-call scons install prefix=..\..\build-msvc use_vc=yes frontend=qt4 mode=release version_suffix=16 gettext=system nls=yes extra_inc_path=..\..\lyx-windows-deps-msvc2008\include extra_lib_path=..\..\lyx-windows-deps-msvc2008\lib extra_bin_path=..\..\lyx-windows-deps-msvc2008\bin qt_dir=..\..\lyx-windows-deps-msvc2008\qt-4
\ No newline at end of file
+call scons install prefix=..\..\build-msvc use_vc=yes frontend=qt4 mode=release version_suffix=16 gettext=system nls=yes extra_inc_path=..\..\lyx-windows-deps-msvc-qt4\include extra_lib_path=..\..\lyx-windows-deps-msvc-qt4\lib extra_bin_path=..\..\lyx-windows-deps-msvc-qt4\bin qt_dir=..\..\lyx-windows-deps-msvc-qt4\qt-4
\ No newline at end of file
EmbeddedObjects.lyx
Extended.lyx
FAQ.lyx
+ Formula-numbering.lyx
Intro.lyx
LaTeXConfig.lyx
+ Math.lyx
Reference.lyx
Shortcuts.lyx
Tutorial.lyx
EmbeddedObjects.lyx
Extended.lyx
FAQ.lyx
+ Formelnummerierung.lyx
Intro.lyx
+ Math.lyx
Tutorial.lyx
UserGuide.lyx
''')
linguistics.lyx
listerrors.lyx
listings.lyx
- mathed.lyx
modernCV.lyx
multicol.lyx
noweb2lyx.lyx
Minipage.lyx
beispiel_gelyxt.lyx
beispiel_roh.lyx
- mathed.lyx
multicol.lyx
splash.lyx
''')
examples/de/beispiel_roh.lyx \
examples/de/Dezimal.lyx \
examples/de/splash.lyx \
- examples/de/mathed.lyx \
examples/de/multicol.lyx
esexamplesdir = $(pkgdatadir)/examples/es
examples/linguistics.lyx \
examples/listerrors.lyx \
examples/listings.lyx \
- examples/mathed.lyx \
examples/modernCV.lyx \
examples/multicol.lyx \
examples/noweb2lyx.lyx \
--- /dev/null
+#LyX 1.5.4svn created this file. For more info see http://www.lyx.org/
+\lyxformat 276
+\begin_document
+\begin_header
+\textclass scrartcl
+\begin_preamble
+\usepackage{ifpdf}
+
+\ifpdf
+
+\usepackage[colorlinks=true,
+ pdftitle=Formelnummerierung, pdfpagemode=none,
+ pdfpagelayout=OneColumn, pdfstartview=XYZ,
+ pdfauthor={Uwe Stöhr},
+ pdfsubject={LaTeX/LyX numbering example},
+ pdfkeywords={LaTeX, numbering, LyX}]{hyperref}
+
+\else % if DVI
+
+\usepackage[colorlinks=true, hypertex]{hyperref}
+
+\fi
+
+% define Roman counter
+\newcounter{rom}
+\renewcommand{\therom}{\roman{rom}}
+
+% remember the original counter
+\newcommand{\c@org@eq}{}
+\let\c@org@eq\c@equation
+\newcommand{\org@theeq}{}
+\let\org@theeq\theequation
+
+% \setrom activates the Roman counter
+\newcommand{\setrom}{
+ \let\c@equation\c@rom
+ \let\theequation\therom}
+
+% \setarab activates the original Arabic counter
+\newcommand{\setarab}{
+ \let\c@equation\c@org@eq
+ \let\theequation\org@theeq}
+\end_preamble
+\options fleqn
+\language english
+\inputencoding auto
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+\graphics default
+\paperfontsize 12
+\spacing single
+\papersize default
+\use_geometry false
+\use_amsmath 2
+\use_esint 0
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 4
+\tocdepth 3
+\paragraph_separation skip
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle empty
+\tracking_changes false
+\output_changes false
+\author ""
+\author ""
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+This document demonstrates the usage of two different formula categories.
+ One is Arabic, one is Roman numbered.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+A=B\label{eq:B}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=C\label{eq:C}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setrom
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=D\label{eq:D}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=E\label{eq:E}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setarab
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=F\label{eq:F}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=G\label{eq:G}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setrom
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=H\label{eq:H}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A=I\label{eq:I}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Cross-references:
+\begin_inset LatexCommand eqref
+reference "eq:B"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:C"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:F"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:G"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:D"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:E"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:H"
+
+\end_inset
+
+ ,
+\begin_inset LatexCommand eqref
+reference "eq:I"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\lyxline
+
+\begin_inset VSpace medskip
+\end_inset
+
+To create this example, first a counter must be defined for the Roman numbered
+ formulas.
+ To do this the following is inserted to the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcounter{rom}
+\newline
+
+\backslash
+renewcommand{
+\backslash
+therom}{
+\backslash
+roman{rom}}
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+To save the value of the Arabic counter
+\series bold
+equation
+\series default
+, this is added to the preamble
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+c@org@eq}{}
+\newline
+
+\backslash
+let
+\backslash
+c@org@eq
+\backslash
+c@equation
+\newline
+
+\backslash
+newcommand{
+\backslash
+org@theeq}{}
+\newline
+
+\backslash
+let
+\backslash
+org@theeq
+\backslash
+theequation
+\end_layout
+
+\begin_layout Standard
+To be able to switch in the document between the two numbering schemes,
+ the following commands are defined in the preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+setrom}{
+\backslash
+let
+\backslash
+c@equation
+\backslash
+c@rom
+\backslash
+let
+\backslash
+theequation
+\backslash
+therom}
+\end_layout
+
+\begin_layout Standard
+for Roman numbering and
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+setarab}{
+\backslash
+let
+\backslash
+c@equation
+\backslash
+c@org@eq
+\backslash
+let
+\backslash
+theequation
+\backslash
+org@theeq}
+\end_layout
+
+\begin_layout Standard
+for Arabic numbering.
+\end_layout
+
+\begin_layout Standard
+Every formula will be by default numbered Arabic.
+ To switch to Roman numbering, the command
+\series bold
+
+\backslash
+setrom
+\series default
+ is inserted in TeX-mode.
+ With the command
+\series bold
+
+\backslash
+setarab
+\series default
+ the numbering is switched to Arabic.
+\end_layout
+
+\end_body
+\end_document
de/EmbeddedObjects.lyx \
de/Extended.lyx \
de/FAQ.lyx \
+ de/Formelnummerierung.lyx \
de/Intro.lyx \
+ de/Math.lyx \
de/Tutorial.lyx \
de/UserGuide.lyx
EmbeddedObjects.lyx \
Extended.lyx \
FAQ.lyx \
+ Formula-numbering.lyx \
Intro.lyx \
LaTeXConfig.lyx \
+ Math.lyx \
Reference.lyx \
Shortcuts.lyx \
Tutorial.lyx \
# First come the rules for each xx/TOC.lyx file. Then comes the
# TOCs target, which prints all the TOC files.
-cs/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Intro.lyx $(srcdir)/UserGuide.lyx $(srcdir)/cs/Tutorial.lyx
+cs/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Intro.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/cs/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py cs .
-da/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx $(srcdir)/da/Intro.lyx
+da/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx $(srcdir)/da/Intro.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py da .
-de/TOC.lyx: $(srcdir)/de/Customization.lyx $(srcdir)/de/EmbeddedObjects.lyx $(srcdir)/de/Extended.lyx $(srcdir)/de/FAQ.lyx $(srcdir)/de/Intro.lyx $(srcdir)/de/Tutorial.lyx $(srcdir)/de/UserGuide.lyx
+de/TOC.lyx: $(srcdir)/de/Customization.lyx $(srcdir)/de/EmbeddedObjects.lyx $(srcdir)/de/Extended.lyx $(srcdir)/de/FAQ.lyx $(srcdir)/de/Intro.lyx $(srcdir)/de/Math.lyx $(srcdir)/de/Tutorial.lyx $(srcdir)/de/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py de .
-TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Intro.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx
+TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Intro.lyx $(srcdir)/Math.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py en .
-es/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/es/EmbeddedObjects.lyx $(srcdir)/es/Extended.lyx $(srcdir)/es/FAQ.lyx $(srcdir)/es/Intro.lyx $(srcdir)/es/Tutorial.lyx $(srcdir)/es/UserGuide.lyx
+es/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/es/EmbeddedObjects.lyx $(srcdir)/es/Extended.lyx $(srcdir)/es/FAQ.lyx $(srcdir)/es/Intro.lyx $(srcdir)/Math.lyx $(srcdir)/es/Tutorial.lyx $(srcdir)/es/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py es .
-eu/TOC.lyx: $(srcdir)/eu/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/eu/Extended.lyx $(srcdir)/eu/FAQ.lyx $(srcdir)/eu/Intro.lyx $(srcdir)/eu/Tutorial.lyx $(srcdir)/eu/UserGuide.lyx
+eu/TOC.lyx: $(srcdir)/eu/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/eu/Extended.lyx $(srcdir)/eu/FAQ.lyx $(srcdir)/eu/Intro.lyx $(srcdir)/Math.lyx $(srcdir)/eu/Tutorial.lyx $(srcdir)/eu/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py eu .
-fr/TOC.lyx: $(srcdir)/fr/Customization.lyx $(srcdir)/fr/EmbeddedObjects.lyx $(srcdir)/fr/Extended.lyx $(srcdir)/fr/FAQ.lyx $(srcdir)/fr/Intro.lyx $(srcdir)/fr/Tutorial.lyx $(srcdir)/fr/UserGuide.lyx
+fr/TOC.lyx: $(srcdir)/fr/Customization.lyx $(srcdir)/fr/EmbeddedObjects.lyx $(srcdir)/fr/Extended.lyx $(srcdir)/fr/FAQ.lyx $(srcdir)/fr/Intro.lyx $(srcdir)/Math.lyx $(srcdir)/fr/Tutorial.lyx $(srcdir)/fr/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py fr .
-gl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/gl/Intro.lyx $(srcdir)/gl/Tutorial.lyx
+gl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/gl/Intro.lyx $(srcdir)/gl/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py gl .
-he/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/he/Intro.lyx $(srcdir)/he/Tutorial.lyx
+he/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/he/Intro.lyx $(srcdir)/he/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py he .
-hu/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/hu/Intro.lyx $(srcdir)/hu/Tutorial.lyx
+hu/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/hu/Intro.lyx $(srcdir)/hu/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py hu .
-it/TOC.lyx: $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/it/Customization.lyx $(srcdir)/it/Intro.lyx $(srcdir)/it/Tutorial.lyx $(srcdir)/it/UserGuide.lyx
+it/TOC.lyx: $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/it/Customization.lyx $(srcdir)/it/Intro.lyx $(srcdir)/it/Tutorial.lyx $(srcdir)/it/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py it .
-nb/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx $(srcdir)/nb/Intro.lyx
+nb/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx $(srcdir)/nb/Intro.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py nb .
-nl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/nl/Intro.lyx $(srcdir)/nl/Tutorial.lyx
+nl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/nl/Intro.lyx $(srcdir)/nl/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py nl .
-pl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/pl/Extended.lyx $(srcdir)/pl/Intro.lyx $(srcdir)/pl/Tutorial.lyx
+pl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/pl/Extended.lyx $(srcdir)/pl/Intro.lyx $(srcdir)/pl/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py pl .
-pt/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/pt/Intro.lyx $(srcdir)/pt/Tutorial.lyx
+pt/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/pt/Intro.lyx $(srcdir)/pt/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py pt .
-ro/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx $(srcdir)/ro/Intro.lyx
+ro/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/Tutorial.lyx $(srcdir)/UserGuide.lyx $(srcdir)/ro/Intro.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py ro .
-ru/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/UserGuide.lyx $(srcdir)/ru/FAQ.lyx $(srcdir)/ru/Intro.lyx $(srcdir)/ru/Tutorial.lyx
+ru/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/ru/FAQ.lyx $(srcdir)/ru/Intro.lyx $(srcdir)/ru/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py ru .
-sk/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Intro.lyx $(srcdir)/sk/Tutorial.lyx $(srcdir)/sk/UserGuide.lyx
+sk/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Intro.lyx $(srcdir)/Math.lyx $(srcdir)/sk/Tutorial.lyx $(srcdir)/sk/UserGuide.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py sk .
-sl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/sl/Intro.lyx $(srcdir)/sl/Tutorial.lyx
+sl/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/sl/Intro.lyx $(srcdir)/sl/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py sl .
-sv/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/UserGuide.lyx $(srcdir)/sv/Intro.lyx $(srcdir)/sv/Tutorial.lyx
+sv/TOC.lyx: $(srcdir)/Customization.lyx $(srcdir)/EmbeddedObjects.lyx $(srcdir)/Extended.lyx $(srcdir)/FAQ.lyx $(srcdir)/Math.lyx $(srcdir)/UserGuide.lyx $(srcdir)/sv/Intro.lyx $(srcdir)/sv/Tutorial.lyx
PYTHONPATH=$(top_builddir)/lib/lyx2lyx python -tt $(srcdir)/doc_toc.py sv .
tocfiles = cs/TOC.lyx da/TOC.lyx de/TOC.lyx TOC.lyx es/TOC.lyx eu/TOC.lyx fr/TOC.lyx gl/TOC.lyx he/TOC.lyx hu/TOC.lyx it/TOC.lyx nb/TOC.lyx nl/TOC.lyx pl/TOC.lyx pt/TOC.lyx ro/TOC.lyx ru/TOC.lyx sk/TOC.lyx sl/TOC.lyx sv/TOC.lyx
--- /dev/null
+#LyX 1.5.4svn created this file. For more info see http://www.lyx.org/
+\lyxformat 276
+\begin_document
+\begin_header
+\textclass scrartcl
+\begin_preamble
+% DO NOT ALTER THIS PREAMBLE!!!
+%
+% This preamble is designed to ensure that the file prints
+% out as advertised. If you mess with this preamble,
+% parts of this document may not print out as expected. If you
+% have problems LaTeXing this file, please contact
+% the documentation team
+% email: lyx-docs@lists.lyx.org
+
+
+% if pdflatex is used
+\usepackage{ifpdf}
+\ifpdf
+
+% set fonts for nicer pdf view
+\IfFileExists{lmodern.sty}
+ {\usepackage{lmodern}}{}
+
+% link all cross references and URLs
+% in pdf output
+ \usepackage[colorlinks=true, bookmarks, bookmarksnumbered,
+ bookmarksopen, bookmarksopenlevel=1,
+ linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,
+ pdfpagelayout=OneColumn, pdfnewwindow=true,
+ pdfstartview=XYZ, plainpages=false, pdfpagelabels,
+ pdfauthor={LyX Team}, pdftex,
+ pdftitle={LyX's Math Manual},
+ pdfsubject={LyX-documentation about math},
+ pdfkeywords={LyX, Mathed}]{hyperref}
+
+\else % if dvi or ps is produced
+
+ % link all cross references and URLs in DVI output
+ \usepackage[ps2pdf, colorlinks=true,
+ linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref}
+
+\fi % end if pdflatex is used
+
+% Folgendes Problem lösen:
+% Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
+% Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
+% die Kapitelnummer geschrieben.
+% Als Lösung wird mehr Platz zwischen Nummer und
+% Überschrift eingefügt.
+\renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
+\renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
+
+% To be able to enter the character ° and · directly in LyX,
+% see sec. 22.11
+\DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
+\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
+
+% increase link area for cross-references and autoname them,
+% see sec. 22.18.1
+\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
+%\renewcommand{\sectionautorefname}{sec.\negthinspace}
+\renewcommand{\subsectionautorefname}{sec.\negthinspace}
+\renewcommand{\subsubsectionautorefname}{sec.\negthinspace}
+\newlength{\abc}
+\settowidth{\abc}{\space}
+\renewcommand{\equationautorefname}{\hspace{-\abc}}
+
+% don't load packages twice
+% see first footnote in sec. 9.3
+\@ifundefined{textcolor}{\usepackage{color}}{}
+
+% the pages of the TOC are numbered roman
+% and a PDF-bookmark for the TOC is added
+\pagenumbering{Roman}
+\let\myTOC\tableofcontents
+\renewcommand{\tableofcontents}{%
+ \vspace{1cm}
+ \pdfbookmark[1]{Contents}{}
+ \myTOC
+ \cleardoublepage
+ \pagenumbering{arabic}}
+
+% insert additional vertical space of 1.5 mm between footnotes,
+% see sec. 22.16
+\let\myFoot\footnote
+\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
+
+% provides caption formatting
+\setkomafont{captionlabel}{\bfseries}
+
+% used in Kap. 22.4
+\usepackage{braket}
+
+% used in Kap. 22.6
+\usepackage[samesize]{cancel}
+
+% enables calculation of values,
+\usepackage{calc}
+
+% for multiple table row and column cells
+\usepackage{multirow}
+\usepackage{multicol}
+
+% needed for diagrams
+\usepackage{amscd}
+
+% needed in sec. 19.4
+\usepackage{remreset}
+
+% center multirows (e.g. in sec. 13.3)
+\renewcommand{\multirowsetup}{\centering}
+
+% define a color, used in sec.9.3
+\definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
+
+% declare operators (see sec. 10.4 and sec. 15.2)
+\DeclareMathOperator*{\Lozenge}{\blacklozenge}
+\DeclareMathOperator{\sgn}{sgn}
+
+\newcommand{\spce}{\textvisiblespace}
+
+% example definitions for sec. 20.1
+\newcommand{\gr}{\Longrightarrow}
+\newcommand{\us}[1]{\underline{#1}}
+\newcommand{\fb}[3]{\framebox#1#2{$#3$}}
+\newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
+\newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
+
+% example macro from sec. 19.4
+%\def\tagform@#1{\maketag@@@{|#1|}}
+
+% macro from sec. 10.2
+\def\clap#1{\hbox to 0pt{\hss #1\hss}}
+\def\mathclap {\mathpalette \mathclapinternal}
+\def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
+
+% redefine the greyed out note
+\renewenvironment{lyxgreyedout}
+ {\textcolor{blue}\bgroup}{\egroup}
+
+% check for package eurosym
+% used for the Euro symbol
+\newboolean{eurosym}
+\IfFileExists{eurosym.sty}
+ {\usepackage[gennarrow]{eurosym}
+ \setboolean{eurosym}{true}}
+ {\setboolean{eurosym}{false}}
+
+% needed in sec. 22.10
+% check for package upgreek
+\newboolean{upgreek}
+\IfFileExists{upgreek.sty}
+ {\usepackage{upgreek}
+ \setboolean{upgreek}{true}}
+ {\setboolean{upgreek}{false}}
+\end_preamble
+\options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
+\language english
+\inputencoding auto
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+\graphics default
+\paperfontsize 12
+\spacing single
+\papersize a4paper
+\use_geometry false
+\use_amsmath 2
+\use_esint 1
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 4
+\tocdepth 3
+\paragraph_separation skip
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 2
+\paperpagestyle plain
+\bullet 1 0 6 -1
+\bullet 2 2 35 -1
+\bullet 3 2 7 -1
+\tracking_changes false
+\output_changes false
+\author ""
+\author ""
+\end_header
+
+\begin_body
+
+\begin_layout Title
+LyX's detailed Math manual
+\end_layout
+
+\begin_layout Author
+by the LyX Team
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\noindent
+If you have comments or error corrections, please send them to the LyX Documenta
+tion mailing list:
+\family typewriter
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
+\end_layout
+
+\end_inset
+
+lyx-docs@lists.lyx.org
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+author: Uwe Stöhr
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\newline
+
+\family sans
+Version 1.5.4-
+\family default
+1
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+To export this document to PDF, PS, or DVI the LaTeX-packages
+\series bold
+eurosym,
+\series default
+
+\series bold
+multirow,
+\series default
+ and
+\series bold
+was
+\series default
+ must be installed.
+ If they are not installed you can export the document anyway but the sections
+ where the packages are required won't appear in the output.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Introduction
+\begin_inset LatexCommand label
+name "sec:Introduction"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This document explains LyX's math features and is furthermore a collection
+ of LaTeX-commands used for mathematical characters and constructs.
+ The explanations are designed for the usage of commands.
+ It is therefore required that you have read the section
+\family typewriter
+Mathematical\InsetSpace ~
+Formulas
+\family default
+ of the User's Guide.
+\end_layout
+
+\begin_layout Standard
+Most of the characters and many constructs explained in this manual are
+ also accessible via the menu
+\family sans
+Insert
+\series bold
+\SpecialChar \menuseparator
+
+\series default
+Math
+\family default
+, or the
+\family sans
+math
+\family default
+\series bold
+
+\family sans
+\series default
+toolbar
+\family default
+.
+ But everybody who has to write lots of formulas will notice that it is
+ much faster to use commands instead of the math toolbar.
+ Therefore this manual is focused on commands but also mentions the correspondin
+g toolbar buttons when available.
+\end_layout
+
+\begin_layout Standard
+If not specially mentioned the commands are only available within formulas.
+ To be able to use all commands explained in this document, the option
+\family sans
+Use AMS math package
+\family default
+ must be used in the document settings (menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings\SpecialChar \menuseparator
+Math\InsetSpace ~
+Options
+\family default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+The option
+\family sans
+Use AMS math package automatically
+\family default
+ only uses
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-math when math constructs are found that are supported by LyX.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+This document doesn't list all
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-math commands
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+A list with all
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-math commands is in the file
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
+\end_layout
+
+\end_inset
+
+
+\family sans
+amsguide.ps
+\family default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+, which is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+ for lucidity reasons.
+\end_layout
+
+\begin_layout Section
+General Instructions
+\begin_inset LatexCommand label
+name "sec:General-Instructions"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To create an inline formula
+\begin_inset LatexCommand index
+name "Formula ! inline"
+
+\end_inset
+
+ that is embedded into a text line, press
+\family sans
+Ctrl-m
+\family default
+ or the toolbar button
+\begin_inset Graphics
+ filename ../images/math-mode.png
+ scale 85
+
+\end_inset
+
+
+\newline
+To create a display style formula
+\begin_inset LatexCommand index
+name "Formula ! display style"
+
+\end_inset
+
+ that will appear bigger and in an own paragraph, press
+\family sans
+Ctrl-M
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To change a display style formula to an inline formula, set the cursor into
+ the formula and press
+\family sans
+Ctrl-M
+\family default
+ or use the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Change formula type
+\family default
+.
+ The same way is used to change an inline formula to a display style formula.
+\end_layout
+
+\begin_layout Standard
+To display parts of an inline formula in the size of a display style formula,
+ enter the command
+\series bold
+
+\backslash
+displaystyle
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash displaystyle"
+
+\end_inset
+
+
+\series default
+ to a formula.
+ Then a new blue box appears in which the desired formula part is inserted.
+\end_layout
+
+\begin_layout Standard
+Only inline formulas are allowed inside tables.
+\end_layout
+
+\begin_layout Standard
+The
+\family sans
+math toolbar
+\family default
+ can be turned on in the menu
+\family sans
+View\SpecialChar \menuseparator
+Toolbars
+\family default
+.
+ When you click there on
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ the toolbar will be shown permanently at the bottom; this state is visualized
+ in the
+\family sans
+Toolbars
+\family default
+ menu with a checkmark.
+ When you click in this state again on
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ in the
+\family sans
+Toolbars
+\family default
+ menu, the
+\family sans
+math toolbar
+\family default
+ is only shown when the cursor is within a formula; this state is visualized
+ by the renaming of the menu entry from
+\begin_inset Quotes eld
+\end_inset
+
+Math
+\begin_inset Quotes erd
+\end_inset
+
+ to
+\begin_inset Quotes eld
+\end_inset
+
+Math\InsetSpace ~
+(auto)
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The TeX-mode
+\begin_inset LatexCommand index
+name "T@\\TeX-mode"
+
+\end_inset
+
+ is invoked by pressing the toolbar button
+\begin_inset Graphics
+ filename ../images/ert-insert.png
+ scale 85
+
+\end_inset
+
+ or by using the menu
+\family sans
+Insert\SpecialChar \menuseparator
+T
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+e
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+X Code
+\family default
+ (shortcut
+\family sans
+Ctrl-l
+\family default
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+In LyX there are three
+\begin_inset Quotes eld
+\end_inset
+
+proper names
+\begin_inset Quotes erd
+\end_inset
+
+ that appear in the output with sub- and superscript letters: TeX, LaTeX,
+ and LyX
+\end_layout
+
+\begin_layout Standard
+To avoid that these names are recognized as proper names, TeX-braces are
+ set around one of the letters of the name.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To change the LaTeX-preamble
+\begin_inset LatexCommand index
+name "L@\\LaTeX-preamble"
+
+\end_inset
+
+, use the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings\SpecialChar \menuseparator
+La
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+T
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+eX
+\family default
+
+\family sans
+Preamble
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+To edit matrices, case differentiations, and multiline formulas subsequently,
+ the menus
+\family sans
+Edit\SpecialChar \menuseparator
+Math
+\family default
+ and
+\family sans
+Edit\SpecialChar \menuseparator
+Rows\InsetSpace \thinspace{}
+&\InsetSpace \thinspace{}
+Columns,
+\family default
+ or the
+\family sans
+table toolbar
+\family default
+ can be used.
+ When lines and columns are swapped via the menu, the column or line where
+ the cursor is in is exchanged with the column to the right or the line
+ below, respectively.
+ Is the cursor in the last column or row, the exchange is done with the
+ column to the left or the line above.
+\end_layout
+
+\begin_layout Standard
+To write text in formulas
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+For multiline formulas the command
+\series bold
+
+\backslash
+intertext
+\series default
+ is used, see
+\begin_inset LatexCommand ref
+reference "sub:Text-in-multiline"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\emph on
+mathematical text
+\emph default
+
+\begin_inset LatexCommand index
+name "Text ! in formulas"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Mathematical text"
+
+\end_inset
+
+ is used.
+ This mode is invoked with the the shortcut
+\family sans
+Alt-m\InsetSpace ~
+m
+\family default
+ or by the insertion of the command
+\series bold
+
+\backslash
+text
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash text"
+
+\end_inset
+
+
+\series default
+.
+ The text appears black in LyX and can therefore be distinguished from the
+ other formula parts that appear blue.
+ In the output mathematical text is set upright, in contrary to other formula
+ parts.
+\end_layout
+
+\begin_layout Subsection*
+Command Scheme
+\end_layout
+
+\begin_layout Standard
+Most of the LaTeX-commands for math constructs have the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+commandname[optional
+\series default
+
+\series bold
+argument]{required
+\series default
+
+\series bold
+argument}
+\end_layout
+
+\begin_layout Standard
+A command starts always with a backslash
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+
+\backslash
+
+\series default
+
+\begin_inset Quotes grd
+\end_inset
+
+.
+ To omit optional arguments, also omit the associated brackets.
+ The braces around the required arguments are named in this document as
+ TeX-braces
+\begin_inset LatexCommand index
+name "T@\\TeX-braces"
+
+\end_inset
+
+.
+ If you add in a formula a left brace to a command name, LyX creates automatical
+ly a TeX-brace.
+ In all other cases TeX-braces are created in formulas with the command
+
+\series bold
+
+\backslash
+{
+\series default
+.
+ TeX-braces appear red in LyX, in contrary to normal braces that appear
+ blue.
+ In TeX-mode no command is needed to get TeX-braces.
+ TeX-braces don't appear in the output.
+\end_layout
+
+\begin_layout Standard
+When commands without arguments, like commands for symbols are entered in
+ TeX-mode, a space character must
+\emph on
+always
+\emph default
+ be behind the command to end it.
+ This space doesn't appear in the output.
+ When the space should appear in the output, the space must be followed
+ by a protected space in normal text.
+\end_layout
+
+\begin_layout Standard
+A protected space is inserted with
+\family sans
+Ctrl-Space
+\family default
+.
+\end_layout
+
+\begin_layout Subsection*
+
+\newpage
+Syntax Explanation
+\end_layout
+
+\begin_layout Itemize
+The symbol
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+This visible space character can be created with the command
+\series bold
+
+\backslash
+textvisiblespace
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash textvisiblespace"
+
+\end_inset
+
+, inserted in TeX-mode.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+denotes a space character to be input.
+\end_layout
+
+\begin_layout Itemize
+An arrow like
+\begin_inset Formula $\to$
+\end_inset
+
+ denotes the usage of the corresponding arrow key on the keyboard.
+\end_layout
+
+\begin_layout Subsection*
+Used units
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Used-units"
+
+\end_inset
+
+Used units
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Unit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Name / Description
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Millimeter
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Centimeter
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+in
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Inch (1\InsetSpace \thinspace{}
+in = 2,54\InsetSpace \thinspace{}
+cm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+pt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Point (72.27\InsetSpace \thinspace{}
+pt = 1\InsetSpace \thinspace{}
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+pc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Pica (1\InsetSpace \thinspace{}
+pc = 12\InsetSpace \thinspace{}
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+sp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+scaled point (65536\InsetSpace \thinspace{}
+sp = 1\InsetSpace \thinspace{}
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+bp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+big point (72\InsetSpace \thinspace{}
+bp = 1\InsetSpace \thinspace{}
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+dd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Didot (1\InsetSpace \thinspace{}
+dd
+\begin_inset Formula $\approx$
+\end_inset
+
+ 0.376\InsetSpace \thinspace{}
+mm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Cicero (1\InsetSpace \thinspace{}
+cc = 12\InsetSpace \thinspace{}
+dd)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+ex
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Height of letter
+\emph on
+
+\begin_inset Quotes eld
+\end_inset
+
+x
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ in the current font
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+em
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+width of letter
+\begin_inset Quotes eld
+\end_inset
+
+
+\emph on
+M
+\emph default
+
+\begin_inset Quotes erd
+\end_inset
+
+ in the current font
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+math unit (1\InsetSpace \thinspace{}
+mu =
+\begin_inset Formula $\nicefrac{1}{18}$
+\end_inset
+
+\InsetSpace \thinspace{}
+em)
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+textfrac
+\series default
+ is explained in sec.\InsetSpace \thinspace{}
+
+\begin_inset LatexCommand ref
+reference "sub:Self-defined-Fractions"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Basic Functions
+\end_layout
+
+\begin_layout Subsection
+Exponents
+\begin_inset LatexCommand index
+name "Exponents"
+
+\end_inset
+
+ and Indices
+\begin_inset LatexCommand index
+name "Indices"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Superscripts|see{Exponents}"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Subscripts|see{Indices}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Indices are created with an underscore
+\begin_inset Quotes eld
+\end_inset
+
+_
+\begin_inset Quotes erd
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math-subscript.png
+ scale 85
+
+\end_inset
+
+ , exponents with a caret
+\begin_inset Quotes eld
+\end_inset
+
+^
+\begin_inset Quotes erd
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math-superscript.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B_V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $B_{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B^V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}B^{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}B^{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+As the caret is in some languages an accent, vowels will be accentuated
+ in this case and not set as exponents
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Depending on the used keyboard settings this can also happen for other character
+s than vowels.
+\end_layout
+
+\end_inset
+
+.
+ To get in this case exponents, press
+\family sans
+Space
+\family default
+ after the caret as in the last example.
+\end_layout
+
+\begin_layout Subsection
+Fractions
+\begin_inset LatexCommand label
+name "sub:Fractions"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Fractions"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Fractions are generated with the command
+\series bold
+
+\backslash
+frac
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! F ! \\textbackslash frac"
+
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/frac.png
+ scale 50
+
+\end_inset
+
+.
+ The font size is adjusted automatically, depending on whether the fraction
+ is in an inline or display style formula.
+ With the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/frac-square.png
+ scale 85
+
+\end_inset
+
+ you can select different fraction types.
+\end_layout
+
+\begin_layout Standard
+With the command
+\series bold
+
+\backslash
+dfrac
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash dfrac"
+
+\end_inset
+
+
+\series default
+ a fraction can be created that has in any case the size of a display style
+ formula.
+ With
+\series bold
+
+\backslash
+tfrac
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash tfrac"
+
+\end_inset
+
+
+\series default
+ the fraction appears always with the size of an inline formula.
+ An example:
+\end_layout
+
+\begin_layout Standard
+A line with the fraction
+\begin_inset Formula $\frac{1}{2}$
+\end_inset
+
+ that was created with the command
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+A line with the fraction
+\begin_inset Formula $\dfrac{1}{2}$
+\end_inset
+
+ that was created with the command
+\series bold
+
+\backslash
+dfrac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+1
+\begin_inset Formula $\downarrow$
+\end_inset
+
+2
+\begin_inset Formula $\downarrow\downarrow$
+\end_inset
+
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\newpage
+For nested fractions the command
+\series bold
+
+\backslash
+cfrac
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! C ! \\textbackslash cfrac"
+
+\end_inset
+
+ can be used.
+ Here an example:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\
+\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for the example above is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac{A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{B+
+\backslash
+cfrac{C+
+\backslash
+cfrac{E
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{F
+\begin_inset Formula $\to\to$
+\end_inset
+
+
+\backslash
+{D
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ sets the fraction always in the size of a displayed formula, also when
+ it is part of another fraction.
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ has the following command scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac[numerator position]{numerator}{denominator}
+\end_layout
+
+\begin_layout Standard
+The numerator position can be
+\emph on
+l
+\emph default
+ ,
+\emph on
+c
+\emph default
+, or
+\emph on
+r
+\emph default
+ .
+ l or r aligns the numerator to the left or right, resp.\InsetSpace ~
+with the fraction
+ stroke.
+ When
+\emph on
+c
+\emph default
+ or no position is given, the numerator appears centered.
+ These fractions demonstrate the different alignments:
+\newline
+
+\series bold
+
+\begin_inset Formula $\cfrac[l]{A}{B+C}$
+\end_inset
+
+,
+\begin_inset Formula $\cfrac{A}{B+C}$
+\end_inset
+
+,
+\begin_inset Formula $\cfrac[r]{A}{B+C}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+It is often advantageous to combine
+\series bold
+
+\backslash
+cfrac
+\series default
+ and
+\series bold
+
+\backslash
+frac
+\series default
+:
+\begin_inset Formula \[
+\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For inline fractions with a sloped fraction stroke you can use the command
+
+\series bold
+
+\backslash
+nicefrac
+\begin_inset LatexCommand index
+name "Commands ! N ! \\textbackslash nicefrac"
+
+\end_inset
+
+
+\series default
+:
+\begin_inset Formula $\nicefrac{5}{31}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to define own fractions where the fraction stroke can be changed, is
+ explained in
+\begin_inset LatexCommand ref
+reference "sub:Self-defined-Fractions"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Roots
+\begin_inset LatexCommand index
+name "Roots"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Square roots are created with
+\series bold
+
+\backslash
+sqrt
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash sqrt"
+
+\end_inset
+
+ or the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/sqrt.png
+ scale 85
+
+\end_inset
+
+, all other roots with the command
+\series bold
+
+\backslash
+root
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash root"
+
+\end_inset
+
+ or with the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/root.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqrt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+root
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+3
+\begin_inset Formula $\downarrow$
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A square root can also be created with
+\series bold
+
+\backslash
+root
+\series default
+ when the root index field is left empty.
+\end_layout
+
+\begin_layout Standard
+With certain indices the distance to the root is too small, like in this
+ formula:
+\begin_inset Formula $\sqrt[\beta]{B}$
+\end_inset
+
+
+\newline
+The
+\begin_inset Formula $\beta$
+\end_inset
+
+ touches the root.
+ To avoid this, the commands
+\series bold
+
+\backslash
+leftroot
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash leftroot"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+uproot
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! U ! \\textbackslash uproot"
+
+\end_inset
+
+ are used with the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+leftroot{distance}
+\series default
+ and
+\series bold
+
+\backslash
+uproot{distance}
+\end_layout
+
+\begin_layout Standard
+Distance is the number of Big Points (unit bp;
+\begin_inset Formula $\mathrm{72\, bp=1\, inch}$
+\end_inset
+
+), that the index should be moved to the left or top, resp..
+ The commands are written to the index.
+ This way the command
+\newline
+
+\series bold
+
+\backslash
+root
+\backslash
+leftroot{-1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+uproot{2
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+beta
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\newline
+
+\series default
+produces a correct typeset formula:
+\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Binomial coefficients
+\begin_inset LatexCommand index
+name "Binomial coefficient s"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binomial coefficients are inserted with the command
+\series bold
+
+\backslash
+binom
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash binom"
+
+\end_inset
+
+ or with the submenu of the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/frac-square.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+binom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dbinom{A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Analog to fractions (
+\series bold
+
+\backslash
+frac
+\series default
+) there are besides
+\series bold
+
+\backslash
+binom
+\series default
+ the commands
+\series bold
+
+\backslash
+dbinom
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash dbinom"
+
+\end_inset
+
+
+\series default
+ and
+\series bold
+
+\backslash
+tbinom
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash tbinom"
+
+\end_inset
+
+ with the following command scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+dbinom{numerator}{denominator}
+\series default
+ and
+\newline
+
+\series bold
+
+\backslash
+tbinom{numerator}{denominator}
+\end_layout
+
+\begin_layout Subsection
+Case differentiations
+\begin_inset LatexCommand index
+name "Case differentiations "
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cases
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+B>0
+\begin_inset LatexCommand index
+name "Commands ! C ! \\textbackslash cases"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{cases}
+A & B>0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cases
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+Ctrl-Enter
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{cases}
+A & \textrm{für }x>0\\
+B & \textrm{für }x=0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+After inserting
+\series bold
+
+\backslash
+cases
+\series default
+ or the usage of the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/cases.png
+ scale 85
+
+\end_inset
+
+ you can create new lines with the shortcut
+\family sans
+Ctrl-Return
+\family default
+ or the table toolbar button
+\begin_inset Graphics
+ filename ../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Umlauts and accents in formulas, like in the table above, are explained
+ in
+\begin_inset LatexCommand ref
+reference "sub:Accents-for-one"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+cases
+\series default
+ is also available via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Cases-Environment
+\family default
+.
+\end_layout
+
+\begin_layout Subsection
+Negations
+\begin_inset LatexCommand index
+name "Negations"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+By inserting of
+\series bold
+
+\backslash
+not
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! N ! \\textbackslash not"
+
+\end_inset
+
+ every character can be displayed canceled.
+ The characters are quasi accentuated by a slash.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The last example shows, that not all negations look good.
+ Therefore there are for some negations special commands (see
+\begin_inset LatexCommand ref
+reference "sub:Mathematical-Symbols"
+
+\end_inset
+
+ and
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+sectionautorefname}{
+\backslash
+hspace{-
+\backslash
+abc}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand ref
+reference "sec:Relations"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+sectionautorefname}{sec.
+\backslash
+negthinspace}
+\end_layout
+
+\end_inset
+
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+The
+\series bold
+
+\backslash
+renewcommand
+\series default
+-commands in TeX-mode are necessary that the cross-reference name
+\begin_inset Quotes eld
+\end_inset
+
+sec.
+\begin_inset Quotes erd
+\end_inset
+
+ don't appear twice, see sec.\InsetSpace \thinspace{}
+
+\begin_inset LatexCommand ref
+reference "sub:Verlinkte-Querverweise"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Placeholders
+\begin_inset LatexCommand label
+name "sub:Placeholders"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Placeholders"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Chemical characters ! Isotopes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Isotopes|see{Chemical characters}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When displaying e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+isotopes
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+More about chemical symbols is written in
+\begin_inset LatexCommand ref
+reference "sub:Chemical-Symbols-and"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ the following problem occurs:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Indices created with sub- and superscripts:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+correct indices:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The shorter index is by default placed below or above the first character
+ of the longer index.
+ To avoid this there is the command
+\series bold
+
+\backslash
+phantom
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! P ! \\textbackslash phantom"
+
+\end_inset
+
+ or the math toolbar button \InsetSpace ~
+
+\begin_inset Graphics
+ filename ../images/math/phantom.png
+ scale 85
+
+\end_inset
+
+ that creates one or more phantom characters.
+ When inserting
+\series bold
+
+\backslash
+phantom
+\series default
+ a small blue box appears that is superposed with two red arrows.
+ The arrows indicate that the complete width and height of the box content
+ will be created as placeholder.
+ Phantom characters are accordingly placeholders with the size of the characters.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^19
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+1
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^235
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+23
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Lambda^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+ii
+\begin_inset Formula $\to$
+\end_inset
+
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_MMt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Furthermore there are the commands
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! V ! \\textbackslash vphantom"
+
+\end_inset
+
+ (toolbar button \InsetSpace ~
+
+\begin_inset Graphics
+ filename ../images/math/vphantom.png
+ scale 85
+
+\end_inset
+
+) and
+\series bold
+
+\backslash
+hphantom
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash hphantom"
+
+\end_inset
+
+ (toolbar button \InsetSpace ~
+
+\begin_inset Graphics
+ filename ../images/math/hphantom.png
+ scale 85
+
+\end_inset
+
+).
+
+\series bold
+
+\backslash
+hphantom
+\series default
+ creates only space for the maximal height of the characters in the box
+ but not for its width.
+
+\series bold
+
+\backslash
+vphantom
+\series default
+ creates only space for the width of the box content.
+ Therefore the boxes of both commands have only one red arrow.
+\end_layout
+
+\begin_layout Standard
+For example creates
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+a
+\backslash
+int
+\series default
+ space for the height of the integral sign,
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+int
+\series default
+ creates an integral sign, see
+\begin_inset LatexCommand ref
+reference "sub:Big-Operators"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ because this is the larger character.
+ An example application is in
+\begin_inset LatexCommand ref
+reference "sub:Multiline-Brackets"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Lines
+\begin_inset LatexCommand index
+name "Lines"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! underlined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset LatexCommand index
+name "Commands ! O ! \\textbackslash overline"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset LatexCommand index
+name "Commands ! U ! \\textbackslash underline"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+underline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example it doesn't matter if first
+\series bold
+
+\backslash
+overline
+\series default
+ or
+\series bold
+
+\backslash
+underline
+\series default
+ is inserted.
+\end_layout
+
+\begin_layout Standard
+To double underline e.\InsetSpace \thinspace{}
+g.
+ results, one uses
+\series bold
+
+\backslash
+underline
+\series default
+ twice.
+\end_layout
+
+\begin_layout Standard
+It is possible to place up to 6 lines above or below characters.
+\end_layout
+
+\begin_layout Subsection
+Ellipses
+\begin_inset LatexCommand index
+name "Ellipses"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are different types of ellipses available.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+In the math toolbar in the submenu of the button
+\begin_inset Graphics
+ filename ../images/math/ldots.png
+ scale 85
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ For listings dots at the baseline are used (
+\series bold
+
+\backslash
+ldots
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash ldots"
+
+\end_inset
+
+), while for operations dots are needed that are on the same height as the
+ operators (
+\series bold
+
+\backslash
+cdots
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! C ! \\textbackslash cdots"
+
+\end_inset
+
+).
+ When using the command
+\series bold
+
+\backslash
+dots
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash dots"
+
+\end_inset
+
+, LaTeX decides on the basis of the next character what type is used.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,
+\backslash
+dots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1},\dots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++
+\backslash
+dots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1}+\dots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,
+\backslash
+ldots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1},\ldots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++
+\backslash
+cdots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1}+\cdots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vdots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vdots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3×3\InsetSpace \thinspace{}
+matrix with the different dots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{array}{ccc}
+A_{11} & \cdots & A_{1m}\\
+\vdots & \ddots & \vdots\\
+A_{n1} & \cdots & A_{nm}\end{array}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The ellipses available in menu
+\family sans
+Insert\SpecialChar \menuseparator
+Special\InsetSpace ~
+Character
+\family default
+ are
+\series bold
+
+\backslash
+ldots
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Specially for matrices there are ellipses that span over several columns.
+ They are created with the command
+\series bold
+
+\backslash
+hdotsfor
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash hdotsfor"
+
+\end_inset
+
+, that has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hdotsfor[distance]{number of columns}
+\end_layout
+
+\begin_layout Standard
+The number of columns specifies how many columns should be spanned.
+ Distance is a factor for the distance between the dots.
+\end_layout
+
+\begin_layout Standard
+In the following matrix the command
+\series bold
+
+\backslash
+hdotsfor[2]{4}
+\series default
+ was inserted in the first box of the second line, to get an ellipsis with
+ a dot distance twice as long as with the command
+\series bold
+
+\backslash
+dots
+\series default
+:
+\begin_inset Formula \[
+\left(\begin{array}{cccc}
+A & B & C & D\\
+\hdotsfor[2]{4}\\
+q & w & e & r\end{array}\right)\]
+
+\end_inset
+
+Note that the matrix fields that should be spanned must be empty, otherwise
+ you get LaTeX-errors.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore you can fill with the command
+\series bold
+
+\backslash
+dotfill
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash dotfill"
+
+\end_inset
+
+ the rest of a line with dots.
+ The effect of these commands is the same like with
+\series bold
+
+\backslash
+hfill
+\series default
+, see
+\begin_inset LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+A
+\backslash
+dotfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\series default
+ produces
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\dotfill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Analog to
+\series bold
+
+\backslash
+dotfill
+\series default
+ there is for a line the command
+\series bold
+
+\backslash
+hrulefill
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash hrulefill"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\hrulefill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use the commands for text, they have to be inserted in TeX-mode.
+\end_layout
+
+\begin_layout Section
+Matrices
+\begin_inset LatexCommand label
+name "sec:Matrices"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Matrices"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Matrices can be inserted via the math toolbar button
+\begin_inset Graphics
+ filename ../images/dialog-show_mathmatrix.png
+ scale 85
+
+\end_inset
+
+ or the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Matrix
+\family default
+.
+ You will be asked for the number of matrix columns and rows, and the alignment.
+ The vertical alignment is hereby only of importance for matrices in inline
+ formulas:
+\end_layout
+
+\begin_layout Standard
+The first matrix is top
+\begin_inset Formula $\begin{array}[t]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+, the second middle
+\begin_inset Formula $\begin{array}{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+, and the third bottom
+\begin_inset Formula $\begin{array}[b]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+ aligned.
+\end_layout
+
+\begin_layout Standard
+The horizontal alignment specifies how the column entries should be aligned.
+ It is set by entering a letter for every column.
+
+\emph on
+l
+\emph default
+ denotes left aligned,
+\emph on
+c
+\emph default
+ centered, and
+\emph on
+r
+\emph default
+ right aligned.
+ To create for example a 4
+\series bold
+×
+\series default
+4\InsetSpace ~
+matrix where the first column is left aligned, the second and third are
+ centered, and the last one is right aligned, one enters for the horizontal
+ alignment
+\series bold
+lccr
+\series default
+.
+ Normally are in a matrix all columns centered, therefore the default is
+ for every column is a
+\series bold
+c
+\series default
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+pagebreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Horizontal alignment:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+lll
+\series default
+ :
+\begin_inset Formula $\begin{array}{lll}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+ ,
+\series bold
+ccc
+\series default
+ :
+\begin_inset Formula $\begin{array}{ccc}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+ ,
+\series bold
+rrr
+\series default
+ :
+\begin_inset Formula $\begin{array}{rrr}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To add or delete rows and columns subsequently, the math toolbar buttons
+
+\begin_inset Graphics
+ filename ../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+,
+\begin_inset Graphics
+ filename ../images/tabular-feature_delete-row.png
+ scale 85
+
+\end_inset
+
+, etc.\InsetSpace \thinspace{}
+, or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows & Columns
+\family default
+ can be used.
+ New rows can also be created with
+\family sans
+Ctrl-Return
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Parentheses around a matrix can can either be created with the commands
+
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash left"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash right"
+
+\end_inset
+
+ (shortcut
+\family sans
+Alt-m\InsetSpace ~
+parenthesis
+\family default
+), see
+\begin_inset LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+, or by using the following commands:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Vmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+matrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+
+\series bold
+
+\backslash
+vmatrix
+\series default
+ is inserted, a blue box appears between two vertical lines where the matrix
+ is inserted.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+As all multiline formulas are matrices, the length
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash arraycolsep"
+
+\end_inset
+
+ that is described in
+\begin_inset LatexCommand ref
+reference "sub:Column-Separation"
+
+\end_inset
+
+ can also be used to change the column separation of matrices.
+\end_layout
+
+\begin_layout Standard
+To change the row separation, the command
+\series bold
+
+\backslash
+arraystretch
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash arraystretch"
+
+\end_inset
+
+ is used.
+ It is used as follows:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+arraystretch}{stretch factor}
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash renewcommand"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ assigns the stretch factor to the predefined command
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+ To double e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+the row separation, use the factor 2.
+ This is then used for all following matrices.
+ To go back to the original separation, assign the factor 1 to
+\series bold
+
+\backslash
+arraystretch
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+To set matrices into a text line, the command
+\series bold
+
+\backslash
+smallmatrix
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash smallmatrix"
+
+\end_inset
+
+ is used.
+ When it is inserted a blue box with two dashed lines appears.
+ In this box the matrix is inserted.
+\end_layout
+
+\begin_layout Standard
+This is a matrix
+\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
+C & D\end{smallmatrix}\right)$
+\end_inset
+
+ in a text line.
+\end_layout
+
+\begin_layout Section
+Brackets and Delimiters
+\begin_inset LatexCommand index
+name "Brackets"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Delimiters"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical Brackets and Delimiters
+\begin_inset LatexCommand index
+name "Brackets ! vertical"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $($
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+{
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\{$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+[
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $[$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+langle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\langle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+/
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $/$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\backslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\series medium
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ In TeX-mode the command
+\series bold
+
+\backslash
+textbackslash
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash textbackslash"
+
+\end_inset
+
+ must be used for the backslash, because the command
+\series bold
+
+\backslash
+
+\backslash
+
+\series default
+ produces there a line break.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For all characters listed above the size can be adjusted with the commands
+ described in the following two subsections.
+ When using these commands, the characters < and > can directly be used
+ instead of the commands
+\series bold
+
+\backslash
+langle
+\series default
+ and
+\series bold
+
+\backslash
+rangle
+\series default
+.
+\end_layout
+
+\begin_layout Subsubsection
+Manual Bracket Size
+\begin_inset LatexCommand label
+name "sub:Manual-Bracket-Size"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Bracket size ! manual"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The bracket size can be specified manually by the LaTeX-commands
+\series bold
+
+\backslash
+big
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash big"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+Big
+\series default
+,
+\series bold
+
+\backslash
+bigg
+\series default
+, and
+\series bold
+
+\backslash
+Bigg
+\series default
+.
+
+\series bold
+
+\backslash
+big
+\series default
+ denotes the smallest and
+\series bold
+
+\backslash
+Bigg
+\series default
+ the largest bracket size.
+\end_layout
+
+\begin_layout Standard
+These commands are used to emphasize levels of brackets:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+all brackets in the same size:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+this looks better:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For the second formula the command
+\series bold
+
+\backslash
+Big((A+B)(A-B)
+\backslash
+Big)^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+C
+\series default
+ has been used.
+\end_layout
+
+\begin_layout Standard
+Here is an overview about all bracket sizes:
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\backslash
+Bigg(
+\backslash
+exp
+\backslash
+bigg<
+\backslash
+Big[
+\backslash
+big{
+\backslash
+ln(3x)
+\backslash
+big}^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+sin(x)
+\backslash
+Big]^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+bigg>
+\backslash
+Bigg)^0,5
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+Besides the
+\series bold
+
+\backslash
+big
+\series default
+-commands there is the variant
+\series bold
+
+\backslash
+bigm
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash bigm"
+
+\end_inset
+
+ that adds a bit more space between the bracket and its content, and the
+ variant
+\series bold
+
+\backslash
+bigl
+\series default
+-
+\series bold
+
+\backslash
+bigr
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"
+
+\end_inset
+
+, that don't add additional space.
+ The
+\emph on
+l
+\emph default
+ at the end of the command
+\series bold
+
+\backslash
+bigl
+\series default
+ is for a left bracket; for a right bracket this will be replaced by an
+
+\emph on
+r
+\emph default
+.
+ A left or right bracket can each be an opening or closing bracket.
+\end_layout
+
+\begin_layout Standard
+In the following table is a comparison of the variants:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="0">
+<column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bigm(
+\backslash
+bigm(
+\backslash
+ln(3x)
+\backslash
+bigm)^2
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\backslash
+Bigm)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Big(
+\backslash
+big(
+\backslash
+ln(3x)
+\backslash
+big)^2
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\backslash
+Big)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bigl(
+\backslash
+bigl(
+\backslash
+ln(3x)
+\backslash
+bigr)^2
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\backslash
+Bigr)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigl)
+\backslash
+ln(3x)
+\backslash
+bigr(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Automatic Bracket Size
+\begin_inset LatexCommand label
+name "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Bracket size ! automatic"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Brackets with variable size can be inserted with the commands
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash left"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash right"
+
+\end_inset
+
+ or via the math toolbar button
+\begin_inset Graphics
+ filename ../images/dialog-show_mathdelimiter.png
+ scale 85
+
+\end_inset
+
+.
+ Directly behind
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ the wanted bracket must be inserted.
+ The bracket size will then automatically be calculated for the output.
+\end_layout
+
+\begin_layout Standard
+\align center
+normal bracket: The command
+\series bold
+
+\backslash
+ln(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+)
+\series default
+ creates
+\begin_inset Formula \[
+\ln(\frac{A}{C})\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+multiline bracket: The command
+\series bold
+
+\backslash
+ln
+\backslash
+left(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+right)
+\series default
+ creates
+\begin_inset Formula \[
+\ln\left(\frac{A}{C}\right)\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Instead of
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ the shortcut
+\family sans
+Alt-m\InsetSpace ~
+bracket
+\family default
+ can be used.
+ This has the advantage that you can see in LyX immediately the real bracket
+ size and that the matching right bracket will be created too.
+\newline
+The command
+ for the last example would then be:
+\series bold
+
+\backslash
+ln Alt-m
+\series default
+
+\series bold
+(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\end_layout
+
+\begin_layout Standard
+To omit a left or right bracket, a dot is inserted for the omitted bracket.
+ For example the command
+\series bold
+
+\backslash
+left.
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+right}
+\series default
+ creates:
+\series bold
+
+\begin_inset Formula \[
+\left.\frac{A}{B}\right\} \]
+
+\end_inset
+
+
+\series default
+The commands
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ will be converted by LyX to brackets in the right size when the document
+ is reloaded and an omitted bracket will appear as dashed line.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
+ the command
+\series bold
+
+\backslash
+middle
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash middle"
+
+\end_inset
+
+ is additionally available for all brackets and limits.
+ With this command the height of the following character is adapted to the
+ one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+needed for physical vectors:
+\begin_inset Formula \[
+\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
+
+\end_inset
+
+For physical vectors there is a special LaTeX-package, described in
+\begin_inset LatexCommand ref
+reference "sub:Physical-Vectors"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Brackets
+\begin_inset LatexCommand index
+name "Brackets ! horizontal"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{2.3mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+overbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+3
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commands ! O ! \\textbackslash overbrace"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\overbrace{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-2.2mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+underbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_5
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commands ! U ! \\textbackslash underbrace"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\underbrace{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overbrace
+\backslash
+underbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A+B_w
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_7
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example it doesn't matter if
+\series bold
+
+\backslash
+overbrace
+\series default
+ or
+\series bold
+
+\backslash
+underbrace
+\series default
+ is inserted at first.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When brackets are needed that overlap each other, multiline formulas, as
+ described in
+\begin_inset LatexCommand ref
+reference "sec:Multiline-Formulas"
+
+\end_inset
+
+, must be used:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
+ & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
+
+\end_inset
+
+In the first row the formula is inserted together with the first brace.
+ It is hereby important that the space command
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Space commands are explained in
+\begin_inset LatexCommand ref
+reference "sub:Predefined-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+:
+\series default
+ is inserted before the first
+\begin_inset Formula $d$
+\end_inset
+
+, because the brace that ends behind the
+\begin_inset Formula $q$
+\end_inset
+
+ prevents that the following
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ is surrounded by space.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+because a bracket is not handled as character, see
+\begin_inset LatexCommand ref
+reference "sub:Binary-Operators"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ In the second row the second brace is inserted.
+ As it should begin before the
+\begin_inset Formula $b$
+\end_inset
+
+, first the command
+\series bold
+
+\backslash
+hphantom{gggg+
+\backslash
+:}
+\series default
+ is inserted.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+more about
+\series bold
+
+\backslash
+hphantom
+\series default
+ see
+\begin_inset LatexCommand ref
+reference "sub:Placeholders"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ This space is needed because the
+\begin_inset Quotes eld
+\end_inset
+
++
+\begin_inset Quotes erd
+\end_inset
+
+ is also surrounded by space in the formula.
+ The brace is placed under the command
+\series bold
+
+\backslash
+hphantom{bbqq+dddd}
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+It gets more complicated when brackets overlap each other, like in the following
+ example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+ & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+The first formula row is the same as the second row of the previous example,
+ with the difference that the brace is above.
+ The second row contains the formula together with the second brace.
+ To avoid that there is space between the upper brace in the first row and
+ the formula, the row spacing need to be reduced.
+ This is not easily possible due to a bug in LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1505
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ As solution for the problem, the global formula row separation
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! J ! \\textbackslash jot"
+
+\end_inset
+
+ must be changed to -6\InsetSpace \thinspace{}
+pt before the formula with the command
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\series default
+ in TeX-mode.
+
+\series bold
+
+\backslash
+jot
+\series default
+ is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
+pt using the same
+ command.
+ More about the row separation in formulas is explained in
+\begin_inset LatexCommand ref
+reference "sub:Line-Separation"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Arrows
+\begin_inset LatexCommand index
+name "Arrows"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Arrows can be inserted via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/leftarrow.png
+ scale 85
+
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Arrows
+\begin_inset LatexCommand index
+name "Arrows ! horizontal"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gets$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Leftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hookleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hookleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\to$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Rightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hookrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hookrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightleftharpoons
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightleftharpoons$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{25pt}
+\end_layout
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longmapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longmapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leadsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leadsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dasharrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Arrows used as accent like e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+vector arrows are listed in
+\begin_inset LatexCommand ref
+reference "sec:Accents"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore there are the labeled arrows
+\begin_inset LatexCommand index
+name "Arrows ! labeled"
+
+\end_inset
+
+
+\series bold
+
+\backslash
+xleftarrow
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! X ! \\textbackslash xleftarrow"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+xrightarrow
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
+
+\end_inset
+
+.
+ When inserting one of these commands in a formula, an arrow with two blue
+ boxes appear where the label can be inserted.
+ The length of the arrow adapts to the label width.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+F(a)
+\backslash
+xleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+F(x)
+\backslash
+xrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(a)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical and diagonal Arrows
+\begin_inset LatexCommand index
+name "Arrows ! diagonal"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Arrows ! vertical"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nearrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nearrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+searrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\searrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+swarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\swarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nwarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nwarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Vertical arrows can be used also as delimiter together with the commands
+ described in
+\begin_inset LatexCommand ref
+reference "sub:Manual-Bracket-Size"
+
+\end_inset
+
+ and
+\begin_inset LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Accents
+\begin_inset LatexCommand label
+name "sec:Accents"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Accents can be inserted via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/hat.png
+ scale 85
+
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Accents for one Character
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+accents in text see
+\begin_inset LatexCommand ref
+reference "sub:Accents-in-Text"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand label
+name "sub:Accents-for-one"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents ! for one character"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddddot{A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vec
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset LatexCommand index
+name "Vectors"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\vec{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bar
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\bar{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathring
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tilde
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hat
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\hat{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+check
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\check{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+acute
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\acute{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+grave
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\grave{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+breve
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\breve{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To create umlauts
+\begin_inset LatexCommand index
+name "Umlauts"
+
+\end_inset
+
+ in formulas, a quotation mark is inserted before the vowel.
+ These two characters are then treated by LaTeX as
+\emph on
+one
+\emph default
+ character when the formula part with the umlaut is marked as German.
+ In contrary to
+\series bold
+
+\backslash
+ddot
+\series default
+, with this method
+\begin_inset Quotes eld
+\end_inset
+
+real
+\begin_inset Quotes erd
+\end_inset
+
+ umlauts are created as demonstrated in the following example:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\lang ngerman
+\begin_inset Quotes grd
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\lang ngerman
+\begin_inset Formula $"i$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Another advantage to
+\series bold
+
+\backslash
+ddot
+\series default
+ is that umlauts can directly be converted to mathematical text because
+ the accent commands above are
+\emph on
+not allowed
+\emph default
+
+\emph on
+in mathematical text
+\emph default
+.
+ To convert an accented character to mathematical text, only the character
+ under the accent may be converted.
+ This applies also for all other conversions, e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+to italic or bold.
+\end_layout
+
+\begin_layout Standard
+In mathematical text, umlauts and other accented characters can directly
+ be inserted.
+\end_layout
+
+\begin_layout Subsection
+Accents for Operators
+\begin_inset LatexCommand index
+name "Accents ! for operators"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! O ! \\textbackslash overset"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! U ! \\textbackslash underset"
+
+\end_inset
+
+ characters can be placed above or below an operator, respectively, to accent
+ it.
+ With the command
+\series bold
+
+\backslash
+sideset
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash sideset"
+
+\end_inset
+
+ characters can be set before and behind an operator.
+ The command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset{character
+\series default
+
+\series bold
+before}{character
+\series default
+
+\series bold
+behind}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset
+\series default
+ must always be before the operator that should be accented.
+ You can accent with several characters and even with other operators and
+ symbols.
+ To place with
+\series bold
+
+\backslash
+sideset
+\series default
+ for example only characters behind an operator, write nothing between the
+ first braces but don't omit the braces.
+\end_layout
+
+\begin_layout Standard
+For example the command
+\series bold
+
+\backslash
+sideset{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\series default
+'
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+sum_k=1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+^
+\series bold
+n
+\series default
+ produces:
+\begin_inset Formula \[
+\sideset{}{'}\sum_{k=1}^{n}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+overset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\series bold
+a
+\series default
+ produces:
+\begin_inset Formula \[
+\overset{a}{\maltese}\]
+
+\end_inset
+
+As seen in the last example, with
+\series bold
+
+\backslash
+overset
+\series default
+ and
+\series bold
+
+\backslash
+underset
+\series default
+ also symbols and characters can be accented; with
+\series bold
+
+\backslash
+sideset
+\series default
+ this is not possible.
+\end_layout
+
+\begin_layout Subsection
+Accents for several Characters
+\begin_inset LatexCommand label
+name "sub:Accents-for-several"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents ! for several characters"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overleftrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underleftrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widetilde
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widehat
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+With these commands as many characters as you like can be accented.
+ But the accents
+\series bold
+
+\backslash
+widetilde
+\series default
+ and
+\series bold
+
+\backslash
+widehat
+\series default
+ will only be set in the output with a length of three characters, as shown
+ in the following example:
+\begin_inset Formula \[
+\widetilde{A+B=C-D}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! O ! \\textbackslash overset"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! U ! \\textbackslash underset"
+
+\end_inset
+
+ described in the previous subsection it is also possible to accent several
+ characters.
+ The command
+\series bold
+
+\backslash
+underset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\begin_inset Formula $\downarrow$
+\end_inset
+
+***
+\series default
+ creates:
+\begin_inset Formula \[
+\underset{***}{A=B}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Space
+\begin_inset LatexCommand label
+name "sub:Space"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Space ! horizontal"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Predefined Space
+\begin_inset LatexCommand label
+name "sub:Predefined-Space"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Space ! horizontal ! predefined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sometimes it is necessary to insert horizontal space to a formula.
+ This is done by inserting a protected space (shortcut
+\family sans
+Ctrl-Space
+\family default
+).
+ A blue
+\begin_inset Quotes eld
+\end_inset
+
+
+\series bold
+\color blue
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ appears and by pressing
+\family sans
+Space
+\family default
+ several times one can select one of eight different space sizes.
+ The spaces can also be inserted using the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/space.png
+ scale 85
+
+\end_inset
+
+ or special commands.
+ Independent from the inserted command, one can select the size again by
+ pressing
+\family sans
+Space
+\family default
+ afterwards.
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="7">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="6.8cm">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+,
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+;
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+quad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+qquad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+!
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Number of
+\family sans
+Space
+\family default
+ keystrokes after inserting the protected space
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+4
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+5
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\, B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\: B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\; B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\quad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\qquad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\! B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The last size seem to produce no space.
+ It is displayed red in LyX contrary to the other sizes, because it is a
+ negative space.
+ There are two more negative spaces:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="6.8cm">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+negmedspace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+negthickspace
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Number of
+\family sans
+Space
+\family default
+ keystrokes after inserting the protected space
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+6
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+7
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\negmedspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\negthickspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative spaces can lead to characters overlapping each other.
+ Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+useful for summation
+ operators:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\backslash
+sum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Relations like for example equal signs, are always surrounded by space.
+ To suppress this, the equal sign is placed into a TeX-brace.
+ The following example demonstrates this:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+normal equation
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\raisebox{5mm}{}$
+\end_inset
+
+equation without space
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A{=}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+The command for the last formula is:
+\series bold
+A
+\backslash
+{=
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Spaces are needed for physical units, because the space between the value
+ and the unit is the smallest one and not a normal space.
+ For units in text, the smallest space is inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Formatting\SpecialChar \menuseparator
+Thin\InsetSpace ~
+Space
+\family default
+ (shortcut
+\family sans
+Ctrl-Shift-Space
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+An example to visualize the difference:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+24 kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+space between value and unit
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+24\InsetSpace \thinspace{}
+kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+smallest space between value and unit
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Variable Space
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+for vertical space in formulas see
+\begin_inset LatexCommand ref
+reference "sub:Line-Separation"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand label
+name "sub:Variable-Space"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Space ! horizontal ! variable"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Space with a defined length can be inserted in LyX with the command
+\newline
+
+\series bold
+
+\backslash
+hspace{length}
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash hspace"
+
+\end_inset
+
+.
+ For the length all units listed in
+\begin_inset LatexCommand ref
+reference "tab:Used-units"
+
+\end_inset
+
+ are allowed, except of the unit
+\begin_inset Quotes eld
+\end_inset
+
+mu
+\begin_inset Quotes erd
+\end_inset
+
+.
+ The length may also be negative.
+ To insert so many space that the formula uses all available space, the
+ command
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash hfill"
+
+\end_inset
+
+ is used.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -1mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=B
+\backslash
+hspace{3cm
+\begin_inset Formula $\to$
+\end_inset
+
+A
+\backslash
+not=C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=B\hspace{3cm}A\not=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+hspace{-1mm
+\begin_inset Formula $\to$
+\end_inset
+
+A
+\backslash
+not=A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\hspace{-1mm}A\not=A$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=A
+\backslash
+hfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=A\hfill B=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the last example the available space is given by the longest column entry
+ of the table.
+ In an inline formula the space depends on the length of the line in which
+
+\series bold
+
+\backslash
+hfill
+\series default
+ is inserted.
+ Thus, when the line uses the full width, no space will be created.
+
+\series bold
+
+\backslash
+hfill
+\series default
+ has only an effect on displayed formulas when the formula style
+\series bold
+Indented
+\series default
+ is used.
+ (Formula styles are explained in
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+.)
+\end_layout
+
+\begin_layout Standard
+The commands
+\series bold
+
+\backslash
+hspace
+\series default
+ and
+\series bold
+
+\backslash
+hfill
+\series default
+ can also be inserted in TeX-mode to use them for text:
+\end_layout
+
+\begin_layout Standard
+This is a line with
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{2cm}
+\end_layout
+
+\end_inset
+
+2\InsetSpace \thinspace{}
+cm space.
+\end_layout
+
+\begin_layout Standard
+This is a line with
+\hfill
+maximum space.
+\end_layout
+
+\begin_layout Standard
+In the last example
+\series bold
+
+\backslash
+hfill
+\series default
+ was inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Formatting\SpecialChar \menuseparator
+Horizontal\InsetSpace ~
+Fill
+\family default
+, what is not possible in formulas.
+ This has the advantage that one can directly see in LyX that this is a
+ stretch space.
+\end_layout
+
+\begin_layout Standard
+When the commands are at the begin of a text line but not at the beginning
+ of a paragraph, they will be ignored by LaTeX.
+ To avoid that, the command
+\series bold
+
+\backslash
+hspace*
+\series default
+ is used instead of
+\series bold
+
+\backslash
+hspace
+\series default
+.
+ To get the same with
+\series bold
+
+\backslash
+hfill
+\series default
+, a line break and an empty placeholder
+\series bold
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+for placeholders see
+\begin_inset LatexCommand ref
+reference "sub:Placeholders"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is inserted in TeX-mode with the command
+\series bold
+
+\backslash
+vphantom{}
+\series default
+before
+\series bold
+
+\backslash
+hfill
+\series default
+.
+
+\end_layout
+
+\begin_layout Subsection
+Space besides inline Formulas
+\begin_inset LatexCommand index
+name "Space ! besides inline formulas"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The space that surrounds inline formulas can be adjusted with the length
+
+\series bold
+
+\backslash
+mathsurround
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mathsurround"
+
+\end_inset
+
+
+\series default
+.
+ The value of a length is set with the command
+\series bold
+
+\backslash
+setlength
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash setlength"
+
+\end_inset
+
+
+\series default
+ that has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{length name}{value}
+\end_layout
+
+\begin_layout Standard
+To set
+\series bold
+
+\backslash
+mathsurround
+\series default
+ to the value 5\InsetSpace \thinspace{}
+mm, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\begin_layout Standard
+is inserted in TeX-mode.
+ 5\InsetSpace \thinspace{}
+mm space will now be set around all inline formulas:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This is a line with an inline formula
+\begin_inset Formula $A=B$
+\end_inset
+
+ with 5\InsetSpace \thinspace{}
+mm surrounding space.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{0pt}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To return to the predefined value,
+\series bold
+
+\backslash
+mathsurround
+\series default
+ is set to the value 0\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Section
+Boxes and Frames
+\begin_inset LatexCommand index
+name "Boxes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Frames | see {Boxes}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Boxes for text are described in chapter
+\family typewriter
+Boxes
+\family default
+ in the
+\family typewriter
+Embedded\InsetSpace ~
+Objects
+\family default
+ manual.
+\end_layout
+
+\begin_layout Subsection
+Boxes with Frame
+\begin_inset LatexCommand label
+name "sub:Boxes-with-Frame"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxes ! with frame"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+It is possible to frame formulas or parts of it with the commands
+\series bold
+
+\backslash
+fbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! F ! \\textbackslash fbox"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+boxed
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash boxed"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+When one of these commands is inserted to a formula, a blue box appears
+ within a frame to enter formula parts.
+ For
+\series bold
+
+\backslash
+fbox
+\series default
+ an additional formula has to be created by
+\family sans
+Ctrl-m
+\family default
+ within this box
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Due to a bug in LyX it is not possible to create a new formula with
+\family sans
+Ctrl-m
+\family default
+, see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+, because the box content will otherwise be treated as mathematical text.
+ When
+\series bold
+
+\backslash
+boxed
+\series default
+ is used, a new formula is automatically created inside the frame.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+fbox
+\series default
+ is not suitable to frame displayed formulas, because the formula will always
+ be set in the size of the text.
+
+\series bold
+
+\backslash
+boxed
+\series default
+ is in contrary not suitable to frame inline formulas, because the formula
+ will always be set in the size of a displayed formula.
+\end_layout
+
+\begin_layout Standard
+As extension to
+\series bold
+
+\backslash
+fbox
+\series default
+ there is the command
+\series bold
+
+\backslash
+framebox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! F ! \\textbackslash framebox"
+
+\end_inset
+
+ where additionally the frame width and the alignment can be specified.
+
+\series bold
+
+\backslash
+framebox
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+framebox[frame width][position]{box content}
+\end_layout
+
+\begin_layout Standard
+The position can either be
+\emph on
+l
+\emph default
+ or
+\emph on
+r
+\emph default
+.
+
+\emph on
+l
+\emph default
+ left aligns,
+\emph on
+r
+\emph default
+ right aligns the formula in the box.
+ When no position is given, the formula will be centered.
+\newline
+Is no width given,
+ also no position can be given.
+ In this case the frame width is adjusted to the box content like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+When the command
+\series bold
+
+\backslash
+framebox
+\series default
+ is inserted, a box appears containing three blue boxes.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Due to a bug in LyX the cursor has to be placed left beside blue the boxes
+ to fill them, see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
+\end_layout
+
+\end_inset
+
+LyX-bug #2461
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ The first two boxes are surrounded by brackets and denote the two optional
+ arguments.
+ The third box is for formula parts like for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+The table has been set into a minipage to make the footnote appearing.
+ Otherwise the footnote text would not be displayed.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Box Frameless
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "c"
+use_parbox 0
+width "100col%"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Due to a bug in LyX it is not possible to create a new formula with
+\family sans
+Ctrl-m
+\family default
+, see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\family sans
+Ctrl-m
+\family default
+
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+boxed
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+framebox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+20mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\family sans
+Ctrl-m
+\family default
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}$
+\end_inset
+
+
+\begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The frame thickness can also be adjusted.
+ To do this the following commands have to be inserted in TeX-mode before
+ the formula
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+thickness
+\begin_inset Quotes erd
+\end_inset
+
+
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Quotes eld
+\end_inset
+
+distance
+\begin_inset Quotes erd
+\end_inset
+
+ specifies the minimal distance between the frame and the first character
+ in the box.
+ An example for this is the following framed formula:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 2mm
+\backslash
+fboxsep 3mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\boxed{A+B=C}\]
+
+\end_inset
+
+Before this formula the commands
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+2mm
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3mm
+\end_layout
+
+\begin_layout Standard
+were inserted in TeX-mode.
+ The given values are used for all following boxes.
+\end_layout
+
+\begin_layout Standard
+To return to the standard frame size, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+0.4pt
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3pt
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+is inserted in TeX-mode before the next formula.
+\end_layout
+
+\begin_layout Subsection
+Boxes without Frame
+\begin_inset LatexCommand label
+name "sub:Boxes-without-Frame"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxes ! without frame"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For boxes without a frame there are the following box commands:
+\series bold
+
+\backslash
+mbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mbox"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+makebox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash makebox"
+
+\end_inset
+
+, and
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash raisebox"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With
+\series bold
+
+\backslash
+raisebox
+\series default
+ a box can be super- or subscripted.
+ But in contrary to normal super- and subscripting, the characters in the
+ box keep their font size.
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox{height}{box content}
+\end_layout
+
+\begin_layout Standard
+When the box should contain a formula, an extra formula is needed like for
+
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+H
+\backslash
+raisebox{2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+ lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $H\raisebox{2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+H
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $H\raisebox{-2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Ctrl-m
+\family default
+
+\backslash
+sqrt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+$A=
+\backslash
+raisebox{-2mm}{$
+\backslash
+sqrt{B}$}$
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The last formula can currently only be created using TeX-mode because LyX
+ inserts a box instead of the needed extra formula.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+mbox
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+fbox
+\series default
+ and
+\series bold
+
+\backslash
+makebox
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+framebox
+\series default
+, with the difference that there is no frame.
+\end_layout
+
+\begin_layout Subsection
+Colored Boxes
+\begin_inset LatexCommand label
+name "sub:Colored-Boxes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxes ! colored"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all commands explained in this section, the LaTeX-package
+
+\series bold
+color
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+The LaTeX-package
+\series bold
+color
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! color"
+
+\end_inset
+
+ has to be loaded in the LaTeX-preamble with the line
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+When text is colored somewhere in the document with a predefined color,
+ LyX loads the LaTeX-package
+\series bold
+color
+\series default
+ automatically.
+ Thus it is possible that the package is loaded twice, but this doesn't
+ arise problems.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
+amble.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{color}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To color boxes, the command
+\series bold
+
+\backslash
+colorbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! C ! \\textbackslash colorbox"
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox{color}{box content}
+\end_layout
+
+\begin_layout Standard
+The box content can also be a box and a
+\series bold
+
+\backslash
+colorbox
+\series default
+ can also be part of another box (see the 2nd and 3rd example).
+ When the box should contain a formula, an extra formula has to be created,
+ the same as for
+\series bold
+
+\backslash
+fbox
+\series default
+.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+This also applies for the command
+\series bold
+
+\backslash
+fcolorbox
+\series default
+.
+ Thereby note
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One of the following predefined colors can be chosen:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+black
+\series default
+,
+\series bold
+blue
+\series default
+,
+\series bold
+cyan
+\series default
+,
+\series bold
+green
+\series default
+,
+\series bold
+magenta
+\series default
+,
+\series bold
+red
+\series default
+,
+\series bold
+white
+\series default
+, and
+\series bold
+yellow
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+colorbox{yellow
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox
+\series default
+ only colors the box but not the characters in the box.
+ To color all characters, the whole formula is highlighted and the wanted
+ color is chosen in the
+\family sans
+Text\InsetSpace ~
+Style
+\family default
+ dialog.
+ The dialog can be called with the toolbar button
+\begin_inset Graphics
+ filename ../images/dialog-show_character.png
+ scale 85
+
+\end_inset
+
+ or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Text\InsetSpace ~
+Style\SpecialChar \menuseparator
+Customized
+\family default
+.
+ The formula number has then the same color as the formula.
+ When the formula number should get another color than the formula characters,
+ the color must be changed within the formula.
+\end_layout
+
+\begin_layout Standard
+An example:
+\end_layout
+
+\begin_layout Standard
+
+\color red
+\begin_inset Formula \begin{equation}
+\int A=B\label{eq:red}\end{equation}
+
+\end_inset
+
+
+\color green
+
+\begin_inset Formula \begin{equation}
+\textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formula
+\begin_inset LatexCommand eqref
+reference "eq:red"
+
+\end_inset
+
+ is completely colored red.
+\newline
+Formula
+\begin_inset LatexCommand eqref
+reference "eq:redgreen"
+
+\end_inset
+
+ was first completely colored green to set the color for the formula number.
+ Subsequently the formula characters were colored red.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To color the frame different than the rest of the box, the command
+\series bold
+
+\backslash
+fcolorbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! F ! \\textbackslash fcolorbox"
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fcolorbox{frame color}{color}{box content}
+\end_layout
+
+\begin_layout Standard
+So
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ is an extension of the command
+\series bold
+
+\backslash
+colorbox
+\series default
+.
+ The frame width is set, like for
+\series bold
+
+\backslash
+framebox
+\series default
+, with
+\series bold
+
+\backslash
+fboxrule
+\series default
+ and
+\series bold
+
+\backslash
+fboxsep
+\series default
+.
+ An example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 1mm
+\backslash
+fboxsep 1mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\fcolorbox{cyan}{magenta}{A=B}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This formula was created with the command
+\newline
+
+\series bold
+
+\backslash
+fcolorbox{cyan
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{magenta
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To use other colors than the predefined ones, they have to be defined first.
+\end_layout
+
+\begin_layout Standard
+One can for example define the color
+\begin_inset Quotes eld
+\end_inset
+
+
+\series bold
+darkgreen
+\series default
+
+\begin_inset Quotes erd
+\end_inset
+
+ with the LaTeX-preamble line:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+definecolor{darkgreen}{cmyk}{0.5,
+\series default
+
+\series bold
+0,
+\series default
+
+\series bold
+1,
+\series default
+
+\series bold
+0.5}
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash definecolor"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+cmyk
+\series default
+ is the color space that denotes the colors
+\series bold
+cyan
+\series default
+,
+\series bold
+magenta
+\series default
+,
+\series bold
+yellow
+\series default
+, and
+\series bold
+black
+\series default
+.
+ The four comma separated numbers are the portion factor for the corresponding
+ colors of the color space.
+ The factors can be in the range of 0\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+1.
+ Instead of
+\series bold
+cmyk
+\series default
+ also the color space
+\series bold
+rgb
+\series default
+ can be used for definitions.
+
+\series bold
+rgb
+\series default
+ denotes
+\series bold
+red
+\series default
+,
+\series bold
+green
+\series default
+, and
+\series bold
+blue
+\series default
+, so that there are in this case three portion factors for the corresponding
+ colors.
+ Furthermore there is the color space
+\series bold
+gray
+\series default
+ with one portion factor for the gray value.
+\end_layout
+
+\begin_layout Standard
+As example a framed box with the new defined color
+\series bold
+darkgreen
+\series default
+ where the characters have been colored
+\series bold
+yellow
+\series default
+:
+\begin_inset Formula \begin{equation}
+\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Self-defined colors can also be be used for text with the help of the command
+
+\series bold
+
+\backslash
+textcolor
+\series default
+:
+\begin_inset LatexCommand index
+name "Text ! colored"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textcolor{darkgreen}{
+\end_layout
+
+\end_inset
+
+This sentence is
+\begin_inset Quotes eld
+\end_inset
+
+darkgreen
+\begin_inset Quotes erd
+\end_inset
+
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+textcolor
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash textcolor"
+
+\end_inset
+
+ is used in the scheme
+\series bold
+
+\backslash
+textcolor{color}{characters to color}
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Paragraph Boxes
+\begin_inset LatexCommand label
+name "sub:Paragraph-Boxes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxes ! as paragraph"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+A box that can contain several lines and paragraphs, a so called paragraph
+ box (parbox), can be created with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Box
+\family default
+ or the toolbar button
+\begin_inset Graphics
+ filename ../images/box-insert.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The following example shows a framed parbox in a line:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+This is a line
+\begin_inset Box Boxed
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 1
+width "5cm"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Standard
+This is a paragraph box.
+ It is exactly 5\InsetSpace \thinspace{}
+cm long and can also contain formulas:
+\begin_inset Formula $\int A\,\mathrm{d}s=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ with a parbox.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Such a box is created by right-clicking on the gray box inset.
+ A dialog pops up showing the box properties.
+ In our case set:
+\emph on
+Decoration
+\emph default
+: Recangular box,
+\emph on
+Inner Box
+\emph default
+: Parbox,
+\emph on
+Width
+\emph default
+: 5\InsetSpace \thinspace{}
+cm,
+\emph on
+Vertical Box Alignment
+\emph default
+: Middle
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+In LaTeX a parbox is created with the command
+\series bold
+
+\backslash
+parbox
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! P ! \\textbackslash parbox"
+
+\end_inset
+
+ that has the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+parbox[position]{width}{box content}
+\end_layout
+
+\begin_layout Standard
+The positions
+\emph on
+b
+\emph default
+ and
+\emph on
+t
+\emph default
+ are possible.
+
+\emph on
+b
+\emph default
+ for bottom means that the box is aligned within the surrounding text with
+ its last line.
+ With
+\emph on
+t
+\emph default
+ for top this is done with the first line.
+ When no position is given, the box will be vertically centered, see section
+
+\emph on
+Boxes
+\emph default
+ of the
+\emph on
+Embedded\InsetSpace ~
+Objects
+\emph default
+ manual for examples.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To frame formulas completely, including the formula number, the formula
+ must be set into a parbox.
+ To do this, the command
+\series bold
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\series default
+ is inserted in TeX-mode before the formula.
+
+\series bold
+
+\backslash
+linewidth
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash linewidth"
+
+\end_inset
+
+
+\series default
+ is hereby the line width set for the document.
+ Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
+times the frame separation and
+ the frame thickness must be subtracted from the line width.
+ As this is not automatically done by LyX due to a bug
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
+\end_layout
+
+\end_inset
+
+LyX-bug #4483
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, TeX-mode has to be used.
+ To be able to multiply and subtract in arguments, the LaTeX-package
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+calc
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! calc"
+
+\end_inset
+
+ must be loaded in the LaTeX-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+Behind the formula both boxes are closed by entering
+\series bold
+}}
+\series default
+ in TeX-mode.
+ Here is an example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxsep 5mm
+\backslash
+fboxrule 5mm
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+As a parbox is used as argument of
+\series bold
+
+\backslash
+fbox
+\series default
+, there is in this case no difference between
+\series bold
+
+\backslash
+fbox
+\series default
+ and
+\series bold
+
+\backslash
+boxed
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Paragraph boxes are very useful to comment formulas directly.
+ To do this,
+\series bold
+
+\backslash
+parbox
+\series default
+ is used in combination with the command
+\series bold
+
+\backslash
+tag
+\series default
+.
+ (more about
+\series bold
+
+\backslash
+tag
+\series default
+ see
+\begin_inset LatexCommand ref
+reference "sub:User-defined-Numbering"
+
+\end_inset
+
+)
+\end_layout
+
+\begin_layout Standard
+An example of a formula commented with
+\series bold
+
+\backslash
+parbox
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*{
+\backslash
+parbox{5cm}{
+\end_layout
+
+\end_inset
+
+This is a description.
+ It is distinctly separated from the formula and multiline.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}}
+\backslash
+]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Such a formula must be inserted completely in TeX-mode because LyX does
+ not yet support the command
+\series bold
+
+\backslash
+parbox
+\series default
+ in formulas.
+ The formula is created with the following command sequence:
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*
+\backslash
+{
+\backslash
+parbox{5cm}{
+\series default
+ is inserted in TeX-mode.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+When the formula style
+\series bold
+Indented
+\series default
+ is used,
+\series bold
+
+\backslash
+tag*
+\backslash
+{
+\series default
+ can also be replaced by
+\series bold
+
+\backslash
+hfill
+\series default
+.
+ (formula styles see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+)
+\end_layout
+
+\end_inset
+
+ Then the description follows as normal text, and finally
+\series bold
+}}
+\backslash
+]
+\series default
+ is inserted in TeX-mode.
+ The commands
+\series bold
+
+\backslash
+[
+\series default
+ and
+\series bold
+
+\backslash
+]
+\series default
+ hereby create a displayed formula.
+\end_layout
+
+\begin_layout Standard
+The advantages of
+\series bold
+
+\backslash
+parbox
+\series default
+ can be seen in this example that was
+\begin_inset Quotes eld
+\end_inset
+
+commented
+\begin_inset Quotes erd
+\end_inset
+
+ using the mathematical textmode:
+\begin_inset Formula \[
+5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Operators
+\begin_inset LatexCommand index
+name "Operators"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Big Operators
+\begin_inset LatexCommand label
+name "sub:Big-Operators"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operators ! big"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Sums"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Integrals"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To be able to use all integral operators listed here, the option
+\family sans
+Use esint package automatically
+\family default
+ must be set in the document settings under
+\family sans
+Math\InsetSpace ~
+Options
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash sum"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sum$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+int
+\begin_inset LatexCommand index
+name "Commands ! I ! \\textbackslash int"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\int$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+intop
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\intop$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointop
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointop$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointctrclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointctrclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prod
+\begin_inset LatexCommand index
+name "Commands ! P ! \\textbackslash prod"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+coprod
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\coprod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigodot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigodot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigotimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigotimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigoplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigoplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigwedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigwedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigvee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigvee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigsqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigsqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+biguplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\biguplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+All big operators can also be inserted via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/intop.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The operators are called big because they are bigger than the sometimes
+ equal looking binary operators.
+ All big operators can have limits as described in the next subsection.
+\end_layout
+
+\begin_layout Standard
+The operators
+\series bold
+
+\backslash
+intop
+\series default
+ and
+\series bold
+
+\backslash
+ointop
+\series default
+ are different from
+\series bold
+
+\backslash
+int
+\series default
+ and
+\series bold
+
+\backslash
+oint
+\series default
+, resp.\InsetSpace ~
+in the style the operator limits are displayed, see
+\begin_inset LatexCommand ref
+reference "sub:Operator-Limits"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Subsubsection*
+Advices for Integrals
+\end_layout
+
+\begin_layout Standard
+The letter
+\emph on
+d
+\emph default
+ in an integral is an operator, that therefore has to be set upright.
+ This is done by highlighting the
+\emph on
+d
+\emph default
+ and using the keyboard shortcut
+\family sans
+Alt-c\InsetSpace ~
+r
+\family default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Font styles
+\series bold
+
+\series default
+see
+\begin_inset LatexCommand ref
+reference "sub:Font-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Finally the smallest space is inserted before the
+\emph on
+d
+\emph default
+, as this is usual for operators.
+ An example:
+\end_layout
+
+\begin_layout Standard
+incorrect:
+\begin_inset Formula $\int A(x)dx$
+\end_inset
+
+
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{in}
+\end_layout
+
+\end_inset
+
+correct:
+\begin_inset Formula $\int A(x)\,\mathrm{d}x$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For multiple integrals there are the following commands:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iiiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dotsint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Subsection
+Operator Limits
+\begin_inset LatexCommand label
+name "sub:Operator-Limits"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operators ! Limits"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits are created by super- and subscripts:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prod^
+\backslash
+infty
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+_0
+\begin_inset Formula $\to$
+\end_inset
+
+A(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Limits of inline formulas are set right beside the operator.
+ Limits in displayed formulas are set above or below the operator, except
+ of integral limits.
+\end_layout
+
+\begin_layout Standard
+To force that the limits are set beside the operator, the cursor is set
+ directly behind the operator and the limits type is changed with the menu
+
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Change Limits Type
+\family default
+ to
+\family sans
+\series bold
+Inline
+\family default
+\series default
+ (shortcut
+\family sans
+Alt-m\InsetSpace ~
+l
+\family default
+).
+ An example:
+\end_layout
+
+\begin_layout Standard
+The default limits type is this:
+\begin_inset Formula \[
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
+
+\end_inset
+
+This is how it looks when the limits type was changed to
+\family sans
+\series bold
+Inline
+\family default
+\series default
+:
+\begin_inset Formula \[
+\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
+
+\end_inset
+
+For integrals, except of
+\series bold
+
+\backslash
+intop
+\series default
+ and
+\series bold
+
+\backslash
+ointop
+\series default
+, the limits are by default set beside the operator.
+ But for multiple integrals the limits are often set below the operator.
+ In the following example the limits type was therefore set to
+\series bold
+Display
+\series default
+ and so set below the integrals:
+\begin_inset Formula \begin{equation}
+\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To specify conditions for limits, the commands
+\series bold
+
+\backslash
+subarray
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash subarray"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+substack
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash substack"
+
+\end_inset
+
+ are used.
+ To create for example this expression
+\begin_inset Formula \begin{equation}
+\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+the following has to be done:
+\newline
+First the command
+\series bold
+
+\backslash
+sum
+\series default
+^
+\series bold
+n
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+_
+\series default
+ is typed in.
+ One is now in a blue box under the summation operator and insert there
+ the command
+\series bold
+
+\backslash
+subarray
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+.
+ The blue box is now within a purple box and now several lines can be written
+ among each other.
+ A new line is created by inserting a line break (
+\family sans
+Ctrl-Return
+\family default
+).
+ When now
+\newline
+
+\series bold
+0<k<1000 Ctrl-Return
+\newline
+
+\series default
+is typed in, a new box appears below for the new line.
+\end_layout
+
+\begin_layout Standard
+The alignment of the lines can be changed to left aligned with the
+\family sans
+table
+\family default
+
+\family sans
+toolbar
+\family default
+ or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows &Columns
+\family default
+.
+ To get right alignment,
+\series bold
+
+\backslash
+hfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+ is inserted at the beginning of the line.
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+substack
+\series default
+ is equivalent to
+\series bold
+
+\backslash
+subarray
+\series default
+ with the difference that the lines are always centered.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Like in formula
+\begin_inset LatexCommand eqref
+reference "eq:substack"
+
+\end_inset
+
+ there can be too much space beside an operator, because the characters
+ following the operator are set beside the limits.
+\end_layout
+
+\begin_layout Standard
+To avoid this, the following macro can be used in the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+def
+\backslash
+clap#1{
+\backslash
+hbox to 0pt{
+\backslash
+hss #1
+\backslash
+hss}}
+\newline
+
+\backslash
+def
+\backslash
+mathclap {
+\backslash
+mathpalette
+\backslash
+mathclapinternal}
+\newline
+
+\backslash
+def
+\backslash
+mathclapinternal #1#2{
+\backslash
+clap{$
+\backslash
+mathsurround =0pt #1{#2}$}}
+\end_layout
+
+\begin_layout Standard
+This defines the command
+\series bold
+
+\backslash
+mathclap
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mathclap"
+
+\end_inset
+
+ that sets the width of the limit to 0\InsetSpace \thinspace{}
+pt.
+ The command scheme is
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathclap{limit}
+\end_layout
+
+\begin_layout Standard
+where the limit can consist of several conditions.
+\end_layout
+
+\begin_layout Standard
+Applied on formula
+\begin_inset LatexCommand eqref
+reference "eq:substack"
+
+\end_inset
+
+, one uses the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sum_
+\backslash
+mathclap{
+\backslash
+substack
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+0<k<1000 Ctrl-Enter
+\end_layout
+
+\begin_layout Standard
+to create the lower limit.
+ The summand is now directly behind the summation operator:
+\begin_inset Formula \[
+\sum_{\mathclap{\substack{0<k<1000\\
+\\k\,\in\,\mathbb{N}}
+}}^{n}k^{-2}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+How to use one limit for several operators is described in
+\begin_inset LatexCommand ref
+reference "sub:Self-defined-Operators"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Binary Operators
+\begin_inset LatexCommand label
+name "sub:Binary-Operators"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operators ! binary"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binary operators are surrounded by space when there is a character before
+ and behind them.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
++
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $+$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $-$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pm$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cdot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cdot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+times
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\times$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+div
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\div$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $*$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+star
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\star$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nabla
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nabla$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigtriangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigtriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigtriangleup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigtriangleup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Box$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcirc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcirc$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ominus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ominus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+otimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\otimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+odot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\odot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+amalg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\amalg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+uplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\uplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+setminus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\setminus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangleleft
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangleleft$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangleright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+All binary operators can also be inserted via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/pm.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+To typeset the Laplace operator also
+\series bold
+
+\backslash
+Delta
+\series default
+ or
+\series bold
+
+\backslash
+nabla
+\series default
+^
+\series bold
+2
+\series default
+ (
+\begin_inset Formula $\nabla^{2}$
+\end_inset
+
+) can be used instead of
+\series bold
+
+\backslash
+bigtriangleup
+\series default
+ .
+\end_layout
+
+\begin_layout Standard
+The character
+\family sans
+Menu Separator
+\family default
+ from the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Special Character
+\family default
+ is the operator
+\series bold
+
+\backslash
+triangleright
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Operators
+\begin_inset LatexCommand label
+name "sub:Self-defined-Operators"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operators ! self-defined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the help of the command
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
+
+\end_inset
+
+ custom operators can be defined in the LaTeX-preamble.
+ Its command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator{new command}{display}
+\end_layout
+
+\begin_layout Standard
+Display can be characters or symbols that define how the operator looks
+ in the output.
+ To define a big operator a * is set behind the command.
+ All self-defined big operators can have limits as described in
+\begin_inset LatexCommand ref
+reference "sub:Operator-Limits"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For example the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator*{
+\backslash
+Lozenge}{
+\backslash
+blacklozenge}
+\end_layout
+
+\begin_layout Standard
+defines the command
+\series bold
+
+\backslash
+Lozenge
+\series default
+, that inserts a big operator consisting of the lozenge symbol from
+\begin_inset LatexCommand ref
+reference "sub:Miscellaneous-Symbols"
+
+\end_inset
+
+:
+\begin_inset Formula \[
+\Lozenge_{n=1}^{\infty}\]
+
+\end_inset
+
+The command for this formula is:
+\series bold
+
+\backslash
+Lozenge
+\series default
+^
+\series bold
+
+\backslash
+infty
+\begin_inset Formula $\to$
+\end_inset
+
+_n=1
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When self-defined operators are not used several times in the document,
+ they can also be defined with the commands
+\series bold
+
+\backslash
+mathop
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mathop"
+
+\end_inset
+
+ and
+\series bold
+
+\backslash
+mathbin
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mathbin"
+
+\end_inset
+
+, which have the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop{display}
+\series default
+ and
+\series bold
+
+\backslash
+mathbin{display}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ defines big operators,
+\series bold
+
+\backslash
+mathbin
+\series default
+ binary operators.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ can e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+be used to use one limit for several operators:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for the formula above is:
+\newline
+
+\series bold
+
+\backslash
+mathop{
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+^N
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+_i,j=1
+\end_layout
+
+\begin_layout Section
+Fonts
+\begin_inset LatexCommand index
+name "Fonts"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Font Styles
+\begin_inset LatexCommand label
+name "sub:Font-Styles"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Font ! style"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Latin letters in formulas can be set in one of the following font styles:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+shortcut
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathbb
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathbb{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z k
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathbf
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathbf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z f
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+boldsymbol
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\boldsymbol{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathcal
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z h
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathfrak
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathfrak{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+shortcut
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathit
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathit{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathrm
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathrm{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z r
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathsf
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathsf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z s
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathtt
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathtt{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ The styles
+\series bold
+
+\backslash
+mathbb
+\series default
+ and
+\series bold
+
+\backslash
+mathcal
+\series default
+ can only be used for big letters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Predefined is the style
+\series bold
+
+\backslash
+mathnormal
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+The style commands work also for letters in mathematical constructs:
+\begin_inset Formula \[
+\mathfrak{A=\frac{b}{C}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Characters in mathematical text don't appear in a math font style but in
+ the text font style
+\series bold
+
+\backslash
+textrm
+\series default
+.
+ That their style can't be set correctly via the text style dialog is a
+ bug in LyX.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
+\end_layout
+
+\end_inset
+
+LyX-bug #4091
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Instead of the style commands the dialog
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Text Style
+\family default
+ or the toolbar button
+\begin_inset Graphics
+ filename ../images/math/font.png
+ scale 85
+
+\end_inset
+
+ can be used.
+\end_layout
+
+\begin_layout Subsection
+Bold Formulas
+\begin_inset LatexCommand label
+name "sub:Bold-Formulas"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! bold"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To make a complete formula bold, the command
+\series bold
+
+\backslash
+mathbf
+\series default
+ from the previous subsection cannot be used, because it doesn't work for
+ small Greek letters.
+ Furthermore it prints Latin letters always upright, like in the following
+ equation:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To display the formula correctly, the command
+\series bold
+
+\backslash
+boldsymbol
+\series default
+ is used:
+\begin_inset Formula \[
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
+
+\end_inset
+
+It is also possible to set the formula in a
+\series bold
+boldmath environment
+\series default
+.
+ This environment is created by inserting the command
+\series bold
+
+\backslash
+boldmath
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash boldmath"
+
+\end_inset
+
+
+\series default
+ in TeX-mode.
+ To end the environment, the command
+\series bold
+
+\backslash
+unboldmath
+\begin_inset LatexCommand index
+name "Commands ! U ! \\textbackslash unboldmath"
+
+\end_inset
+
+
+\series default
+ is inserted in TeX-mode.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Font Sizes
+\begin_inset LatexCommand label
+name "sub:Font-Sizes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Font ! size"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For characters in formulas there are, analog to characters in text, the
+ following size commands:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Huge
+\series default
+,
+\series bold
+
+\backslash
+huge
+\series default
+,
+\series bold
+
+\backslash
+LARGE
+\series default
+,
+\series bold
+
+\backslash
+Large
+\series default
+,
+\series bold
+
+\backslash
+large
+\series default
+,
+\series bold
+
+\backslash
+normalsize
+\series default
+,
+\series bold
+
+\backslash
+small
+\series default
+,
+\newline
+
+\series bold
+
+\backslash
+footnotesize
+\series default
+,
+\series bold
+
+\backslash
+scriptsize
+\series default
+, and
+\series bold
+
+\backslash
+tiny
+\end_layout
+
+\begin_layout Standard
+The size produced by the commands depends on the document font size, that
+ corresponds with the command
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ The other commands produce smaller or larger sizes than
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ The font size can however not exceed a certain value.
+ Is for example the document font size 12\InsetSpace \thinspace{}
+pt, the command
+\series bold
+
+\backslash
+Huge
+\series default
+ switches to the same size as
+\series bold
+
+\backslash
+huge
+\series default
+.
+
+\end_layout
+
+\begin_layout Standard
+A size command is inserted in TeX-mode before the formula and sets the size
+ for all following formula and text characters.
+ To switch back to the initial size, the command
+\series bold
+
+\backslash
+normalsize
+\series default
+ is inserted behind the formula in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+Within a formula the size can only be changed for symbols or letters in
+ mathematical text.
+ To do this, the size command is inserted in mathematical text.
+ All following characters until the end of the mathematical text or until
+ another size command will have the selected size.
+ Two examples:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+huge
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+A=\frac{B}{c}\cdot\maltese\]
+
+\end_inset
+
+
+\begin_inset Formula \[
+\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+normalsize
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Before both formulas the command
+\series bold
+
+\backslash
+huge
+\series default
+ was inserted.
+ The command for the second formula is:
+\newline
+
+\series bold
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A Alt-m m
+\backslash
+Large
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+textit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace*{1cm}
+\end_layout
+
+\end_inset
+
+Alt-m
+\series default
+
+\series bold
+m
+\backslash
+tiny
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+textit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\begin_layout Standard
+If a symbol cannot be displayed in different sizes, it will always be displayed
+ in the default size.
+\end_layout
+
+\begin_layout Section
+Greek Letters
+\begin_inset LatexCommand index
+name "Greek letters"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All Greek letters can also be inserted via the toolbar button
+\begin_inset Graphics
+ filename ../images/math/alpha.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Small Letters
+\begin_inset LatexCommand label
+name "sub:Small-Letters"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Greek letters ! small"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+alpha
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\alpha$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+beta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\beta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+epsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\epsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varepsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+zeta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\zeta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+eta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\eta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vartheta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vartheta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iota
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\iota$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+kappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\kappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varkappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varkappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $o$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varpi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varpi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varrho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varrho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varsigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varsigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tau
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\tau$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varphi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varphi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+chi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\chi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to create upright Greek letters is explained in
+\begin_inset LatexCommand ref
+reference "sub:Upright-small-Greek"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Big Letters
+\begin_inset LatexCommand index
+name "Greek letters ! big"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+That the big Greek letters appear upright is caused by a design bug when
+ TeX was developed.
+ To get correct italic big letters, begin every command with
+\series bold
+var
+\series default
+.
+ For example the command
+\series bold
+
+\backslash
+varGamma
+\series default
+ produces:
+\begin_inset Formula $\varGamma$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Bold Letters
+\begin_inset LatexCommand index
+name "Greek letters ! bold"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Greek letters cannot be set with different font styles like Latin letters.
+ They can only be made bold with the command
+\series bold
+
+\backslash
+boldsymbol
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! B ! \\textbackslash boldsymbol"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Upsilon
+\backslash
+boldsymbol
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+theta
+\backslash
+boldsymbol
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\theta\boldsymbol{\theta}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Symbols
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+A list with all symbols of most of the LaTeX-packages can be found in
+\begin_inset LatexCommand cite
+key "Symbole"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbols"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Many of the symbols listed in this section can also be inserted via the
+ toolbar buttons
+\begin_inset Graphics
+ filename ../images/math/nabla.png
+ scale 85
+
+\end_inset
+
+ and
+\begin_inset Graphics
+ filename ../images/math/digamma.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Mathematical Symbols
+\begin_inset LatexCommand label
+name "sub:Mathematical-Symbols"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbols ! mathematical"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\neg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Im
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Im$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Re
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Re$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+aleph
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\aleph$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+partial
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\partial$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+infty
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+imath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\imath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+jmath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\jmath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+forall
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\forall$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+exists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\exists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nexists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nexists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+emptyset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\emptyset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varnothing
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varnothing$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+complement
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-0.8mm}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\complement$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bbbk
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Bbbk$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+backprime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\backprime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+angle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\angle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+measuredangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\measuredangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sphericalangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sphericalangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+top
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\top$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Subsection
+Miscellaneous Symbols
+\begin_inset LatexCommand label
+name "sub:Miscellaneous-Symbols"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbols ! miscellaneous"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+flat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\flat$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+natural
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\natural$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sharp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sharp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+surd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\surd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+checkmark
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\checkmark$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+yen
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\yen$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pounds
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pounds$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+$
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\$$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+§
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $§$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hbar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hbar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+clubsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\clubsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+spadesuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\spadesuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigstar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigstar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacklozenge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacklozenge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacktriangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacktriangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacktiangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacktriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diamondsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diamondsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+heartsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\heartsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+P
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\P$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+copyright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\copyright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circledR
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circledR$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+maltese
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\maltese$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diagup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diagup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diagdown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diagdown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+More symbols are listed in
+\begin_inset LatexCommand ref
+reference "sub:Miscellaneous-Special-Characters"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Some symbols can be displayed in different sizes, see
+\begin_inset LatexCommand ref
+reference "sub:Font-Sizes"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+The Euro-Symbol €
+\begin_inset LatexCommand index
+name "Symbols ! Euro-symbol"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "\\textcent@\\officialeuro"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use the Euro symbol in formulas, the LaTeX-package
+\series bold
+eurosym
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! eurosym"
+
+\end_inset
+
+ must be installed and loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[gennarrow]{eurosym}
+\end_layout
+
+\begin_layout Standard
+The Euro symbol can now be inserted with the command
+\series bold
+
+\backslash
+euro
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! E ! \\textbackslash euro"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The Euro symbol can directly be inserted with the € key in mathematical
+ text, without having
+\series bold
+eurosym
+\series default
+ installed.
+ When
+\series bold
+eurosym
+\series default
+ is installed,
+\series bold
+
+\backslash
+euro
+\series default
+ can also be inserted in TeX-mode.
+ The official currency symbol can then be inserted with the command
+\series bold
+
+\backslash
+officialeuro
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! O ! \\textbackslash officialeuro"
+
+\end_inset
+
+, that is only available in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+ifeurosym
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+The following table will only be displayed when the LaTeX-package
+\series bold
+eurosym
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An overview about the different Euro symbols:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+formula
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+euro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\euro$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mathematical text
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+€
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mbox{€}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+TeX-mode
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+</cell>
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+\series default
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+\end_layout
+
+\end_inset
+
+
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+
+\begin_layout Standard
+You need to install the package
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+
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+status collapsed
+
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+
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+
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+
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+
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+
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+
+
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+
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+All relations can also be inserted via the toolbar button
+\begin_inset Graphics
+ filename ../images/math/leq.png
+ scale 85
+
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+
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+
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+
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+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+succ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\succ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+succeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\succeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+supset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\supset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+supseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\supseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqsupseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqsupseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ni$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dashv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dashv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+frown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\frown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+unrhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\unrhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lessgtr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lessgtr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nparallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nparallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The characters
+\series bold
+
+\backslash
+lhd
+\series default
+ and
+\series bold
+
+\backslash
+rhd
+\series default
+ are bigger than the equal looking operators
+\series bold
+
+\backslash
+triangleleft
+\series default
+ and
+\series bold
+
+\backslash
+triangleright
+\series default
+, respectively.
+\end_layout
+
+\begin_layout Standard
+Relations are, in contrary to symbols, always surrounded by space.
+\end_layout
+
+\begin_layout Standard
+Relations with labels can be created with the command
+\series bold
+
+\backslash
+stackrel
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash stackrel"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A(r)
+\backslash
+stackrel
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+r
+\backslash
+to
+\backslash
+infty
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\backslash
+approx
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Functions
+\end_layout
+
+\begin_layout Subsection
+Predefined Functions
+\begin_inset LatexCommand label
+name "sub:Predefined-Functions"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Functions ! predefined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In general, variables are set
+\emph on
+italic
+\emph default
+ in mathematical expressions, but not function names, because
+\begin_inset Formula $sin$
+\end_inset
+
+ could be misunderstood as
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+.
+ Therefore there are predefined functions, that are additionally a bit separated
+ from prefactors.
+ They are inserted as commands starting with a backslash before their name.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="4">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Asin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $Asin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+sin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\sin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+pagebreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following functions are predefined:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="4">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sinh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arcsin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cosh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arccos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+inf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tanh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arctan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lim
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+coth
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+liminf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+min
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+deg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+limsup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+csc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+max
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+det
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Pr
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ln
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+exp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+log
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ker
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gcd
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+They can also be inserted with the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/functions.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Functions
+\begin_inset LatexCommand index
+name "Functions ! self-defined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use a function that is not predefined, like for example the sign function
+ sgn(x), there are two possibilities:
+\end_layout
+
+\begin_layout Itemize
+Define the function by inserting the following line to the LaTeX-preamble
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+For more about
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+ see
+\begin_inset LatexCommand ref
+reference "sub:Self-defined-Operators"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\newline
+
+\series bold
+
+\backslash
+DeclareMathOperator{
+\backslash
+sgn}{sgn}
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
+
+\end_inset
+
+
+\newline
+
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\newline
+Now the new defined function can be called with the command
+\series bold
+
+\backslash
+sgn
+\series default
+.
+\end_layout
+
+\begin_layout Itemize
+Write the the formula as usual, mark the formula name, in our example the
+ letters
+\emph on
+sgn
+\emph default
+, and change it to mathematical text.
+ At last a space is inserted between prefactor and function.
+\end_layout
+
+\begin_layout Standard
+The result is the same with both methods as with a predefined function
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+In LyX self-defined functions are displayed red, predefined ones black.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+sgn(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\sgn(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+,
+\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
+\end_inset
+
+(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\,\textrm{sgn}(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The first method is more suitable when the self-defined function should
+ be used several times.
+\end_layout
+
+\begin_layout Subsection
+Limits
+\begin_inset LatexCommand index
+name "Limits"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For limits there are defined besides
+\series bold
+
+\backslash
+lim
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash lim"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+liminf
+\series default
+ and
+\series bold
+
+\backslash
+limsup
+\series default
+ furthermore the following functions:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varliminf
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varliminf$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varlimsup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varlimsup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varprojlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varprojlim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varinjlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varinjlim$
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The limit is created by inserting a subscript.
+ It is set right beside the function in an inline formula:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{1cm}
+\end_layout
+
+\end_inset
+
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace
+\series default
+ and
+\series bold
+
+\backslash
+raisebox
+\series default
+ are used here as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lim_x
+\backslash
+to
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+x=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In a displayed formula the limit is set below the formula, as usual:
+\begin_inset Formula \[
+\lim_{x\to A}x=B\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Modulo-Functions
+\begin_inset LatexCommand index
+name "Functions ! modulo-"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The modulo-function is special, because it exists in four variants.
+\end_layout
+
+\begin_layout Standard
+The variants in a displayed formula:
+\begin_inset Formula \begin{align*}
+\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\
+\mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\
+\mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\
+\mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\
+\mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In an inline formula less space is set before the function names for all
+ variants.
+\end_layout
+
+\begin_layout Section
+Special Characters
+\begin_inset LatexCommand index
+name "Special characters"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Special Characters in Mathematical Text
+\end_layout
+
+\begin_layout Standard
+The following commands can only be used in mathematical text or in TeX-mode:
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oe
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\oe}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+OE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\OE}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ae
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\ae}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+AE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\AE}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+aa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\aa}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+AA
+\begin_inset LatexCommand index
+name "\\@\\textrm{\\AA}"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\AA}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace{0mm}
+\series default
+ is used for separation, because otherwise the output will be ¡ and ¿ respective
+ly.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\o}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+O
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\O}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+l
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\l}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+L
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\L}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+!
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{!`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+?
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{?`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+j
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\j}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+The characters
+\begin_inset Formula $\textrm{\textrm{Å}}$
+\end_inset
+
+ and
+\begin_inset Formula $\textrm{\textrm{Ø}}$
+\end_inset
+
+ can also be inserted via the math toolbar button
+\begin_inset Graphics
+ filename ../images/math/digamma.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+An exception are the commands
+\series bold
+!
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\series default
+ and
+\series bold
+?
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\series default
+, because they can be inserted in LyX directly to text.
+\end_layout
+
+\begin_layout Subsection
+Accents in Text
+\begin_inset LatexCommand label
+name "sub:Accents-in-Text"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Accents ! in text"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the following commands all letters can be accented.
+ The commands must be inserted in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\begin_inset Quotes grd
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+"e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+^e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+=e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+u
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+u e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+b
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+b e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+ee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+t ee
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+H
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+H e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+~e
+\begin_inset LatexCommand index
+name "Tilde"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+~e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+v
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+v e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+d
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+d e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+c
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+c e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+With the command
+\series bold
+
+\backslash
+t
+\series default
+ also two different characters can be accented.
+ The command
+\series bold
+
+\backslash
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+sz
+\series default
+ creates:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+t sz
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The accents
+\series bold
+`
+\series default
+ ,
+\series bold
+'
+\series default
+ , and
+\series bold
+^
+\series default
+ can in combination with vowels directly be inserted with the keyboard without
+ using TeX-mode.
+ The same applies for the tilde
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+This only applies for keyboards where the tilde is defined as accent.
+\end_layout
+
+\end_inset
+
+
+\series bold
+~
+\series default
+ in combination with
+\emph on
+a
+\emph default
+ ,
+\emph on
+n
+\emph default
+ , or
+\emph on
+o
+\emph default
+.
+\end_layout
+
+\begin_layout Standard
+The commands
+\series bold
+
+\backslash
+b
+\series default
+ ,
+\series bold
+
+\backslash
+c
+\series default
+ ,
+\series bold
+
+\backslash
+d
+\series default
+ ,
+\series bold
+
+\backslash
+H
+\series default
+ ,
+\series bold
+
+\backslash
+t
+\series default
+ ,
+\series bold
+
+\backslash
+u
+\series default
+ ,
+\series bold
+
+\backslash
+v
+\series default
+, and accents inserted directly with the keyboard are also available in
+ mathematical text.
+ For the other accents there are special math commands to be used in formulas,
+ see
+\begin_inset LatexCommand ref
+reference "sub:Accents-for-one"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Furthermore, with the command
+\series bold
+
+\backslash
+textcircled
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash textcircled"
+
+\end_inset
+
+ all numbers and letters can be set into a circle, quasi accented with a
+ circle, similar to the the copyright symbol.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}{W}}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}W}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+One has to take care that the character fits in the circle.
+
+\series bold
+
+\backslash
+Large
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset LatexCommand ref
+reference "sub:Font-Sizes"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ specifies thereby the size of the circle.
+ With the help of
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset LatexCommand ref
+reference "sub:Boxes-without-Frame"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ the character can be centered.
+\end_layout
+
+\begin_layout Subsection
+Minuscule Numbers
+\begin_inset LatexCommand index
+name "Minuscule numbers"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Minuscule numbers are created with the command
+\series bold
+
+\backslash
+oldstylenums
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! O ! \\textbackslash oldstylenums"
+
+\end_inset
+
+.
+ The command can be used in formulas and in TeX-mode.
+ The command scheme is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+oldstylenums{number}
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+oldstylenums{0123456789
+\series default
+ produces:
+\begin_inset Formula $\oldstylenums{0123456789}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Miscellaneous Special Characters
+\begin_inset LatexCommand label
+name "sub:Miscellaneous-Special-Characters"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Special characters ! miscellaneous"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The following characters can only be inserted to formulas by using commands:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathcircumflex$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+_
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\_$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\backslash
+circ
+\begin_inset LatexCommand index
+name "°"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $^{\circ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
+ contains the following line
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+More about this is described in
+\begin_inset LatexCommand ref
+reference "sub:Text-Characters-in"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputtext{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+The tilde
+\begin_inset LatexCommand index
+name "Tilde"
+
+\end_inset
+
+ is designed as accent, thus is looks alone a bit misplaced: ~
+\newline
+But for web
+ addresses (URLs) sometimes a single tilde is needed.
+ In this case the relation sign
+\series bold
+
+\backslash
+sim
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset LatexCommand ref
+reference "sec:Relations"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used in a formula.
+ As a formula cannot be created in an URL-box (menu
+\family sans
+Insert\SpecialChar \menuseparator
+URL
+\family default
+), the URL is inserted as normal text with the font style '
+\family typewriter
+typewriter
+\family default
+'.
+ Should the URL be a hyperlink in the DVI- or PDF-output, the command
+\series bold
+
+\backslash
+href
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+href
+\series default
+ can only be used together with the LaTeX-package
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! hyperref"
+
+\end_inset
+
+.
+ More about
+\series bold
+
+\backslash
+href
+\series default
+ is written in the section
+\family typewriter
+URL
+\family default
+ in the
+\family typewriter
+Embedded\InsetSpace ~
+Objects
+\family default
+ manual.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash href"
+
+\end_inset
+
+ is used.
+\end_layout
+
+\begin_layout Standard
+As example an URL with a tilde:
+\end_layout
+
+\begin_layout Standard
+as text:
+\family typewriter
+http://www.lyx.org/
+\begin_inset Formula $\sim$
+\end_inset
+
+mustermann
+\end_layout
+
+\begin_layout Standard
+with
+\series bold
+
+\backslash
+href
+\series default
+:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://www.lyx.org/~mustermann}{
+\end_layout
+
+\end_inset
+
+http://www.lyx.org/
+\begin_inset Formula $\sim$
+\end_inset
+
+mustermann
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Styles
+\begin_inset LatexCommand label
+name "sec:Formula-Styles"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! styles"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+There are two different alignment styles:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Centered is the predefined standard
+\end_layout
+
+\begin_layout Description
+Indented for this the option
+\series bold
+fleqn
+\series default
+ must be inserted in the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings
+\family default
+ under
+\family sans
+Document\InsetSpace ~
+Class
+\end_layout
+
+\begin_layout Standard
+When
+\series bold
+Indented
+\series default
+ is used, the indentation can be adjusted with the length
+\series bold
+
+\backslash
+mathindent
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mathindent"
+
+\end_inset
+
+.
+ Should the distance be 15\InsetSpace \thinspace{}
+mm, the following command line is inserted in
+ the LaTeX-preamble
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathindent}{15mm}
+\end_layout
+
+\begin_layout Standard
+When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
+pt will be used.
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+And two different numbering styles:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Right is the predefined standard
+\end_layout
+
+\begin_layout Description
+Left for this the option
+\series bold
+leqno
+\series default
+ must be inserted in the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings
+\family default
+ under
+\family sans
+Document\InsetSpace ~
+Class
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+
+\series bold
+fleqn
+\series default
+ and
+\series bold
+leqno
+\series default
+ can also be used together.
+ In this case both options are inserted, separated by a comma.
+\end_layout
+
+\begin_layout Standard
+The chosen styles are used for all displayed formulas of the document.
+ When both, centered and indented formulas should be created in a document,
+ the style
+\series bold
+Centered
+\series default
+ is used.
+ The indented formulas are then set in a flalign environment, see
+\begin_inset LatexCommand ref
+reference "sub:Flalign-Environment"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Multiline Formulas
+\begin_inset LatexCommand label
+name "sec:Multiline-Formulas"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+In LyX multiline formulas are created by pressing
+\family sans
+\series bold
+Ctrl-Return
+\family default
+\series default
+ inside a formula.
+ This creates an
+\series bold
+align environment
+\series default
+ that is described in
+\begin_inset LatexCommand ref
+reference "sub:Standard-align-Environment"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+There are other multiline formula environments that can be created via the
+ menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math
+\family default
+.
+ These environments are described in the following sections.
+\end_layout
+
+\begin_layout Standard
+In all multiline formula environments a new line is created by pressing
+
+\family sans
+Ctrl-Return
+\family default
+.
+ To add or delete lines, the math toolbar buttons
+\begin_inset Graphics
+ filename ../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+ or
+\begin_inset Graphics
+ filename ../images/tabular-feature_delete-row.png
+ scale 85
+
+\end_inset
+
+, respectively, or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows & Columns
+\family default
+ can be used.
+\end_layout
+
+\begin_layout Subsubsection
+Line Separation
+\begin_inset LatexCommand label
+name "sub:Line-Separation"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! Line separation"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There is sometimes not enough space in multiline formulas between the lines:
+\begin_inset Formula \begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In LaTeX additional line space is specified as optional argument of the
+ new line command.
+ This is not yet possible in LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1505
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, therefore the whole formula must be inserted in TeX-mode.
+ To add in our example space, the command
+\series bold
+
+\backslash
+
+\backslash
+[3mm]
+\series default
+ is inserted at the end of the first line.
+ One gets:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{eqnarray*}
+\end_layout
+
+\begin_layout Standard
+
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
+ = &
+\backslash
+textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
+\backslash
+
+\backslash
+[3mm]
+\end_layout
+
+\begin_layout Standard
+
+4x^{2}
+\backslash
+left(B^{2}+x_{0}^{2}
+\backslash
+right)+4x_{0}x
+\backslash
+left(D-B^{2}
+\backslash
+right)+B^{2}
+\backslash
+left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
+\backslash
+right) & = & 0
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+end{eqnarray*}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To set the the line separation for all lines in a formula, the length
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! J ! \\textbackslash jot"
+
+\end_inset
+
+ is changed.
+ The definition is:
+\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
+\end_inset
+
+.
+ Predefined for
+\series bold
+
+\backslash
+jot
+\series default
+ is the value 3\InsetSpace \thinspace{}
+pt.
+ To create 3\InsetSpace \thinspace{}
+mm additional line separation as in the previous example, the
+ command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\begin_layout Standard
+is inserted in TeX-mode before the formula.
+ This requires that the LaTeX-package
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+calc
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! calc"
+
+\end_inset
+
+ was loaded in LaTeX-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+One gets:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+ To get back to the predefined distance,
+\series bold
+
+\backslash
+jot
+\series default
+ is set to the value 3\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Subsubsection
+Column Separation
+\begin_inset LatexCommand label
+name "sub:Column-Separation"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! Column separation"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Multiline formulas form a matrix.
+ A formula in the eqnarray environment is for example a matrix with three
+ columns.
+ By changing the column separation in this environment, the space beside
+ the relation sign can be changed.
+\end_layout
+
+\begin_layout Standard
+The column separation is specified with the length
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash arraycolsep"
+
+\end_inset
+
+ according to:
+\newline
+column separation = 2\InsetSpace \thinspace{}
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\newline
+Thus, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\begin_layout Standard
+inserted in TeX-mode, sets for all following formulas a column separation
+ of 2\InsetSpace \thinspace{}
+cm.
+ To get back to the predefined distance,
+\series bold
+
+\backslash
+arraycolsep
+\series default
+ is set to 5\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Standard
+A formula with 2\InsetSpace \thinspace{}
+cm column separation:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+A & = & B\\
+C & \ne & A\end{eqnarray*}
+
+\end_inset
+
+A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
+pt:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{5pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+A & = & B\\
+C & \ne & A\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Long Formulas
+\begin_inset LatexCommand index
+name "Formula ! long"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Long formulas can be typeset using these methods:
+\end_layout
+
+\begin_layout Itemize
+When one side of the equation is much shorther than the line width, this
+ one is chosen for the left side and the right side is typeset over two
+ lines:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
+ & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+smallskip
+\end_layout
+
+\end_inset
+
+
+\newline
+The minus sign at the beginning of the second line does normally not appear
+ as operator because it is the first character of the line.
+ Thus it would not be surrounded by space and could not be distinguished
+ from the fraction bar.
+ To avoid this, space was inserted behind the minus sign with the command
+
+\series bold
+
+\backslash
+hspace{3pt}
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+more about
+\series bold
+
+\backslash
+hspace
+\series default
+ see
+\begin_inset LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commands ! H ! \\textbackslash hspace"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+When both sides of the equation are too long, the command
+\series bold
+
+\backslash
+lefteqn
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash lefteqn"
+
+\end_inset
+
+ is used.
+ It is inserted to the first column of the first line and effects that all
+ further insertions overwrite the following columns:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
+ & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
+ & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+smallskip
+\end_layout
+
+\end_inset
+
+
+\newline
+After the insertion of
+\series bold
+
+\backslash
+lefteqn
+\series default
+, the cursor is in a purple box that is a bit shifted to the left from the
+ blue one.
+ In this the formula is inserted.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+The content of the further lines is inserted to the second or another formula
+ column.
+ The greater the column number where it was inserted, the larger the indentation.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Note the following when using
+\series bold
+
+\backslash
+lefteqn
+\series default
+:
+\end_layout
+
+\begin_layout Itemize
+The formula doesn't use the full page width.
+ When e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+the term
+\begin_inset Formula $-B^{2}$
+\end_inset
+
+ is added to the first line in the above example, it would have been outside
+ the page margin.
+ To better use the width, negative space can be inserted at the beginning
+ of the first line.
+\end_layout
+
+\begin_layout Itemize
+Due to a bug in LyX the cursor cannot be set with the mouse into the first
+ line.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
+\end_layout
+
+\end_inset
+
+LyX-bug #1429
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ One can only set the cursor at the beginning of the line and move it with
+ the arrow keys.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Other methods to set long formulas are offered by the environments described
+ in
+\begin_inset LatexCommand ref
+reference "sub:Multline-Environment"
+
+\end_inset
+
+ and
+\begin_inset LatexCommand ref
+reference "sub:Multiline-Formula-Parts"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsubsection
+Multiline Brackets
+\begin_inset LatexCommand label
+name "sub:Multiline-Brackets"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Brackets ! for multiline expressions"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+For brackets spanning multiple lines the following problem occurs:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\cdots+B-D\right]\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The closing bracket is smaller than the opening bracket because brackets
+ with variable size may not span multiple lines.
+\end_layout
+
+\begin_layout Standard
+To set the bracket size for the second line correctly, the first line is
+ ended with
+\series bold
+
+\backslash
+right.
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash right"
+
+\end_inset
+
+ and the second line with
+\series bold
+
+\backslash
+left.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+for more about
+\series bold
+
+\backslash
+left
+\series default
+ and
+\series bold
+
+\backslash
+right
+\series default
+ see
+\begin_inset LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! L ! \\textbackslash left"
+
+\end_inset
+
+.
+ After
+\series bold
+
+\backslash
+left.
+
+\series default
+ the command
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+prod
+\series default
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+infty
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_R=1}
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! V ! \\textbackslash vphantom"
+
+\end_inset
+
+ is inserted, because the multiplication operator with its limits is the
+ largest symbol in the first line and this should be the size for the bracket
+ in the second line.
+\end_layout
+
+\begin_layout Standard
+The result is this:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Align Environments
+\end_layout
+
+\begin_layout Standard
+Align environments can be used for every kind of multiline formulas.
+ They are specially useful to set several formulas side by side.
+\end_layout
+
+\begin_layout Standard
+Align environments consist of columns.
+ The odd columns are right aligned, the even ones left aligned.
+ Every line in an Align environment can be numbered.
+\end_layout
+
+\begin_layout Standard
+Align environments are created via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math
+\family default
+.
+ With the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Change Formula Type
+\family default
+ already existing existing formulas can be converted to Align environments.
+\end_layout
+
+\begin_layout Standard
+To add or delete columns, the math toolbar buttons
+\begin_inset Graphics
+ filename ../images/tabular-feature_append-column.png
+ scale 85
+
+\end_inset
+
+ or
+\begin_inset Graphics
+ filename ../images/tabular-feature_delete-column.png
+ scale 85
+
+\end_inset
+
+, respectively, or the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Rows & Columns
+\family default
+ can be used.
+\end_layout
+
+\begin_layout Subsubsection
+Standard align Environment
+\begin_inset LatexCommand label
+name "sub:Standard-align-Environment"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! align environment"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This Align environment is created by presssing
+\family sans
+Ctrl-Return
+\family default
+ in a formula or by the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+AMS align Environment
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+An example for two formulas set side by side, that are created with a four
+ column align environment:
+\begin_inset Formula \begin{align*}
+A & =\sin(B) & C & =D\\
+C & \ne A & B & \ne D\end{align*}
+
+\end_inset
+
+As it can be seen, the formulas in this environment are placed so as if
+ there would be a
+\series bold
+
+\backslash
+hfill
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+more about
+\series bold
+
+\backslash
+hfill
+\series default
+ see
+\begin_inset LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ before the first and after every even column.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+formula styles see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, the formula is set without the
+\series bold
+
+\backslash
+hfill
+\series default
+ before the first column.
+\end_layout
+
+\begin_layout Subsubsection
+Alignat Environment
+\begin_inset LatexCommand index
+name "Formula ! multiline ! alignat environment"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The alignat environment has no predefined column separation.
+ It can be inserted manually with the spaces that are described
+\begin_inset LatexCommand ref
+reference "sub:Space"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+The above example in the alignat environment where 1\InsetSpace \thinspace{}
+cm space was inserted
+ at the beginning of the second formula:
+\begin_inset Formula \begin{alignat*}{2}
+A & =\sin(B) & \hspace{1cm}C & =D\\
+C & \ne A & B & \ne D\end{alignat*}
+
+\end_inset
+
+Because the column separation can be set separately for every column, this
+ environment is especially suitable to set three and more formulas side
+ by side.
+\end_layout
+
+\begin_layout Subsubsection
+Flalign Environment
+\begin_inset LatexCommand label
+name "sub:Flalign-Environment"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! flalign environment"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In this environment the first two columns are always set as much as possible
+ to the left and the last two ones to the right.
+ An example:
+\begin_inset Formula \begin{flalign*}
+A & =1 & B & =2 & C & =3\\
+X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+By creating a flalign environment with an odd number of columns where an
+ empty TeX-brace is inserted to the last column, several formulas in a document
+ can be set to the left, although the formula style
+\series bold
+Centered
+\series default
+ is used.
+ As example the indented formula
+\begin_inset LatexCommand eqref
+reference "eq:VolInt"
+
+\end_inset
+
+:
+\begin_inset Formula \begin{flalign}
+\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
+
+\end_inset
+
+The first two columns contain the formula.
+ To indent it as with the formula style
+\series bold
+Indented
+\series default
+, 30\InsetSpace \thinspace{}
+pt space was inserted at the beginning of the first column.
+\end_layout
+
+\begin_layout Subsection
+Eqnarray Environment
+\begin_inset LatexCommand index
+name "Formula ! multiline ! eqnarray environment"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When this environment has been created, three blue boxes appear.
+ The content of the first box is right aligned, the content of the last
+ one left aligned.
+ The content of the middle box appears centered and a bit smaller, because
+ it is designed to insert there only relation characters.
+\begin_inset Formula \begin{eqnarray*}
+\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
+AB & AB & AB\\
+A & = & A\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Gather Environment
+\begin_inset LatexCommand index
+name "Formula ! multiline ! gather environment"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This environment consists of only one centered column.
+ Every line can be numbered.
+\begin_inset Formula \begin{gather}
+A=1\\
+X=\textrm{-}1\end{gather}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Multline Environment
+\begin_inset LatexCommand label
+name "sub:Multline-Environment"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! multline environment"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The multline environment consists, like the gather environment, of only
+ one column.
+ But the first line is left aligned, the last one right aligned.
+ All other lines are centered.
+ Therefore this environment is suitable for long formulas.
+ As example formula
+\begin_inset LatexCommand eqref
+reference "eq:lefteqn"
+
+\end_inset
+
+ in the multline environment:
+\begin_inset Formula \begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the output only the the last (first) line of a multline environment appears
+ numbered when the document numbering is right (left).
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+numbering styles see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ This is also the case when there is a formula number displayed after every
+ line in LyX.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+This is
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
+\end_layout
+
+\end_inset
+
+LyX-bug #518
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the commands
+\series bold
+
+\backslash
+shoveright
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash shoveright"
+
+\end_inset
+
+
+\series default
+ and
+\series bold
+
+\backslash
+shoveleft
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash shoveleft"
+
+\end_inset
+
+
+\series default
+ a centered line can be right or left aligned, respectively.
+ The commands are used as follows:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+shoveright{line content}
+\series default
+ and
+\series bold
+
+\backslash
+shoveleft{line content}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+The length
+\series bold
+
+\backslash
+multlinegap
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash multlinegap"
+
+\end_inset
+
+
+\series default
+ specifies the distance of the first line from the left page margin.
+ Predefined is the length 0\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Standard
+As example the above formula where the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\begin_layout Standard
+was inserted in TeX-mode before:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{0pt}
+\end_layout
+
+\end_inset
+
+The second line was left aligned using
+\series bold
+
+\backslash
+shoveleft
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Multiline Formula Parts
+\begin_inset LatexCommand label
+name "sub:Multiline-Formula-Parts"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! formula parts"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To display only parts of a formula with multiple lines, one of the following
+ environments are used:
+\series bold
+aligned
+\series default
+,
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+ or
+\series bold
+split
+\series default
+.
+ They can be inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math
+\family default
+ or by using the commands described in this section.
+\end_layout
+
+\begin_layout Standard
+The first three have the same properties as the corresponding multiline
+ formula environments, but it is possible to set further formula parts beside
+ them.
+ An example:
+\begin_inset Formula \[
+\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
+\Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
+\right\} \textrm{Uncertainty relations}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To get this formula, a displayed formula is created where the command
+\series bold
+
+\backslash
+aligned
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash aligned"
+
+\end_inset
+
+
+\series default
+ is inserted.
+ A purple box appears around the blue formula box where now columns and
+ lines can be added.
+ Outside the multiline environment other formula parts can be set, like
+ the brace.
+\end_layout
+
+\begin_layout Standard
+The aligned environment is also suitable for long formulas whose lines are
+ horizontally aligned.
+ Using aligned in a displayed formula has the advantage that the formula
+ number is vertically centered behind the lines.
+ As example formula
+\begin_inset LatexCommand eqref
+reference "eq:kurzlang"
+
+\end_inset
+
+ in the aligned environment:
+\begin_inset Formula \begin{equation}
+\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
+ & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\end{aligned}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use the environments
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+, or
+\series bold
+split
+\series default
+, the command
+\series bold
+
+\backslash
+alignedat
+\series default
+,
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash alignedat"
+
+\end_inset
+
+
+\series bold
+
+\backslash
+gathered
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! G ! \\textbackslash gathered"
+
+\end_inset
+
+, or
+\series bold
+
+\backslash
+split
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! S ! \\textbackslash split"
+
+\end_inset
+
+ are inserted, respectively.
+ The split environment has the same properties as the aligned environment
+ but it can only have two columns.
+\end_layout
+
+\begin_layout Subsection
+Text in multiline Formulas
+\begin_inset LatexCommand label
+name "sub:Text-in-multiline"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Text ! in formulas"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! multiline ! text"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In the Align environments, and the multline and gather environment, text
+ can be inserted that will appear in a separate line and doesn't affect
+ the column alignment.
+ To do this, the command
+\series bold
+
+\backslash
+intertext
+\begin_inset LatexCommand index
+name "Commands ! I ! \\textbackslash intertext"
+
+\end_inset
+
+
+\series default
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext{text}
+\end_layout
+
+\begin_layout Standard
+The text should not be longer than a line because it cannot be hyphenated.
+ As LyX doesn't yet support
+\series bold
+
+\backslash
+intertext
+\series default
+ directly, the text is written as mathematical text.
+
+\series bold
+
+\backslash
+intertext
+\series default
+ must hereby be at the beginning of a line and appears in the output above
+ this line.
+ An example where the text was inserted at the beginning of the second line:
+\begin_inset Formula \begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formula Numbering
+\begin_inset LatexCommand index
+name "Formula numbering"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! numbering|see{Formula numbering}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+General
+\end_layout
+
+\begin_layout Standard
+Numbered formulas can be created with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Numbered\InsetSpace ~
+Formula
+\family default
+ (shortcut
+\family sans
+Ctrl-Alt\InsetSpace ~
+n
+\family default
+).
+ Existing formulas can be numbered with the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Toggle\InsetSpace ~
+Numbering
+\family default
+ (shortcut
+\family sans
+Alt-m\InsetSpace ~
+n
+\family default
+).
+ The formula number is displayed in LyX behind the formula as number sign
+ in parentheses.
+ The number sign is replaced in the output by the formula number.
+\end_layout
+
+\begin_layout Standard
+When numbering is turned on in multiline formulas, all lines will be numbered.
+ But the numbering can be controlled with the menu
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Toggle\InsetSpace ~
+Numbering\InsetSpace ~
+of\InsetSpace ~
+Line
+\family default
+ (shortcut
+\family sans
+Alt-m\InsetSpace ~
+N
+\family default
+) for every line.
+\end_layout
+
+\begin_layout Standard
+Except of inline formulas, all formulas can be numbered with two different
+ styles, see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Cross-References
+\begin_inset LatexCommand label
+name "sub:Cross-References"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Cross-references ! to formulas"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+All labeled formulas can be cross-referenced.
+ A label is added by the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Label
+\family default
+ or the toolbar button
+\begin_inset Graphics
+ filename ../images/label-insert.png
+ scale 85
+
+\end_inset
+
+.
+ The cursor must hereby be inside a displayed formula.
+ A dialog pops up displaying the prefix
+\series bold
+eq:
+\series default
+ in a text field.
+ The label is inserted there behind the prefix.
+ The predefined prefix means
+\begin_inset Quotes eld
+\end_inset
+
+equation
+\begin_inset Quotes erd
+\end_inset
+
+ and makes it easier to find labels in large documents because it marks
+ it as formula label to divide it from e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+section labels.
+ To change a label, the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Label
+\family default
+ is used again.
+\end_layout
+
+\begin_layout Standard
+The name of the label is displayed in LyX within two parentheses behind
+ formula.
+ A formula with a label is always numbered.
+ The label is deleted when the numbering is turned off.
+ This is at the moment the only way to delete a label, see
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
+\end_layout
+
+\end_inset
+
+LyX-bug #2556
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Cross-references are inserted via the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Cross-Reference
+\family default
+ or with the toolbar button
+\begin_inset Graphics
+ filename ../images/dialog-show-new-inset_ref.png
+ scale 85
+
+\end_inset
+
+.
+ A formula cross-reference appears in the output as formula number.
+ When in the cross-reference dialog window the format
+\series bold
+(<reference>)
+\series default
+ is chosen, the cross-reference appears in the output as formula number
+ in parentheses.
+\newline
+By right-clicking on a cross-reference in LyX, one jumps
+ to the formula that is referenced.
+\end_layout
+
+\begin_layout Standard
+Here are as examples cross-references to formulas of the following subsections:
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Note the different cross-reference types.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The equations
+\begin_inset LatexCommand eqref
+reference "eq:tag"
+
+\end_inset
+
+ and
+\begin_inset LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ are equivalent.
+ In (
+\begin_inset LatexCommand ref
+reference "eq:Lat"
+
+\end_inset
+
+) big Latin letters are used for the numbering in contrary to (
+\begin_inset LatexCommand ref
+reference "eq:Rom"
+
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+When the argument of
+\series bold
+
+\backslash
+tag
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+tag
+\series default
+ is described in
+\begin_inset LatexCommand ref
+reference "sub:User-defined-Numbering"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\series default
+ contains a box like in
+\begin_inset LatexCommand ref
+reference "sub:Paragraph-Boxes"
+
+\end_inset
+
+, the formula cannot be referenced.
+\end_layout
+
+\begin_layout Subsection
+Subnumbering
+\begin_inset LatexCommand index
+name "Formula numbering ! subnumbering"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With the help of the commands
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+ and
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ formulas can be subnumbered.
+ Both commands are inserted in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+An example:
+\begin_inset Formula \begin{equation}
+A=C-B\label{eq:a}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+addtocounter{equation}{-1}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{subequations}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+B=C-A\label{eq:b}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+C=A+B\label{eq:c}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{subequations}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To create the example, the following is done:
+\end_layout
+
+\begin_layout Enumerate
+first formula is inserted
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+
+\backslash
+addtocounter{equation}{-1}
+\backslash
+begin{subequations}
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash addtocounter"
+
+\end_inset
+
+
+\newline
+
+\series default
+is inserted after the first formula
+\end_layout
+
+\begin_layout Enumerate
+second formula is inserted
+\end_layout
+
+\begin_layout Enumerate
+third formula is inserted
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ is inserted after the third formula
+\end_layout
+
+\begin_layout Standard
+Every formula between the commands
+\series bold
+
+\backslash
+begin
+\series default
+ and
+\series bold
+
+\backslash
+end
+\series default
+ is subnumbered as a, b,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+c, \SpecialChar \ldots{}
+ For multiline formulas every line will be subnumbered.
+ All subnumbered formulas are treated as
+\emph on
+one
+\emph default
+ numbered formula.
+ But as every numbered formula increases the counter
+\series bold
+equation
+\series default
+ by one, the command
+\series bold
+
+\backslash
+addtocounter
+\series default
+ is needed to decrease it.
+ Otherwise the formulas
+\begin_inset LatexCommand eqref
+reference "eq:a"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:b"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ would be numbered as
+\begin_inset LatexCommand eqref
+reference "eq:a"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:d"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:f"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+By inserting the commands in TeX-mode, a space is created between the first
+ two formulas.
+ To revert this -5\InsetSpace \thinspace{}
+mm vertical space is inserted after the command
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+formula styles see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, -7\InsetSpace \thinspace{}
+mm space is inserted instead.
+\end_layout
+
+\begin_layout Standard
+Here is an example for a multiline formula where the numbering was turned
+ off for the second line:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{subequations}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
+ & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
+ & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{subequations}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+User-defined Numbering
+\begin_inset LatexCommand label
+name "sub:User-defined-Numbering"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula numbering ! user-defined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand index
+name "Formula numbering ! self-defined delimiters"
+
+\end_inset
+
+With the standard numbering parentheses are set around the formula number.
+ To replace the parentheses for example by vertical bars, the following
+ line is added to the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+def
+\backslash
+tagform@#1{
+\backslash
+maketag@@@{|#1|}}
+\series default
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+This macro is already declared in the LaTeX-preamble for testing.
+ To activate it, remove the percent sign at the beginning.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To use other characters, the vertical bars besides the
+\series bold
+#1
+\series default
+ are replaced by one ore more characters.
+ To get only the formula number the vertical bars are omitted.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When there should be an expression of your choice instead of the consecutive
+ formula number in parentheses behind the formula, the command
+\series bold
+
+\backslash
+tag{expression}
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash tag"
+
+\end_inset
+
+ is used:
+\begin_inset Formula \begin{equation}
+A+B=C\tag{something}\label{eq:tag}\end{equation}
+
+\end_inset
+
+In this example the command
+\series bold
+
+\backslash
+tag
+\backslash
+{something
+\series default
+ was inserted to the formula.
+\end_layout
+
+\begin_layout Standard
+When the command
+\series bold
+
+\backslash
+tag*
+\backslash
+{something
+\series default
+ is inserted instead, the star prevents the parentheses around the expression:
+\begin_inset Formula \[
+A+B=C\tag*{something}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+To restart the formula numbering with new document parts or sections, the
+ following command is used:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+@addtoreset{equation}{part}
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"
+
+\end_inset
+
+
+\newline
+resp.
+\newline
+
+\series bold
+
+\backslash
+@addtoreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+To be able to use these commands in TeX-mode, the
+\begin_inset Quotes eld
+\end_inset
+
+@
+\begin_inset Quotes erd
+\end_inset
+
+ character has to be made
+\begin_inset Quotes eld
+\end_inset
+
+active
+\begin_inset Quotes erd
+\end_inset
+
+ for LaTeX using the command
+\series bold
+
+\backslash
+makeatletter.
+
+\series default
+ The command
+\series bold
+
+\backslash
+makeatother
+\series default
+ reverts this.
+ So the command sequence in TeX-mode is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+makeatletter
+\newline
+
+\backslash
+@addtoreset{equation}{section}
+\newline
+
+\backslash
+makeatother
+\end_layout
+
+\begin_layout Standard
+In the LaTeX-preamble
+\series bold
+
+\backslash
+makeatletter
+\series default
+ and
+\series bold
+
+\backslash
+makeatother
+\series default
+ can be omitted as they are automatically internally inserted by LyX.
+\end_layout
+
+\begin_layout Standard
+To revert
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, the file
+\series bold
+remreset.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+remreset
+\series default
+ is part of the LaTeX-package
+\series bold
+carlisle
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! carlisle"
+
+\end_inset
+
+ that is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! remreset"
+
+\end_inset
+
+ has to be loaded in the LaTeX-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{remreset}
+\end_layout
+
+\begin_layout Standard
+Then the command
+\series bold
+
+\backslash
+@removefromreset
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"
+
+\end_inset
+
+ can be used with the same scheme as
+\series bold
+
+\backslash
+@addtoreset
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Sometimes formulas should be numbered in the following form:
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+(section number.formula number)
+\end_layout
+
+\begin_layout Standard
+The formula number should start with every section with
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+For this case there is the command
+\series bold
+
+\backslash
+numberwithin
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! N ! \\textbackslash numberwithin"
+
+\end_inset
+
+, which is used with the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{counter}{sectioning}
+\end_layout
+
+\begin_layout Standard
+Counter denotes what kind of numbering is affected, sectioning denotes what
+ number is before the dot.
+\end_layout
+
+\begin_layout Standard
+Thus in our case the following LaTeX-preamble or ERT line is used:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\begin_layout Standard
+This is the result:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A+B=C\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To number e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+tables so that the number of the part is the sectioning,
+\newline
+
+\series bold
+
+\backslash
+numberwithin{table}{part}
+\series default
+ is used.
+\end_layout
+
+\begin_layout Standard
+To go back to the standard numbering or to prevent this kind of numbering
+ when it is defined by the document class, the following command is inserted
+ as ERT or to the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash arabic"
+
+\end_inset
+
+
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+or
+\series bold
+
+\newline
+
+\backslash
+renewcommand{
+\backslash
+thetable}{
+\backslash
+arabic{table}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin
+\series default
+ uses internally the command
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, described above, that also needs to be reverted.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+makeatletter
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+@removefromreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+makeatother
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Numbering with Roman Numbers and Letters
+\begin_inset LatexCommand label
+name "sub:Numbering-with-Roman"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula numbering ! with letters"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula numbering ! with Roman numbers"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas can also be numbered with Roman numbers and Latin letters.
+ To number for example with small Roman numbers, the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+is inserted before the formula in TeX-mode.
+
+\series bold
+
+\backslash
+renewcommand
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash renewcommand"
+
+\end_inset
+
+ redefines the predefined command
+\series bold
+
+\backslash
+theequation
+\series default
+ to the command
+\series bold
+
+\backslash
+roman{equation}
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+renewcommand
+\series default
+ has the same scheme like the command
+\series bold
+
+\backslash
+newcommand
+\series default
+ that is described in
+\begin_inset LatexCommand ref
+reference "sec:User-defined-commands"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+.
+
+\series bold
+equation
+\series default
+ is the formula counter.
+ When the command
+\series bold
+
+\backslash
+the
+\series default
+ is used as prefix for a counter, the value of the counter is output as
+ Arabic number.
+ When a formula is numbered, LaTeX sets internally the command
+\series bold
+
+\backslash
+theequation
+\series default
+ behind the formula.
+
+\series bold
+
+\backslash
+roman{equation}
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash roman"
+
+\end_inset
+
+
+\series default
+ outputs the counter as small Roman number.
+\end_layout
+
+\begin_layout Standard
+All formulas behind the command
+\series bold
+
+\backslash
+renew
+\series default
+c
+\series bold
+ommand
+\series default
+ are now numbered Roman.
+ To switch to numbering with big Roman numbers, the command is inserted
+ again, but
+\series bold
+
+\backslash
+roman
+\series default
+ is replaced by
+\series bold
+
+\backslash
+Roman
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"
+
+\end_inset
+
+.
+ To
+\begin_inset Quotes eld
+\end_inset
+
+number
+\begin_inset Quotes erd
+\end_inset
+
+ with small Latin letters there is the command
+\series bold
+
+\backslash
+alph
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash alph"
+
+\end_inset
+
+, for big ones there is the command
+\series bold
+
+\backslash
+Alph
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ Only maximal 26 formulas can be numbered with Latin letters in one document.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+A=\textrm{small roman}\label{eq:rom}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+B=\textrm{big Roman}\label{eq:Rom}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+C=\textrm{small Latin}\label{eq:lat}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+D=\textrm{big Latin}\label{eq:Lat}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To switch back to the default numbering, insert the command:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset LatexCommand index
+name "Commands ! A ! \\textbackslash arabic"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+E=\textrm{Arabic}\label{eq:arab}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+As you see, formulas are numbered serially independent from the numbering
+ style.
+ When then numbering should start with
+\begin_inset Quotes eld
+\end_inset
+
+1
+\begin_inset Quotes erd
+\end_inset
+
+ when the style is changed, new equation counters have to be defined.
+ A description about this can be found in the file
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{Formula-numbering.pdf}{
+\end_layout
+
+\end_inset
+
+Formula-numbering.pdf
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+More about the command
+\series bold
+
+\backslash
+href
+\series default
+, see section
+\begin_inset LatexCommand ref
+reference "sub:Links-in-DVI-"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+User-defined commands
+\begin_inset LatexCommand label
+name "sec:User-defined-commands"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "User-defined commands"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Many LaTeX-commands are too long to be used frequently.
+ But it is possible to define with the command
+\series bold
+
+\backslash
+newcommand
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! N ! \\textbackslash newcommand"
+
+\end_inset
+
+ new shorter commands.
+\end_layout
+
+\begin_layout Standard
+The command scheme of
+\series bold
+
+\backslash
+newcommand
+\series default
+ is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{new command name}[number of arguments][optional
+\series default
+
+\series bold
+value]
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+phantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+newcommand
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+{command definition}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ Assure that the name of the new command is not already used in your document
+ or by LaTeX-packages that you use.
+ When you for example define the command
+\series bold
+
+\backslash
+le
+\series default
+ for
+\series bold
+
+\backslash
+Leftarrow
+\series default
+, you get an error message because
+\series bold
+
+\backslash
+le
+\series default
+ is already defined as command for
+\begin_inset Quotes eld
+\end_inset
+
+
+\begin_inset Formula $\le$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Note:
+\series default
+ The names of user-defined commands may only consist of Latin letters.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+9 and specifies how
+ many arguments the new command should have.
+ With the optional value a value for an optional argument can be predefined.
+ When this is done, the
+\emph on
+first
+\emph default
+
+\emph on
+a
+\emph default
+rgument of the new command is automatically an optional one.
+\end_layout
+
+\begin_layout Standard
+Here are some examples:
+\end_layout
+
+\begin_layout Itemize
+To define the command
+\series bold
+
+\backslash
+gr
+\series default
+ for
+\series bold
+
+\backslash
+Longrightarrow
+\series default
+, the LaTeX-preamble line is:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+gr}{
+\backslash
+Longrightarrow}
+\end_layout
+
+\begin_layout Itemize
+To define the command
+\series bold
+
+\backslash
+us
+\series default
+ for
+\series bold
+
+\backslash
+underline
+\series default
+, the argument (that should be underlined) must be taken into account.
+ For this the preamble line is:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+us}[1]{
+\backslash
+underline{#1}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+The character
+\series bold
+#
+\series default
+ acts as argument placeholder, the
+\series bold
+1
+\series default
+ behind it denotes that it is the placeholder for the first argument.
+\end_layout
+
+\begin_layout Itemize
+For
+\series bold
+
+\backslash
+framebox
+\series default
+ one can e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+define the command
+\series bold
+
+\backslash
+fb
+\series default
+:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+fb}[3]{
+\backslash
+framebox#1#2{$#3$}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+The two Dollar signs creates the extra formula needed for
+\series bold
+
+\backslash
+framebox
+\series default
+, see
+\begin_inset LatexCommand ref
+reference "sub:Boxes-with-Frame"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+To create a new command for
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ where the color for the box needn't to be specified, the argument for the
+ color is defined optional:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+cb}[3][white]{
+\backslash
+fcolorbox{#2}{#1}{$#3$}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+When the color is not specified when using
+\series bold
+
+\backslash
+cb
+\series default
+, the predefined color
+\series bold
+white
+\series default
+ will be used.
+\end_layout
+
+\begin_layout Standard
+A test of the new defined commands:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+gr
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\gr B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+us{ABcd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fb{[2cm]
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cb{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cb[green]
+\backslash
+{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Diagrams
+\begin_inset LatexCommand index
+name "Diagrams"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To create diagrams, the LaTeX-package
+\series bold
+amscd
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+amscd
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! amscd"
+
+\end_inset
+
+ is needed.
+ It is loaded in the LaTeX-preamble with the line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{amscd}
+\end_layout
+
+\begin_layout Standard
+Diagrams visualize relations and look like this:
+\begin_inset Formula \[
+\begin{CD}A@>>>B@>>>C\\
+@AAA@.@VVV\\
+F@<<<E@<<<D\end{CD}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To get them, the command
+\series bold
+
+\backslash
+CD
+\begin_inset LatexCommand index
+name "Commands ! C ! \\textbackslash CD"
+
+\end_inset
+
+
+\series default
+ is inserted to a formula.
+ A blue box appears with two dashed lines where further commands can be
+ inserted.
+ With
+\family sans
+Ctrl-Return
+\family default
+ a new line is created.
+ Horizontal relations are inserted in odd, vertical in even formula lines.
+\end_layout
+
+\begin_layout Standard
+To create the relations there are the following commands:
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@<<<
+\series default
+ creates a left arrow,
+\series bold
+@>>>
+\series default
+ a right arrow, and
+\series bold
+@=
+\series default
+ a long equal sign
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@AAA
+\series default
+ creates an up arrow,
+\series bold
+@VVV
+\series default
+ an down arrow, and
+\series bold
+@|
+\series default
+ a vertical equal sign
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@.
+
+\series default
+ is a placeholder for non-existent relations
+\end_layout
+
+\begin_layout Standard
+All arrows can be labeled as follows:
+\end_layout
+
+\begin_layout Itemize
+Is text inserted between the first and second < or >, resp., it is placed
+ above the arrow.
+ When it is inserted between the second and third one, it appears under
+ the arrow.
+\end_layout
+
+\begin_layout Itemize
+When text for vertical arrows is inserted between the first and second A
+ or V, resp., it is placed left beside the arrow.
+ When it is inserted between the second and third one, it appears right
+ beside the arrow.
+ If the text contains an A or V, these letters must be set into a TeX-brace.
+\end_layout
+
+\begin_layout Standard
+As example a diagram with all possible relations:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\begin{CD}A@>j>>B@>>k>C@=F\\
+@AmAA@.@VV{V}V@|\\
+D@<<j<E@>k>>F@=C\end{CD}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command for this is:
+\newline
+
+\series bold
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A@>j>>B@>>k>C@=F Ctrl-Enter
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+@AmAA@.@VV
+\backslash
+{V
+\series default
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\series bold
+V@| Ctrl-Enter
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+D@<<j<E@>k>>F@=C
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Tips
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Other useful math tips can be found in
+\begin_inset LatexCommand cite
+key "Voss"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\backslash
+texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+More about
+\backslash
+texorpdfstring is in section
+\begin_inset LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Tips"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Ions|see{Chemical characters}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Chemical Symbols and Equations
+\begin_inset LatexCommand label
+name "sub:Chemical-Symbols-and"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Chemical characters ! Symbols"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Chemical equations"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbols ! chemical"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An example text from chemistry:
+\end_layout
+
+\begin_layout Quote
+The
+\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
+\end_inset
+
+-ion reacts with two
+\begin_inset Formula $\mathrm{Na^{+}}$
+\end_inset
+
+-ions to sodium sulfate
+\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
+\end_inset
+
+.
+ The chemical equation for this is:
+\begin_inset Formula \[
+\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This chemical equation can directly be created as formula.
+ To avoid that the symbols appear italic, everything is highlighted and
+ changed by the shortcut
+\family sans
+Alt-c\InsetSpace ~
+r
+\family default
+ to the upright font style.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+font styles
+\series bold
+
+\series default
+see
+\begin_inset LatexCommand ref
+reference "sub:Font-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Negative Numbers
+\begin_inset LatexCommand index
+name "Numbers ! negative"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative numbers often look ugly in formulas because the minus sign before
+ the number is set with the same length as the minus operator sign.
+ When writing the negative number in normal text, the minus sign appears
+ correctly.
+\end_layout
+
+\begin_layout Standard
+Thus, the problem disappears when converting the minus sign to mathematical
+ text.
+\end_layout
+
+\begin_layout Standard
+An example to visualize the problem:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="right" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" rightline="true" width="0">
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+normal text:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+x = -2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+formula:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $x=-2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+solution:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $x=\textrm{-}2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Comma as Decimal Separator
+\begin_inset LatexCommand index
+name "Comma"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In LaTeX a comma inside a formula is used, according to the English convention,
+ as number group separator.
+ So there will be space added behind all commas in formulas.
+\end_layout
+
+\begin_layout Standard
+To avoid this, the comma is highlighted and changed to mathematical text
+ (shortcut
+\family sans
+Alt-m\InsetSpace ~
+m
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+To use all formula commas in the document as decimal separator, the file
+
+\series bold
+icomma.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+icomma
+\series default
+ is part of the LaTeX-package
+\series bold
+was
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! was\\vspace{4mm}"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! icomma"
+
+\end_inset
+
+ is loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{icomma}
+\end_layout
+
+\begin_layout Subsection
+Physical Vectors
+\begin_inset LatexCommand label
+name "sub:Physical-Vectors"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Vectors ! physical"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Predefined vectors are offered by the LaTeX-package
+\series bold
+braket
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+braket
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! braket"
+
+\end_inset
+
+ that is loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{braket}
+\end_layout
+
+\begin_layout Standard
+The following commands are defined:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bra{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Bra{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Ket{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Ket{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Braket{
+\backslash
+psi|
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Braket{\psi|\phi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The command
+\series bold
+
+\backslash
+Braket
+\series default
+ assures that all vertical bars are set in the size of the surrounding brackets:
+\begin_inset Formula \[
+\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The effect of
+\series bold
+
+\backslash
+Braket
+\series default
+ can also be achieved using the command
+\series bold
+
+\backslash
+middle
+\series default
+, that is described in
+\begin_inset LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Self-defined Fractions
+\begin_inset LatexCommand label
+name "sub:Self-defined-Fractions"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Fractions ! self-defined"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To define custom commands for fractions, the command
+\series bold
+
+\backslash
+genfrac
+\series default
+
+\begin_inset LatexCommand index
+name "Commands ! G ! \\textbackslash genfrac"
+
+\end_inset
+
+ is used in the following scheme:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+genfrac{left
+\series default
+
+\series bold
+bracket}{right
+\series default
+
+\series bold
+bracket}{fraction bar thickness}{style}
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+phantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+genfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+{numerator}{denominator}
+\end_layout
+
+\begin_layout Standard
+The style is a number in the range of 0\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+3.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Number
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Style (Size)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+display style formula
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+inline formula
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+small
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+tiny
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When no style is given, the size is adjusted to the surrounding environment
+ like for the command
+\series bold
+
+\backslash
+frac
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
+pt will
+ be used.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+For example, the commands
+\series bold
+
+\backslash
+dfrac
+\series default
+ and
+\series bold
+
+\backslash
+tbinom
+\series default
+ from
+\begin_inset LatexCommand ref
+reference "sub:Fractions"
+
+\end_inset
+
+ are defined with the commands
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+dfrac}[2]{
+\backslash
+genfrac{}{}{}{0}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+and
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+tbinom}[2]{
+\backslash
+genfrac{(}{)}{0pt}{1}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+To define a fraction where the fraction bar thickness can be given as optional
+ argument, the following line is inserted to the LaTeX-preamble:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+fracS}[3][]{
+\backslash
+genfrac{}{}{#1}{}{#2}{#3}}
+\end_layout
+
+\begin_layout Standard
+A test:
+\begin_inset Formula \begin{align*}
+\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
+\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
+
+\end_inset
+
+As one can see, the distance of the numerator and the denominator to the
+ fraction bar is round about three times the bar thickness.
+\end_layout
+
+\begin_layout Subsection
+Canceled Formulas
+\begin_inset LatexCommand label
+name "sub:Canceled-Formulas"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! canceled"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To cancel formulas or formula parts, the LaTeX-package
+\series bold
+cancel
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+cancel
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! cancel"
+
+\end_inset
+
+ has to be loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[samesize]{cancel}
+\end_layout
+
+\begin_layout Standard
+There are four ways to cancel formulas:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Result
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace
+\series default
+ and
+\series bold
+
+\backslash
+raisebox
+\series default
+ are used here as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bcancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+xcancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cancelto{1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+spce
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cancelto
+\series default
+ is especially suitable to visualize the reduction of fractions within formulas:
+\begin_inset Formula \[
+\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formulas in Section Headings
+\begin_inset LatexCommand label
+name "sub:Formulas-in-Section"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formula ! in section headings"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When formulas are used in section headings, the following has to be taken
+ into account:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+When the LaTeX-package
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! hyperref"
+
+\end_inset
+
+ is used, PDF-bookmarks are automatically created for every section heading
+ in the table of contents.
+ If a section heading contains formulas, they are incorrectly displayed
+ in the bookmark text, because formulas in bookmarks infringe the PDF convention
+s.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Both problems can be solved by inserting at the end of the section heading
+ a short title with the menu
+\family sans
+Insert\SpecialChar \menuseparator
+Short\InsetSpace ~
+Title
+\family default
+.
+ Short titles are used as alternative for multiline section headings to
+ keep the table of contents clearly arranged.
+ Only the short title appears in the table of contents and therefore also
+ in the PDF-bookmark.
+\end_layout
+
+\begin_layout Standard
+When formulas should be used in the table of contents but
+\series bold
+hyperref
+\series default
+ is used, one can use the following command in TeX-mode:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring{part}{alternative}
+\begin_inset LatexCommand index
+name "Commands ! T ! \\textbackslash texorpdfstring"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Part is the part of the heading that shouldn't appear in the PDF-bookmark.
+ This can be characters, formulas, footnotes, but also cross-references.
+ The alternative is used instead of the part for the bookmark.
+\end_layout
+
+\begin_layout Standard
+Here are two example headings:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Heading without formula in table of contents
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset OptArg
+status collapsed
+
+\begin_layout Standard
+Heading without formula in table of contents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Heading with formula in table of contents
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+In the first heading a short title was used, in the second one
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+To get the same formatting as for the other headings, the complete heading
+ was set into a
+\series bold
+boldmath environment
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset LatexCommand ref
+reference "sub:Bold-Formulas"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Formulas in multi-column Text
+\begin_inset LatexCommand index
+name "Formula ! in multi-column text"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formulas in multi-column text are often too wide to fit into a column and
+ thus need to be set over the whole page width.
+ This is done by using the LaTeX-package
+\series bold
+multicol
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+multicol
+\series default
+ is part of every LaTeX standard installation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! multicol"
+
+\end_inset
+
+, that is loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{multicol}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Note herby that the setting
+\family sans
+Two-column\InsetSpace ~
+document
+\family default
+ in the menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings
+\family default
+ under
+\family sans
+Text\InsetSpace ~
+Layout
+\family default
+\emph on
+
+\emph default
+must
+\emph on
+not
+\emph default
+ be selected.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Before the multi-column text the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+begin{multicols}{column number}
+\end_layout
+
+\begin_layout Standard
+is written in TeX-mode.
+ The column number is a number in the range of 2\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+10.
+ Before the formula the multi-column text is ended by inserting the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+end{multicols}
+\end_layout
+
+\begin_layout Standard
+in TeX-mode.
+\end_layout
+
+\begin_layout Standard
+Due to the command some space is automatically added before the formula.
+ To revert this, -6\InsetSpace \thinspace{}
+mm vertical space is inserted before the formula.
+ When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+formula styles see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, -9\InsetSpace \thinspace{}
+mm space is inserted instead.
+\end_layout
+
+\begin_layout Standard
+As example a multi-column text with a displayed formula:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+Das Spektrum wird fouriertransformiert.
+ the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
+, Lösungsmittel) zu trennen.
+ Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
+ nun das Aussehen des Ausgangssignals.
+ Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
+ über alle Phasen integrieren muss.
+ Sei nun
+\begin_inset Formula $S$
+\end_inset
+
+ unser normiertes Ausgangssignal and
+\begin_inset Formula $P$
+\end_inset
+
+ the Phasenverteilungsfunktion, so ergibt sich the Beziehung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -6mm
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+wobei
+\begin_inset Formula $S_{0}$
+\end_inset
+
+ das Signal ohne Gradient ist and the Normierungsbedingung
+\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
+\end_inset
+
+ gilt.
+ Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
+ Direkt nach the
+\begin_inset Formula $\nicefrac{\pi}{2}$
+\end_inset
+
+\InsetSpace \thinspace{}
+-rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
+ das Signal zusätzlich abschwächt.
+ Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
+
+\begin_inset Formula $T_{2}$
+\end_inset
+
+-Zeit.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formulas with Description of Variables
+\begin_inset LatexCommand index
+name "Formula ! with description of variables"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+To describe variables within a formula, like in formula
+\begin_inset LatexCommand eqref
+reference "eq:within"
+
+\end_inset
+
+, a 2
+\series bold
+×
+\series default
+
+\begin_inset Formula $n$
+\end_inset
+
+\InsetSpace ~
+matrix is used with left aligned columns for the
+\begin_inset Formula $n$
+\end_inset
+
+ used variables.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+matrices see
+\begin_inset LatexCommand ref
+reference "sec:Matrices"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
+g.\InsetSpace ~
+the command
+
+\series bold
+
+\backslash
+footnotesize
+\series default
+ is inserted.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+font sizes see
+\begin_inset LatexCommand ref
+reference "sub:Font-Sizes"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+When the formula style
+\series bold
+Indented
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+formula styles see
+\begin_inset LatexCommand ref
+reference "sec:Formula-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ is used, a
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hfill
+\series default
+ only works in formulas with the style
+\series bold
+Indented
+\series default
+, see
+\begin_inset LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ is inserted before and after the matrix to have the same separation of
+ the matrix from the equation and the side margin.
+\end_layout
+
+\begin_layout Standard
+When the formula style
+\series bold
+Centered
+\series default
+ is used, the method described in
+\begin_inset LatexCommand ref
+reference "sub:Flalign-Environment"
+
+\end_inset
+
+ is used to indent formulas.
+ Formula
+\begin_inset LatexCommand eqref
+reference "eq:within"
+
+\end_inset
+
+ consists of five columns whereas in the first two columns contain the equation,
+ the third the matrix, and the last one an empty TeX-brace.
+\begin_inset Formula \begin{flalign}
+\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
+\rho & \textrm{density}\\
+V & \textrm{volume}\\
+g & \textrm{gravitational acceleration}\end{array} & & {}\label{eq:within}\end{flalign}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Upright small Greek Letters
+\begin_inset LatexCommand label
+name "sub:Upright-small-Greek"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Greek letters ! upright"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Most of the math fonts only provide italic small Greek letters.
+ But for symbols of elementary particles like pions and neutrinos, upright
+ Greek letters are needed.
+ The file
+\series bold
+upgreek.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+upgreek
+\series default
+ is part of the LaTeX-package
+\series bold
+was
+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! was\\vspace{4mm}"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Packages ! upgreek"
+
+\end_inset
+
+ that is loaded with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{upgreek}
+\end_layout
+
+\begin_layout Standard
+provides them.
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+ifupgreek
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+The following table will only be displayed when the LaTeX-package
+\series bold
+upgreek
+\series default
+ is installed.
+\end_layout
+
+\end_inset
+
+ They are created when the command for a small Greek letters is started
+ with
+\series bold
+up
+\series default
+.
+ For example the command
+\series bold
+
+\backslash
+uptau
+\series default
+ creates this:
+\begin_inset Formula $\uptau$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+With these commands reactions of elementary particles can be typeset:
+\begin_inset Formula \[
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+The upright letters are more bold and wider than the italic ones.
+ They should therefore not be used for units like
+\begin_inset Quotes eld
+\end_inset
+
+µm
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+The following will be displayed when the LaTeX-package
+\series bold
+upgreek
+\series default
+ is not installed:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+You need to install the package
+\series bold
+upgreek
+\series default
+ to see the rest of this subsection in the output.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Text Characters in Formulas
+\begin_inset LatexCommand label
+name "sub:Text-Characters-in"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Text ! in formulas"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In some cases you might want to insert text characters directly into formulas.
+ When for example the centered dot · is often used in formulas like
+\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
+\end_inset
+
+, one would have to insert the command
+\series bold
+
+\backslash
+cdot
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+see
+\begin_inset LatexCommand ref
+reference "sub:Binary-Operators"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ all the time, because this character is defined in all encodings as text
+ character.
+ But the encoding can be changed by this LaTeX-preamble line:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Declare Inputtext{183}{
+\backslash
+ifmmode
+\backslash
+cdot
+\backslash
+else
+\backslash
+textperiodcentered
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+The character encoding (menu
+\family sans
+Document\SpecialChar \menuseparator
+Settings\SpecialChar \menuseparator
+Language
+\family default
+) specifies what character appears when a keyboard key is pressed.
+ When the key for the character '·' is pressed, internally the command
+\series bold
+
+\backslash
+textperiodcentered
+\series default
+ is used.
+ But this command is not available in a formula so that you would get LaTeX-erro
+rs.
+ With the changed encoding the right command is chosen automatically, depending
+ on if the character was inserted into a formula or not.
+\end_layout
+
+\begin_layout Standard
+The encoding of several characters is saved in definition files.
+ Fore example the encoding
+\series bold
+latin9
+\series default
+ is defined in the file
+\series bold
+latin9.def
+\series default
+ that is in the installation folder of LaTeX.
+ Encodings should only be changed via the LaTeX-preamble and not in the
+ definition files.
+ Otherwise own documents could not be edited by other LyX users working
+ on other computers.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Besides the centered dot, in this document the degree sign ° is defined
+ with the following LaTeX-preamble line so that it can directly be inserted
+ to a formula:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputtext{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+\start_of_appendix
+Typographic Advises
+\begin_inset LatexCommand index
+name "Typographic Advises"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+This section is a summary of the most important typographic rules, listed
+ in ISO norms.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+This collection was partly taken from the German semi-official dictionary
+ called
+\begin_inset Quotes eld
+\end_inset
+
+Duden
+\begin_inset Quotes erd
+\end_inset
+
+
+\begin_inset LatexCommand cite
+key "Duden"
+
+\end_inset
+
+ that lists some of the ISO rules.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Physical units are
+\emph on
+always
+\emph default
+ set upright
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+done with font styles, see
+\begin_inset LatexCommand ref
+reference "sub:Font-Styles"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+: 30\InsetSpace \thinspace{}
+km/h
+\newline
+Between the value and the unit is the smallest space, see
+\begin_inset LatexCommand ref
+reference "sub:Predefined-Space"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Percent and perthousand signs are set like physical units:
+\newline
+1,2\InsetSpace \thinspace{}
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textperthousand
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+alcohol in blood
+\end_layout
+
+\begin_layout Itemize
+The degree sign follows directly on the value: 15°, but not when it is used
+ in units: 15\InsetSpace \thinspace{}
+°C
+\end_layout
+
+\begin_layout Itemize
+In numbers with more than four digits the smallest space is inserted before
+ every third digit to group them:
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+18\InsetSpace \thinspace{}
+473\InsetSpace \thinspace{}
+588
+\end_layout
+
+\begin_layout Itemize
+For dimensionings like 120×90×40\InsetSpace \thinspace{}
+cm the multiplication sign
+\begin_inset Quotes eld
+\end_inset
+
+×
+\begin_inset Quotes erd
+\end_inset
+
+ is used.
+ It is available with the LaTeX-command
+\series bold
+
+\backslash
+texttimes
+\series default
+, but can also directly be inserted with some keyboard definitions.
+\end_layout
+
+\begin_layout Itemize
+Functions with names consisting of several letters are set upright to avoid
+ confusions, see
+\begin_inset LatexCommand ref
+reference "sub:Predefined-Functions"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Indices consisting of several letters, are set upright:
+\begin_inset Formula $E_{\mathrm{kin}}$
+\end_inset
+
+
+\newline
+Components of matrices are set italic:
+\begin_inset Formula $\hat{H}_{kl}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+The differentiation/integration operator 'd', the Euler's number 'e', and
+ the imaginary unit 'i' should be set upright, to avoid mixing them up with
+ other variables.
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Synonyms
+\begin_inset LatexCommand index
+name "Synonyms"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Some characters and symbols can be created with several commands.
+ Here is a list of the synonym commands:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+equivalent to
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ast
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+choose
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+binom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+geq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+{
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+[
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+slash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+/
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vert
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+|
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+equivalent to
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+backslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dashrightarrow
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+land
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+]
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lnot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ne
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+owns
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+square
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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+
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+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "TLC2"
+
+\end_inset
+
+
+\shape smallcaps
+Mittelbach, F.
+ ; Goossens, M.
+\shape default
+:
+\shape italic
+The LaTeX Companion
+\shape default
+.
+ Addison Wesley, 2004
+\end_layout
+
+\begin_layout Bibliography
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+
+\end_inset
+
+
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+
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+
+ of LaTeX's math abilities
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
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+
+\end_inset
+
+LaTeX tips and tricks-
+\begin_inset ERT
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+
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+
+\end_inset
+
+-LaTeX
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Symbole"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
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+
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+
+\end_inset
+
+List
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ of all symbols available with LaTeX-packages
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "hyperref"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
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+
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+\begin_inset ERT
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+
+}
+\end_layout
+
+\end_inset
+
+ of the LaTeX-package
+\series bold
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+\series default
+
+\begin_inset LatexCommand index
+name "Packages ! hyperref"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Mathclap"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
+\end_layout
+
+\end_inset
+
+Description
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ of the command
+\series bold
+
+\backslash
+mathclap
+\series default
+, described in
+\begin_inset LatexCommand ref
+reference "sub:Operator-Limits"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Commands ! M ! \\textbackslash mathclap"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Duden"
+
+\end_inset
+
+
+\emph on
+Duden Band 1
+\emph default
+.
+ 22.
+ Auflage, Duden 2001
+\end_layout
+
+\begin_layout Subsubsection*
+\begin_inset LatexCommand printindex
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
--- /dev/null
+#LyX 1.5.4svn created this file. For more info see http://www.lyx.org/
+\lyxformat 276
+\begin_document
+\begin_header
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+
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+
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+ pdfpagelayout=OneColumn, pdfstartview=XYZ,
+ pdfauthor={Uwe Stöhr},
+ pdfsubject={LaTeX/LyX-Nummerierungsbeispiel},
+ pdfkeywords={LaTeX, Nummerierung, LyX}]{hyperref}
+
+\else % if DVI
+
+\usepackage[colorlinks=true, hypertex]{hyperref}
+
+\fi
+
+%Roemischen Gleichungszaehler einrichten
+\newcounter{roem}
+\renewcommand{\theroem}{\roman{roem}}
+
+%Merken des Originalzaehlers
+\newcommand{\c@org@eq}{}
+\let\c@org@eq\c@equation
+\newcommand{\org@theeq}{}
+\let\org@theeq\theequation
+
+%\setroem aktiviert den roemischen Gleichungszaehler
+\newcommand{\setroem}{
+ \let\c@equation\c@roem
+ \let\theequation\theroem}
+
+%\setarab aktiviert den urspruenglichen arabischen Gleichungszaehler
+\newcommand{\setarab}{
+ \let\c@equation\c@org@eq
+ \let\theequation\org@theeq}
+\end_preamble
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+Diese Datei ist ein Beispiel zur Verwendung von zwei verschiedenen Formelkategor
+ien.
+ Die eine wird arabisch, die andere römisch nummeriert.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+A=B\label{eq:B}\end{equation}
+
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+
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+\begin_inset LatexCommand eqref
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+\begin_inset LatexCommand eqref
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+
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+
+
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+
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+
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+\begin_inset VSpace medskip
+\end_inset
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+Um dieses Beispiel zu erzeugen, muss zuerst für die römisch zu nummerierenden
+ Formeln ein eigener Gleichungszähler angelegt werden.
+ Dazu gibt man im LaTeX-Vorspann Folgendes ein:
+\end_layout
+
+\begin_layout Standard
+
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+
+\begin_layout Standard
+
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+Damit sich LaTeX den Zählerstand des arabischen Zählers
+\series bold
+equation
+\series default
+ merkt, gibt man im Vorspann
+\end_layout
+
+\begin_layout Standard
+
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+
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+\backslash
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+
+\backslash
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+\backslash
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+\backslash
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+\newline
+
+\backslash
+newcommand{
+\backslash
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+\newline
+
+\backslash
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+\backslash
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+\end_layout
+
+\begin_layout Standard
+ein.
+ Um im Dokument zwischen den beiden Nummerierungen umschalten zu können,
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+
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+
+\begin_layout Standard
+für römische Nummerierung und
+\end_layout
+
+\begin_layout Standard
+
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+
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+\end_layout
+
+\begin_layout Standard
+für arabische.
+\end_layout
+
+\begin_layout Standard
+Jede Formel im Dokument wird standardmäßig arabisch nummeriert.
+ Um auf römische Nummerierung umzuschalten, wird im TeX-Modus der Befehl
+
+\series bold
+
+\backslash
+setroem
+\series default
+ eingegeben.
+ Auf arabische Nummerierung wird mit dem Befehl
+\series bold
+
+\backslash
+setarab
+\series default
+ umgeschaltet.
+\end_layout
+
+\end_body
+\end_document
--- /dev/null
+#LyX 1.5.4svn created this file. For more info see http://www.lyx.org/
+\lyxformat 276
+\begin_document
+\begin_header
+\textclass scrartcl
+\begin_preamble
+% DO NOT ALTER THIS PREAMBLE!!!
+%
+% This preamble is designed to ensure that the file prints
+% out as advertised. If you mess with this preamble,
+% parts of this document may not print out as expected. If you
+% have problems LaTeXing this file, please contact
+% the documentation team
+% email: lyx-docs@lists.lyx.org
+
+
+% if pdflatex is used
+\usepackage{ifpdf}
+\ifpdf
+
+% set fonts for nicer pdf view
+\IfFileExists{lmodern.sty}
+ {\usepackage{lmodern}}{}
+
+% link all cross references and URLs
+% in pdf output
+ \usepackage[colorlinks=true, bookmarks, bookmarksnumbered,
+ bookmarksopen, bookmarksopenlevel=1,
+ linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,
+ pdfpagelayout=OneColumn, pdfnewwindow=true,
+ pdfstartview=XYZ, plainpages=false, pdfpagelabels,
+ pdfauthor={LyX Team}, pdftex,
+ pdftitle={LyXs Mathehandbuch},
+ pdfsubject={LyX-Dokumentation der Mathefunktionen},
+ pdfkeywords={LyX, Mathed}]{hyperref}
+
+\else % if dvi or ps is produced
+
+ % link all cross references and URLs in DVI output
+ \usepackage[ps2pdf, colorlinks=true,
+ linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref}
+
+\fi % end if pdflatex is used
+
+% Folgendes Problem lösen:
+% Besteht die Kapitelnummer aus zu vielen Ziffern, wird die
+% Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
+% die Kapitelnummer geschrieben.
+% Als Lösung wird mehr Platz zwischen Nummer und
+% Überschrift eingefügt.
+\renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}}
+\renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}}
+
+% Damit die Zeichen ° und · in LyX direkt eingegeben werden können,
+% siehe Kap. 22.11
+\DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
+\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi}
+
+% Linkfläche für Querverweise vergrößern und automatisch benennen,
+% siehe Kap. 22.18.1
+\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
+\renewcommand{\sectionautorefname}{Kap.\negthinspace}
+\renewcommand{\subsectionautorefname}{Kap.\negthinspace}
+\renewcommand{\subsubsectionautorefname}{Kap.\negthinspace}
+\newlength{\abc}
+\settowidth{\abc}{\space}
+\renewcommand{\equationautorefname}{\hspace{-\abc}}
+
+% Makros damit Pakete nicht doppelt geladen werden.
+% siehe erste Fußnote in Kap. 9.3
+\@ifundefined{textcolor}{\usepackage{color}}{}
+
+% damit die Seiten des Inhaltsverzeichnisses römisch
+% nummeriert werden und damit das Inhaltsverzeichnis
+% ein eigenes pdf-Lesezeichen erhält
+\pagenumbering{Roman}
+\let\myTOC\tableofcontents
+\renewcommand{\tableofcontents}{%
+ \vspace{1cm}
+ \pdfbookmark[1]{Inhaltsverzeichnis}{}
+ \myTOC
+ \cleardoublepage
+ \pagenumbering{arabic}}
+
+% Damit die Fußnoten einen zusätzlichen vertikalen Abstand von 1,5 mm haben,
+% siehe Kap. 22.16
+\let\myFoot\footnote
+\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}}
+
+% provides caption formatting
+\setkomafont{captionlabel}{\bfseries}
+
+% benutzt in Kap. 22.4
+\usepackage{braket}
+
+% benutzt in Kap. 22.6
+\usepackage[samesize]{cancel}
+
+% enables calculation of values,
+\usepackage{calc}
+
+% für Mehrfachzeilen und -spalten
+\usepackage{multirow}
+\usepackage{multicol}
+
+% für Diagramme
+\usepackage{amscd}
+
+% benutzt in Kap. 19.4
+\usepackage{remreset}
+
+%Mehrfachzeilen zentriert ausrichten (z.B. in Kap. 13.3)
+\renewcommand{\multirowsetup}{\centering}
+
+% Farbdefinition aus Kap. 9.3
+\definecolor{dunkelgruen}{cmyk}{0.5, 0, 1, 0.5}
+
+% Operatoren deklarieren (siehe Kap. 10.4 und 15.2)
+\DeclareMathOperator*{\Raute}{\blacklozenge}
+\DeclareMathOperator{\sgn}{sgn}
+
+\newcommand{\leer}{\textvisiblespace}
+
+% Beispielbefehle aus Kap. 20.1
+\newcommand{\gr}{\Longrightarrow}
+\newcommand{\us}[1]{\underline{#1}}
+\newcommand{\fb}[3]{\framebox#1#2{$#3$}}
+\newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}}
+\newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}}
+
+% Beispielmakro aus Kap. 19.4
+%\def\tagform@#1{\maketag@@@{|#1|}}
+
+% Makro aus Kap. 10.2
+\def\clap#1{\hbox to 0pt{\hss #1\hss}}
+\def\mathclap {\mathpalette \mathclapinternal}
+\def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
+
+% Grauschrift Notiz umdefinieren
+\renewenvironment{lyxgreyedout}
+ {\textcolor{blue}\bgroup}{\egroup}
+
+% Damit der Index einen anderen Namen erhält.
+\usepackage[ngerman]{babel}
+\addto\captionsngerman
+{\renewcommand{\indexname}
+{Stichwort- und Befehlsverzeichnis}}
+
+% testen ob das Paket eurosym installiert ist
+% wird benutzt für das Euro-Symbol
+\newboolean{eurosym}
+\IfFileExists{eurosym.sty}
+ {\usepackage[gennarrow]{eurosym}
+ \setboolean{eurosym}{true}}
+ {\setboolean{eurosym}{false}}
+
+% benutzt in Kap. 22.10
+% testen ob Paket upgreek instaliert ist
+\newboolean{upgreek}
+\IfFileExists{upgreek.sty}
+ {\usepackage{upgreek}
+ \setboolean{upgreek}{true}}
+ {\setboolean{upgreek}{false}}
+
+% benötigt für Kommas in Formeln, siehe Kap. 22.3
+\IfFileExists{icomma.sty}
+ {\usepackage{icomma}}{}
+\end_preamble
+\options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
+\language ngerman
+\inputencoding auto
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+\graphics default
+\paperfontsize 12
+\spacing single
+\papersize a4paper
+\use_geometry false
+\use_amsmath 2
+\use_esint 1
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\secnumdepth 4
+\tocdepth 3
+\paragraph_separation skip
+\defskip medskip
+\quotes_language german
+\papercolumns 1
+\papersides 2
+\paperpagestyle plain
+\bullet 1 0 6 -1
+\bullet 2 2 35 -1
+\bullet 3 2 7 -1
+\tracking_changes false
+\output_changes false
+\author ""
+\author ""
+\end_header
+
+\begin_body
+
+\begin_layout Title
+LyXs Mathehandbuch
+\end_layout
+
+\begin_layout Author
+vom LyX Team
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\noindent
+Für Anmerkungen oder Korrekturen senden sie bitte eine Email an LyXs Dokumentati
+ons-Liste:
+\family typewriter
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{mailto:lyx-docs@lists.lyx.org?subject=LyXs Mathehandbuch}{
+\end_layout
+
+\end_inset
+
+lyx-docs@lists.lyx.org
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Verfasser: Uwe Stöhr
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\newline
+
+\family sans
+Version 1.5.4-
+\family default
+1
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand tableofcontents
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Um diese Datei als PDF, PS oder DVI zu exportieren, müssen die LaTeX-Pakete
+
+\series bold
+eurosym,
+\series default
+
+\series bold
+multirow,
+\series default
+ und
+\series bold
+was
+\series default
+ installiert sein.
+ Wenn sie nicht installiert sind, kann das Dokument trotzdem exportiert
+ werden, die Abschnitte in denen die Pakete benötigt werden, erscheinen
+ dann aber nicht im Ausdruck.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Einleitung
+\begin_inset LatexCommand label
+name "sec:Einleitung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dieses Dokument ist eine Zusammenstellung und Erläuterung der wichtigsten
+ LaTeX-Befehle für mathematische Zeichen und Konstruktionen.
+ Die Erläuterungen sind speziell auf die Benutzung der Befehle mit LyX zugeschni
+tten.
+ Das setzt voraus, dass bereits das Kapitel
+\family typewriter
+Mathematische
+\family default
+
+\family typewriter
+Formeln
+\family default
+ des Benutzerhandbuchs gelesen worden ist.
+\end_layout
+
+\begin_layout Standard
+Die meisten Zeichen und viele Konstruktionen sind auch über das Menü
+\family sans
+Einfügen
+\series bold
+\SpecialChar \menuseparator
+
+\series default
+Mathe
+\family default
+ oder die
+\family sans
+Mathe-Werkzeugleiste
+\family default
+ aufrufbar.
+ Wer viele Formeln zu schreiben hat, wird jedoch feststellen, dass man mit
+ den LaTeX-Befehlen viel schneller eine Formel setzen kann.
+ Daher wird in diesem Handbuch der Fokus auf Befehle gesetzt wobei entsprechende
+ Werkzeugleistenknöpfe, falls vorhanden, erwähnt werden.
+\end_layout
+
+\begin_layout Standard
+Sofern nicht anders angegeben, sind Befehle nur in der Formel-Umgebung von
+ LyX verfügbar.
+ Um alle Befehle nutzen zu können, muss die Option
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+AMS-Mathe-Paket verwenden
+\family default
+ im Menü
+\family sans
+Dokument\SpecialChar \menuseparator
+Einstellungen\SpecialChar \menuseparator
+Mathe Optionen
+\family default
+ aktiviert sein
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Die
+\family sans
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+\family default
+
+\family sans
+AMS-Mathe-Paket automatisch verwenden
+\family default
+ verwendet
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-Mathe nur wenn im Dokument mathematische Konstrukte gefunden wurden die
+ LyX unterstützt.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Es wird in diesem Dokument der Übersichtlichkeit halber auf die Auf\SpecialChar \textcompwordmark{}
+listung
+ aller
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-Mathe Befehle
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Eine Liste mit allen
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-Mathe Befehlen findet sich in der Datei
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
+\end_layout
+
+\end_inset
+
+
+\family sans
+amsguide.ps
+\family default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+, die Teil jeder LaTeX-Standardinstallation ist.
+\end_layout
+
+\end_inset
+
+ verzichtet.
+\end_layout
+
+\begin_layout Section
+Allgemeine Hinweise
+\begin_inset LatexCommand label
+name "sec:Allgemeine-Hinweise"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um eine in einer Textzeile eingebettete Formel
+\begin_inset LatexCommand index
+name "Formel ! eingebettete"
+
+\end_inset
+
+ zu erstellen, drückt man
+\family sans
+Strg-m
+\family default
+ oder den Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math-mode.png
+ scale 85
+
+\end_inset
+
+.
+\newline
+Um eine abgesetzte Formel
+\begin_inset LatexCommand index
+name "Formel ! abgesetzte"
+
+\end_inset
+
+ zu erstellen, drückt man
+\family sans
+Strg-M
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Um eine abgesetzte Formel in eine eingebettete umzuwandeln, setzt man den
+ Cursor in die Formel und drückt
+\family sans
+Strg-M
+\family default
+ oder benutzt das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+Formelart ändern
+\family default
+.
+ Auf die selbe Weise lässt sich eine eingebettete in eine abgesetzte Formel
+ umwandeln.
+\end_layout
+
+\begin_layout Standard
+Um Teile einer eingebetteten Formel in der Größe einer abgesetzten darzustellen,
+ gibt man in die Formel den Befehl
+\series bold
+
+\backslash
+displaystyle
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash displaystyle"
+
+\end_inset
+
+
+\series default
+ ein.
+ Es erscheint ein neues blaues Kästchen, in das dann der Formelteil eingegeben
+ wird.
+\end_layout
+
+\begin_layout Standard
+In einer Tabelle dürfen nur eingebettete Formeln verwendet werden.
+\end_layout
+
+\begin_layout Standard
+Die
+\family sans
+Mathe-Werkzeugleiste
+\family default
+ kann über das Menü
+\family sans
+Ansicht\SpecialChar \menuseparator
+Werkzeugleisten
+\family default
+ eingeblendet werden.
+ Wenn dort auf
+\begin_inset Quotes eld
+\end_inset
+
+Mathe
+\begin_inset Quotes erd
+\end_inset
+
+ geklickt wird, wird die Werkzeugleiste permanent am unteren Rand eingeblendet;
+ diese Einstellung wird durch ein Häkchen im Menü
+\family sans
+Werkzeugleisten
+\family default
+ angezeigt.
+ Wenn nun im Menü
+\family sans
+Werkzeugleisten
+\family default
+ nochmal auf
+\begin_inset Quotes eld
+\end_inset
+
+Mathe
+\begin_inset Quotes erd
+\end_inset
+
+ geklickt wird, wird die Werkzeugleiste nur angezeigt, wenn sich der Cursor
+ in einer Formel befindet; diese Einstellung wird durch die Umbenennung
+ des Menüeintrags von
+\begin_inset Quotes eld
+\end_inset
+
+Mathe
+\begin_inset Quotes erd
+\end_inset
+
+ zu
+\begin_inset Quotes eld
+\end_inset
+
+Mathe\InsetSpace ~
+(automatisch)
+\begin_inset Quotes erd
+\end_inset
+
+ angezeigt.
+\end_layout
+
+\begin_layout Standard
+In den TeX-Modus
+\begin_inset LatexCommand index
+name "T@\\TeX-Modus"
+
+\end_inset
+
+ gelangt man über den Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/ert-insert.png
+ scale 85
+
+\end_inset
+
+ oder das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+T
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+e
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+X\InsetSpace ~
+Code
+\family default
+ (Tastenkürzel
+\family sans
+Strg-l
+\family default
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+In LyX gibt es drei
+\begin_inset Quotes gld
+\end_inset
+
+Eigennamen
+\begin_inset Quotes grd
+\end_inset
+
+, die im Ausdruck mit hoch bzw.
+ tief gestellten Großbuchstaben erscheinen: TeX, LaTeX und LyX
+\end_layout
+
+\begin_layout Standard
+Um zu verhindern, dass diese Wörter als Eigennamen erkannt werden, setzt
+ man einen der Buchstaben in TeX-Klammern.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In den LaTeX-Vorspann
+\begin_inset LatexCommand index
+name "L@\\LaTeX-Vorspann"
+
+\end_inset
+
+ gelangt man über das Menü
+\family sans
+Dokument\SpecialChar \menuseparator
+Einstellungen\SpecialChar \menuseparator
+La
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+{
+\end_layout
+
+\end_inset
+
+T
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+eX-Vorspann
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Zur nachträglichen Bearbeitung von Matrizen, Fallunterscheidungen und mehrzeilig
+en Formeln kann man die Menüs
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe
+\family default
+ und
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Zeilen\InsetSpace \thinspace{}
+&\InsetSpace \thinspace{}
+Spalten
+\family default
+ oder die
+\family sans
+Tabellen-Werkzeugleiste
+\family default
+ verwenden.
+ Beim Vertauschen von Zeilen und Spalten mit Hilfe dieses Menüs wird immer
+ die Spalte bzw.
+ Zeile, in der der Cursor steht, mit der rechts daneben stehenden Spalte
+ bzw.
+ darunter liegenden Zeile vertauscht.
+ Befindet sich der Cursor in der letzten Spalte bzw.
+ Zeile, wird mit der links daneben stehenden Spalte bzw.
+ darüber liegenden Zeile vertauscht.
+\end_layout
+
+\begin_layout Standard
+Zum Schreiben von Text in einer Formel
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Bei mehrzeiligen Formeln wird der Befehl
+\series bold
+
+\backslash
+intertext
+\series default
+ verwendet, siehe
+\begin_inset LatexCommand ref
+reference "sub:Text-in-mehrzeiligen"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ verwendet man den
+\emph on
+mathematischen Textmodus
+\emph default
+
+\begin_inset LatexCommand index
+name "Text ! in Formeln"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Mathematischer Textmodus"
+
+\end_inset
+
+, in den man mit dem Tastenkürzel
+\family sans
+Alt-m\InsetSpace ~
+m
+\family default
+ oder durch Eingabe des Befehls
+\series bold
+
+\backslash
+text
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash text"
+
+\end_inset
+
+
+\series default
+ gelangt.
+ Der Text erscheint in LyX schwarz und lässt sich dadurch gut vom Rest der
+ Formel unterscheiden.
+ Im fertigen Dokument erscheint mathematischer Text im Gegensatz zu allen
+ anderen Zeichen einer Formel nicht kursiv.
+\end_layout
+
+\begin_layout Subsection*
+Befehlsschema
+\end_layout
+
+\begin_layout Standard
+Die meisten LaTeX-Befehle für mathematische Konstruktionen besitzen folgendes
+ Schema:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Befehlsname[optionales
+\series default
+
+\series bold
+Argument]{anzugebendes
+\series default
+
+\series bold
+Argument}
+\end_layout
+
+\begin_layout Standard
+Ein Befehl muss immer mit einem Backslash
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+
+\backslash
+
+\series default
+
+\begin_inset Quotes grd
+\end_inset
+
+ beginnen.
+ Möchte man ein optionales Argument nicht angeben, müssen auch die zugehörigen
+ eckigen Klammern weggelassen werden.
+ Die geschweiften Klammern werden in diesem Dokument als TeX-Klammern
+\begin_inset LatexCommand index
+name "T@\\TeX-Klammern"
+
+\end_inset
+
+ bezeichnet.
+ Hängt man in einer Formel an Befehlsnamen eine linke geschweifte Klammer
+ an, erzeugt LyX automatisch eine TeX-Klammer.
+ Ansonsten werden sie in Formeln mit dem Befehl
+\series bold
+
+\backslash
+{
+\series default
+ erzeugt.
+ TeX-Klammern erscheinen in LyX rot, im Gegensatz zu normalen geschweiften
+ Klammern, die blau erscheinen.
+ Im TeX-Modus sind für TeX-Klammern keine Befehle notwendig.
+ TeX-Klammern erscheinen nicht im Ausdruck.
+\end_layout
+
+\begin_layout Standard
+Werden Befehle ohne Argumente, wie z.\InsetSpace \thinspace{}
+B.
+ Symbolbefehle, im TeX-Modus eingegeben, muss auf den Befehl
+\emph on
+immer
+\emph default
+ ein Leerzeichen folgen um ihn zu beenden.
+ Dieses Leerzeichen erscheint nicht im Ausdruck.
+ Soll das Leerzeichen auch im Ausdruck erscheinen, muss auf den Befehl im
+ normalen Text ein geschütztes Leerzeichen folgen.
+\end_layout
+
+\begin_layout Standard
+Ein geschütztes Leerzeichen gibt man mit
+\family sans
+Strg-Leertaste
+\family default
+ ein.
+\end_layout
+
+\begin_layout Subsection*
+Zeichenerklärung
+\end_layout
+
+\begin_layout Itemize
+Das Symbol
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Dieses sichtbare Leerzeichen erhält man über den Befehl
+\series bold
+
+\backslash
+textvisiblespace
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash textvisiblespace"
+
+\end_inset
+
+, der im TeX-Modus einzugeben ist.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+steht für ein einzugebendes Leerzeichen.
+\end_layout
+
+\begin_layout Itemize
+Ein Pfeil wie z.\InsetSpace \thinspace{}
+B.
+
+\begin_inset Formula $\to$
+\end_inset
+
+ steht für den Druck der jeweiligen Pfeiltaste auf der Tastatur.
+\end_layout
+
+\begin_layout Subsection*
+Verwendete Einheiten
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Caption
+
+\begin_layout Standard
+\begin_inset LatexCommand label
+name "tab:Verwendete-Einheiten"
+
+\end_inset
+
+Verwendete Einheiten
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Einheit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Name / Beschreibung
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Millimeter
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Zentimeter
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+in
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Inch / Zoll (1\InsetSpace \thinspace{}
+in = 2,54\InsetSpace \thinspace{}
+cm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+pt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Punkt (72,27\InsetSpace \thinspace{}
+pt = 1\InsetSpace \thinspace{}
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+pc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Pica (1\InsetSpace \thinspace{}
+pc = 12\InsetSpace \thinspace{}
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+sp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+scaled point (65536\InsetSpace \thinspace{}
+sp = 1\InsetSpace \thinspace{}
+pt)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+bp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+big point (72\InsetSpace \thinspace{}
+bp = 1\InsetSpace \thinspace{}
+in)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+dd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Didot (1\InsetSpace \thinspace{}
+dd
+\begin_inset Formula $\approx$
+\end_inset
+
+ 0,376\InsetSpace \thinspace{}
+mm)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Cicero (1\InsetSpace \thinspace{}
+cc = 12\InsetSpace \thinspace{}
+dd)
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+ex
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Höhe des Buchstabens
+\emph on
+x
+\emph default
+ in der aktuellen Schrift
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+em
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Breite des Buchstabens
+\emph on
+M
+\emph default
+ in der aktuellen Schrift
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+math unit (1\InsetSpace \thinspace{}
+mu =
+\begin_inset Formula $\nicefrac{1}{18}$
+\end_inset
+
+\InsetSpace \thinspace{}
+em)
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+textfrac
+\series default
+ ist in Kap.
+
+\begin_inset LatexCommand ref
+reference "sub:Selbstdefinierte-Brüche"
+
+\end_inset
+
+ erklärt.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Grundlegende Funktionen
+\end_layout
+
+\begin_layout Subsection
+Exponenten
+\begin_inset LatexCommand index
+name "Exponenten"
+
+\end_inset
+
+ und Indizes
+\begin_inset LatexCommand index
+name "Indizes"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Hochstellen|see{Exponenten}"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Tiefstellen|see{Indizes}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Indizes werden mit dem Unterstrich _ oder mit dem Mathe-Werkzeugleistenknopf
+
+\begin_inset Graphics
+ filename ../../images/math-subscript.png
+ scale 85
+
+\end_inset
+
+, Exponenten mit dem Zirkumflexzeichen ^ oder mit dem Mathe-Werkzeugleistenknopf
+
+\begin_inset Graphics
+ filename ../../images/math-superscript.png
+ scale 85
+
+\end_inset
+
+ erzeugt.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B_V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $B_{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B^V
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}B^{V}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+B^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}B^{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Da der Zirkumflex ein Akzent ist, werden Selbstlaute akzentuiert statt hochgeste
+llt
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Je nach Tastatureinstellung werden auch andere Buchstaben akzentuiert.
+\end_layout
+
+\end_inset
+
+.
+ Um in diesem Fall Exponenten zu erzeugen, muss nach dem Zirkumflex ein
+ Leerzeichen eingegeben werden, siehe letztes Beispiel.
+\end_layout
+
+\begin_layout Subsection
+Brüche
+\begin_inset LatexCommand label
+name "sub:Brüche"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Brüche"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Brüche werden mit dem Befehl
+\series bold
+
+\backslash
+frac
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! F ! \\textbackslash frac"
+
+\end_inset
+
+ oder mit dem Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/frac.png
+ scale 50
+
+\end_inset
+
+ erstellt.
+ Die Zeichengröße wird automatisch angepasst, je nachdem, ob sich der Bruch
+ in einer eingebetteten oder abgesetzten Formel befindet.
+ Mit dem Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/frac-square.png
+ scale 85
+
+\end_inset
+
+ können verschieden Bruchtypen gewählt werden.
+\end_layout
+
+\begin_layout Standard
+Mit dem Befehl
+\series bold
+
+\backslash
+dfrac
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash dfrac"
+
+\end_inset
+
+
+\series default
+ kann man einen Bruch erzeugen, der immer in der Größe einer abgesetzten
+ Formel erscheint.
+ Mit
+\series bold
+
+\backslash
+tfrac
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash tfrac"
+
+\end_inset
+
+
+\series default
+ erscheint der Bruch immer in der Größe einer eingebetteten Formel.
+ Ein Beispiel:
+\end_layout
+
+\begin_layout Standard
+Eine Zeile mit dem Bruch
+\begin_inset Formula $\frac{1}{2}$
+\end_inset
+
+, der mit dem Befehl
+\series bold
+
+\backslash
+frac
+\series default
+ erstellt wurde.
+\end_layout
+
+\begin_layout Standard
+Eine Zeile mit dem Bruch
+\begin_inset Formula $\dfrac{1}{2}$
+\end_inset
+
+, der mit dem Befehl
+\series bold
+
+\backslash
+dfrac
+\series default
+ erstellt wurde.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+1
+\begin_inset Formula $\downarrow$
+\end_inset
+
+2
+\begin_inset Formula $\downarrow\downarrow$
+\end_inset
+
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\newpage
+Für Mehrfachbrüche gibt es den Befehl
+\series bold
+
+\backslash
+cfrac
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! C ! \\textbackslash cfrac"
+
+\end_inset
+
+.
+ Dazu ein Beispiel:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{align*}
+\textrm{mit \textbf{\textbackslash frac} erstellt} & & \textrm{mit \textbf{\textbackslash cfrac} erstellt}\\
+\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl für obiges Beispiel lautet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac{A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{B+
+\backslash
+cfrac{C+
+\backslash
+cfrac{E
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{F
+\begin_inset Formula $\to\to$
+\end_inset
+
+
+\backslash
+{D
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ bewirkt, dass der Bruch immer in der Größe einer abgesetzten Formel erscheint,
+ auch wenn er selbst Teil eines Bruches ist.
+
+\series bold
+
+\backslash
+cfrac
+\series default
+ besitzt folgendes Befehlsschema:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cfrac[Zählerposition]{Zähler}{Nenner}
+\end_layout
+
+\begin_layout Standard
+Zählerposition kann
+\emph on
+l
+\emph default
+ ,
+\emph on
+c
+\emph default
+ oder
+\emph on
+r
+\emph default
+ sein.
+ Bei
+\emph on
+l
+\emph default
+ oder
+\emph on
+r
+\emph default
+ wird der Zähler links- bzw.\InsetSpace ~
+rechtsbündig am Bruchstrich ausgerichtet.
+ Wird
+\emph on
+c
+\emph default
+ oder keine Position angegeben, erscheint der Zähler wie gewohnt mittig.
+ Diese Brüche demonstrieren die verschiedenen Ausrichtungen:
+\newline
+
+\series bold
+
+\begin_inset Formula $\cfrac[l]{A}{B+C}$
+\end_inset
+
+,
+\begin_inset Formula $\cfrac{A}{B+C}$
+\end_inset
+
+,
+\begin_inset Formula $\cfrac[r]{A}{B+C}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Oftmals ist es am günstigsten
+\series bold
+
+\backslash
+cfrac
+\series default
+ und
+\series bold
+
+\backslash
+frac
+\series default
+ zu kombinieren:
+\begin_inset Formula \[
+\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um Brüche mit schrägem Bruchstrich zu erzeugen, kann der Befehl
+\series bold
+
+\backslash
+nicefrac
+\begin_inset LatexCommand index
+name "Befehle ! N ! \\textbackslash nicefrac"
+
+\end_inset
+
+
+\series default
+ benutzt werden:
+\begin_inset Formula $\nicefrac{5}{31}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Wie man eigene Brüche definiert, um die Bruchstrichdicke zu ändern, ist
+ in
+\begin_inset LatexCommand ref
+reference "sub:Selbstdefinierte-Brüche"
+
+\end_inset
+
+ erklärt.
+\end_layout
+
+\begin_layout Subsection
+Wurzeln
+\begin_inset LatexCommand index
+name "Wurzeln"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Quadratwurzeln werden mit
+\series bold
+
+\backslash
+sqrt
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash sqrt"
+
+\end_inset
+
+ oder dem Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/sqrt.png
+ scale 85
+
+\end_inset
+
+ gesetzt, alle anderen Wurzeln mit dem Befehl
+\series bold
+
+\backslash
+root
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash root"
+
+\end_inset
+
+ oder dem Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/root.png
+ scale 85
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqrt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+root
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+3
+\begin_inset Formula $\downarrow$
+\end_inset
+
+A-B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Eine Quadratwurzel kann man auch mit
+\series bold
+
+\backslash
+root
+\series default
+ erstellen, indem man das Feld über der Wurzel frei lässt.
+\end_layout
+
+\begin_layout Standard
+Bei manchen Indizes ist der Abstand zur Wurzel zu gering, wie bei dieser
+ Formel:
+\begin_inset Formula $\sqrt[\beta]{B}$
+\end_inset
+
+
+\newline
+Das
+\begin_inset Formula $\beta$
+\end_inset
+
+ berührt die Wurzel.
+ Um dies zu verhindern, verwendet man die Befehle
+\series bold
+
+\backslash
+leftroot
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash leftroot"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+uproot
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! U ! \\textbackslash uproot"
+
+\end_inset
+
+, die folgendes Schema besitzen:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+leftroot{Abstand}
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+uproot{Abstand}
+\end_layout
+
+\begin_layout Standard
+Abstand ist die Anzahl der Big Points (Einheit bp;
+\begin_inset Formula $\mathrm{72\, bp=1\, inch}$
+\end_inset
+
+), um die der Index nach links bzw.
+ nach oben verschoben werden soll.
+ Die Befehle werden in den Index geschrieben.
+ So ergibt der Befehl
+\newline
+
+\series bold
+
+\backslash
+root
+\backslash
+leftroot{-1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+uproot{2
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+beta
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\newline
+
+\series default
+eine korrekt gesetzte Formel:
+\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Binomialkoeffizienten
+\begin_inset LatexCommand index
+name "Binomialkoeffizienten"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binomialkoeffizienten können mit dem Befehl
+\series bold
+
+\backslash
+binom
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash binom"
+
+\end_inset
+
+ oder über das Untermenü des Mathe-Werkzeugleistenknopfs
+\begin_inset Graphics
+ filename ../../images/math/frac-square.png
+ scale 85
+
+\end_inset
+
+eingefügt werden.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+binom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dbinom{A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Analog zu Brüchen (
+\series bold
+
+\backslash
+frac
+\series default
+) gibt es außer
+\series bold
+
+\backslash
+binom
+\series default
+ noch die Befehle
+\series bold
+
+\backslash
+dbinom
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash dbinom"
+
+\end_inset
+
+
+\series default
+ und
+\series bold
+
+\backslash
+tbinom
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash tbinom"
+
+\end_inset
+
+, die folgendes Befehlsschema besitzen:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+dbinom{Zähler}{Nenner}
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+tbinom{Zähler}{Nenner}
+\end_layout
+
+\begin_layout Subsection
+Fallunterscheidungen
+\begin_inset LatexCommand index
+name "Fallunterscheidungen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cases
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+B>0
+\begin_inset LatexCommand index
+name "Befehle ! C ! \\textbackslash cases"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{cases}
+A & B>0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cases
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+Strg-Enter
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{cases}
+A & \textrm{für }x>0\\
+B & \textrm{für }x=0\end{cases}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Nach der Eingabe von
+\series bold
+
+\backslash
+cases
+\series default
+ oder der Benutzung des Mathe-Werkzeugleistenknopfs
+\begin_inset Graphics
+ filename ../../images/math/cases.png
+ scale 85
+
+\end_inset
+
+ können mit
+\family sans
+Strg-Enter
+\family default
+ oder dem Tabellen-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+ neue Zeilen erstellt werden.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Umlaute in Formeln, wie in obiger Tabelle, sind in
+\begin_inset LatexCommand ref
+reference "sub:Akzente-für-ein"
+
+\end_inset
+
+ beschrieben.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+cases
+\series default
+ ist auch über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Cases-Umgebung
+\family default
+ verfügbar.
+\end_layout
+
+\begin_layout Subsection
+Verneinungen
+\begin_inset LatexCommand index
+name "Verneinungen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Durch die Eingabe von
+\series bold
+
+\backslash
+not
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! N ! \\textbackslash not"
+
+\end_inset
+
+ kann jedes beliebige Zeichen durchgestrichen dargestellt werden.
+ Die Zeichen werden quasi mit einem Schrägstrich akzentuiert.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Das letzte Beispiel zeigt, dass nicht alle Verneinungen gut aussehen.
+ Deswegen gibt es für Einige spezielle Befehle (siehe
+\begin_inset LatexCommand ref
+reference "sub:Mathematische-Symbole"
+
+\end_inset
+
+ und
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+sectionautorefname}{
+\backslash
+hspace{-
+\backslash
+abc}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand ref
+reference "sec:Relationen"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+sectionautorefname}{Kap.
+\backslash
+negthinspace}
+\end_layout
+
+\end_inset
+
+).
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Die
+\series bold
+
+\backslash
+renewcommand
+\series default
+-Befehle im TeX-Modus sind notwendig, damit der Querverweisname
+\begin_inset Quotes gld
+\end_inset
+
+Kap.
+\begin_inset Quotes grd
+\end_inset
+
+ nicht zweimal geschrieben wird, siehe Kap.\InsetSpace \thinspace{}
+
+\begin_inset LatexCommand ref
+reference "sub:Verlinkte-Querverweise"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Platzhalter
+\begin_inset LatexCommand label
+name "sub:Platzhalter"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Platzhalter\\vspace{4mm}"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "chemische Zeichen ! Isotope"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Isotope|see{chemische Zeichen}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man z.\InsetSpace \thinspace{}
+B.
+ Isotope
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Weiteres zu chemischen Symbolen steht in
+\begin_inset LatexCommand ref
+reference "sub:Chemische-Symbole-und"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ darstellen, tritt folgendes Problem auf:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+durch Hoch- und Tiefstellen erzeugte Indizes:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+korrekte Indizes:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur
+\end_layout
+
+\begin_layout Standard
+als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der kürzere Index wird standardmäßig unter oder über das erste Zeichen des
+ längeren Index gesetzt.
+ Um das zu verhindern gibt es den Befehl
+\series bold
+
+\backslash
+phantom
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! P ! \\textbackslash phantom"
+
+\end_inset
+
+ oder den Mathe-Werkzeugleistenknopf \InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/phantom.png
+ scale 85
+
+\end_inset
+
+, der ein oder mehrere Phantomzeichen erstellt.
+ Wenn
+\series bold
+
+\backslash
+phantom
+\series default
+ eingegeben wird, erscheint ein kleines blaues Kästchen, dass von zwei roten
+ Pfeilen überlagert wird.
+ Die Pfeile geben an, dass die komplette Breite und Höhe des Kästcheninhalts
+ als Leerraum erstellt wird.
+ Phantomzeichen sind dementsprechend Platzhalter mit der Größe der angegebenen
+ Zeichen.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^19
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+1
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^235
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+_
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+23
+\begin_inset Formula $\to$
+\end_inset
+
+9
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+F
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Lambda^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+phantom
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+ii
+\begin_inset Formula $\to$
+\end_inset
+
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+_MMt
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Des Weiteren gibt es noch die Befehle
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! V ! \\textbackslash vphantom"
+
+\end_inset
+
+ (Werkzeugleistenknopf \InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/vphantom.png
+ scale 85
+
+\end_inset
+
+) und
+\series bold
+
+\backslash
+hphantom
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash hphantom"
+
+\end_inset
+
+ (Werkzeugleistenknopf \InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/math/hphantom.png
+ scale 85
+
+\end_inset
+
+).
+
+\series bold
+
+\backslash
+hphantom
+\series default
+ erzeugt nur Platz für die maximale Höhe der im Kästchen angegebenen Zeichen,
+ nicht jedoch für deren Breite.
+ Bei
+\series bold
+
+\backslash
+vphantom
+\series default
+ wird nur Platz mit der Breite des Kästchens erstellt.
+ Daher haben die Kästchen der beiden Befehle nur einen roten Pfeil.
+\end_layout
+
+\begin_layout Standard
+Zum Beispiel erzeugt
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series bold
+a
+\backslash
+int
+\series default
+ Platz der Höhe des Integralzeichens,
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+int
+\series default
+ erzeugt ein Integralzeichen, siehe
+\begin_inset LatexCommand ref
+reference "sub:Große-Operatoren"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ da dieses das größere Zeichen ist.
+ Eine Beispielanwendung ist in
+\begin_inset LatexCommand ref
+reference "sub:Mehrzeilige-Klammern"
+
+\end_inset
+
+ zu finden.
+\end_layout
+
+\begin_layout Subsection
+Linien
+\begin_inset LatexCommand index
+name "Linien"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! unterstrichene"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset LatexCommand index
+name "Befehle ! O ! \\textbackslash overline"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset LatexCommand index
+name "Befehle ! U ! \\textbackslash underline"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+underline
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Beim letzten Beispiel spielt es keine Rolle, ob man zuerst
+\series bold
+
+\backslash
+overline
+\series default
+ oder
+\series bold
+
+\backslash
+underline
+\series default
+ eingibt.
+\end_layout
+
+\begin_layout Standard
+Will man Ergebnisse doppelt unterstreichen, verwendet man zweimal hintereinander
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+underline
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Man kann bis zu 6 Striche über oder unter Zeichen setzen.
+\end_layout
+
+\begin_layout Subsection
+Fortsetzungspunkte
+\begin_inset LatexCommand index
+name "Fortsetzungspunkte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Es gibt unterschiedliche Arten von Fortsetzungspunkten.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+In der Mathe-Werkzeugleiste zu finden im Untermenü des Knopfs
+\begin_inset Graphics
+ filename ../../images/math/ldots.png
+ scale 85
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ Für Aufzählungen verwendet man unten sitzende Punkte (
+\series bold
+
+\backslash
+ldots
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash ldots"
+
+\end_inset
+
+), während man für Operationen Punkte braucht, die auf der selben Höhe wie
+ die Operatoren sind (
+\series bold
+
+\backslash
+cdots
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! C ! \\textbackslash cdots"
+
+\end_inset
+
+).
+ Verwendet man den Befehl
+\series bold
+
+\backslash
+dots
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash dots"
+
+\end_inset
+
+, entscheidet LaTeX anhand des nachfolgenden Zeichens, welche Punktart verwendet
+ wird.
+\newpage
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+,
+\backslash
+dots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1},\dots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
++
+\backslash
+dots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1}+\dots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+,
+\backslash
+ldots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+,A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1},\ldots,A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A_1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
++
+\backslash
+cdots
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
++A_n
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A_{1}+\cdots+A_{n}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vdots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vdots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddots
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddots$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\series bold
+×
+\series default
+3\InsetSpace \thinspace{}
+Matrix mit obigen Befehlen
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\begin{array}{ccc}
+A_{11} & \cdots & A_{1m}\\
+\vdots & \ddots & \vdots\\
+A_{n1} & \cdots & A_{nm}\end{array}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die im Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Sonderzeichen
+\family default
+ verfügbaren Fortsetzungspunkte sind
+\series bold
+
+\backslash
+ldots
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Speziell für Matrizen gibt es Fortsetzungspunkte, die sich über mehrere
+ Spalten erstrecken.
+ Man erhält sie mit dem Befehl
+\series bold
+
+\backslash
+hdotsfor
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash hdotsfor"
+
+\end_inset
+
+, der folgendes Schema besitzt:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hdotsfor[Abstand]{Anzahl der Spalten}
+\end_layout
+
+\begin_layout Standard
+Anzahl der Spalten gibt an, über wie viele Spalten sich die Punkte erstrecken
+ sollen.
+ Abstand ist ein Faktor, der den Punktabstand festlegt.
+\end_layout
+
+\begin_layout Standard
+In folgender Matrix wurde in das erste Kästchen der zweiten Zeile der Befehl
+
+\series bold
+
+\backslash
+hdotsfor[2]{4}
+\series default
+ eingegeben, um Fortsetzungspunkte mit doppelt so großem Punktabstand wie
+ beim Befehl
+\series bold
+
+\backslash
+dots
+\series default
+ zu erhalten:
+\begin_inset Formula \[
+\left(\begin{array}{cccc}
+A & B & C & D\\
+\hdotsfor[2]{4}\\
+q & w & e & r\end{array}\right)\]
+
+\end_inset
+
+Es ist zu beachten, dass die Matrixfelder über die sich die Punkte erstrecken
+ sollen leer sein müssen, ansonsten kommt es zu LaTeX-Fehlern.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Des Weiteren kann man mit dem Befehl
+\series bold
+
+\backslash
+dotfill
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash dotfill"
+
+\end_inset
+
+ den Rest einer Zeile mit Punkten füllen.
+ Die Wirkungsweise des Befehls entspricht der von
+\series bold
+
+\backslash
+hfill
+\series default
+, siehe
+\begin_inset LatexCommand ref
+reference "sub:Variabler-Leerraum"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Z.\InsetSpace \thinspace{}
+B.
+ ergibt der Befehl
+\series bold
+A
+\backslash
+dotfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\dotfill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Analog dazu gibt es für eine Linie den Befehl
+\series bold
+
+\backslash
+hrulefill
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash hrulefill"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $A\hrulefill B$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um die Befehle für Text zu verwenden, müssen sie im TeX-Modus eingegeben
+ werden.
+\end_layout
+
+\begin_layout Section
+Matrizen
+\begin_inset LatexCommand label
+name "sec:Matrizen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Matrizen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Matrizen können über den Mathe-Werkzeugleistenknopf
+\family sans
+
+\family default
+
+\begin_inset Graphics
+ filename ../../images/dialog-show_mathmatrix.png
+ scale 85
+
+\end_inset
+
+ oder das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Matrix
+\family default
+ eingefügt werden.
+ Sie werden nach der Spalten- und Zeilenanzahl und der Ausrichtung gefragt.
+ Die vertikale Ausrichtung ist dabei nur bei Matrizen in eingebetteten Formeln
+ von Bedeutung:
+\end_layout
+
+\begin_layout Standard
+Die erste Matrix ist oben
+\begin_inset Formula $\begin{array}[t]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+, die zweite mittig
+\begin_inset Formula $\begin{array}{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+ und die dritte unten
+\begin_inset Formula $\begin{array}[b]{cccc}
+A & D & G & J\\
+B & E & H & K\\
+C & F & I & L\end{array}$
+\end_inset
+
+ ausgerichtet.
+\end_layout
+
+\begin_layout Standard
+Die horizontale Ausrichtung gibt an, wie die Spalteneinträge ausgerichtet
+ werden sollen.
+ Dazu wird für jede Spalte ein Buchstabe eingegeben.
+
+\emph on
+l
+\emph default
+ steht für linksbündig,
+\emph on
+c
+\emph default
+ für mittig und
+\emph on
+r
+\emph default
+ für rechtsbündig.
+ Möchte man z.\InsetSpace \thinspace{}
+B.
+ eine 4
+\series bold
+×
+\series default
+4\InsetSpace ~
+Matrix erstellen, bei der der Inhalt der ersten Spalte linksbündig, der
+ Inhalt der zweiten und dritten mittig und der Inhalt der letzten rechtsbündig
+ ausgerichtet ist, gibt man für die horizontale Ausrichtung
+\series bold
+lccr
+\series default
+ an.
+ Normalerweise sind in einer Matrix alle Spalteninhalte zentriert, weswegen
+ die Voreinstellung für jede Spalte ein
+\series bold
+c
+\series default
+ ist.
+\end_layout
+
+\begin_layout Standard
+Horizontale Ausrichtung:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+lll
+\series default
+ :
+\begin_inset Formula $\begin{array}{lll}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+ ,
+\series bold
+ccc
+\series default
+ :
+\begin_inset Formula $\begin{array}{ccc}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+ ,
+\series bold
+rrr
+\series default
+ :
+\begin_inset Formula $\begin{array}{rrr}
+10000 & D & G\\
+B & 10000 & H\\
+C & F & 10000\end{array}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um nachträglich Zeilen und Spalten hinzuzufügen oder zu entfernen, kann
+ man die Mathe-Werkzeugleistenknöpfe
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+,
+\begin_inset Graphics
+ filename ../../images/tabular-feature_delete-row.png
+ scale 85
+
+\end_inset
+
+, usw.\InsetSpace ~
+oder das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Zeilen & Spalten
+\family default
+ verwenden.
+ Neue Zeilen können auch mit
+\family sans
+Strg-Enter
+\family default
+ erstellt werden.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Klammern um eine Matrix können entweder mit den Befehlen
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash left"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash right"
+
+\end_inset
+
+ erstellt werden (Tastenkürzel
+\family sans
+Alt-m\InsetSpace ~
+Klammer
+\family default
+), siehe
+\begin_inset LatexCommand ref
+reference "sub:Automatische-Klammergrößen"
+
+\end_inset
+
+, oder man verwendet folgende Befehle:
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+Matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+Matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+Matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+Matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Vmatrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+Matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+matrix
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+2
+\series bold
+×
+\series default
+2\InsetSpace \thinspace{}
+Matrix
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc}
+0 & \textrm{-}\mathrm{i}\\
+\mathrm{i} & 0\end{array}\end{matrix}\raisebox{-5.3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Wurde z.\InsetSpace \thinspace{}
+B.
+
+\series bold
+
+\backslash
+vmatrix
+\series default
+ eingegeben, erscheint ein blaues Kästchen zwischen zwei senkrechten Strichen,
+ in das die Matrix eingefügt wird.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Da alle mehrzeiligen Formeln Matrizen sind, kann man die in
+\begin_inset LatexCommand ref
+reference "sub:Spaltenabstand"
+
+\end_inset
+
+ beschriebene Länge
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash arraycolsep"
+
+\end_inset
+
+ auch zur Änderung des Spaltenabstands von Matrizen verwenden.
+\end_layout
+
+\begin_layout Standard
+Möchte man den Zeilenabstand ändern, verwendet man den Befehl
+\series bold
+
+\backslash
+arraystretch
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash arraystretch"
+
+\end_inset
+
+.
+ Dieser wird folgendermaßen benutzt:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+arraystretch}{Dehnungsfaktor}
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash renewcommand"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+renewcommand
+\series default
+ weist dabei dem vordefinierten Befehl
+\series bold
+
+\backslash
+arraystretch
+\series default
+ den Dehnungsfaktor zu.
+ Möchte man z.\InsetSpace \thinspace{}
+B.
+ den Zeilenabstand verdoppeln, gibt man für den Faktor eine 2 an.
+ Dieser wird dann für alle folgenden Matrizen verwendet.
+ Um wieder zum ursprünglichen Abstand zurückzukehren, weist man
+\series bold
+
+\backslash
+arraystretch
+\series default
+ den Faktor 1 zu.
+\end_layout
+
+\begin_layout Standard
+Um Matrizen in eine Textzeile zu setzen, benutzt man den Befehl
+\series bold
+
+\backslash
+smallmatrix
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash smallmatrix"
+
+\end_inset
+
+.
+ Gibt man ihn in eine Formel ein, erscheint ein blaues Kästchen mit zwei
+ gestrichelten Linien.
+ In dieses Kästchen wird die Matrix eingegeben.
+ Man verwendet stattdessen das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Zeilen\InsetSpace ~
+&\InsetSpace ~
+Spalten
+\family default
+ oder die Mathe-Werkzeugleiste um neue Spalten zu erstellen.
+ Neue Zeilen können auch mit
+\family sans
+Strg-Enter
+\family default
+ erstellt werden.
+\end_layout
+
+\begin_layout Standard
+Dies ist eine Matrix
+\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
+C & D\end{smallmatrix}\right)$
+\end_inset
+
+ in einer Textzeile.
+\end_layout
+
+\begin_layout Section
+Klammern und Begrenzungszeichen
+\begin_inset LatexCommand index
+name "Klammern"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Begrenzungszeichen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertikale Klammern und Begrenzungszeichen
+\begin_inset LatexCommand index
+name "Klammern ! vertikale"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $($
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+{
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\{$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+[
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $[$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+langle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\langle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+/
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $/$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $)$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+}
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+]
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rceil
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rceil$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rfloor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rfloor$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\backslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+|
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\|$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\series medium
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Achtung:
+\series default
+ Im TeX-Modus muss für den Backslash der Befehl
+\series bold
+
+\backslash
+textbackslash
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash textbackslash"
+
+\end_inset
+
+ verwendet werden, denn der Befehl
+\series bold
+
+\backslash
+
+\backslash
+
+\series default
+ steht dort für einen Zeilenumbruch.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Für alle oben aufgelisteten Zeichen kann die Größe mit den in den folgenden
+ zwei Unterkapiteln beschriebenen Befehlen eingestellt werden.
+ Dabei können dann statt den Befehlen
+\series bold
+
+\backslash
+langle
+\series default
+ und
+\series bold
+
+\backslash
+rangle
+\series default
+ direkt die Zeichen < und > verwendet werden.
+\end_layout
+
+\begin_layout Subsubsection
+Manuelle Klammergrößen
+\begin_inset LatexCommand label
+name "sub:Manuelle-Klammergrößen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Klammergrößen ! manuelle"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man die Klammergröße manuell festlegen, kann man dies mittels der
+ LaTeX-Befehle
+\series bold
+
+\backslash
+big
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash big"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+Big
+\series default
+,
+\series bold
+
+\backslash
+bigg
+\series default
+ und
+\series bold
+
+\backslash
+Bigg
+\series default
+ tun.
+
+\series bold
+
+\backslash
+big
+\series default
+ steht hierbei für die kleinste und
+\series bold
+
+\backslash
+Bigg
+\series default
+ für die größte Klammergröße.
+\end_layout
+
+\begin_layout Standard
+Diese Befehle werden benutzt um Klammerebenen optisch hervorzuheben:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+einheitliche Klammergröße:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+besser sieht das so aus:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur
+\end_layout
+
+\begin_layout Standard
+als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Für die zweite Formel wurde der Befehl
+\series bold
+
+\backslash
+Big((A+B)(A-B)
+\backslash
+Big)^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+C
+\series default
+ verwendet.
+\end_layout
+
+\begin_layout Standard
+Hier alle Klammergrößen in der Übersicht:
+\end_layout
+
+\begin_layout Standard
+\align center
+
+\backslash
+Bigg(
+\backslash
+exp
+\backslash
+bigg<
+\backslash
+Big[
+\backslash
+big{
+\backslash
+ln(3x)
+\backslash
+big}^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+sin(x)
+\backslash
+Big]^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+bigg>
+\backslash
+Bigg)^0,5
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Es gibt außer den
+\series bold
+
+\backslash
+big
+\series default
+-Befehlen noch die Variante
+\series bold
+
+\backslash
+bigm
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash bigm"
+
+\end_inset
+
+, die etwas mehr Leerraum zwischen Klammer und Klammerinhalt erzeugt und
+ die Variante
+\series bold
+
+\backslash
+bigl
+\series default
+-
+\series bold
+
+\backslash
+bigr
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash bigl - \\textbackslash bigr"
+
+\end_inset
+
+, die keinen zusätzlichen Leerraum erzeugt.
+ Das
+\emph on
+l
+\emph default
+ am Ende des Befehls
+\series bold
+
+\backslash
+bigl
+\series default
+ steht für eine linke Klammer; für eine rechte Klammer wird dieses durch
+ ein
+\emph on
+r
+\emph default
+ ersetzt.
+ Eine linke oder rechte Klammer kann je eine öffnende oder schließende Klammer
+ sein.
+\end_layout
+
+\begin_layout Standard
+In der folgenden Tabelle sind die Varianten miteinander verglichen:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="0">
+<column alignment="center" valignment="middle" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bigm(
+\backslash
+bigm(
+\backslash
+ln(3x)
+\backslash
+bigm)^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+Bigm)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Big(
+\backslash
+big(
+\backslash
+ln(3x)
+\backslash
+big)^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+Big)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bigl(
+\backslash
+bigl(
+\backslash
+ln(3x)
+\backslash
+bigr)^2
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+Bigr)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigl)
+\backslash
+ln(3x)
+\backslash
+bigr(
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Automatische Klammergrößen
+\begin_inset LatexCommand label
+name "sub:Automatische-Klammergrößen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Klammergrößen ! automatische"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Klammern variabler Größe können mit den Befehlen
+\series bold
+
+\backslash
+left
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash left"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+right
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash right"
+
+\end_inset
+
+ oder über den Mathe-Werkzeugleistenknopf
+\family sans
+
+\family default
+
+\begin_inset Graphics
+ filename ../../images/dialog-show_mathdelimiter.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+ Auf
+\series bold
+
+\backslash
+left
+\series default
+ und
+\series bold
+
+\backslash
+right
+\series default
+ muss unmittelbar die gewünschte Klammer folgen.
+ Die Klammergröße wird dann bei der Ausgabe automatisch berechnet.
+\end_layout
+
+\begin_layout Standard
+\align center
+normale Klammer: Der Befehl
+\series bold
+
+\backslash
+ln(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+)
+\series default
+ ergibt
+\begin_inset Formula \[
+\ln(\frac{A}{C})\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+mehrzeilige Klammer: Der Befehl
+\series bold
+
+\backslash
+ln
+\backslash
+left(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+right)
+\series default
+ ergibt
+\begin_inset Formula \[
+\ln\left(\frac{A}{C}\right)\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+An Stelle von
+\series bold
+
+\backslash
+left
+\series default
+ und
+\series bold
+
+\backslash
+right
+\series default
+ kann man die Tastenkürzel
+\family sans
+Alt-m\InsetSpace ~
+Klammer
+\family default
+ verwenden.
+ Das hat den Vorteil, dass man in LyX sofort die wahre Klammergröße sieht
+ und dass die rechte Klammer gleich mit erstellt wird.
+\newline
+Der Befehl für das
+ letzte Beispiel würde dann lauten:
+\series bold
+
+\backslash
+ln Alt-m
+\series default
+
+\series bold
+(
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+C
+\end_layout
+
+\begin_layout Standard
+Will man nur eine Klammerhälfte erstellen, schreibt man für die weggelassene
+ Klammer einen Punkt.
+ So ergibt z.\InsetSpace \thinspace{}
+B.
+ der Befehl
+\series bold
+
+\backslash
+left.
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+right}
+\series default
+\InsetSpace \thinspace{}
+:
+\series bold
+
+\begin_inset Formula \[
+\left.\frac{A}{B}\right\} \]
+
+\end_inset
+
+
+\series default
+Die Befehle
+\series bold
+
+\backslash
+left
+\series default
+ und
+\series bold
+
+\backslash
+right
+\series default
+ werden beim Neu laden des Dokuments von LyX in Klammern der richtigen Größe
+ umgewandelt.
+ Für eine weggelassene Klammer erscheint in LyX eine gestrichelte Linie.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Da alle gängigen LaTeX-Distributionen eTeX, eine Erweiterung von LaTeX,
+ verwenden, steht für alle Klammern und Begrenzungszeichen zusätzlich der
+ Befehl
+\series bold
+
+\backslash
+middle
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash middle"
+
+\end_inset
+
+ zur Verfügung.
+ Durch diesen wird das folgende Zeichen an die Höhe der umgebenden Klammern
+ angepasst, was z.\InsetSpace \thinspace{}
+B.
+ für physikalische Vektoren von Nutzen ist:
+\begin_inset Formula \[
+\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
+
+\end_inset
+
+Für physikalische Vektoren gibt es ein spezielles LaTeX-Paket, das in
+\begin_inset LatexCommand ref
+reference "sub:Physikalische-Vektoren"
+
+\end_inset
+
+ beschrieben ist.
+\end_layout
+
+\begin_layout Subsection
+Horizontale Klammern
+\begin_inset LatexCommand index
+name "Klammern ! horizontale"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{2.3mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+overbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+3
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Befehle ! O ! \\textbackslash overbrace"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\overbrace{A+B}^{3}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-2.2mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+underbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A+B
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+_5
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Befehle ! U ! \\textbackslash underbrace"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\underbrace{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overbrace
+\backslash
+underbrace
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A+B_w
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+_7
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Beim letzten Beispiel spielt es keine Rolle, ob man zuerst
+\series bold
+
+\backslash
+overbrace
+\series default
+ oder
+\series bold
+
+\backslash
+underbrace
+\series default
+ eingibt.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Benötigt man Klammern, die sich überschneiden, muss man die in
+\begin_inset LatexCommand ref
+reference "sec:Mehrzeilige-Formeln"
+
+\end_inset
+
+ beschriebenen mehrzeiligen Formeln verwenden:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
+ & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}
+
+\end_inset
+
+In die erste Zeile wird die Formel zusammen mit der ersten Klammer eingegeben.
+ Dabei ist es wichtig, dass vor dem ersten
+\begin_inset Formula $d$
+\end_inset
+
+ der Abstandsbefehl
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Abstandsbefehle sind in
+\begin_inset LatexCommand ref
+reference "sub:Vordefinierter-Leerraum"
+
+\end_inset
+
+ erklärt.
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+:
+\series default
+ eingegeben wird, denn die nach dem
+\begin_inset Formula $q$
+\end_inset
+
+ endende Klammer verhindert, dass das nachfolgende
+\begin_inset Quotes gld
+\end_inset
+
++
+\begin_inset Quotes grd
+\end_inset
+
+ von Leerraum umgeben ist.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+weil eine Klammer nicht als Zeichen gilt, siehe
+\begin_inset LatexCommand ref
+reference "sub:Binäre-Operatoren"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ In die zweite Zeile wird die zweite Klammer eingegeben.
+ Da sie vor dem
+\begin_inset Formula $b$
+\end_inset
+
+ beginnen soll, gibt man zuerst
+\series bold
+
+\backslash
+hphantom{gggg+
+\backslash
+:}
+\series default
+ ein.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+mehr zu
+\series bold
+
+\backslash
+hphantom
+\series default
+ siehe
+\begin_inset LatexCommand ref
+reference "sub:Platzhalter"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ Dieser Leerraum wird benötigt, weil das
+\begin_inset Quotes gld
+\end_inset
+
++
+\begin_inset Quotes grd
+\end_inset
+
+ in der Formel auch von Leerraum umgeben ist.
+ Die Klammer wird unter den Befehl
+\series bold
+
+\backslash
+hphantom{bbqq+dddd}
+\series default
+ gesetzt.
+\end_layout
+
+\begin_layout Standard
+Komplizierter wird es, wenn sich Klammern über und unter der Formel überschneide
+n, wie in folgendem Beispiel:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+ & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
+A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+Die erste Formelzeile ist gleich der zweiten Zeile des vorigen Beispiels,
+ mit dem Unterschied, dass sich die Klammer oben befindet.
+ Die zweite Zeile enthält die Formel zusammen mit der zweiten Klammer.
+ Damit sich zwischen oberer Klammer in der ersten Zeile und der Formel in
+ der zweiten Zeile kein Leerraum befindet, muss der Zeilenabstand verändert
+ werden.
+ Aufgrund eines Fehlers in LyX ist dies nicht ohne Weiteres möglich
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1505
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+ Es muss als Lösung des Problems der globale Formelzeilenabstand
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! J ! \\textbackslash jot"
+
+\end_inset
+
+ vor der Formel mit dem Befehl
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{-6pt}
+\series default
+ im TeX-Modus auf den Wert -6\InsetSpace \thinspace{}
+pt geändert.
+ Nach der Formel wird
+\series bold
+
+\backslash
+jot
+\series default
+ mit demselben Befehl wieder auf den Standardwert 3\InsetSpace \thinspace{}
+pt zurückgesetzt.
+ Genaueres zum Zeilenabstand in Formeln ist in
+\begin_inset LatexCommand ref
+reference "sub:Zeilenabstand"
+
+\end_inset
+
+ erklärt.
+\end_layout
+
+\begin_layout Section
+Pfeile
+\begin_inset LatexCommand index
+name "Pfeile"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Pfeile können über den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/leftarrow.png
+ scale 85
+
+\end_inset
+
+ oder mit den Befehlen eingefügt werden die in den folgenden Unterkapiteln
+ aufgelistet sind.
+\end_layout
+
+\begin_layout Subsection
+Horizontale Pfeile
+\begin_inset LatexCommand index
+name "Pfeile ! horizontale"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gets$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Leftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hookleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hookleftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\to$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Rightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightharpoonup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightharpoondown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightharpoondown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hookrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hookrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Leftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Leftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Longleftrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightleftharpoons
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rightleftharpoons$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{25pt}
+\end_layout
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+longmapsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\longmapsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leadsto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\leadsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dasharrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Als Akzent verwendete Pfeile, wie z.\InsetSpace \thinspace{}
+B.
+ Vektorpfeile, sind in
+\begin_inset LatexCommand ref
+reference "sec:Akzente"
+
+\end_inset
+
+ aufgelistet.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Des Weiteren gibt es die beschriftbaren Pfeile
+\begin_inset LatexCommand index
+name "Pfeile ! beschriftbare"
+
+\end_inset
+
+
+\series bold
+
+\backslash
+xleftarrow
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! X ! \\textbackslash xleftarrow"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+xrightarrow
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! X ! \\textbackslash xrightarrow\\vspace{4mm}"
+
+\end_inset
+
+.
+ Gibt man einen dieser Befehle in eine Formel ein, erscheint ein Pfeil mit
+ zwei blauen Kästchen, in die man die Beschriftung eingeben kann.
+ Die Pfeillänge passt sich der Breite der Beschriftung an.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+F(a)
+\backslash
+xleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+F(x)
+\backslash
+xrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(a)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertikale und diagonale Pfeile
+\begin_inset LatexCommand index
+name "Pfeile ! diagonale"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pfeile ! vertikale"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Uparrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Uparrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Updownarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Updownarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+downarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nearrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nearrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+searrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\searrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+swarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\swarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nwarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nwarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Vertikale Pfeile können auch als Begrenzungszeichen zusammen mit den in
+
+\begin_inset LatexCommand ref
+reference "sub:Manuelle-Klammergrößen"
+
+\end_inset
+
+ und
+\begin_inset LatexCommand ref
+reference "sub:Automatische-Klammergrößen"
+
+\end_inset
+
+ beschriebenen Befehlen verwendet werden.
+\end_layout
+
+\begin_layout Section
+Akzente
+\begin_inset LatexCommand label
+name "sec:Akzente"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Akzente"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Akzente können über den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/hat.png
+ scale 85
+
+\end_inset
+
+ oder mit den Befehlen eingefügt werden die in den folgenden Unterkapiteln
+ aufgelistet sind.
+\end_layout
+
+\begin_layout Subsection
+Akzente für ein Zeichen
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Akzente im Text siehe
+\begin_inset LatexCommand ref
+reference "sub:Sonderzeichen-Akzente"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ dient dazu, dass die Fußnote nicht im PDF-Lesezeichen erscheint.
+\end_layout
+
+\begin_layout Standard
+Näheres zu
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ steht in Kapitel
+\begin_inset LatexCommand ref
+reference "sub:Formeln-in-Überschriften"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand label
+name "sub:Akzente-für-ein"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Akzente ! für ein Zeichen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddddot{A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vec
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset LatexCommand index
+name "Vektoren"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\vec{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bar
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\bar{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathring
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tilde
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hat
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\hat{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+check
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\check{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+acute
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\acute{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+grave
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\grave{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+breve
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\breve{A}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Wenn man in einer Formel Umlaute
+\begin_inset LatexCommand index
+name "Umlaute"
+
+\end_inset
+
+ erstellen will, schreibt man ein Anführungszeichen vor den Selbstlaut.
+ Diese beiden Zeichen bilden dann für LaTeX
+\emph on
+ein
+\emph default
+ Zeichen.
+ Im Gegensatz zu
+\series bold
+
+\backslash
+ddot
+\series default
+ entstehen damit
+\begin_inset Quotes gld
+\end_inset
+
+echte
+\begin_inset Quotes grd
+\end_inset
+
+ Umlaute, was folgendes Beispiel zeigt:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Quotes grd
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $"i$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddot
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ein weiterer Vorteil gegenüber
+\series bold
+
+\backslash
+ddot
+\series default
+ ist, dass man Umlaute direkt in mathematischen Text konvertieren kann,
+ denn die obigen Akzentbefehle sind
+\emph on
+im mathematischen Text\SpecialChar \-
+modus nicht erlaubt
+\emph default
+.
+ Um ein akzentuiertes Zeichen in mathematischen Text zu überführen, darf
+ nur das Zeichen unter dem Akzent umgewandelt werden.
+ Das gilt auch für alle anderen Umwandlungen wie z.\InsetSpace \thinspace{}
+B.
+ in kursiv oder fett.
+\end_layout
+
+\begin_layout Standard
+Im mathematischen Textmodus können Umlaute und andere akzentuierten Zeichen
+ direkt eingegeben werden.
+\end_layout
+
+\begin_layout Subsection
+Akzente für Operatoren
+\begin_inset LatexCommand index
+name "Akzente ! für Operatoren"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Zum Akzentuieren von Operatoren gibt es die Befehle
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! O ! \\textbackslash overset"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! U ! \\textbackslash underset"
+
+\end_inset
+
+, mit denen man Zeichen über bzw.
+ unter einen Operator setzen kann.
+ Mit dem Befehl
+\series bold
+
+\backslash
+sideset
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash sideset"
+
+\end_inset
+
+ können Zeichen vor und nach einen Operator gesetzt werden.
+ Das Befehlsschema lautet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset{Zeichen
+\series default
+
+\series bold
+davor}{Zeichen
+\series default
+
+\series bold
+dahinter}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sideset
+\series default
+ mussen immer vor dem zu akzentuierenden Operator stehen.
+ Es kann auch mit mehreren Zeichen und sogar mit anderen Operatoren und
+ Symbolen akzentuiert werden.
+ Will man mit
+\series bold
+
+\backslash
+sideset
+\series default
+ z.\InsetSpace \thinspace{}
+B.
+ nur Zeichen hinter einen Operator setzen, schreibt man nichts zwischen
+ die ersten geschweiften Klammern, lässt die Klammern aber nicht weg.
+\end_layout
+
+\begin_layout Standard
+Z.\InsetSpace \thinspace{}
+B.
+ ergibt der Befehl
+\series bold
+
+\backslash
+sideset{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\series default
+'
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+sum_k=1
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+^
+\series bold
+n
+\series default
+ :
+\begin_inset Formula \[
+\sideset{}{'}\sum_{k=1}^{n}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+overset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset Formula $\uparrow$
+\end_inset
+
+
+\series bold
+a
+\series default
+ ergibt:
+\begin_inset Formula \[
+\overset{a}{\maltese}\]
+
+\end_inset
+
+Wie man am letzten Beispiel sieht, kann man mit
+\series bold
+
+\backslash
+overset
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+underset
+\series default
+ außer Operatoren auch Symbole und Zeichen akzentuieren; mit
+\series bold
+
+\backslash
+sideset
+\series default
+ ist dies nicht möglich.
+\end_layout
+
+\begin_layout Subsection
+Akzente für mehrere Zeichen
+\begin_inset LatexCommand label
+name "sub:Akzente-für-mehrere"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Akzente ! für mehrere Zeichen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underleftarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overleftrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underleftrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+overrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+underrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widetilde
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widehat
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Mit diesen Befehlen können beliebig viele Zeichen akzentuiert werden.
+ Die Akzente
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+widetilde
+\series default
+ und
+\series bold
+
+\backslash
+widehat
+\series default
+ werden aber im Ausdruck nur mit einer Länge von etwa drei Zeichen gesetzt,
+ was folgendes Beispiel verdeutlicht:
+\begin_inset Formula \[
+\widetilde{A+B=C-D}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Mit den im vorigen Kapitel beschriebenen Befehlen
+\series bold
+
+\backslash
+overset
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! O ! \\textbackslash overset"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+underset
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! U ! \\textbackslash underset"
+
+\end_inset
+
+ ist es auch möglich mehrere Zeichen zu akzentuieren.
+ Der Befehl
+\series bold
+
+\backslash
+underset
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\begin_inset Formula $\downarrow$
+\end_inset
+
+***
+\series default
+ ergibt:
+\begin_inset Formula \[
+\underset{***}{A=B}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Leerraum
+\begin_inset LatexCommand label
+name "sub:Leerraum"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Leerraum ! horizontaler"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vordefinierter Leerraum
+\begin_inset LatexCommand label
+name "sub:Vordefinierter-Leerraum"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Leerraum ! horizontaler ! vordefiniert"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ab und an ist es notwendig in einer Formel horizontalen Leerraum einzufügen.
+ Dazu gibt man ein geschütztes Leerzeichen ein.
+ Es erscheint ein blaues
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+\color blue
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+\color inherit
+
+\begin_inset Quotes grd
+\end_inset
+
+ und man kann durch mehrfaches Drücken der Leertaste aus acht verschiedenen
+ Leerraum-Größen wählen.
+ Man kann die Leerräume auch über den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/space.png
+ scale 85
+
+\end_inset
+
+ oder mit einzelnen Befehlen aufrufen.
+ Unabhängig vom eingegebenen Befehl kann man durch Drücken der Leertaste
+ danach wieder aus allen Größen wählen.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="7">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="6.8cm">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+,
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+;
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+quad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+qquad
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+!
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" leftline="true" usebox="none" width="7cm">
+\begin_inset Text
+
+\begin_layout Standard
+Anzahl der Leertastendrücke nach Eingabe des geschützten Leerzeichens
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+4
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+5
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\, B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\: B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\; B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\quad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\qquad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\! B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die letzte Größe scheint überhaupt keinen Leerraum zu produzieren.
+ In LyX ist diese allerdings auch im Gegensatz zu allen anderen rot eingefärbt,
+ denn sie erstellt negativen Leerraum.
+ Es gibt noch zwei weitere negative Leerräume:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="3">
+<features>
+<column alignment="center" valignment="middle" leftline="true" width="6.8cm">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+negmedspace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+negthickspace
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Anzahl der Leertastendrücke nach Eingabe des geschützten Leerzeichens
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+6
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+7
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\negmedspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\negthickspace B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative Leerräume bewirken, dass sich benachbarte Zeichen überschneiden.
+ Man kann auf diese Weise Ligaturen erzwingen, was z.\InsetSpace \thinspace{}
+B.
+ für Summenzeichen von Nutzen ist:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\backslash
+sum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+f_kl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Relationen, wie z.\InsetSpace \thinspace{}
+B.
+ Gleichheitszeichen, sind immer von Leerraum umgeben.
+ Will man dies unterdrücken, schreibt man das Gleichheitszeichen in eine
+ TeX-Klammer.
+ Die Wirkung kann man an folgendem Beispiel gut erkennen:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+normale Gleichung
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\raisebox{5mm}{}$
+\end_inset
+
+Gleichung ohne Leerraum
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A{=}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl für die letzte Formel lautet:
+\series bold
+A
+\backslash
+{=
+\begin_inset Formula $\to$
+\end_inset
+
+B
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Leerräumen werden für physikalische Einheiten benötigt, denn zwischen Wert
+ und Einheit ist der kleinste Leerraum und kein normales Leerzeichen.
+ Bei Einheiten im Text fügt man den kleinsten Leerraum über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Formatierung\SpecialChar \menuseparator
+Kleiner\InsetSpace ~
+Abstand
+\family default
+ (Tastenkürzel
+\family sans
+Strg-Shift-Leertaste
+\family default
+) ein.
+\end_layout
+
+\begin_layout Standard
+Ein Beispiel zur Veranschaulichung:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="left" valignment="top" width="0">
+<column alignment="left" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+24 kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Leerzeichen zwischen Wert und Einheit
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+24\InsetSpace \thinspace{}
+kW
+\begin_inset Formula $\cdot$
+\end_inset
+
+h
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+kleinster Leerraum zwischen Wert und Einheit
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Variabler Leerraum
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+für vertikalen Leerraum in Formeln siehe
+\begin_inset LatexCommand ref
+reference "sub:Zeilenabstand"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ dient dazu, dass die Fußnote nicht mit im PDF-Lesezeichen erscheint.
+\end_layout
+
+\begin_layout Standard
+Näheres zu
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ steht in Kapitel
+\begin_inset LatexCommand ref
+reference "sub:Formeln-in-Überschriften"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand label
+name "sub:Variabler-Leerraum"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Leerraum ! horizontaler ! variabel"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Leerraum mit vorgegebener Länge lässt sich in LyX mit dem Befehl
+\series bold
+
+\backslash
+hspace{Länge}
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash hspace"
+
+\end_inset
+
+ einfügen.
+ Dabei können alle Längeneinheiten verwendet werden, die in
+\begin_inset LatexCommand ref
+reference "tab:Verwendete-Einheiten"
+
+\end_inset
+
+ aufgelistet sind, mit Ausnahme der Einheit
+\begin_inset Quotes gld
+\end_inset
+
+mu
+\begin_inset Quotes grd
+\end_inset
+
+.
+ Die Länge darf auch negativ sein.
+ Um so viel Leerraum einzufügen, dass die Formel allen verfügbaren Platz
+ einnimmt, benutzt man den Befehl
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash hfill"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -1mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=B
+\backslash
+hspace{3cm
+\begin_inset Formula $\to$
+\end_inset
+
+A
+\backslash
+not=C
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=B\hspace{3cm}A\not=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+hspace{-1mm
+\begin_inset Formula $\to$
+\end_inset
+
+A
+\backslash
+not=A
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\hspace{-1mm}A\not=A$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=A
+\backslash
+hfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+B=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A=A\hfill B=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Im letzten Beispiel ist der verfügbare Platz durch die Länge des längsten
+ Spalteneintrags der Tabelle vorgegeben.
+ In einer eingebetteten Formel ist der Platz von der Länge der Zeile abhängig,
+ in die
+\series bold
+
+\backslash
+hfill
+\series default
+ eingegeben wird.
+ Füllt eine Zeile die Breite komplett aus, wird demnach kein Leerraum erstellt.
+
+\series bold
+
+\backslash
+hfill
+\series default
+ wirkt in abgesetzten Formeln nur, wenn der Formelstil
+\series bold
+Eingerückt
+\series default
+ eingestellt ist.
+ (Formelstile sind in
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+ erklärt.)
+\end_layout
+
+\begin_layout Standard
+Die Befehle
+\series bold
+
+\backslash
+hspace
+\series default
+ und
+\series bold
+
+\backslash
+hfill
+\series default
+ können auch im TeX-Modus eingegeben werden, um sie für Text zu verwenden:
+\end_layout
+
+\begin_layout Standard
+Dies ist eine Zeile mit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{2cm}
+\end_layout
+
+\end_inset
+
+2\InsetSpace \thinspace{}
+cm Leerraum.
+\end_layout
+
+\begin_layout Standard
+Dies ist eine Zeile mit
+\hfill
+maximalem Leerraum.
+\end_layout
+
+\begin_layout Standard
+Im letzten Beispiel wurde
+\series bold
+
+\backslash
+hfill
+\series default
+ über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Formatierung\SpecialChar \menuseparator
+Variabler horiz.
+ Abstand
+\family default
+ eingefügt, was in Formeln nicht möglich ist.
+ Das hat den Vorteil, dass man in LyX direkt sieht, dass es sich um einen
+ gedehnten Leerraum handelt.
+\end_layout
+
+\begin_layout Standard
+Befinden sich die Befehle am Anfang einer Zeile, jedoch nicht am Anfang
+ eines Absatzes, werden sie von LaTeX ignoriert.
+ Um das zu verhindern, verwendet man statt
+\series bold
+
+\backslash
+hspace
+\series default
+ den Befehl
+\series bold
+
+\backslash
+hspace*
+\series default
+.
+ Bei
+\series bold
+
+\backslash
+hfill
+\series default
+ fügt man vor dem Befehl einen Zeilenumbruch und im TeX-Modus mit dem Befehl
+
+\series bold
+
+\backslash
+vphantom{}
+\series default
+ einen leeren Platzhalter
+\series bold
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Platzhalter siehe
+\begin_inset LatexCommand ref
+reference "sub:Platzhalter"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ ein.
+\end_layout
+
+\begin_layout Subsection
+Leerraum neben eingebetteten Formeln
+\begin_inset LatexCommand index
+name "Leerraum ! neben eingebetteten Formeln"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Über die Länge
+\series bold
+
+\backslash
+mathsurround
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mathsurround"
+
+\end_inset
+
+
+\series default
+ lässt sich der Leerraum einstellen, der neben eingebettete Formeln gesetzt
+ wird.
+ Der Wert einer Länge wird mit dem Befehl
+\series bold
+
+\backslash
+setlength
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash setlength"
+
+\end_inset
+
+
+\series default
+ gesetzt.
+ Dieser besitzt folgendes Befehlsschema:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{Längenname}{Wert}
+\end_layout
+
+\begin_layout Standard
+Um
+\series bold
+
+\backslash
+mathsurround
+\series default
+ den Wert 5\InsetSpace \thinspace{}
+mm zuzuweisen, gibt man im TeX-Modus den Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\begin_layout Standard
+ein.
+ Neben alle eingebetteten Formeln, die auf den Befehl folgen, wird nun 5\InsetSpace \thinspace{}
+mm
+ Leerraum gesetzt:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{5mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dies ist eine Zeile in der sich
+\begin_inset Formula $A=B$
+\end_inset
+
+ eine Formel mit 5\InsetSpace \thinspace{}
+mm umgebendem Leerraum befindet.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+mathsurround}{0pt}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um wieder zum voreingestellten Wert zurückzukehren, setzt man
+\series bold
+
+\backslash
+mathsurround
+\series default
+ auf den Wert 0\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Section
+Boxen und Rahmen
+\begin_inset LatexCommand index
+name "Boxen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Rahmen | see {Boxen}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Boxen für Text sind im Kapitel
+\family typewriter
+Boxen
+\family default
+ im Handbuch
+\family typewriter
+Eingebettete\InsetSpace ~
+Objekte
+\family default
+ beschrieben.
+\end_layout
+
+\begin_layout Subsection
+Boxen mit Rahmen
+\begin_inset LatexCommand label
+name "sub:Boxen-mit-Rahmen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxen ! mit Rahmen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Es ist möglich Formeln oder Teile davon mit den Befehlen
+\series bold
+
+\backslash
+fbox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! F ! \\textbackslash fbox"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+boxed
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash boxed"
+
+\end_inset
+
+ zu umranden.
+\end_layout
+
+\begin_layout Standard
+Gibt man einen dieser Befehle in eine Formel ein, erscheint ein Eingabefeld
+ in einem Rahmen.
+ Bei
+\series bold
+
+\backslash
+fbox
+\series default
+ muss in diesem Eingabefeld mit
+\family sans
+Strg-m
+\family default
+ noch eine Formel erstellt werden
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Aufgrund eines Fehlers in LyX ist es nicht möglich mit
+\family sans
+Strg-m
+\family default
+ eine neue Formel zu erzeugen, siehe
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+, denn der Inhalt dieser Box wird sonst als mathematischer Text behandelt.
+ Verwendet man
+\series bold
+
+\backslash
+boxed
+\series default
+, wird automatisch im Rahmen eine neue Formel erzeugt.
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+fbox
+\series default
+ ist nicht zur Umrandung von abgesetzten Formeln geeignet, denn die Formel
+ wird dann immer in Textzeilengröße gesetzt.
+ Im Gegensatz dazu ist
+\series bold
+
+\backslash
+boxed
+\series default
+ nicht zur Umrandung von Formeln in einer Textzeile geeignet, denn die Formel
+ wird dann immer in der Größe einer abgesetzten Formel gesetzt.
+\end_layout
+
+\begin_layout Standard
+Als Erweiterung zu
+\series bold
+
+\backslash
+fbox
+\series default
+ gibt es den Befehl
+\series bold
+
+\backslash
+framebox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! F ! \\textbackslash framebox"
+
+\end_inset
+
+, bei dem man zusätzlich die Rahmenbreite und die Ausrichtung einstellen
+ kann.
+
+\series bold
+
+\backslash
+framebox
+\series default
+ wird nach folgendem Schema verwendet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+framebox[Rahmenbreite][Position]{Boxinhalt}
+\end_layout
+
+\begin_layout Standard
+Die Position kann entweder
+\emph on
+l
+\emph default
+ oder
+\emph on
+r
+\emph default
+ sein.
+
+\emph on
+l
+\emph default
+ bewirkt linksbündige,
+\emph on
+r
+\emph default
+ rechtsbündige Ausrichtung der Formel in der Box.
+ Gibt man keine Position an, wird die Formel zentriert.
+\newline
+Gibt man keine Breite
+ an, darf auch keine Position angegeben werden.
+ In diesem Falle wird die Rahmenbreite wie bei
+\series bold
+
+\backslash
+fbox
+\series default
+ an den Boxinhalt angepasst.
+\end_layout
+
+\begin_layout Standard
+Wenn man den Befehl
+\series bold
+
+\backslash
+framebox
+\series default
+ eingibt, erscheint eine Box mit drei Eingabefeldern.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Aufgrund eines Fehlers in LyX muss der Cursor links neben die Eingabefelder
+ gesetzt werden um sie zu füllen, siehe
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #2461
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ Die ersten beiden sind von eckigen Klammern umgeben und stehen für die
+ beiden optionalen Argumente.
+ In das dritte Feld wird wie bei
+\series bold
+
+\backslash
+fbox
+\series default
+ die Formel eingegeben.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Die Tabelle wurde in eine Minibox gesetzt damit die Fußnote der Tabelle
+ auch erscheint.
+ Denn sonst würde der Fußnotentext im Ausdruck nicht angezeigt werden.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Box Frameless
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "c"
+use_parbox 0
+width "100col%"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Durch einen Fehler in LyX ist es momentan nicht möglich mit
+\family sans
+Strg-m
+\family default
+ eine neue Formel zu erzeugen, siehe
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\family sans
+Strg-m
+\family default
+
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{}
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+boxed
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+framebox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+20mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\family sans
+Strg-m
+\family default
+
+\backslash
+frac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\downarrow$
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}$
+\end_inset
+
+
+\begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die Rahmendicke kann ebenfalls eingestellt werden.
+ Dazu müssen vor der Formel im TeX-Modus die Befehle
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+
+\begin_inset Quotes gld
+\end_inset
+
+Dicke
+\begin_inset Quotes grd
+\end_inset
+
+
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+
+\begin_inset Quotes gld
+\end_inset
+
+Abstand
+\begin_inset Quotes grd
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+eingegeben werden.
+
+\begin_inset Quotes gld
+\end_inset
+
+Abstand
+\begin_inset Quotes grd
+\end_inset
+
+ legt dabei den minimalen Abstand zwischen Rahmen und dem ersten Zeichen
+ in der Box fest.
+ Ein Beispiel dafür ist folgende umrandete Formel:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 2mm
+\backslash
+fboxsep 3mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\boxed{A+B=C}\]
+
+\end_inset
+
+Vor dieser Formel wurde im TeX-Modus
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+2mm
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3mm
+\end_layout
+
+\begin_layout Standard
+eingegeben.
+ Diese angegeben Werte werden für alle folgenden Boxen verwendet.
+\end_layout
+
+\begin_layout Standard
+Möchte man wieder zur Standardrahmengröße zurückkehren, gibt man vor der
+ nächsten Formel im TeX-Modus folgende Befehle ein:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fboxrule
+\series default
+
+\series bold
+0.4pt
+\series default
+
+\series bold
+
+\backslash
+fboxsep
+\series default
+
+\series bold
+3pt
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Boxen ohne Rahmen
+\begin_inset LatexCommand label
+name "sub:Boxen-ohne-Rahmen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxen ! ohne Rahmen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Für Boxen ohne Rahmen gibt es folgende Box-Befehle:
+\series bold
+
+\backslash
+mbox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mbox"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+makebox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash makebox"
+
+\end_inset
+
+ und
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash raisebox"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Mit
+\series bold
+
+\backslash
+raisebox
+\series default
+ kann man eine Box hoch- oder tiefstellen.
+ Allerdings behalten die Zeichen in der Box im Gegensatz zum normalen Hochstelle
+n die Schriftgröße bei.
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ wird dabei mit folgendem Schema benutzt:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox{Höhe}{Boxinhalt}
+\end_layout
+
+\begin_layout Standard
+Soll in der Box eine Formel stehen, muss man wie bei
+\series bold
+
+\backslash
+fbox
+\series default
+ eine weitere Formel erstellen.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+H
+\backslash
+raisebox{2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+ lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $H\raisebox{2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+H
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{al
+\begin_inset Formula $\to$
+\end_inset
+
+lo
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $H\raisebox{-2mm}{al}lo$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A=
+\backslash
+raisebox{-2mm
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\family sans
+Strg-m
+\family default
+
+\backslash
+sqrt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+$A=
+\backslash
+raisebox{-2mm}{$
+\backslash
+sqrt{B}$}$
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die letzte Formel kann derzeit nur im TeX-Modus erstellt werden, da LyX
+ statt der benötigten weiteren Formel eine Box einfügt.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+mbox
+\series default
+ ist äquivalent zu
+\series bold
+
+\backslash
+fbox
+\series default
+ und
+\series bold
+
+\backslash
+makebox
+\series default
+ ist äquivalent zu
+\series bold
+
+\backslash
+framebox
+\series default
+, nur dass es keinen Rahmen gibt.
+\end_layout
+
+\begin_layout Subsection
+Farbige Boxen
+\begin_inset LatexCommand label
+name "sub:Farbige-Boxen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxen ! farbige"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Damit die in diesem Kapitel angegebenen Befehle benutzt werden können, muss
+ im LaTeX-Vorspann das LaTeX-Paket
+\series bold
+color
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Das Paket
+\series bold
+color
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! color"
+
+\end_inset
+
+ mit der Zeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{color}
+\end_layout
+
+\begin_layout Standard
+geladen werden
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Wird irgendwo im Dokument Text mit einer vordefinierten Farbe gefärbt, lädt
+ LyX das LaTeX-Paket
+\series bold
+color
+\series default
+ automatisch.
+ Dadurch kann es vorkommen, dass das Paket doppelt geladen wird, was aber
+ keine Probleme hervorruft.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Damit das Paket nicht doppelt geladen werden kann, wurde im LaTeX-Vorspann
+ ein Makro eingefügt.
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Um Boxen einzufärben, verwendet man den Befehl
+\series bold
+
+\backslash
+colorbox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! C ! \\textbackslash colorbox"
+
+\end_inset
+
+ nach folgendem Schema:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox{Farbe}{Boxinhalt}
+\end_layout
+
+\begin_layout Standard
+Der Boxinhalt kann auch wieder eine Box sein und eine
+\series bold
+
+\backslash
+colorbox
+\series default
+ kann auch ein Teil einer anderen Box sein (siehe 2.
+ und 3.
+ Beispiel).
+ Soll in der Box eine Formel stehen, muss wie bei
+\series bold
+
+\backslash
+fbox
+\series default
+ eine weitere Formel erstellt werden.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Das gilt auch für den Befehl
+\series bold
+
+\backslash
+fcolorbox
+\series default
+.
+ Dabei ist
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1435
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ zu beachten.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Aus folgenden vordefinierten Farben kann gewählt werden:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+black
+\series default
+,
+\series bold
+blue
+\series default
+,
+\series bold
+cyan
+\series default
+,
+\series bold
+green
+\series default
+,
+\series bold
+magenta
+\series default
+,
+\series bold
+red
+\series default
+,
+\series bold
+white
+\series default
+ und
+\series bold
+yellow
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+colorbox{yellow
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fbox
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+colorbox{green
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+colorbox
+\series default
+ färbt nur die Box, nicht aber die Zeichen in der Box ein.
+ Um alle Zeichen zu färben, markiert man die ganze Formel und wählt im Dialog
+
+\family sans
+Textstil
+\family default
+ die gewünschte Farbe aus.
+ Der Dialog kann mit dem Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/dialog-show_character.png
+ scale 85
+
+\end_inset
+
+ oder dem Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Textstil\SpecialChar \menuseparator
+Benutzerdefiniert
+\family default
+ aufgerufen werden.
+ Die Formelnummer hat dann dieselbe Farbe wie die Formel.
+ Soll die Formelnummer eine andere Farbe als die Formelzeichen haben, muss
+ innerhalb der Formel die Farbe geändert werden.
+\end_layout
+
+\begin_layout Standard
+Ein Beispiel:
+\end_layout
+
+\begin_layout Standard
+
+\color red
+\begin_inset Formula \begin{equation}
+\int A=B\label{eq:rot}\end{equation}
+
+\end_inset
+
+
+\color green
+
+\begin_inset Formula \begin{equation}
+\textcolor{red}{\int A=B}\label{eq:rotgruen}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formel
+\begin_inset LatexCommand eqref
+reference "eq:rot"
+
+\end_inset
+
+ ist komplett rot gefärbt.
+\newline
+Formel
+\begin_inset LatexCommand eqref
+reference "eq:rotgruen"
+
+\end_inset
+
+ wurde zuerst komplett grün gefärbt, um die Farbe der Formelnummer festzulegen.
+ Anschließend wurden die Formelzeichen rot gefärbt.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Möchte man den Rahmen anders als den Rest der Box färben, verwendet man
+ den Befehl
+\series bold
+
+\backslash
+fcolorbox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! F ! \\textbackslash fcolorbox"
+
+\end_inset
+
+ nach folgendem Schema:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fcolorbox{Rahmenfarbe}{Farbe}{Boxinhalt}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ stellt also eine Erweiterung des Befehls
+\series bold
+
+\backslash
+colorbox
+\series default
+ dar.
+ Die Rahmenbreite wird, wie bei
+\series bold
+
+\backslash
+framebox
+\series default
+, mit
+\series bold
+
+\backslash
+fboxrule
+\series default
+ und
+\series bold
+
+\backslash
+fboxsep
+\series default
+ festgelegt.
+ Ein Beispiel:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 1mm
+\backslash
+fboxsep 1mm
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\fcolorbox{cyan}{magenta}{A=B}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Diese Formel wurde mit folgendem Befehl erstellt:
+\newline
+
+\series bold
+
+\backslash
+fcolorbox{cyan
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{magenta
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{A=B
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Um andere als die vordefinierten Farben zu verwenden, muss man diese zuerst
+ selbst definieren.
+\end_layout
+
+\begin_layout Standard
+Man kann z.\InsetSpace \thinspace{}
+B.
+ mit folgender LaTeX-Vorspannzeile die Farbe
+\begin_inset Quotes gld
+\end_inset
+
+
+\series bold
+dunkelgruen
+\series default
+
+\begin_inset Quotes grd
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+In Befehlen darf kein Umlaut stehen, siehe
+\begin_inset LatexCommand ref
+reference "sec:Benutzerdefinierte-Befehle"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ definieren:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+definecolor{dunkelgruen}{cmyk}{0.5,
+\series default
+
+\series bold
+0,
+\series default
+
+\series bold
+1,
+\series default
+
+\series bold
+0.5}
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash definecolor"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+cmyk
+\series default
+ ist der Farbraum und steht für die Farben
+\series bold
+cyan
+\series default
+,
+\series bold
+magenta
+\series default
+,
+\series bold
+yellow
+\series default
+ und
+\series bold
+black
+\series default
+.
+ Die vier Zahlen geben der Reihe nach den Anteil der vier Farben an.
+ Für den Anteil kann man Werte im Bereich 0\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+1 angeben.
+ Anstelle von
+\series bold
+cmyk
+\series default
+ kann man zur Definition auch den Farbraum
+\series bold
+rgb
+\series default
+ verwenden.
+
+\series bold
+rgb
+\series default
+ steht für
+\series bold
+red
+\series default
+,
+\series bold
+green
+\series default
+ und
+\series bold
+blue
+\series default
+, so dass man dann mit drei Zahlen die Anteile dieser Farben festlegen kann.
+ Des Weiteren gibt es noch den Farbraum
+\series bold
+gray
+\series default
+, bei dem man mit einer Zahl den Graustufenanteil festlegen kann.
+\end_layout
+
+\begin_layout Standard
+Als Beispiel eine gerahmte Box mit der neu definierten Farbe
+\series bold
+darkgreen
+\series default
+, bei der die Zeichenfarbe
+\series bold
+yellow
+\series default
+ gewählt wurde:
+\begin_inset Formula \begin{equation}
+\colorbox{dunkelgruen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Selbst definierte Farben können mit dem Befehl
+\series bold
+
+\backslash
+textcolor
+\series default
+ auch für Text
+\begin_inset LatexCommand index
+name "Text ! farbiger"
+
+\end_inset
+
+ verwendet werden:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textcolor{dunkelgruen}{
+\end_layout
+
+\end_inset
+
+Dieser Satz ist
+\begin_inset Quotes gld
+\end_inset
+
+dunkelgruen
+\begin_inset Quotes grd
+\end_inset
+
+.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+textcolor
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash textcolor"
+
+\end_inset
+
+ wird nach dem Schema
+\series bold
+
+\backslash
+textcolor{Farbe}{zu
+\series default
+
+\series bold
+färbende
+\series default
+
+\series bold
+Zeichen}
+\series default
+ verwendet.
+\end_layout
+
+\begin_layout Subsection
+Absatzboxen
+\begin_inset LatexCommand label
+name "sub:Absatzboxen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Boxen ! Absatz-"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Mit dem Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Box
+\family default
+ oder dem Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/box-insert.png
+ scale 85
+
+\end_inset
+
+ kann man eine Box erstellen, die mehrere Zeilen und Absätze enthalten kann,
+ eine so genannte
+\emph on
+Parbox
+\emph default
+ (Absatzbox).
+\end_layout
+
+\begin_layout Standard
+Das folgende Beispiel zeigt eine umrahmte Absatzbox in einer Zeile:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Dies ist eine Zeile
+\begin_inset Box Boxed
+position "c"
+hor_pos "c"
+has_inner_box 1
+inner_pos "t"
+use_parbox 1
+width "5cm"
+special "none"
+height "1in"
+height_special "totalheight"
+status open
+
+\begin_layout Standard
+Dies ist die Absatzbox.
+ Sie ist genau 5\InsetSpace \thinspace{}
+cm lang und kann auch Formeln enthalten:
+\begin_inset Formula $\int A\,\mathrm{d}s=C$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ mit einer Absatzbox.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Solch eine Box wird erstellt, indem man mit der rechten Maustaste auf die
+ graue Box mit dem Namen
+\begin_inset Quotes gld
+\end_inset
+
+Box(Gerahmt)
+\begin_inset Quotes grd
+\end_inset
+
+ klickt.
+ Es erscheint dann ein Fenster in dem man die Boxeigenschaften festlegt.
+ In diesem Fall:
+\emph on
+Verzierung
+\emph default
+: Rechteckige Box,
+\emph on
+Innere Box
+\emph default
+: Parbox,
+\emph on
+Breite
+\emph default
+: 5\InsetSpace \thinspace{}
+cm,
+\emph on
+Vertikale Box Ausrichtung
+\emph default
+: Mitte
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+In LaTeX wird eine Absatzbox mit dem Befehl
+\series bold
+
+\backslash
+parbox
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! P ! \\textbackslash parbox"
+
+\end_inset
+
+ erstellt, welcher folgendes Schema besitzt:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+parbox[Position]{Breite}{Boxinhalt}
+\end_layout
+
+\begin_layout Standard
+Die Positionen
+\emph on
+b
+\emph default
+ und
+\emph on
+t
+\emph default
+ sind möglich.
+
+\emph on
+b
+\emph default
+ steht für bottom und bedeutet, dass die letzte Absatzzeile in den umstehenden
+ Text eingepasst wird.
+ Bei
+\emph on
+t
+\emph default
+ wie top geschieht dies für die erste Zeile.
+ Wird keine Position angegeben, wird der Absatz in mittlerer Höhe eingepasst,
+ siehe das Kapitel
+\emph on
+Boxen
+\emph default
+ des Handbuchs
+\emph on
+ Eingebettete\InsetSpace ~
+Objekte
+\emph default
+ für Beispiele.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Möchte man Formeln komplett mit Formelnummer umranden, muss man die Formel
+ in eine Absatzbox setzen.
+ Dazu schreibt man im TeX-Modus vor die Formel den Befehl
+\series bold
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\series default
+.
+ Hierbei steht
+\series bold
+
+\backslash
+linewidth
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash linewidth"
+
+\end_inset
+
+
+\series default
+ für die im Dokument eingestellte Zeilenbreite.
+ Da sich der Rahmen außerhalb der Absatzbox befindet, muss man von der Zeilenbre
+ite zweimal die Rahmendicke und den Rahmenabstand abziehen.
+ Da dies LyX aufgrund eines Fehlers
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #4483
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ nicht automatisch macht, muss der TeX-Modus verwendet werden.
+ Damit man in Argumenten multiplizieren und subtrahieren kann, muss im LaTeX-Vor
+spann das LaTeX-Paket
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+calc
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! calc"
+
+\end_inset
+
+ mit der Zeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+geladen werden.
+ Nach der Formel werden beide Boxen geschlossen, indem man
+\series bold
+}}
+\series default
+ im TeX-Modus eingibt.
+ Dazu ein Beispiel:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxsep 5mm
+\backslash
+fboxrule 5mm
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fbox{
+\backslash
+parbox{
+\backslash
+linewidth-2
+\backslash
+fboxsep-2
+\backslash
+fboxrule}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fboxrule 0.4pt
+\backslash
+fboxsep 3pt
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Da im Argument von
+\series bold
+
+\backslash
+fbox
+\series default
+ eine Absatzbox verwendet wird, gibt es in diesem Fall bei der Formelgröße
+ keinen Unterschied zwischen
+\series bold
+
+\backslash
+fbox
+\series default
+ und
+\series bold
+
+\backslash
+boxed
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Sehr nützlich sind Absatzboxen, wenn man Formeln direkt kommentieren möchte.
+ Dazu verwendet man
+\series bold
+
+\backslash
+parbox
+\series default
+ in Verbindung mit dem Befehl
+\series bold
+
+\backslash
+tag
+\series default
+.
+ (mehr zu
+\series bold
+
+\backslash
+tag
+\series default
+ siehe
+\begin_inset LatexCommand ref
+reference "sub:Benutzerdefinierte-Nummerierung"
+
+\end_inset
+
+)
+\end_layout
+
+\begin_layout Standard
+Ein Beispiel einer mit Hilfe von
+\series bold
+
+\backslash
+parbox
+\series default
+ kommentierten Formel:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*{
+\backslash
+parbox{5cm}{
+\end_layout
+
+\end_inset
+
+Dies ist eine Beschreibung.
+ Sie ist deutlich von der Formel getrennt und mehrzeilig.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}}
+\backslash
+]
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+So eine Formel muss komplett im TeX-Modus eingegeben werden, da LyX den
+ Befehl
+\series bold
+
+\backslash
+parbox
+\series default
+ in Formeln noch nicht unterstützt.
+ Die Formel wird mit folgender Befehlssequenz erstellt:
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+[5x-7b=3b
+\backslash
+tag*
+\backslash
+{
+\backslash
+parbox{5cm}{
+\series default
+ wird im TeX-Modus eingegeben.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Ist der Formelstil
+\series bold
+Eingerückt
+\series default
+ aktiviert, kann
+\series bold
+
+\backslash
+tag*
+\backslash
+{
+\series default
+ auch durch
+\series bold
+
+\backslash
+hfill
+\series default
+ ersetzt werden.
+ (Formelstile siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+)
+\end_layout
+
+\end_inset
+
+ Dann folgt die Beschreibung als normaler Text und zuletzt gibt man
+\series bold
+}}
+\backslash
+]
+\series default
+ im TeX-Modus ein.
+ Die Befehle
+\series bold
+
+\backslash
+[
+\series default
+ und
+\series bold
+
+\backslash
+]
+\series default
+ erstellen hierbei eine abgesetzte Formel.
+\end_layout
+
+\begin_layout Standard
+Die Vorteile von
+\series bold
+
+\backslash
+parbox
+\series default
+ erkennt man an folgendem Beispiel, in dem mit Hilfe des mathematischen
+ Textmodus
+\begin_inset Quotes gld
+\end_inset
+
+kommentiert
+\begin_inset Quotes grd
+\end_inset
+
+ wurde:
+\begin_inset Formula \[
+5x-7b=3b\textrm{Dies ist eine Beschreibung. Sie ist nicht von der Formel getrennt ...}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Operatoren
+\begin_inset LatexCommand index
+name "Operatoren"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Große Operatoren
+\begin_inset LatexCommand label
+name "sub:Große-Operatoren"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operatoren ! große"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Summen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Integrale"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um alle großen Integraloperatoren nutzen zu können, die im Folgenden aufgelistet
+ sind, muss die Option
+\family sans
+esint-Paket automatisch verwenden
+\family default
+ in den Dokumenteinstellungen unter
+\family sans
+Mathe-Optionen
+\family default
+ gewählt sein.
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sum
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash sum"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sum$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+int
+\begin_inset LatexCommand index
+name "Befehle ! I ! \\textbackslash int"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\int$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+intop
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\intop$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointop
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointop$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointctrclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointctrclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ointclockwise
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ointclockwise$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqint$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prod
+\begin_inset LatexCommand index
+name "Befehle ! P ! \\textbackslash prod"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+coprod
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\coprod$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigodot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigodot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigotimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigotimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigoplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigoplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigwedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigwedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigvee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigvee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigsqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigsqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+biguplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\biguplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+Alle großen Operatoren können auch über den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/intop.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Standard
+Die Operatoren werden als groß bezeichnet, da sie größer sind als die zum
+ Teil gleich aussehenden binären Operatoren.
+ Zu allen großen Operatoren kann man Grenzen angeben, wie im nächsten Abschnitt
+ beschrieben.
+\end_layout
+
+\begin_layout Standard
+Die Operatoren
+\series bold
+
+\backslash
+intop
+\series default
+ und
+\series bold
+
+\backslash
+ointop
+\series default
+ unterscheiden sich von
+\series bold
+
+\backslash
+int
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+oint
+\series default
+ in der Art wie die Operatorgrenzen dargestellt werden, siehe
+\begin_inset LatexCommand ref
+reference "sub:Operatorgrenzen"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Subsubsection*
+Hinweise zu Integralen
+\end_layout
+
+\begin_layout Standard
+Der Buchstabe
+\emph on
+d
+\emph default
+ in einer Integralen ist ein Operator, der deswegen aufrecht erscheinen
+ muss.
+ Dazu markiert man das
+\emph on
+d
+\emph default
+ und wandelt es mit der Tastenkombination
+\family sans
+Alt-z\InsetSpace ~
+r
+\family default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Schriftstile siehe
+\begin_inset LatexCommand ref
+reference "sub:Schriftstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ um.
+ Anschließend fügt man vor dem
+\emph on
+d
+\emph default
+, wie bei Operatoren üblich, den kleinsten Leerraum ein.
+ Dazu ein Beispiel:
+\end_layout
+
+\begin_layout Standard
+inkorrekt:
+\begin_inset Formula $\int A(x)dx$
+\end_inset
+
+
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{in}
+\end_layout
+
+\end_inset
+
+korrekt:
+\begin_inset Formula $\int A(x)\,\mathrm{d}x$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Für Mehrfachintegrale gibt es folgende Befehle:
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iiiint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dotsint
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\newpage
+
+\end_layout
+
+\begin_layout Subsection
+Operatorgrenzen
+\begin_inset LatexCommand label
+name "sub:Operatorgrenzen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operatoren ! Grenzen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Grenzen werden durch Hoch- bzw.
+ Tiefstellen erzeugt:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prod^
+\backslash
+infty
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+_0
+\begin_inset Formula $\to$
+\end_inset
+
+A(x)
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Bei einer Formel in einer Textzeile werden die Grenzen rechts neben den
+ Operator gesetzt.
+ In einer abgesetzten Formel werden, außer bei Integralen, die Grenzen über
+ bzw.
+ unter den Operator gesetzt.
+\end_layout
+
+\begin_layout Standard
+Um zu erzwingen, dass die Grenzen neben den Operator gesetzt werden, setzt
+ man den Cursor direkt hinter den Operator und setzt über das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Art der Operatorgrenzen ändern
+\family default
+ die Grenzen auf
+\series bold
+Eingebettet
+\series default
+ (Tastenkombination
+\family sans
+Alt-m\InsetSpace ~
+l
+\family default
+).
+ Dazu folgendes Beispiel:
+\end_layout
+
+\begin_layout Standard
+Die normalen Grenzen sehen so aus:
+\begin_inset Formula \[
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
+
+\end_inset
+
+So sieht die Formel aus, wenn man die Grenzen neben das Summenzeichen setzt:
+\begin_inset Formula \[
+\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
+
+\end_inset
+
+Bei Integralen werden mit Ausnahme von
+\series bold
+
+\backslash
+intop
+\series default
+ und
+\series bold
+
+\backslash
+ointop
+\series default
+ die Grenzen standardmäßig neben den Operator gesetzt.
+ Bei Mehrfachintegralen werden die Grenzen jedoch meistens unter den Operator
+ gesetzt.
+ Im folgenden Beispiel wurde die Grenze deswegen auf
+\series bold
+Anzeige
+\series default
+ gesetzt und damit unter die Integrale geschrieben:
+\begin_inset Formula \begin{equation}
+\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Um Bedingungen für Grenzen anzugeben, gibt es die Befehle
+\series bold
+
+\backslash
+subarray
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash subarray"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+substack
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash substack"
+
+\end_inset
+
+.
+ Um z.\InsetSpace \thinspace{}
+B.
+ diesen Ausdruck
+\begin_inset Formula \begin{equation}
+\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
+
+\end_inset
+
+zu erstellen, muss man Folgendes tun:
+\newline
+Zuerst gibt man den Befehl
+\series bold
+
+\backslash
+sum
+\series default
+^
+\series bold
+n
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+_
+\series default
+ ein.
+ Man befindet sich nun in einem blauen Kästchen unter dem Summenzeichen.
+ In dieses gibt man den Befehl
+\series bold
+
+\backslash
+subarray
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+ ein.
+ Das blaue Kästchen hat nun eine lila Umrahmung und man kann jetzt mehrere
+ Zeilen untereinander schreiben.
+ Mit Eingabe des Zeilenumbruchs (
+\family sans
+Strg-Enter
+\family default
+) wird eine neue Zeile erstellt.
+ Gibt man
+\newline
+
+\series bold
+0<k<1000 Strg-Enter
+\newline
+
+\series default
+ein, erscheint darunter ein Kästchen für die neue Zeile.
+\end_layout
+
+\begin_layout Standard
+Die Ausrichtung der Zeilen kann mit der
+\family sans
+Tabellen-Werkzeugleiste
+\family default
+ oder dem Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Zeilen & Spalten
+\family default
+ auf links geändert werden.
+ Um rechts ausgerichtete Zeilen zu erhalten, wird am Anfang der Zeile
+\series bold
+
+\backslash
+hfill
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+ eingegeben.
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+substack
+\series default
+ ist äquivalent zu
+\series bold
+
+\backslash
+subarray
+\series default
+, mit dem Unterschied dass die Zeilen immer zentriert ausgerichtet sind.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Wie bei Formel
+\begin_inset LatexCommand eqref
+reference "eq:substack"
+
+\end_inset
+
+ kann es vorkommen, dass sich neben dem Operator zu viel Leerraum befindet,
+ denn das dem Operator folgende Zeichen wird neben die Grenzen gesetzt.
+\end_layout
+
+\begin_layout Standard
+Um das zu verhindern, kann man folgendes Makro in den LaTeX-Vorspann einfügen:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+def
+\backslash
+clap#1{
+\backslash
+hbox to 0pt{
+\backslash
+hss #1
+\backslash
+hss}}
+\newline
+
+\backslash
+def
+\backslash
+mathclap {
+\backslash
+mathpalette
+\backslash
+mathclapinternal}
+\newline
+
+\backslash
+def
+\backslash
+mathclapinternal #1#2{
+\backslash
+clap{$
+\backslash
+mathsurround =0pt #1{#2}$}}
+\end_layout
+
+\begin_layout Standard
+Dadurch wird der Befehl
+\series bold
+
+\backslash
+mathclap
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mathclap"
+
+\end_inset
+
+ definiert, der die Breite der Grenze auf 0\InsetSpace \thinspace{}
+pt setzt.
+ Das Befehlsschema lautet
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathclap{Grenze}
+\end_layout
+
+\begin_layout Standard
+wobei die Grenze auch aus mehreren Bedingungen bestehen kann.
+\end_layout
+
+\begin_layout Standard
+Auf Formel
+\begin_inset LatexCommand eqref
+reference "eq:substack"
+
+\end_inset
+
+ angewandt, gibt man also den Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+sum_
+\backslash
+mathclap{
+\backslash
+substack
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+0<k<1000 Strg-Enter
+\end_layout
+
+\begin_layout Standard
+ein, um die untere Grenze zu erstellen.
+ Der Summand befindet sich nun direkt hinter dem Summenzeichen:
+\begin_inset Formula \[
+\sum_{\mathclap{\substack{0<k<1000\\
+\\k\,\in\,\mathbb{N}}
+}}^{n}k^{-2}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+In
+\begin_inset LatexCommand ref
+reference "sub:Selbstdefinierte-Operatoren"
+
+\end_inset
+
+ ist beschrieben, wie man eine Grenze für mehrere Operatoren verwenden kann.
+\end_layout
+
+\begin_layout Subsection
+Binäre Operatoren
+\begin_inset LatexCommand label
+name "sub:Binäre-Operatoren"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operatoren ! binäre"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Binäre Operatoren sind von Leerraum umgeben, wenn sich vor und hinter ihnen
+ ein Zeichen befindet.
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
++
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $+$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $-$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pm$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cdot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cdot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+times
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\times$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+div
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\div$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $*$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+star
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\star$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nabla
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nabla$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigtriangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigtriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigtriangleup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigtriangleup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Box$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddagger
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddagger$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigcirc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigcirc$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wedge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vee$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="13" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ominus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ominus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+otimes
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\otimes$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\oslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+odot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\odot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+amalg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\amalg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+uplus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\uplus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+setminus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\setminus$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqcap
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqcap$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqcup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqcup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangleleft
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangleleft$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangleright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangleright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+Alle binären Operatoren können auch über den Mathe-Werkzeugleistenknopf
+
+\begin_inset Graphics
+ filename ../../images/math/pm.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Standard
+Um den Laplace-Operator darzustellen, kann man statt
+\series bold
+
+\backslash
+bigtriangleup
+\series default
+ auch
+\series bold
+
+\backslash
+Delta
+\series default
+ verwenden oder man benutzt
+\series bold
+
+\backslash
+nabla
+\series default
+^
+\series bold
+2
+\series default
+ (
+\begin_inset Formula $\nabla^{2}$
+\end_inset
+
+).
+\end_layout
+
+\begin_layout Standard
+Das Zeichen
+\family sans
+Menütrenner
+\family default
+ im Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Sonderzeichen
+\family default
+ ist der Operator
+\series bold
+
+\backslash
+triangleright
+\series default
+.
+\end_layout
+
+\begin_layout Subsection
+Selbst definierte Operatoren
+\begin_inset LatexCommand label
+name "sub:Selbstdefinierte-Operatoren"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Operatoren ! selbstdefinierte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Mit Hilfe des Befehls
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
+
+\end_inset
+
+ kann man im LaTeX-Vorspann eigene Operatoren definieren.
+ Das Befehlsschema dazu lautet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator{neuer Befehl}{Anzeige}
+\end_layout
+
+\begin_layout Standard
+Anzeige können Zeichen und Symbole sein, die festlegen, wie der Operator
+ im Ausdruck aussieht.
+ Will man einen großen Operator definieren, setzt man hinter den Befehl
+ ein
+\series bold
+*
+\series default
+.
+ Zu allen selbst definierten großen Operatoren kann man Grenzen angeben,
+ wie in
+\begin_inset LatexCommand ref
+reference "sub:Operatorgrenzen"
+
+\end_inset
+
+ beschrieben.
+\end_layout
+
+\begin_layout Standard
+Beispielsweise definiert die LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareMathOperator*{
+\backslash
+Raute}{
+\backslash
+blacklozenge}
+\end_layout
+
+\begin_layout Standard
+den Befehl
+\series bold
+
+\backslash
+Raute
+\series default
+, mit dem man einen großen Operator aufrufen kann, der aus dem Raute Symbol
+ aus
+\begin_inset LatexCommand ref
+reference "sub:Sonstige-Symbole"
+
+\end_inset
+
+ besteht:
+\begin_inset Formula \[
+\Raute_{n=1}^{\infty}\]
+
+\end_inset
+
+Der Befehl für diese Formel lautet:
+\series bold
+
+\backslash
+Raute
+\series default
+^
+\series bold
+
+\backslash
+infty
+\begin_inset Formula $\to$
+\end_inset
+
+_n=1
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Benötigt man eigene Operatoren nicht mehrfach im Dokument, kann man diese
+ auch mit den Befehlen
+\series bold
+
+\backslash
+mathop
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mathop"
+
+\end_inset
+
+ und
+\series bold
+
+\backslash
+mathbin
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mathbin"
+
+\end_inset
+
+ definieren, die folgendes Schema besitzen:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop{Anzeige}
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+mathbin{Anzeige}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ definiert große,
+\series bold
+
+\backslash
+mathbin
+\series default
+ binäre Operatoren.
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+mathop
+\series default
+ lässt sich z.\InsetSpace \thinspace{}
+B.
+ nutzen, um eine Grenze für mehrere Operatoren zu verwenden:
+\begin_inset Formula \[
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl für obige Formel lautet:
+\newline
+
+\series bold
+
+\backslash
+mathop{
+\backslash
+sum
+\backslash
+negmedspace
+\backslash
+sum
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\to$
+\end_inset
+
+^N
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series bold
+_i,j=1
+\end_layout
+
+\begin_layout Section
+Schriften
+\begin_inset LatexCommand index
+name "Schriften"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Schriftstile
+\begin_inset LatexCommand label
+name "sub:Schriftstile"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Schriften ! Schriftstile"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Lateinische Buchstaben in einer Formel können in folgenden Schriftstilen
+ gesetzt werden:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Tastenkürzel
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathbb
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathbb{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z k
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathbf
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathbf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z f
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+boldsymbol
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\boldsymbol{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathcal
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+ABC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{ABC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z h
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathfrak
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathfrak{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Tastenkürzel
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathit
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathit{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathrm
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathrm{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z r
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathsf
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathsf{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Alt-z s
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mathtt
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series default
+AbC
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathtt{AbC}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Achtung:
+\series default
+ Die Stile
+\series bold
+
+\backslash
+mathbb
+\series default
+ und
+\series bold
+
+\backslash
+mathcal
+\series default
+ können nur für Großbuchstaben verwendet werden.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Voreingestellt ist der Stil
+\series bold
+
+\backslash
+mathnormal
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Die Stilbefehle wirken auch auf Buchstaben in mathematischen Konstruktionen:
+\begin_inset Formula \[
+\mathfrak{A=\frac{b}{C}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Zeichen im mathematischen Textmodus erscheinen nicht in einem der Matheschriftst
+ile, sondern in dem Textschriftstil
+\series bold
+
+\backslash
+textrm
+\series default
+.
+ Dass ihr Stil nicht über den Textstil Dialog geändert werden kann ist ein
+ Fehler in LyX .
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #4091
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Anstelle der Stilbefehle kann man auch den Dialog
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Text-Stil
+\family default
+ oder den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/font.png
+ scale 85
+
+\end_inset
+
+ verwenden.
+\end_layout
+
+\begin_layout Subsection
+Fett gedruckte Formeln
+\begin_inset LatexCommand label
+name "sub:Fett-gedruckte-Formeln"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! fett gedruckte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man komplette Formeln fett setzen, kann man nicht den im vorigen
+ Kapitel angegebenen Befehl
+\series bold
+
+\backslash
+mathbf
+\series default
+ verwenden, denn dieser wirkt nicht auf kleine griechische Buchstaben.
+ Außerdem setzt er lateinische Buchstaben immer aufrecht, was man an folgender
+ Formel gut erkennt:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{Formel mit \textbackslash mathbf}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um die Formel korrekt darzustellen, verwendet man den Befehl
+\series bold
+
+\backslash
+boldsymbol
+\series default
+:
+\begin_inset Formula \[
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{Formel mit \textbackslash boldsymbol}}\]
+
+\end_inset
+
+Es gibt auch die Möglichkeit die Formel in eine
+\series bold
+boldmath-Umgebung
+\series default
+ zu setzen.
+ Diese Umgebung wird erzeugt, indem man im TeX-Modus den Befehl
+\series bold
+
+\backslash
+boldmath
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash boldmath"
+
+\end_inset
+
+
+\series default
+ eingibt.
+ Um die Umgebung wieder zu beenden, gibt man im TeX-Modus den Befehl
+\series bold
+
+\backslash
+unboldmath
+\begin_inset LatexCommand index
+name "Befehle ! U ! \\textbackslash unboldmath"
+
+\end_inset
+
+
+\series default
+ ein.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{Formel in boldmath-Umgebung}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Schriftgrößen
+\begin_inset LatexCommand label
+name "sub:Schriftgrößen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Schriften ! Schriftgrößen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Für Zeichen in einer Formel gibt es, analog zu Textzeichen, folgende Größenbefeh
+le:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+Huge
+\series default
+,
+\series bold
+
+\backslash
+huge
+\series default
+,
+\series bold
+
+\backslash
+LARGE
+\series default
+,
+\series bold
+
+\backslash
+Large
+\series default
+,
+\series bold
+
+\backslash
+large
+\series default
+,
+\series bold
+
+\backslash
+normalsize
+\series default
+,
+\series bold
+
+\backslash
+small
+\series default
+,
+\series bold
+
+\backslash
+footnotesize
+\series default
+,
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+scriptsize
+\series default
+ und
+\series bold
+
+\backslash
+tiny
+\end_layout
+
+\begin_layout Standard
+Welche Größe die Befehle produzieren, hängt von der Dokumentschriftgröße
+ ab, die dem Befehl
+\series bold
+
+\backslash
+normalsize
+\series default
+ entspricht.
+ Die anderen Befehle produzieren kleinere oder größere Schriften als
+\series bold
+
+\backslash
+normalsize
+\series default
+.
+ Die Schriftgröße kann jedoch einen bestimmten Wert nicht übertreffen.
+ Beträgt z.\InsetSpace \thinspace{}
+B.
+ die Dokumentschriftgröße 12\InsetSpace \thinspace{}
+pt, produziert der Befehl
+\series bold
+
+\backslash
+Huge
+\series default
+ dasselbe wie
+\series bold
+
+\backslash
+huge
+\series default
+.
+
+\end_layout
+
+\begin_layout Standard
+Ein Größenbefehl wird im TeX-Modus vor der Formel eingegeben und legt die
+ Größe aller nachfolgenden Formel- und Textzeichen fest.
+ Um wieder zur Ausgangsgröße zurückzukehren, gibt man nach der Formel im
+ TeX-Modus den Befehl
+\series bold
+
+\backslash
+normalsize
+\series default
+ ein.
+\end_layout
+
+\begin_layout Standard
+Innerhalb einer Formel kann die Größe nur für Symbole oder Buchstaben im
+ mathematischen Text geändert werden.
+ Dazu wird der Größenbefehl im mathematischen Textmodus eingegeben.
+ Alle diesem Befehl folgenden Zeichen bis zum Ende des mathematischen Textes
+ oder bis zu einem anderen Größenbefehl haben dann die angegebene Größe.
+ Dazu zwei Beispiele:
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+huge
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \[
+A=\frac{B}{c}\cdot\maltese\]
+
+\end_inset
+
+
+\begin_inset Formula \[
+\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+normalsize
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Vor beiden Formeln wurde der Befehl
+\series bold
+
+\backslash
+huge
+\series default
+ eingegeben.
+ Der Befehl für die zweite Formel lautet:
+\newline
+
+\series bold
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A M-m m
+\backslash
+Large
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+textit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset Formula $\to$
+\end_inset
+
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace*{1cm}
+\end_layout
+
+\end_inset
+
+M-m
+\series default
+
+\series bold
+m
+\backslash
+tiny
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+maltese
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+textit
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\end_layout
+
+\begin_layout Standard
+Kann ein Symbol nicht in verschiedenen Größen dargestellt werden, wird es
+ immer in der Standardgröße dargestellt.
+\end_layout
+
+\begin_layout Section
+Griechische Buchstaben
+\begin_inset LatexCommand index
+name "griechische Buchstaben"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Alle griechischen Buchstaben können auch über den Mathe-Werkzeugleistenknopf
+
+\begin_inset Graphics
+ filename ../../images/math/alpha.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Subsection
+Kleine Buchstaben
+\begin_inset LatexCommand label
+name "sub:Kleine-Buchstaben"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "griechische Buchstaben ! kleine"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+alpha
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\alpha$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+beta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\beta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+epsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\epsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varepsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varepsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+zeta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\zeta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+eta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\eta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vartheta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vartheta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+iota
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\iota$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+kappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\kappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varkappa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varkappa$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nu
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nu$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $o$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varpi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varpi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="11" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varrho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varrho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varsigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varsigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tau
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\tau$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varphi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varphi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+chi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\chi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Wie man aufrechte griechische Buchstaben erstellt, ist in
+\begin_inset LatexCommand ref
+reference "sub:Aufrechte-kleine-griechische"
+
+\end_inset
+
+ beschrieben.
+\end_layout
+
+\begin_layout Subsection
+Große Buchstaben
+\begin_inset LatexCommand index
+name "griechische Buchstaben ! große"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Gamma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Gamma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Delta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Delta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Theta$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Lambda
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Lambda$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Xi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Xi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Pi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Pi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Sigma
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Sigma$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Upsilon$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Phi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Psi$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Omega
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Omega$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Dass die großen griechischen Buchstaben aufrecht erscheinen, ist einem Fehler
+ geschuldet, der während der Entwicklung von TeX gemacht wurde.
+ Um korrekte kursive Großbuchstaben zu erhalten, beginnt man einen Befehl
+ mit
+\series bold
+var
+\series default
+.
+ So ergibt z.\InsetSpace \thinspace{}
+B.
+ der Befehl
+\series bold
+
+\backslash
+varGamma
+\series default
+:
+\begin_inset Formula $\varGamma$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Fett gedruckte Buchstaben
+\begin_inset LatexCommand index
+name "griechische Buchstaben ! fett gedruckte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Griechische lassen sich nicht wie lateinische Buchstaben in verschiedenen
+ Schriftstilen darstellen.
+ Es besteht nur die Möglichkeit, sie mit dem Befehl
+\series bold
+
+\backslash
+boldsymbol
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! B ! \\textbackslash boldsymbol"
+
+\end_inset
+
+ fett gedruckt auszugeben.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Upsilon
+\backslash
+boldsymbol
+\backslash
+Upsilon
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+theta
+\backslash
+boldsymbol
+\backslash
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\theta\boldsymbol{\theta}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Symbole
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Eine Liste mit sämtlichen Symbolen der meisten LaTeX-Pakete findet man in
+
+\begin_inset LatexCommand cite
+key "Symbole"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ dient dazu, dass die Fußnote nicht mit im pdf-Lesezeichen erscheint.
+\end_layout
+
+\begin_layout Standard
+Näheres zu
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ steht in Kapitel
+\begin_inset LatexCommand ref
+reference "sub:Formeln-in-Überschriften"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbole"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Viele der im Folgenden aufgelisteten Symbole können auch über die Mathe-Werkzeug\SpecialChar \-
+
+leistenknöpfe
+\begin_inset Graphics
+ filename ../../images/math/nabla.png
+ scale 85
+
+\end_inset
+
+ und
+\begin_inset Graphics
+ filename ../../images/math/digamma.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Subsection
+Mathematische Symbole
+\begin_inset LatexCommand label
+name "sub:Mathematische-Symbole"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbole ! mathematische"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\neg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Im
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Im$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Re
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Re$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+aleph
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\aleph$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+partial
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\partial$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+infty
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\wp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+imath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\imath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+jmath
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\jmath$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+forall
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\forall$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+exists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\exists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nexists
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nexists$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+emptyset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\emptyset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varnothing
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varnothing$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ddag
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ddag$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+complement
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-0.8mm}{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\complement$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bbbk
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Bbbk$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+backprime
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\backprime$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mho
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mho$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+triangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\triangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+angle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\angle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+measuredangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\measuredangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sphericalangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sphericalangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+top
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\top$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bot$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Subsection
+Sonstige Symbole
+\begin_inset LatexCommand label
+name "sub:Sonstige-Symbole"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbole ! sonstige"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+flat
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\flat$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+natural
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\natural$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sharp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sharp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+surd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\surd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+checkmark
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\checkmark$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+yen
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\yen$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+pounds
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\pounds$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+$
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\$$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+§
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $§$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hbar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hbar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hslash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+clubsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\clubsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+spadesuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\spadesuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bigstar
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bigstar$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacklozenge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacklozenge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacktriangle
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacktriangle$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+blacktiangledown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\blacktriangledown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bullet
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bullet$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diamondsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diamondsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Diamond
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Diamond$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+heartsuit
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\heartsuit$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+P
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\P$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+copyright
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\copyright$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circledR
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circledR$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+maltese
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\maltese$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diagup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diagup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+diagdown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\diagdown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Weitere Symbole sind in
+\begin_inset LatexCommand ref
+reference "sub:Sonstige-Sonderzeichen"
+
+\end_inset
+
+ aufgelistet.
+\end_layout
+
+\begin_layout Standard
+Einige Symbole können in unterschiedlicher Größe dargestellt werden, siehe
+
+\begin_inset LatexCommand ref
+reference "sub:Schriftgrößen"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Das Euro-Symbol €
+\begin_inset LatexCommand index
+name "Symbole ! Euro-Symbol"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "\\textcent@\\officialeuro"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Wenn man in einer Formel das Euro-Symbol verwenden will, muss man das LaTeX-Pake
+t
+\series bold
+eurosym
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! eurosym"
+
+\end_inset
+
+ installieren und dieses mit der LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[gennarrow]{eurosym}
+\end_layout
+
+\begin_layout Standard
+aktivieren.
+ Das Euro-Symbol kann man nun mit dem Befehl
+\series bold
+
+\backslash
+euro
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! E ! \\textbackslash euro"
+
+\end_inset
+
+ aufrufen.
+\end_layout
+
+\begin_layout Standard
+Das Euro-Symbol kann man direkt übder die Tastatur in mathematischen Text
+ eingeben, ohne
+\series bold
+eurosym
+\series default
+ installiert zu haben.
+ Ist
+\series bold
+eurosym
+\series default
+ installiert, kann man
+\series bold
+
+\backslash
+euro
+\series default
+ auch im TeX-Modus eingeben.
+ Das offizielle Währungssymbol erhält man dann über den Befehl
+\series bold
+
+\backslash
+officialeuro
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! O ! \\textbackslash officialeuro"
+
+\end_inset
+
+, der nur im TeX-Modus verfügbar ist.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+ifeurosym
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Die folgende Tabelle erscheint nur im Ausdruck wenn das LaTeX-Paket
+\series bold
+eurosym
+\series default
+ installiert ist:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Eine Übersicht der verschiedenen Euro-Symbole:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="3">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Formel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+euro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\euro$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+mathematischer Text
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+€
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mbox{€}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+TeX-Modus
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+officialeuro
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Folgendes erscheint im Ausdruck wenn das LaTeX-Paket
+\series bold
+eurosym
+\series default
+ nicht installiert ist:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Das LaTeX-Paket
+\series bold
+eurosym
+\series default
+muss installiert sein, um den Rest dieses Abschnitts im Ausdruck zu sehen.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Relationen
+\begin_inset LatexCommand label
+name "sec:Relationen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Relationen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Vergleiche|see{Relationen}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Alle griechischen Buchstaben können auch über den Mathe-Werkzeugleistenknopf
+
+\begin_inset Graphics
+ filename ../../images/math/leq.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+<
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $<$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\le$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ll
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ll$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+prec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\prec$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+preceq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\preceq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+subset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\subset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+subseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\subseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqsubseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqsubseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+in
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\in$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vdash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\vdash$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+smile
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\smile$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+unlhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\unlhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gtrless
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gtrless$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+mid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nmid
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nmid$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\not=$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+equiv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\equiv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+simeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\simeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+approx
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\approx$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cong
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\cong$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bowtie
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\bowtie$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+notin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\notin$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+perp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\perp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+propto
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\propto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+asymp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\asymp$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+doteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\doteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+circeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\circeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+models
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\models$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+widehat=
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\widehat{=}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="17" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+>
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $>$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ge$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\gg$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+succ
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\succ$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+succeq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\succeq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+supset
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\supset$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+supseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\supseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sqsupseteq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\sqsupseteq$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\ni$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dashv
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\dashv$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+frown
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\frown$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\rhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+unrhd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\unrhd$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lessgtr
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\lessgtr$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+parallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\parallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+nparallel
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\nparallel$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Die Zeichen
+\series bold
+
+\backslash
+lhd
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+rhd
+\series default
+ sind größer als die gleich aussehenden Operatoren
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+triangleleft
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+triangleright
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Relationen sind im Gegensatz zu Symbolen immer von Leerraum umgeben.
+\end_layout
+
+\begin_layout Standard
+Relationen mit Beschriftungen können mit Hilfe des Befehls
+\series bold
+
+\backslash
+stackrel
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash stackrel"
+
+\end_inset
+
+ erstellt werden:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A(r)
+\backslash
+stackrel
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+r
+\backslash
+to
+\backslash
+infty
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+
+\backslash
+approx
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Funktionen
+\end_layout
+
+\begin_layout Subsection
+Vordefinierte Funktionen
+\begin_inset LatexCommand label
+name "sub:Vordefinierte-Funktionen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Funktionen ! vordefinierte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Allgemein werden in mathematischen Ausdrücken Variablen
+\shape italic
+kursiv
+\shape default
+ gesetzt, Funktionsnamen hingegen nicht, denn
+\begin_inset Formula $sin$
+\end_inset
+
+ könnte als
+\begin_inset Formula $s\cdot i\cdot n$
+\end_inset
+
+ missverstanden werden.
+ Aus diesem Grund gibt es vordefinierte Funktionen, die zusätzlich von Vorfaktor
+en etwas abgesetzt sind.
+ Sie werden als Befehle mit einem Backslash vor dem Funktionsnamen eingefügt.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="4">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Asin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $Asin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+sin(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\sin(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Folgende Funktionen sind vordefiniert:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="9" columns="4">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sinh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arcsin
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cosh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arccos
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+inf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+tanh
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arctan
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lim
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+coth
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+arg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+liminf
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+sec
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+min
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+deg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+limsup
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+csc
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+max
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+det
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Pr
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ln
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+exp
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+hom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lg
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+log
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ker
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gcd
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Sie können auch über den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/functions.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Subsection
+Selbst definierte Funktionen
+\begin_inset LatexCommand index
+name "Funktionen ! selbstdefinierte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Will man eine Funktion verwenden, die nicht vordefiniert ist, wie z.\InsetSpace \thinspace{}
+B.
+ die Signumfunktion sgn(x), hat man zwei Möglichkeiten:
+\end_layout
+
+\begin_layout Itemize
+Man definiert die Funktion selbst.
+ Dazu gibt man im LaTeX-Vorspann die Zeile
+\newline
+
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\newline
+
+\series bold
+
+\backslash
+DeclareMathOperator{
+\backslash
+sgn}{sgn}
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"
+
+\end_inset
+
+
+\newline
+
+\begin_inset VSpace -2mm
+\end_inset
+
+
+\newline
+ein
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Näheres zu
+\series bold
+
+\backslash
+DeclareMathOperator
+\series default
+ siehe
+\begin_inset LatexCommand ref
+reference "sub:Selbstdefinierte-Operatoren"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+.
+ Nun kann man mit dem Befehl
+\series bold
+
+\backslash
+sgn
+\series default
+ die neu definierte Funktion aufrufen.
+\end_layout
+
+\begin_layout Itemize
+Man schreibt die Formel wie gewohnt, markiert den Formelnamen, also in unserem
+ Beispiel die Buchstaben
+\emph on
+sgn
+\emph default
+, und wandelt ihn in in mathematischen Text um.
+ Zwischen Vorfaktor und Funktion fügt man einen kleinen Leerraum ein.
+\end_layout
+
+\begin_layout Standard
+Das Ergebnis ist bei beiden Methoden dasselbe wie bei einer vordefinierten
+ Funktion
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Selbst definierte Funktionen werden in LyX rot, vordefinierte schwarz angezeigt.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+sgn(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\sgn(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+,
+\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt-m}\,\textrm{m}}$
+\end_inset
+
+(x)+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\,\textrm{sgn}(x)+B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die erste Methode ist besser geeignet, wenn die selbst definierte Funktion
+ mehrfach verwendet werden soll.
+\end_layout
+
+\begin_layout Subsection
+Grenzwerte
+\begin_inset LatexCommand index
+name "Grenzwerte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Für Grenzwerte sind außer
+\series bold
+
+\backslash
+lim
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash lim"
+
+\end_inset
+
+,
+\series bold
+
+\backslash
+liminf
+\series default
+ und
+\series bold
+
+\backslash
+limsup
+\series default
+ noch folgende Funktionen definiert:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varliminf
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varliminf$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varlimsup
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varlimsup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varprojlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varprojlim$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+varinjlim
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\varinjlim$
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Der Grenzwert wird durch Tiefstellen erzeugt.
+ Bei einer eingebetteten Formel wird er rechts neben die Funktion gesetzt:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{1cm}
+\end_layout
+
+\end_inset
+
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace
+\series default
+ und
+\series bold
+
+\backslash
+raisebox
+\series default
+ dienen nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lim_x
+\backslash
+to
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+x=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In einer abgesetzten Formel steht der Grenzwert wie gewohnt darunter:
+\begin_inset Formula \[
+\lim_{x\to A}x=B\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Modulo-Funktionen
+\begin_inset LatexCommand index
+name "Funktionen ! Modulo-"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Eine Besonderheit stellt die Modulo-Funktion dar, denn es gibt sie in vier
+ Varianten.
+\newpage
+
+\end_layout
+
+\begin_layout Standard
+Die Varianten in einer abgesetzten Formel:
+\begin_inset Formula \begin{align*}
+\underline{\textrm{Befehl}\raisebox{-0.9mm}{}} & & \underline{\textrm{Ergebnis}}\\
+\mathrm{a\backslash mod\textrm{\leer}b} & & a\mod b\\
+\mathrm{a\backslash pmod\textrm{\leer}b} & & a\pmod b\\
+\mathrm{a\backslash bmod\textrm{\leer}b} & & a\bmod b\\
+\mathrm{a\backslash pod\textrm{\leer}b} & & a\pod b\end{align*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In einer eingebetteten Formel wird bei allen Varianten vor den Funktionsnamen
+ weniger Leerraum gesetzt.
+\end_layout
+
+\begin_layout Section
+Sonderzeichen
+\begin_inset LatexCommand index
+name "Sonderzeichen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Sonderzeichen im mathematischen Text
+\end_layout
+
+\begin_layout Standard
+Die folgenden Befehle können nur im mathematischen Textmodus oder im TeX-Modus
+ verwendet werden:
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+oe
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\oe}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+OE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\OE}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ae
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\ae}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+AE
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\AE}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+aa
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\aa}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+AA
+\begin_inset LatexCommand index
+name "\\@\\textrm{\\AA}"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\AA}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+i
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\i}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace{0mm}
+\series default
+ dient nur zur Trennung,da sonst im Ausdruck ¡ bzw.
+ ¿ erscheinen würde.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+o
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\o}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+O
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\O}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+l
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\l}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+L
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\L}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+!
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{!`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+?
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{?`}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+j
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\textrm{\j}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+Die Zeichen
+\begin_inset Formula $\textrm{\textrm{Å}}$
+\end_inset
+
+ und
+\begin_inset Formula $\textrm{\textrm{Ø}}$
+\end_inset
+
+ können auch über den Mathe-Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/math/digamma.png
+ scale 85
+
+\end_inset
+
+ eingefügt werden.
+\end_layout
+
+\begin_layout Standard
+Eine Ausnahme bilden die Befehle
+\series bold
+!
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\series default
+ und
+\series bold
+?
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hspace{0mm}
+\end_layout
+
+\end_inset
+
+`
+\series default
+, denn man kann sie in LyX direkt in den Text eingeben.
+\end_layout
+
+\begin_layout Subsection
+Akzente im Text
+\begin_inset LatexCommand label
+name "sub:Sonderzeichen-Akzente"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Akzente ! im Text"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Man kann mit den folgenden Befehlen sämtliche Buchstaben akzentuieren.
+ Die Befehle müssen dazu im TeX-Modus eingegeben werden.
+\end_layout
+
+\begin_layout Standard
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="block" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\begin_inset Quotes grd
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+"e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+`e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
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+
+\begin_layout Standard
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+\end_layout
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+\end_inset
+
+
+\end_layout
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+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
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+\backslash
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
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+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
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+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+u e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+b
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+b e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
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+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+ee
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+t ee
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features>
+<column alignment="block" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
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+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+H e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
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+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+'e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+~e
+\begin_inset LatexCommand index
+name "Tilde"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+~e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+.e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+v
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+v e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+d
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+d e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+c
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+e
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+c e
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Mit dem Befehl
+\series bold
+
+\backslash
+t
+\series default
+ können auch zwei verschiedene Zeichen akzentuiert werden.
+ Der Befehl
+\series bold
+
+\backslash
+t
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+sz
+\series default
+ ergibt:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+t sz
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die Akzente
+\series bold
+`
+\series default
+ ,
+\series bold
+'
+\series default
+ und
+\series bold
+^
+\series default
+ können in Verbindung mit Selbstlauten auch direkt über die Tastatur eingegeben
+ werden ohne den TeX-Modus zu benutzen.
+ Dasselbe gilt für die Tilde
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Gilt nur für Tastaturen, bei denen die Tilde als Akzent definiert ist.
+\end_layout
+
+\end_inset
+
+
+\series bold
+~
+\series default
+ in Verbindung mit
+\emph on
+a
+\emph default
+ ,
+\emph on
+n
+\emph default
+ oder
+\emph on
+o
+\emph default
+.
+\end_layout
+
+\begin_layout Standard
+Die Befehle
+\series bold
+
+\backslash
+b
+\series default
+ ,
+\series bold
+
+\backslash
+c
+\series default
+ ,
+\series bold
+
+\backslash
+d
+\series default
+ ,
+\series bold
+
+\backslash
+H
+\series default
+ ,
+\series bold
+
+\backslash
+t
+\series default
+ ,
+\series bold
+
+\backslash
+u
+\series default
+ ,
+\series bold
+
+\backslash
+v
+\series default
+ und direkt über die Tastatur eingegebene Akzente sind auch im mathematischen
+ Textmodus verfügbar.
+ Für die restlichen Akzente gibt es in Formeln spezielle Mathebefehle, siehe
+
+\begin_inset LatexCommand ref
+reference "sub:Akzente-für-ein"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Des Weiteren kann man mit dem Befehl
+\series bold
+
+\backslash
+textcircled
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash textcircled"
+
+\end_inset
+
+, ähnlich dem Copyrightsymbol, sämtliche Zahlen und Buchstaben in einen
+ Kreis setzen, quasi mit einem Kreis akzentuieren.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ in der Formel dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textcircled{w}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}{W}}
+\end_layout
+
+\end_inset
+</cell>
+<cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+Large
+\backslash
+textcircled{
+\backslash
+normalsize
+\backslash
+protect
+\backslash
+raisebox{-1.5pt}W}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Man muss darauf achten, dass das Zeichen in einen Kreis passt.
+
+\series bold
+
+\backslash
+Large
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset LatexCommand ref
+reference "sub:Schriftgrößen"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ bestimmt dabei die Größe des Kreises.
+ Mit Hilfe von
+\series bold
+
+\backslash
+raisebox
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset LatexCommand ref
+reference "sub:Boxen-ohne-Rahmen"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ kann man das Zeichen zentrieren.
+\end_layout
+
+\begin_layout Subsection
+Minuskelziffern
+\begin_inset LatexCommand index
+name "Minuskelziffern"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Minuskelziffern werden mit dem Befehl
+\series bold
+
+\backslash
+oldstylenums
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! O ! \\textbackslash oldstylenums"
+
+\end_inset
+
+ erzeugt.
+ Der Befehl ist sowohl in einer Formel als auch im TeX-Modus verwendbar.
+ Das Befehlsschema lautet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+oldstylenums{Ziffer}
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+oldstylenums{0123456789
+\series default
+ ergibt:
+\begin_inset Formula $\oldstylenums{0123456789}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Sonstige Sonderzeichen
+\begin_inset LatexCommand label
+name "sub:Sonstige-Sonderzeichen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Sonderzeichen ! sonstige"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Folgende Zeichen können in eine Formel nur mit Befehlen eingegeben werden:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\mathcircumflex$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+_
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\_$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\backslash
+circ
+\begin_inset LatexCommand index
+name "°"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $^{\circ}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Das Gradzeichen ° kann dennoch direkt eingegeben werden, wenn der LaTeX-Vorspann
+ folgende Zeile enthält
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Mehr dazu ist in
+\begin_inset LatexCommand ref
+reference "sub:Textzeichen-in-Formeln"
+
+\end_inset
+
+ beschrieben.
+\end_layout
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputText{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Die Tilde
+\begin_inset LatexCommand index
+name "Tilde"
+
+\end_inset
+
+ ist nur für Akzente gedacht, weswegen sie alleine deplatziert wirkt: ~
+\newline
+Aber
+ für Webadressen (URLs) wird manchmal eine einzelne Tilde benötigt.
+ Man verwendet in diesem Fall das Relationszeichen
+\series bold
+
+\backslash
+sim
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset LatexCommand ref
+reference "sec:Relationen"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ in einer Formel.
+ Da in einer URL-Box (Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+URL
+\family default
+) keine Formel erstellt werden kann, gibt man die URL als normalen Text
+ in der Stilart '
+\family typewriter
+Schreibmaschine
+\family default
+' ein.
+ Soll die URL in der DVI- oder PDF-Ausgabe einen Link produzieren, verwendet
+ man den Befehl
+\series bold
+
+\backslash
+href
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+href
+\series default
+ kann nur zusammen mit dem LaTeX-Paket
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! hyperref"
+
+\end_inset
+
+ verwendet werden.
+ Mehr zu
+\series bold
+
+\backslash
+href
+\series default
+ steht im Kapitel
+\family typewriter
+URL
+\family default
+ im Handbuch
+\family typewriter
+Eingebettete\InsetSpace ~
+Objekte
+\family default
+.
+\end_layout
+
+\end_inset
+
+.
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash href"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Als Beispiel eine URL mit einer Tilde:
+\end_layout
+
+\begin_layout Standard
+als Text:
+\family typewriter
+http://www.lyx.org/
+\begin_inset Formula $\sim$
+\end_inset
+
+mustermann
+\end_layout
+
+\begin_layout Standard
+mit
+\series bold
+
+\backslash
+href
+\series default
+:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://www.lyx.org/~mustermann}{
+\end_layout
+
+\end_inset
+
+http://www.lyx.org/
+\begin_inset Formula $\sim$
+\end_inset
+
+mustermann
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formelstile
+\begin_inset LatexCommand label
+name "sec:Formelstile"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! Stile"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Für abgesetzte Formeln gibt es zwei verschiedene Anordnungsstile:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Zentriert ist der voreingestellte Standard
+\end_layout
+
+\begin_layout Description
+Eingerückt dazu muss im Menü
+\family sans
+Dokument\SpecialChar \menuseparator
+Einstellungen
+\family default
+ unter
+\family sans
+Dokumentklasse
+\family default
+ die Option
+\series bold
+fleqn
+\series default
+ eingeben werden
+\end_layout
+
+\begin_layout Standard
+Wird
+\series bold
+Eingerückt
+\series default
+ verwendet, kann mit der Länge
+\series bold
+
+\backslash
+mathindent
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mathindent"
+
+\end_inset
+
+ die Einrückung eingestellt werden.
+ Soll der Abstand 15\InsetSpace \thinspace{}
+mm betragen, gibt man im LaTeX-Vorspann die Zeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+mathindent}{15mm}
+\end_layout
+
+\begin_layout Standard
+ein.
+ Wenn keine Länge vorgegeben wird, wird der voreingestellte Wert von 30\InsetSpace \thinspace{}
+pt
+ verwendet.
+\end_layout
+
+\end_deeper
+\begin_layout Itemize
+Und zwei verschiedene Nummerierungsstile:
+\end_layout
+
+\begin_deeper
+\begin_layout Description
+Rechts ist der voreingestellte Standard
+\end_layout
+
+\begin_layout Description
+Links dazu muss im Menü
+\family sans
+Dokument\SpecialChar \menuseparator
+Einstellungen
+\family default
+ unter
+\family sans
+Dokumentklasse
+\family default
+ die Option
+\series bold
+leqno
+\series default
+ eingeben werden
+\end_layout
+
+\end_deeper
+\begin_layout Standard
+
+\series bold
+fleqn
+\series default
+ und
+\series bold
+leqno
+\series default
+ können auch gemeinsam verwendet werden.
+ Dazu werden beide Optionen, durch ein Komma getrennt, hintereinander geschriebe
+n.
+\end_layout
+
+\begin_layout Standard
+Die eingestellten Stile gelten für alle abgesetzten Formeln eines Dokuments.
+ Möchte man jedoch in einem Dokument sowohl zentrierte als auch eingerückte
+ ausgerichtete Formeln setzen, verwendet man den Stil
+\series bold
+Zentriert
+\series default
+.
+ Die einzurückenden Formeln setzt man dann in eine flalign-Umgebung, siehe
+
+\begin_inset LatexCommand ref
+reference "sub:Flalign-Umgebung"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Mehrzeilige Formeln
+\begin_inset LatexCommand label
+name "sec:Mehrzeilige-Formeln"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Allgemeines
+\end_layout
+
+\begin_layout Standard
+In LyX werden mehrzeilige Formeln erstellt, wenn man in einer Formel
+\family sans
+\series bold
+Strg-Enter
+\family default
+\series default
+ drückt.
+ Dies erzeugt eine
+\series bold
+align-Umgebung
+\series default
+, die in
+\begin_inset LatexCommand ref
+reference "sub:Standard-align-Umgebung"
+
+\end_inset
+
+ beschrieben ist.
+\end_layout
+
+\begin_layout Standard
+Es gibt noch weitere mehrzeilige Formelumgebungen, die über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe
+\family default
+ erstellt werden können.
+ Diese Umgebungen werden in den folgenden Kapiteln beschrieben.
+\end_layout
+
+\begin_layout Standard
+In allen mehrzeiligen Formelumgebungen erstellt man eine neue Zeile, indem
+ man
+\family sans
+Strg-Enter
+\family default
+ drückt.
+ Um Spalten hinzuzufügen oder zu entfernen, können die Mathe-Werkzeugleistenknöp
+fe
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-row.png
+ scale 85
+
+\end_inset
+
+ bzw.\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/tabular-feature_delete-row.png
+ scale 85
+
+\end_inset
+
+ oder das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Zeilen & Spalten
+\family default
+ verwendet werden.
+\end_layout
+
+\begin_layout Subsubsection
+Zeilenabstand
+\begin_inset LatexCommand label
+name "sub:Zeilenabstand"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Zeilenabstand"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Bei mehrzeiligen Formeln fehlt manchmal etwas Platz zwischen den Zeilen:
+\begin_inset Formula \begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In LaTeX wird zusätzlicher Zeilenabstand als optionales Argument des Zeilenumbru
+chbefehls angegeben.
+ Dies ist in LyX aber nicht möglich
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1505
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, weshalb man die ganze Formel im TeX-Modus eingeben muss.
+ Um für unser Beispiel Leerraum einzufügen, gibt man am Ende der ersten
+ Zeile den Befehl
+\series bold
+
+\backslash
+
+\backslash
+[3mm]
+\series default
+ ein.
+ Damit erhält man:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{eqnarray*}
+\end_layout
+
+\begin_layout Standard
+
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
+ = &
+\backslash
+textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
+\backslash
+
+\backslash
+[3mm]
+\end_layout
+
+\begin_layout Standard
+
+4x^{2}
+\backslash
+left(B^{2}+x_{0}^{2}
+\backslash
+right)+4x_{0}x
+\backslash
+left(D-B^{2}
+\backslash
+right)+B^{2}
+\backslash
+left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
+\backslash
+right) & = & 0
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+end{eqnarray*}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Möchte man den Zeilenabstand für alle Zeilen einer Formel festlegen, verändert
+ man die Länge
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! J ! \\textbackslash jot"
+
+\end_inset
+
+.
+ Es gilt
+\begin_inset Formula $\mbox{Zeilenabstand}=\mathrm{6\, pt+\backslash jot}$
+\end_inset
+
+.
+ Voreingestellt ist für
+\series bold
+
+\backslash
+jot
+\series default
+ der Wert 3\InsetSpace \thinspace{}
+pt.
+ Um wie im vorigen Beispiel 3\InsetSpace \thinspace{}
+mm zusätzlichen Zeilenabstand zu erzeugen,
+ gibt man den Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\begin_layout Standard
+im TeX-Modus vor der Formel ein.
+ Das setzt voraus, dass das LaTeX-Paket
+\series bold
+calc
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+calc
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! calc"
+
+\end_inset
+
+ im LaTeX-Vorspann mit der Zeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{calc}
+\end_layout
+
+\begin_layout Standard
+geladen wurde.
+\end_layout
+
+\begin_layout Standard
+Man erhält:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3mm+3pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+jot}{3pt}
+\end_layout
+
+\end_inset
+
+ Um wieder zum voreingestellten Abstand zu wechseln, setzt man
+\series bold
+
+\backslash
+jot
+\series default
+ auf den Wert 3\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Subsubsection
+Spaltenabstand
+\begin_inset LatexCommand label
+name "sub:Spaltenabstand"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Spaltenabstand"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Mehrzeilige Formeln bilden eine Matrix.
+ Eine Formel in der Eqnarray-Umgebung ist z.\InsetSpace \thinspace{}
+B.
+ eine dreispaltige Matrix.
+ Durch Änderung des Spaltenabstands in dieser Umgebung, kann man den Leerraum
+ neben den Relationszeichen ändern.
+\end_layout
+
+\begin_layout Standard
+Der Spaltenabstand wird mit der Länge
+\series bold
+
+\backslash
+arraycolsep
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash arraycolsep"
+
+\end_inset
+
+ festgelegt, wobei gilt:
+\newline
+Spaltenabstand = 2\InsetSpace \thinspace{}
+
+\series bold
+
+\backslash
+arraycolsep
+\series default
+.
+\newline
+Der im TeX-Modus eingegebene Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\begin_layout Standard
+bewirkt also für alle folgenden Formeln einen Spaltenabstand von 2\InsetSpace \thinspace{}
+cm.
+ Um wieder zum voreingestellten Abstand zurückzukehren, setzt man
+\series bold
+
+\backslash
+arraycolsep
+\series default
+ auf 5\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Standard
+Eine Formel mit 2\InsetSpace \thinspace{}
+cm Spaltenabstand:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{1cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+A & = & B\\
+C & \ne & A\end{eqnarray*}
+
+\end_inset
+
+Eine Formel mit dem für Matrizen voreingestellten Spaltenabstand von 10\InsetSpace \thinspace{}
+pt:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+arraycolsep}{5pt}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray*}
+A & = & B\\
+C & \ne & A\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Lange Formeln
+\begin_inset LatexCommand index
+name "Formel ! lange"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Lange Formeln kann man wie folgt setzen:
+\end_layout
+
+\begin_layout Itemize
+Ist eine Seite der Gleichung deutlich kürzer als die Zeilenbreite, wählt
+ man man diese als linke Seite und schreibt die rechte über zwei Zeilen:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
+ & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+smallskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Das Minuszeichen zu Beginn der zweiten Zeile erscheint eigentlich nicht
+ als Operator, da es das erste Zeichen der Zeile ist.
+ Deswegen wäre es nicht von Leerraum umgeben und ließe sich schlecht vom
+ Bruchstrich unterscheiden.
+ Um das zu verhindern, wurde mit dem Befehl
+\series bold
+
+\backslash
+hspace{3pt}
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+mehr zu
+\series bold
+
+\backslash
+hspace
+\series default
+ siehe
+\begin_inset LatexCommand ref
+reference "sub:Variabler-Leerraum"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Befehle ! H ! \\textbackslash hspace"
+
+\end_inset
+
+ Leerraum hinter das Minuszeichen eingefügt.
+\end_layout
+
+\begin_layout Itemize
+Sind beide Seiten der Gleichung zu lang, verwendet man den Befehl
+\series bold
+
+\backslash
+lefteqn
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash lefteqn"
+
+\end_inset
+
+.
+ Dieser wird in die erste Spalte der ersten Zeile eingegeben und bewirkt,
+ dass alle weiteren Eingaben die folgenden Spalten überschreiben:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
+ & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
+ & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+smallskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Nachdem man
+\series bold
+
+\backslash
+lefteqn
+\series default
+ eingegeben hat, befindet sich der Cursor in einem pinkfarbenen Kästchen,
+ das gegenüber dem blauen leicht verschoben ist.
+ In dieses wird die Formel eingegeben.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Der Inhalt der weiteren Zeilen wird in die zweite oder eine andere Formelspalte
+ eingegeben.
+ Je größer die Spaltennummer in die eingegeben wurde, desto größer ist die
+ Einrückung.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Bei der Verwendung von
+\series bold
+
+\backslash
+lefteqn
+\series default
+ ist Folgendes zu beachten:
+\end_layout
+
+\begin_layout Itemize
+Die Formel nutzt nicht die gesamte Seitenbreite aus.
+ Würde man in obigem Beispiel der ersten Zeile den Term
+\begin_inset Formula $-B^{2}$
+\end_inset
+
+ anfügen, befände sich dieser außerhalb des Seitenrands.
+ Um die Breite besser auszunutzen, kann man zu Beginn der ersten Zeile negativen
+ Leerraum einfügen.
+\end_layout
+
+\begin_layout Itemize
+Aufgrund eines Fehlers in LyX kann der Cursor nicht mit der Maus in die
+ erste Zeile gesetzt werden.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #1429
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ Man kann den Cursor nur an den Anfang der Zeile setzen und ihn mit den
+ Pfeiltasten bewegen.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Weitere Möglichkeiten lange Formeln zu setzen, bieten die in
+\begin_inset LatexCommand ref
+reference "sub:Multline-Umgebung"
+
+\end_inset
+
+ und
+\begin_inset LatexCommand ref
+reference "sub:Mehrzeilige-Formelteile"
+
+\end_inset
+
+ beschriebenen Umgebungen.
+\end_layout
+
+\begin_layout Subsubsection
+Mehrzeilige Klammern
+\begin_inset LatexCommand label
+name "sub:Mehrzeilige-Klammern"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Klammern ! mehrzeilige"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Bei Klammern, die über mehrere Zeilen gehen, tritt folgendes Problem auf:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\cdots+B-D\right]\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die schließende Klammer ist kleiner als die öffnende, denn Klammern variabler
+ Größe dürfen nicht über mehrere Zeilen gehen.
+\end_layout
+
+\begin_layout Standard
+Um die Größe für die Klammer der zweiten Zeile anzupassen, beendet man die
+ erste Zeile mit
+\series bold
+
+\backslash
+right.
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash right"
+
+\end_inset
+
+ und beginnt die zweite Zeile mit
+\series bold
+
+\backslash
+left.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+mehr zu
+\series bold
+
+\backslash
+left
+\series default
+ und
+\series bold
+
+\backslash
+right
+\series default
+ siehe
+\begin_inset LatexCommand ref
+reference "sub:Automatische-Klammergrößen"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! L ! \\textbackslash left"
+
+\end_inset
+
+.
+ Nach
+\series bold
+
+\backslash
+left.
+
+\series default
+ gibt man den Befehl
+\series bold
+
+\backslash
+vphantom
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+prod
+\series default
+^
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+infty
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\begin_inset Formula $\downarrow$
+\end_inset
+
+_R=1}
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! V ! \\textbackslash vphantom"
+
+\end_inset
+
+ ein, denn der Multiplikationsoperator mit seinen Grenzen ist das größte
+ Symbol der ersten Zeile, und daran soll die zweite Klammer angepasst werden.
+\end_layout
+
+\begin_layout Standard
+Das Ergebnis sieht so aus:
+\begin_inset Formula \begin{eqnarray*}
+A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
+ & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Align-Umgebungen
+\end_layout
+
+\begin_layout Standard
+Align-Umgebungen können für jede Art von mehrzeiligen Formeln verwendet
+ werden.
+ Sie sind besonders geeignet um mehrere Formeln nebeneinander zu setzen.
+\end_layout
+
+\begin_layout Standard
+Align-Umgebungen bestehen aus Spalten.
+ Die ungeradzahligen Spalten sind rechts-, die geradzahligen linksbündig
+ ausgerichtet.
+ Jede Zeile einer Align-Umgebung kann nummeriert werden.
+\end_layout
+
+\begin_layout Standard
+Align-Umgebung werden über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe
+\family default
+ erstellt.
+ Über das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Formelart\InsetSpace ~
+ändern
+\family default
+ können bereits existierende Formeln in Align-Umgebungen umgewandelt werden.
+\end_layout
+
+\begin_layout Standard
+Um Spalten hinzuzufügen oder zu entfernen, können die Mathe-Werkzeugleistenknöpf
+e
+\begin_inset Graphics
+ filename ../../images/tabular-feature_append-column.png
+ scale 85
+
+\end_inset
+
+ bzw.\InsetSpace ~
+
+\begin_inset Graphics
+ filename ../../images/tabular-feature_delete-column.png
+ scale 85
+
+\end_inset
+
+ oder das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Zeilen & Spalten
+\family default
+ verwendet werden.
+\end_layout
+
+\begin_layout Subsubsection
+Standard align-Umgebung
+\begin_inset LatexCommand label
+name "sub:Standard-align-Umgebung"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! align-Umgebung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Diese Align-Umgebung wird erstellt, indem man in einer Formel
+\family sans
+Strg-Enter
+\family default
+ drückt oder das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+AMS align-Umge\SpecialChar \-
+bung
+\family default
+ aufruft.
+\end_layout
+
+\begin_layout Standard
+Ein Beispiel für zwei nebeneinander stehende Formeln, die mit einer vierspaltige
+n align-Umgebung erzeugt wurden:
+\begin_inset Formula \begin{align*}
+A & =\sin(B) & C & =D\\
+C & \ne A & B & \ne D\end{align*}
+
+\end_inset
+
+Wie man sieht, werden die Formeln in dieser Umgebung so angeordnet, als
+ würde sich vor der ersten und hinter jeder geraden Spalte ein
+\series bold
+
+\backslash
+hfill
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+mehr zu
+\series bold
+
+\backslash
+hfill
+\series default
+ siehe
+\begin_inset LatexCommand ref
+reference "sub:Variabler-Leerraum"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ befinden.
+ Ist der Formelstil
+\series bold
+Eingerückt
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Formelstile siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ gewählt, wird die Formel ohne den
+\series bold
+
+\backslash
+hfill
+\series default
+ vor der ersten Spalte gesetzt.
+\end_layout
+
+\begin_layout Subsubsection
+Alignat-Umgebung
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! alignat-Umgebung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In der alignat-Umgebung gibt es keinen vordefinierten Spaltenabstand.
+ Man kann ihn manuell durch die in
+\begin_inset LatexCommand ref
+reference "sub:Leerraum"
+
+\end_inset
+
+ beschriebenen Leerräume einfügen.
+\end_layout
+
+\begin_layout Standard
+Das vorige Beispiel in der alignat-Umgebung, bei dem zu Beginn der zweiten
+ Formel 1\InsetSpace \thinspace{}
+cm Leerraum eingefügt wurde:
+\begin_inset Formula \begin{alignat*}{2}
+A & =\sin(B) & \hspace{1cm}C & =D\\
+C & \ne A & B & \ne D\end{alignat*}
+
+\end_inset
+
+Weil man den Spaltenabstand für jede Spalte einzeln einstellen kann, eignet
+ sich diese Umgebung besonders für drei und mehr nebeneinander gesetzte
+ Formeln.
+\end_layout
+
+\begin_layout Subsubsection
+Flalign-Umgebung
+\begin_inset LatexCommand label
+name "sub:Flalign-Umgebung"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! flalign-Umgebung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Bei dieser Umgebung werden die ersten beiden Spalten immer so weit links
+ und die letzten beiden Spalten so weit rechts wie möglich gesetzt.
+ Dazu ein Beispiel:
+\begin_inset Formula \begin{flalign*}
+A & =1 & B & =2 & C & =3\\
+X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Erzeugt man eine flalign-Umgebung mit ungerader Spaltenanzahl und gibt in
+ die letzte Spalte eine leere TeX-Klammer ein, kann man einzelne Formeln
+ im Dokument links setzen obwohl der Formelstil
+\series bold
+Zentriert
+\series default
+ eingestellt ist.
+ Als Beispiel die eingerückte ausgerichtete Formel
+\begin_inset LatexCommand eqref
+reference "eq:VolInt"
+
+\end_inset
+
+:
+\begin_inset Formula \begin{flalign}
+\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
+
+\end_inset
+
+In den ersten beiden Spalten befindet sich die Formel.
+ Damit sie wie beim Formelstil
+\series bold
+Eingerückt
+\series default
+ vom Rand etwas abgesetzt ist, wurde zu Beginn der ersten Spalte 30\InsetSpace \thinspace{}
+pt Leerraum
+ eingefügt.
+\end_layout
+
+\begin_layout Subsection
+Eqnarray-Umgebung
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Eqnarray-Umgebung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Hat man diese Umgebung erzeugt, erscheinen drei blaue Kästchen.
+ Der Inhalt des ersten Kästchens wird rechtsbündig, der des letzten linksbündig
+ ausgerichtet.
+ Der Inhalt des mittleren Kästchens erscheint zentriert und etwas kleiner,
+ da dieses Kästchen nur für Relationzeichen gedacht ist.
+\begin_inset Formula \begin{eqnarray*}
+\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
+AB & AB & AB\\
+A & = & A\end{eqnarray*}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Gather-Umgebung
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Gather-Umgebung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Diese Umgebung besteht nur aus einer Spalte, deren Inhalt zentriert ist.
+ Jede Zeile kann nummeriert werden.
+\begin_inset Formula \begin{gather}
+A=1\\
+X=\textrm{-}1\end{gather}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Multline-Umgebung
+\begin_inset LatexCommand label
+name "sub:Multline-Umgebung"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Multline-Umgebung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die multline-Umgebung besteht wie die Gather-Umgebung nur aus einer Spalte.
+ Jedoch ist die erste Zeile links, die letzte rechts ausgerichtet.
+ Alle anderen Zeilen sind zentriert.
+ Dadurch eignet sich diese Umgebung besonders für lange Formeln.
+ Als Beispiel Formel
+\begin_inset LatexCommand eqref
+reference "eq:lefteqn"
+
+\end_inset
+
+ in der multline-Umgebung:
+\begin_inset Formula \begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In der Ausgabe erscheint nur die letzte (erste) Zeile einer multline-Umgebung
+ nummeriert, wenn rechts (links) nummeriert wird.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Nummerierungsstile siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ Dies gilt auch wenn in LyX hinter jeder Zeile eine Formelnummer angezeigt
+ wird.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Dies ist
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #518
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Mit den Befehlen
+\series bold
+
+\backslash
+shoveright
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash shoveright"
+
+\end_inset
+
+
+\series default
+ und
+\series bold
+
+\backslash
+shoveleft
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash shoveleft"
+
+\end_inset
+
+
+\series default
+ kann eine zentrierte Zeile rechts bzw.
+ links ausgerichtet werden.
+ Die Befehle werden folgendermaßen verwendet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+shoveright{Zeileninhalt}
+\series default
+ bzw.
+
+\series bold
+
+\backslash
+shoveleft{Zeileninhalt}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Die Länge
+\series bold
+
+\backslash
+multlinegap
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash multlinegap"
+
+\end_inset
+
+
+\series default
+ legt den Abstand der ersten Zeile vom linken Seitenrand fest.
+ Voreingestellt ist die Länge 0\InsetSpace \thinspace{}
+pt.
+\end_layout
+
+\begin_layout Standard
+Als Beispiel obige Formel, vor der im TeX-Modus der Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\begin_layout Standard
+eingegeben wurde:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{2cm}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{multline}
+4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
+\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
+=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+setlength{
+\backslash
+multlinegap}{0pt}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die zweite Zeile wurde mit
+\series bold
+
+\backslash
+shoveleft
+\series default
+ linksbündig ausgerichtet.
+\end_layout
+
+\begin_layout Subsection
+Mehrzeilige Formelteile
+\begin_inset LatexCommand label
+name "sub:Mehrzeilige-Formelteile"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Formelteile"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man nur Teile einer Formel mehrzeilig darstellen, verwendet man eine
+ der folgenden Umgebungen:
+\series bold
+aligned
+\series default
+,
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+ oder
+\series bold
+split
+\series default
+.
+ Sie können über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe
+\family default
+ oder mit Befehlen eingefügt werden, wie in diesem Abschnitt beschrieben.
+\end_layout
+
+\begin_layout Standard
+Die ersten drei haben dieselben Eigenschaften wie die entsprechenden mehrzeilige
+n Formel\SpecialChar \-
+umgebungen.
+ Man kann jedoch zusätzlich weitere Formelteile daneben setzen.
+ Dazu ein Beispiel:
+\begin_inset Formula \[
+\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
+\Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
+\right\} \textrm{Unbestimmtheitsrelationen}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um diese Formel zu erhalten, wird eine abgesetzte Formel erstellt, in die
+ der Befehl
+\series bold
+
+\backslash
+aligned
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash aligned"
+
+\end_inset
+
+
+\series default
+ eingegeben wird.
+ Es erscheint eine lila Box um das blaue Formelkästchen in der man nun Spalten
+ und Zeilen hinzufügen kann.
+ Außerhalb der mehrzeiligen Umgebung können Formelteile, wie die Klammer,
+ gesetzt werden.
+\end_layout
+
+\begin_layout Standard
+Die aligned-Umgebung eignet sich auch für lange Formeln, deren Zeilen horizontal
+ ausgerichtet sind.
+ Verwendet man aligned in einer abgesetzten Formel, hat das den Vorteil,
+ dass die Formelnummer vertikal mittig hinter den Zeilen steht.
+ Als Beispiel Formel
+\begin_inset LatexCommand eqref
+reference "eq:kurzlang"
+
+\end_inset
+
+ in der aligned-Umgebung:
+\begin_inset Formula \begin{equation}
+\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
+ & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\end{aligned}
+\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man die Umgebung
+\series bold
+alignedat
+\series default
+,
+\series bold
+gathered
+\series default
+ oder
+\series bold
+split
+\series default
+ verwenden, gibt man den Befehl
+\series bold
+
+\backslash
+alignedat
+\series default
+,
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash alignedat"
+
+\end_inset
+
+
+\series bold
+
+\backslash
+gathered
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! G ! \\textbackslash gathered"
+
+\end_inset
+
+ bzw.
+
+\series bold
+
+\backslash
+split
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! S ! \\textbackslash split"
+
+\end_inset
+
+ ein.
+ Die split-Umgebung hat dieselben Eigenschaften wie die aligned-Umgebung,
+ jedoch darf sie nur zwei Spalten enthalten.
+\end_layout
+
+\begin_layout Subsection
+Text in mehrzeiligen Formeln
+\begin_inset LatexCommand label
+name "sub:Text-in-mehrzeiligen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Text ! in Formeln"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! mehrzeilige ! Text"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Bei den Align-Umgebungen sowie der multline- und gather-Umgebung besteht
+ die Möglichkeit Text einzufügen, der in einer eigenen Zeile erscheint und
+ die Ausrichtung der Spalten nicht beeinflusst.
+ Dazu wird der Befehl
+\series bold
+
+\backslash
+intertext
+\begin_inset LatexCommand index
+name "Befehle ! I ! \\textbackslash intertext"
+
+\end_inset
+
+
+\series default
+ nach folgendem Schema benutzt:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext{Text}
+\end_layout
+
+\begin_layout Standard
+Der Text sollte nicht länger als eine Zeile sein, da er nicht umgebrochen
+ werden kann.
+ Weil LyX
+\series bold
+
+\backslash
+intertext
+\series default
+ noch nicht direkt unterstützt, schreibt man den Text als mathematischen
+ Text.
+
+\series bold
+
+\backslash
+intertext
+\series default
+ muss dabei zu Beginn einer Zeile stehen und erscheint in der Ausgabe über
+ dieser Zeile.
+ Ein Beispiel bei dem der Text zu Beginn der zweiten Zeile eingegeben wurde:
+\begin_inset Formula \begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\intertext{\text{Integrand ist symmetrisch zu $\phi=\pi$, daher}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Formelnummerierung
+\begin_inset LatexCommand index
+name "Formelnummerierung"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! Nummerierung|see{Formelnummerierung}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Allgemeines
+\end_layout
+
+\begin_layout Standard
+Nummerierte Formeln können mit dem Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Nummerierte\InsetSpace ~
+Formel
+\family default
+ (Tastenkürzel
+\family sans
+Strg-Alt\InsetSpace ~
+n
+\family default
+) erstellt, bestehende Formeln über das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Nummerierung\InsetSpace ~
+an/aus
+\family default
+ (Tastenkürzel
+\family sans
+Alt-m\InsetSpace ~
+n
+\family default
+) nummeriert werden.
+ Die Formelnummer erscheint in LyX hinter der Formel als Raute in runden
+ Klammern.
+ Im Ausdruck erscheint anstelle der Raute die Formelnummer.
+\end_layout
+
+\begin_layout Standard
+Wird in mehrzeiligen Formeln die Nummerierung angeschaltet, werden alle
+ Zeilen nummeriert.
+ Man kann jedoch über das Menü
+\family sans
+Bearbeiten\SpecialChar \menuseparator
+Mathe\SpecialChar \menuseparator
+Zeilennummerierung an/aus
+\family default
+ (Tastenkürzel
+\family sans
+Alt-m\InsetSpace ~
+N
+\family default
+) für jede Zeile die Nummerierung festlegen.
+\end_layout
+
+\begin_layout Standard
+Außer eingebetteten können alle Formeln in zwei verschiedenen Stilen nummeriert
+ werden, siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Subsection
+Querverweise
+\begin_inset LatexCommand label
+name "sub:Querverweise"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Querverweise ! auf Formeln"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Es kann auf alle Formeln verwiesen werden, die eine Marke besitzen.
+ Eine Marke wird mit dem Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Marke
+\family default
+ oder dem Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/label-insert.png
+ scale 85
+
+\end_inset
+
+ gesetzt.
+ Dabei muss sich der Cursor in einer abgesetzten Formel befinden.
+ Es erscheint ein Eingabefeld mit dem voreingestellten Eintrag
+\series bold
+eq:
+\series default
+, nachdem der eigentliche Markenname eingegeben wird.
+ Der voreingestellte Eintrag steht für
+\begin_inset Quotes gld
+\end_inset
+
+equation
+\begin_inset Quotes grd
+\end_inset
+
+ und erleichtert bei größeren Dokumenten die Zuordnung, dass die Marke zu
+ einer Formel und nicht zu einem Kapitel gehört.
+ Um eine Marke zu ändern, wählt man wieder das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Marke
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+Der Name der Marke erscheint in LyX in zwei runden Klammern hinter der Formel.
+ Eine Formel mit Marke wird immer nummeriert.
+ Wird die Nummerierung abgeschaltet, wird die Marke gelöscht.
+ Dies ist momentan die einzige Möglichkeit eine Marke zu löschen, siehe
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
+\end_layout
+
+\end_inset
+
+LyX-Fehler #2556
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+Querverweise werden mit dem Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Querverweis
+\family default
+ oder dem Werkzeugleistenknopf
+\begin_inset Graphics
+ filename ../../images/dialog-show-new-inset_ref.png
+ scale 85
+
+\end_inset
+
+ eingefügt.
+ Ein Querverweis uaf Formeln erscheint im Ausdruck als Formelnummer.
+ Wenn man im Querverweis Dialogfenster das Format
+\series bold
+(<Querverweis>)
+\series default
+ wählt, erscheint der Querverweis als Formelnummer in Klammern.
+\newline
+Drückt man
+ in LyX mit der rechten Maustaste auf einen Querverweis, gelangt man zur
+ Formel auf die verwiesen wird.
+\end_layout
+
+\begin_layout Standard
+Als Beispiel folgen Querverweise zu Formeln aus diesem Kapitel:
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Man beachte die unterschiedlichen Querverweistypen.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die Gleichungen
+\begin_inset LatexCommand eqref
+reference "eq:tag"
+
+\end_inset
+
+ und
+\begin_inset LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ sind äquivalent.
+ In (
+\begin_inset LatexCommand ref
+reference "eq:Lat"
+
+\end_inset
+
+) werden im Gegensatz zu (
+\begin_inset LatexCommand ref
+reference "eq:Roem"
+
+\end_inset
+
+) große lateinische Buchstaben zur Nummerierung verwendet.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Ist im Argument von
+\series bold
+
+\backslash
+tag
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+tag
+\series default
+ ist in
+\begin_inset LatexCommand ref
+reference "sub:Benutzerdefinierte-Nummerierung"
+
+\end_inset
+
+ beschrieben.
+\end_layout
+
+\end_inset
+
+
+\series default
+ wie in
+\begin_inset LatexCommand ref
+reference "sub:Absatzboxen"
+
+\end_inset
+
+ eine Box angegeben, kann nicht auf die Formel verwiesen werden.
+\end_layout
+
+\begin_layout Subsection
+Unternummerierung
+\begin_inset LatexCommand index
+name "Formelnummerierung ! Unternummerierung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man Formeln weiter untergliedern, kann man das mit Hilfe der Befehle
+
+\newline
+
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+ und
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ erreichen.
+ Beide Befehle werden im TeX-Modus eingegeben.
+\end_layout
+
+\begin_layout Standard
+Dazu ein Beispiel:
+\begin_inset Formula \begin{equation}
+A=C-B\label{eq:a}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+addtocounter{equation}{-1}
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{subequations}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -5mm
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+B=C-A\label{eq:b}\end{equation}
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+C=A+B\label{eq:c}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{subequations}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um das Beispiel zu erstellen, geht man folgendermaßen vor:
+\end_layout
+
+\begin_layout Enumerate
+erste Formel eingeben
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+
+\backslash
+addtocounter{equation}{-1}
+\backslash
+begin{subequations}
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash addtocounter"
+
+\end_inset
+
+
+\newline
+
+\series default
+nach der ersten Formel einfügen
+\end_layout
+
+\begin_layout Enumerate
+zweite Formel eingeben
+\end_layout
+
+\begin_layout Enumerate
+dritte Formel eingeben
+\end_layout
+
+\begin_layout Enumerate
+
+\series bold
+
+\backslash
+end{subequations}
+\series default
+ nach der dritten Formel einfügen
+\end_layout
+
+\begin_layout Standard
+Jede Formel, die zwischen den Befehlen
+\series bold
+
+\backslash
+begin
+\series default
+ und
+\series bold
+
+\backslash
+end
+\series default
+ steht, wird mit a, b, c, \SpecialChar \ldots{}
+ untergliedert.
+ Bei mehrzeiligen Formeln wird jede Zeile untergliedert.
+ Alle untergliederten Formeln gelten als
+\emph on
+eine
+\emph default
+ nummerierte Formel.
+ Da jede nummerierte Formel den Formelzähler
+\series bold
+equation
+\series default
+ um Eins erhöht, ist der Befehl
+\series bold
+
+\backslash
+addtocounter
+\series default
+ notwendig um den Zähler wieder zu erniedrigen.
+ Ansonsten würden die Formeln
+\begin_inset LatexCommand eqref
+reference "eq:a"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:b"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:c"
+
+\end_inset
+
+ als
+\begin_inset LatexCommand eqref
+reference "eq:a"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:d"
+
+\end_inset
+
+,
+\begin_inset LatexCommand eqref
+reference "eq:f"
+
+\end_inset
+
+ nummeriert werden.
+\end_layout
+
+\begin_layout Standard
+Durch die Eingabe der Befehle im TeX-Modus wird zwischen den ersten beiden
+ Formeln automatisch etwas Leerraum erstellt.
+ Um dies rückgängig zu machen, fügt man nach dem Befehl
+\series bold
+
+\backslash
+begin{subequations}
+\series default
+ -5\InsetSpace \thinspace{}
+mm vertikalen Leerraum ein.
+ Ist der Formelstil
+\series bold
+Eingerückt
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Formelstile siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ gewählt, fügt man -7\InsetSpace \thinspace{}
+mm Leerraum ein.
+\end_layout
+
+\begin_layout Standard
+Hier ist ein Beispiel für mehrzeilige Formeln, bei dem die Nummerierung
+ der zweiten Zeile abgeschaltet wurde:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{subequations}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{eqnarray}
+A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
+ & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
+ & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{subequations}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Benutzerdefinierte Nummerierung
+\begin_inset LatexCommand label
+name "sub:Benutzerdefinierte-Nummerierung"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formelnummerierung ! benutzerdefinierte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset LatexCommand index
+name "Formelnummerierung ! eigene Klammern"
+
+\end_inset
+
+Bei der Standardnummerierung werden um die Formelnummern runde Klammern
+ gesetzt.
+ Will man diese Klammern z.\InsetSpace \thinspace{}
+B.
+ durch senkrechte Striche ersetzen, gibt man im LaTeX-Vorspann Folgendes
+ an:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+def
+\backslash
+tagform@#1{
+\backslash
+maketag@@@{|#1|}}
+\series default
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Dieses Makro ist zum Testen bereits im LaTeX-Vorspann angegeben.
+ Damit es wirksam wird, muss das Prozentzeichen am Zeilenbeginn entfernt
+ werden.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man andere Zeichen haben, ersetzt man die Striche neben
+\series bold
+#1
+\series default
+ durch ein oder mehrere gewünschte Zeichen.
+ Möchte man nur die Formelnummer haben, lässt man die Striche weg.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Soll statt einer fortlaufenden Nummer ein beliebiger Ausdruck in den Klammern
+ hinter der Formel stehen, benutzt man den Befehl
+\series bold
+
+\backslash
+tag{Ausdruck}
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash tag"
+
+\end_inset
+
+:
+\begin_inset Formula \begin{equation}
+A+B=C\tag{etwas}\label{eq:tag}\end{equation}
+
+\end_inset
+
+ In diesem Beispiel wurde in der Formel der Befehl
+\series bold
+
+\backslash
+tag
+\backslash
+{etwas
+\series default
+ eingegeben.
+\end_layout
+
+\begin_layout Standard
+Gibt man stattdessen
+\series bold
+
+\backslash
+tag*
+\backslash
+{etwas
+\series default
+ ein, verhindert der Stern die Klammern um den Ausdruck:
+\begin_inset Formula \[
+A+B=C\tag*{etwas}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Möchte man die Formelnummerierung neu starten wenn ein neuer Dokumentteil
+ oder
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+mbox{
+\end_layout
+
+\end_inset
+
+-abschnitt
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+mbox
+\series default
+ verhindert, dass am Bindestrich umgebrochen wird.
+ Mehr zu
+\series bold
+
+\backslash
+mbox
+\series default
+ siehe Kap.\InsetSpace \thinspace{}
+
+\begin_inset LatexCommand ref
+reference "sub:Worttrennungen"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ beginnt, verwendet man folgende LaTeX-Vorspannzeile:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+@addtoreset{equation}{part}
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! \"@\" ! \\textbackslash \"@\"addtoreset"
+
+\end_inset
+
+
+\newline
+bzw.
+\newline
+
+\series bold
+
+\backslash
+@addtoreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+Um diese Befehle im TeX-Modus benutzen zu können, muss das
+\begin_inset Quotes gld
+\end_inset
+
+@
+\begin_inset Quotes grd
+\end_inset
+
+ Zeichen für LaTeX mit dem Befehl
+\series bold
+
+\backslash
+makeatletter
+\series default
+
+\begin_inset Quotes gld
+\end_inset
+
+aktiv
+\begin_inset Quotes grd
+\end_inset
+
+ gemacht werden.
+ Der Befehl
+\series bold
+
+\backslash
+makeatother
+\series default
+ macht dies wieder rückgängig.
+ Daher ist die Befehlssequenz im TeX-Modus:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+makeatletter
+\newline
+
+\backslash
+@addtoreset{equation}{section}
+\newline
+
+\backslash
+makeatother
+\end_layout
+
+\begin_layout Standard
+Im LaTeX-Vorspann können
+\series bold
+
+\backslash
+makeatletter
+\series default
+ und
+\series bold
+
+\backslash
+makeatother
+\series default
+ weggelassen werden, da LyX sie automatisch intern einfügt.
+\end_layout
+
+\begin_layout Standard
+Um
+\series bold
+
+\backslash
+@addtoreset
+\series default
+ rückgängig zu machen, muss die Datei
+\series bold
+remreset.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+remreset
+\series default
+ ist Teil des LaTeX-Paketes
+\series bold
+carlisle
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! carlisle"
+
+\end_inset
+
+, das Teil jeder LaTeX-Standardinstallation ist.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! remreset"
+
+\end_inset
+
+ im LaTeX-Vorspann mit der Zeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{remreset}
+\end_layout
+
+\begin_layout Standard
+geladen werden.
+ Dann kann der Befehl
+\series bold
+
+\backslash
+@removefromreset
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! \"@\" ! \\textbackslash \"@\"removefromreset"
+
+\end_inset
+
+ mit dem selben Schema wie
+\series bold
+
+\backslash
+@addtoreset
+\series default
+ benutzt werden.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+Oftmals möchte man Formeln in folgender Art nummerieren:
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+(Kapitelnummer.Formelnummer)
+\end_layout
+
+\begin_layout Standard
+Dabei soll die Formelnummer bei jedem Kapitel wieder mit Eins beginnen.
+\end_layout
+
+\begin_layout Standard
+Für diesen Fall gibt es den Befehl
+\series bold
+
+\backslash
+numberwithin
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! N ! \\textbackslash numberwithin"
+
+\end_inset
+
+, der nach folgendem Schema benutzt wird:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{Zähler}{Gliederung}
+\end_layout
+
+\begin_layout Standard
+Zähler gibt an, welche Nummerierung betroffen ist.
+ Gliederung gibt an, welche Nummer vor dem Punkt steht.
+\end_layout
+
+\begin_layout Standard
+In unserem Fall gibt man demnach folgende LaTeX-Vorspann- oder ERT-zeile
+ ein:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\begin_layout Standard
+Das ist das Ergebnis:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+numberwithin{equation}{section}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+A+B=C\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man z.\InsetSpace \thinspace{}
+B.
+ Tabellen nummerieren, so dass die Nummer des Teils vor dem Punkt steht,
+ gibt man
+\series bold
+
+\backslash
+numberwithin{table}{part}
+\series default
+ ein.
+\end_layout
+
+\begin_layout Standard
+Um wieder auf Standardnummerierung umzuschalten oder um diese Art der Nummerieru
+ng zu vermeiden wenn sie von der Dokumentklasse vorgegeben ist, gibt man
+ folgenden Befehl als ERT oder als LaTeX-Vorspannzeile ein:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash arabic"
+
+\end_inset
+
+
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+bzw.
+\series bold
+
+\newline
+
+\backslash
+renewcommand{
+\backslash
+thetable}{
+\backslash
+arabic{table}}
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+numberwithin
+\series default
+ benutzt intern den oben beschriebenen Befehl
+\series bold
+
+\backslash
+@addtoreset
+\series default
+, der ebenfalls rückgängig gemacht werden muss.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+makeatletter
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+@removefromreset{equation}{section}
+\end_layout
+
+\begin_layout Standard
+
+
+\backslash
+makeatother
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Nummerierung mit römischen Zahlen und Buchstaben
+\begin_inset LatexCommand label
+name "sub:Nummerierung-mit-römischen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formelnummerierung ! mit Buchstaben"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formelnummerierung ! mit römischen Zahlen"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formeln können auch mit römischen Zahlen und lateinischen Buchstaben nummeriert
+ werden.
+ Um z.\InsetSpace \thinspace{}
+B.
+ mit kleinen römischen Zahlen zu nummerieren, gibt man vor der Formel im
+ TeX-Modus den Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\begin_layout Standard
+ein.
+
+\series bold
+
+\backslash
+renewcommand
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash renewcommand"
+
+\end_inset
+
+ weist dem vordefinierten Befehl
+\series bold
+
+\backslash
+theequation
+\series default
+ den Befehl
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+linebreak
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\backslash
+roman{equation}
+\series default
+ zu
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+renewcommand
+\series default
+ besitzt dasselbe Schema wie der in
+\begin_inset LatexCommand ref
+reference "sec:Benutzerdefinierte-Befehle"
+
+\end_inset
+
+ beschriebene Befehl
+\newline
+
+\series bold
+
+\backslash
+newcommand
+\series default
+.
+\end_layout
+
+\end_inset
+
+.
+
+\series bold
+equation
+\series default
+ ist der Formelzähler.
+ Stellt man einem Zähler den Befehl
+\series bold
+
+\backslash
+the
+\series default
+ voran, bewirkt dies, dass der Wert des Zählers als arabische Zahl ausgegeben
+ wird.
+ Gibt man an, dass eine Formel nummeriert wird, setzt LaTeX intern den Befehl
+
+\series bold
+
+\backslash
+theequation
+\series default
+ hinter die Formel.
+
+\series bold
+
+\backslash
+roman{equation}
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash roman"
+
+\end_inset
+
+
+\series default
+ bewirkt, dass der Formelzähler als kleine römische Zahl erscheint.
+\end_layout
+
+\begin_layout Standard
+Alle Formeln nach dem
+\series bold
+
+\backslash
+renewcommand
+\series default
+-Befehl werden nun römisch nummeriert.
+ Um auf Nummerierung mit großen römischen Zahlen umzuschalten, gibt man
+ den Befehl erneut ein, ersetzt aber
+\series bold
+
+\backslash
+roman
+\series default
+ durch
+\series bold
+
+\backslash
+Roman
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! R ! \\textbackslash roman@\\textbackslash Roman"
+
+\end_inset
+
+.
+ Für die
+\begin_inset Quotes gld
+\end_inset
+
+Nummerierung
+\begin_inset Quotes grd
+\end_inset
+
+ mit lateinischen Buchstaben gibt es den Befehl
+\series bold
+
+\backslash
+alph
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash alph"
+
+\end_inset
+
+ für kleine und
+\series bold
+
+\backslash
+Alph
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash alph@\\textbackslash Alph"
+
+\end_inset
+
+ für große Buchstaben.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Achtung:
+\series default
+ Es können nur maximal 26 Formeln in einem Dokument mit lateinischen Buchstaben
+ nummeriert werden.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+A=\textrm{römisch}\label{eq:roem}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Roman{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+B=\textrm{Römisch}\label{eq:Roem}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+C=\textrm{lateinisch}\label{eq:lat}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+Alph{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+D=\textrm{Lateinisch}\label{eq:Lat}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um wieder auf Standardnummerierung umzuschalten, gibt man folgenden Befehl
+ ein:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\begin_inset LatexCommand index
+name "Befehle ! A ! \\textbackslash arabic"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+renewcommand{
+\backslash
+theequation}{
+\backslash
+arabic{equation}}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+E=\textrm{arabisch}\label{eq:arab}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Wie man sieht, werden die Formeln unabhängig von der Nummerierungsart durchnumme
+riert.
+ Soll beim Wechsel der Nummerierungsart die Nummerierung wieder mit Eins
+ beginnen, müssen neue Formelzähler angelegt werden.
+ Eine Beschreibung dazu findet man in der Datei
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{Formelnummerierung.pdf}{
+\end_layout
+
+\end_inset
+
+Formelnummerierung.pdf
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+.
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Mehr zum Befehl
+\series bold
+
+\backslash
+href
+\series default
+, siehe Kapitel
+\begin_inset LatexCommand ref
+reference "sub:Links-in-DVI-"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Benutzerdefinierte Befehle
+\begin_inset LatexCommand label
+name "sec:Benutzerdefinierte-Befehle"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "benutzerdefinierte Befehle"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Viele der LaTeX-Befehle sind für den ständigen Gebrauch viel zu lang.
+ Man kann sich aber mit dem Befehl
+\series bold
+
+\backslash
+newcommand
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! N ! \\textbackslash newcommand"
+
+\end_inset
+
+ neue kürzere Befehle definieren.
+\end_layout
+
+\begin_layout Standard
+Das Befehlsschema von
+\series bold
+
+\backslash
+newcommand
+\series default
+ lautet:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{neuer Befehlsname}[Argumentanzahl][optionaler
+\series default
+
+\series bold
+Wert]
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+phantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+newcommand
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+{Befehlsdefinition}
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Achtung:
+\series default
+ Es muss darauf geachtet werden, dass der Befehlsname nicht schon im Dokument
+ oder von benutzten LaTeX-Paketen verwendet wird.
+ Definiert man beispielsweise für
+\series bold
+
+\backslash
+Leftarrow
+\series default
+ den Befehl
+\series bold
+
+\backslash
+le
+\series default
+, erhält man eine Fehlermeldung, denn
+\series bold
+
+\backslash
+le
+\series default
+ ist schon für
+\begin_inset Quotes gld
+\end_inset
+
+
+\begin_inset Formula $\le$
+\end_inset
+
+
+\begin_inset Quotes grd
+\end_inset
+
+ definiert.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+
+\series bold
+Achtung:
+\series default
+Die Namen von selbst definierten Befehlen dürfen nur aus lateinischen Buchstaben
+ bestehen.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die Argumentanzahl ist eine ganze Zahl im Bereich 0\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+9 und gibt an, wie viele
+ Argumente der neue Befehl haben soll.
+ Als optionalen Wert kann man den Wert für ein optionales Argument voreinstellen.
+ Wenn man dies macht, bedeutet das gleichzeitig, dass das
+\emph on
+erste
+\emph default
+ Argument des neuen Befehls ein optionales ist.
+\end_layout
+
+\begin_layout Standard
+Es folgen einige Beispiele:
+\end_layout
+
+\begin_layout Itemize
+Will man für
+\series bold
+
+\backslash
+Longrightarrow
+\series default
+ den Befehl
+\series bold
+
+\backslash
+gr
+\series default
+ definieren, lautet die LaTeX-Vor\SpecialChar \-
+spannzeile:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+gr}{
+\backslash
+Longrightarrow}
+\end_layout
+
+\begin_layout Itemize
+Um für den Befehl
+\series bold
+
+\backslash
+underline
+\series default
+ den Befehl
+\series bold
+
+\backslash
+us
+\series default
+ zu definieren, muss das Argument (was unterstrichen werden soll) berücksichtigt
+ werden.
+ Dazu sieht die Vorspannzeile wie folgt aus:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+us}[1]{
+\backslash
+underline{#1}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+Das Zeichen
+\series bold
+#
+\series default
+ fungiert als Argumentplatzhalter, die
+\series bold
+1
+\series default
+ dahinter gibt an, dass es der Platzhalter für das erste Argument ist.
+\end_layout
+
+\begin_layout Itemize
+Für
+\series bold
+
+\backslash
+framebox
+\series default
+ kann man z.\InsetSpace \thinspace{}
+B.
+ den Befehl
+\series bold
+
+\backslash
+fb
+\series default
+ definieren:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+fb}[3]{
+\backslash
+framebox#1#2{$#3$}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\series default
+Die beiden Dollarzeichen erstellen hierbei die für
+\series bold
+
+\backslash
+framebox
+\series default
+ geforderte weitere Formel, siehe
+\begin_inset LatexCommand ref
+reference "sub:Boxen-mit-Rahmen"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Um einen neuen Befehl für
+\series bold
+
+\backslash
+fcolorbox
+\series default
+ zu erstellen, bei dem die Farbe der Box nicht mehr angegeben werden muss,
+ definiert man das Argument für die Farbe als optional:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\series bold
+
+\newline
+
+\backslash
+newcommand{
+\backslash
+cb}[3][white]{
+\backslash
+fcolorbox{#2}{#1}{$#3$}}
+\series default
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+medskip
+\end_layout
+
+\end_inset
+
+
+\newline
+Gibt man bei der Verwendung von
+\series bold
+
+\backslash
+cb
+\series default
+ die Farbe nicht an, wird die voreingestellte Farbe
+\series bold
+white
+\series default
+ verwendet.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+pagebreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ein Test der neu definierten Befehle:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+A
+\backslash
+gr
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $A\gr B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+us{ABcd
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+fb{[2cm]
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cb{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cb[green]
+\backslash
+{red
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Diagramme
+\begin_inset LatexCommand index
+name "Diagramme"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um Diagramme zu erstellen, wird das LaTeX-Paket
+\series bold
+amscd
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+amscd
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! amscd"
+
+\end_inset
+
+ benötigt.
+ Es wird im LaTeX-Vorspann mit der Zeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{amscd}
+\end_layout
+
+\begin_layout Standard
+geladen.
+\end_layout
+
+\begin_layout Standard
+Diagramme stellen Beziehungen dar und sehen folgendermaßen aus:
+\begin_inset Formula \[
+\begin{CD}A@>>>B@>>>C\\
+@AAA@.@VVV\\
+F@<<<E@<<<D\end{CD}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um sie zu erstellen, gibt man in einer Formel den Befehl
+\series bold
+
+\backslash
+CD
+\begin_inset LatexCommand index
+name "Befehle ! C ! \\textbackslash CD"
+
+\end_inset
+
+
+\series default
+ ein.
+ Es erscheint ein blaues Kästchen mit zwei gestrichelten Linien, in das
+ man die weiteren Befehle eingibt.
+ Mit
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+mbox{
+\end_layout
+
+\end_inset
+
+
+\family sans
+\series default
+Strg-Enter
+\family default
+\series bold
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\series default
+ wird eine neue Zeile erstellt.
+ Horizontale Beziehungen werden in ungerade Zeilen, vertikale in gerade
+ Zeilen der Formel eingegeben.
+\end_layout
+
+\begin_layout Standard
+Zum Erstellen der Beziehungen gibt es folgende Befehle:
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@<<<
+\series default
+ erstellt einen Linkspfeil,
+\series bold
+@>>>
+\series default
+ einen Rechtspfeil und
+\series bold
+@=
+\series default
+ ein langes Gleichheitszeichen
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@AAA
+\series default
+ erstellt einen Pfeil nach oben,
+\series bold
+@VVV
+\series default
+ einen Pfeil nach unten und
+\series bold
+@|
+\series default
+ ein senkrechtes Gleichheitszeichen
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+@.
+
+\series default
+ dient als Platzhalter für nicht vorhandene Beziehungen
+\end_layout
+
+\begin_layout Standard
+Alle Pfeile sind wie folgt beschriftbar:
+\end_layout
+
+\begin_layout Itemize
+Wird bei horizontalen Pfeilen zwischen dem ersten und zweiten < bzw.
+ > Text eingegeben, erscheint er über dem Pfeil.
+ Wird der Text zwischen dem zweiten und dritten < bzw.
+ > eingegeben, erscheint er unter dem Pfeil.
+\end_layout
+
+\begin_layout Itemize
+Wird bei vertikalen Pfeilen Text zwischen erstem und zweitem A bzw.
+ V eingegeben, erscheint er links neben dem Pfeil.
+ Bei Eingabe zwischen zweitem und drittem A bzw.
+ V erscheint er rechts daneben.
+ Enthält der Text ein A oder V, müssen diese Buchstaben in eine TeX-Klammer
+ gesetzt werden.
+\end_layout
+
+\begin_layout Standard
+Als Beispiel ein Diagramm mit allen möglichen Beziehungen:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\begin{CD}A@>j>>B@>>k>C@=F\\
+@AmAA@.@VV{V}V@|\\
+D@<<j<E@>k>>F@=C\end{CD}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl dazu lautet:
+\newline
+
+\series bold
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A@>j>>B@>>k>C@=F Strg-Enter
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+@AmAA@.@VV
+\backslash
+{V
+\series default
+
+\begin_inset Formula $\to$
+\end_inset
+
+
+\series bold
+V@| Strg-Enter
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+hphantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+CD
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+D@<<j<E@>k>>F@=C
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Tipps
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Weitere gute Tipps gibt es unter
+\begin_inset LatexCommand cite
+key "Voss"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ dient dazu, dass die Fußnote nicht mit im pdf-Lesezeichen erscheint.
+\end_layout
+
+\begin_layout Standard
+Näheres zu
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ steht in Kapitel
+\begin_inset LatexCommand ref
+reference "sub:Formeln-in-Überschriften"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Tipps"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Ionen|see{chemische Zeichen}"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Chemische Symbole und Reaktionsgleichungen
+\begin_inset LatexCommand label
+name "sub:Chemische-Symbole-und"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "chemische Zeichen ! Symbole"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Reaktionsgleichungen"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Symbole ! chemische"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Ein Beispieltext aus der Chemie:
+\end_layout
+
+\begin_layout Quote
+Das
+\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
+\end_inset
+
+-Ion verbindet sich mit zwei
+\begin_inset Formula $\mathrm{Na^{+}}$
+\end_inset
+
+-Ionen zu Natriumsulfat
+\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
+\end_inset
+
+.
+ Die Reaktionsgleichung dazu lautet:
+\begin_inset Formula \[
+\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Diese Reaktionsgleichung kann direkt als Formel erstellt werden.
+ Damit die Symbole nicht kursiv erscheinen, markiert man sämtliche Zeichen
+ in der Formel und wandelt diese mit der Tastenkombination
+\family sans
+Alt-z\InsetSpace ~
+r
+\family default
+ in den aufrechten Schriftstil um.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Schriftstile siehe
+\begin_inset LatexCommand ref
+reference "sub:Schriftstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Negative Zahlen
+\begin_inset LatexCommand index
+name "Zahlen ! negative"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Negative Zahlen sehen im Formelmodus oft schlecht aus, denn das Minuszeichen
+ vor der Ziffer wird mit der gleichen Länge wie das Zeichen der Minus-Operation
+ dargestellt.
+ Schreibt man dagegen eine negative Zahl im normalen Text, erscheint das
+ Minuszeichen korrekt.
+\end_layout
+
+\begin_layout Standard
+Wandelt man also das Minuszeichen in mathematischen Text um, tritt das Problem
+ nicht mehr auf.
+\end_layout
+
+\begin_layout Standard
+Ein Beispiel zur Veranschaulichung der Problematik:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="right" valignment="top" leftline="true" width="0">
+<column alignment="left" valignment="top" rightline="true" width="0">
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+normaler Text:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+x = -2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Formelmodus:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $x=-2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Lösung:
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $x=\textrm{-}2$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Komma als Dezimaltrennzeichen
+\begin_inset LatexCommand index
+name "Komma"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In LaTeX fungiert das Komma in einer Formel, gemäß englischer Konvention,
+ als Gruppentrennzeichen.
+ Es wird demnach automatisch hinter allen Kommas in Formeln ein Leerraum
+ eingefügt.
+\end_layout
+
+\begin_layout Standard
+Um dies zu verhindern, markiert man das Komma und wandelt es in mathematischen
+ Text um (Tastenkürzel
+\family sans
+Alt-m\InsetSpace ~
+m
+\family default
+).
+\end_layout
+
+\begin_layout Standard
+Um hingegen alle Formelkommas des Dokuments als Dezimaltrennzeichen zu setzen,
+ lädt man die Datei
+\series bold
+icomma.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+icomma
+\series default
+ ist Teil des LaTeX-Paketes
+\series bold
+was
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! was\\vspace{4mm}"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! icomma"
+
+\end_inset
+
+ mit der LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{icomma}
+\end_layout
+
+\begin_layout Subsection
+Physikalische Vektoren
+\begin_inset LatexCommand label
+name "sub:Physikalische-Vektoren"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Vektoren ! physikalische"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Vordefinierte Vektoren bietet das LaTeX-Paket
+\series bold
+braket
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+braket
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! braket"
+
+\end_inset
+
+, das mit der LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{braket}
+\end_layout
+
+\begin_layout Standard
+geladen wird.
+\end_layout
+
+\begin_layout Standard
+Folgende Befehle sind definiert:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Bra{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Bra{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Ket{
+\backslash
+psi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Ket{\psi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Braket{
+\backslash
+psi|
+\backslash
+phi
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\Braket{\psi|\phi}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Befehl
+\series bold
+
+\backslash
+Braket
+\series default
+ stellt sicher, dass alle senkrechten Striche in der Größe der umgebenden
+ Klammern gesetzt werden:
+\begin_inset Formula \[
+\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Der Effekt von
+\series bold
+
+\backslash
+Braket
+\series default
+ kann auch mit dem Befehl
+\series bold
+
+\backslash
+middle
+\series default
+ erzielt werden, der in
+\begin_inset LatexCommand ref
+reference "sub:Automatische-Klammergrößen"
+
+\end_inset
+
+ beschrieben ist.
+\end_layout
+
+\begin_layout Subsection
+Selbst definierte Brüche
+\begin_inset LatexCommand label
+name "sub:Selbstdefinierte-Brüche"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Brüche ! selbstdefinierte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um eigene Befehle für Brüche zu definieren, verwendet man den Befehl
+\series bold
+
+\backslash
+genfrac
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! G ! \\textbackslash genfrac"
+
+\end_inset
+
+ in folgendem Schema:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+genfrac{linke
+\series default
+
+\series bold
+Klammer}{rechte
+\series default
+
+\series bold
+Klammer}{Bruchstrichdicke}{Ansichtsstil}
+\newline
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+phantom{
+\end_layout
+
+\end_inset
+
+
+\backslash
+genfrac
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+{Zähler}{Nenner}
+\end_layout
+
+\begin_layout Standard
+Der Ansichtsstil wird mit einer ganzen Zahl im Bereich 0\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+3 angegeben.
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Nummer
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ansichtsstil
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+abgesetzte Formel
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+eingebettete Formel
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+klein
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+winzig
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Wird nichts für den Ansichtsstil angegeben, passt sich die Größe wie bei
+
+\series bold
+
+\backslash
+frac
+\series default
+ der Umgebung an.
+\end_layout
+
+\begin_layout Standard
+Wird keine Bruchstrichdicke angegeben, wird der voreingestellte Wert von
+ 0.4\InsetSpace \thinspace{}
+pt verwendet.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Zum Beispiel sind die Befehle
+\series bold
+
+\backslash
+dfrac
+\series default
+ und
+\series bold
+
+\backslash
+tbinom
+\series default
+ aus
+\begin_inset LatexCommand ref
+reference "sub:Brüche"
+
+\end_inset
+
+ folgendermaßen definiert:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+dfrac}[2]{
+\backslash
+genfrac{}{}{}{0}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+und
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+tbinom}[2]{
+\backslash
+genfrac{(}{)}{0pt}{1}{#1}{#2}}
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Um einen Bruch zu definieren, bei dem man die Bruchstrichdicke als optionales
+ Argument angeben kann, gibt man im LaTeX-Vorspann folgenden Befehl ein:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+newcommand{
+\backslash
+fracS}[3][]{
+\backslash
+genfrac{}{}{#1}{}{#2}{#3}}
+\end_layout
+
+\begin_layout Standard
+Dazu ein Test:
+\begin_inset Formula \begin{align*}
+\text{Befehl} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
+\text{Ergebnis} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*}
+
+\end_inset
+
+Wie man sieht, entspricht der Abstand des Zählers und Nenners vom Strich
+ in etwa der dreifachen Strichdicke.
+\end_layout
+
+\begin_layout Subsection
+Durchgestrichene Formeln
+\begin_inset LatexCommand label
+name "sub:Durchgestrichene-Formeln"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! durchgestrichene"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Um Formeln oder Formelteile durchzustreichen, muss das LaTeX-Paket
+\series bold
+cancel
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+cancel
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! cancel"
+
+\end_inset
+
+ mit der LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[samesize]{cancel}
+\end_layout
+
+\begin_layout Standard
+geladen werden.
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+pagebreak
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Es gibt vier verschiedene Arten durchzustreichen:
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Ergebnis
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hspace
+\series default
+ und
+\series bold
+
+\backslash
+raisebox
+\series default
+ dienen nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+bcancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+xcancel{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+cancelto{1
+\begin_inset Formula $\to$
+\end_inset
+
+
+\backslash
+{
+\backslash
+int
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+leer
+\end_layout
+
+\end_inset
+
+A=B
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+cancelto
+\series default
+ eignet sich besonders, wenn man das Kürzen innerhalb einer Formel darstellen
+ will:
+\begin_inset Formula \[
+\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formeln in Überschriften
+\begin_inset LatexCommand label
+name "sub:Formeln-in-Überschriften"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Formel ! in Überschriften"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Benutzt man Formeln in Überschriften, ist auf Folgendes zu achten:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Verwendet man das LaTeX-Paket
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! hyperref"
+
+\end_inset
+
+, werden automatisch PDF-Lesezeichen für jede Überschrift aus dem Inhaltsverzeic
+hnis erzeugt.
+ Enthält eine Überschrift Formeln, werden diese im Lesezeichentext falsch
+ dargestellt.
+ Denn Formeln in Lesezeichen verstoßen gegen die PDF-Konventionen.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Beide Probleme lassen sich lösen, indem man am Ende der Überschrift einen
+ Kurztitel über das Menü
+\family sans
+Einfügen\SpecialChar \menuseparator
+Kurztitel
+\family default
+ einfügt.
+ Kurztitel werden als Alternative für mehrzeilige Überschriften verwendet,
+ um das Inhaltsverzeichnis übersichtlich zu halten.
+ Nur der Kurztitel erscheint im Inhaltsverzeichnis und damit auch im PDF-Lesezei
+chen.
+\end_layout
+
+\begin_layout Standard
+Möchte man im Inhaltsverzeichnis eine Formel verwenden, benutzt aber
+\series bold
+hyperref
+\series default
+, verwendet man im TeX-Modus den Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+texorpdfstring{Teil}{Alternative}
+\begin_inset LatexCommand index
+name "Befehle ! T ! \\textbackslash texorpdfstring"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Teil ist der Überschriftsteil, der nicht im PDF-Lesezeichen erscheinen solle.
+ Das können Zeichen, Formeln, Fußnoten aber auch Querverweise sein.
+ Als Alternative kann man angeben, was stattdessen im Lesezeichen erscheinen
+ soll.
+\end_layout
+
+\begin_layout Standard
+Es folgen zwei Beispielüberschriften:
+\begin_inset VSpace -3mm
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+boldmath
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Überschrift ohne Formel im Inhaltsverzeichnis
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset OptArg
+status collapsed
+
+\begin_layout Standard
+Überschrift ohne Formel im Inhaltsverzeichnis
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Überschrift mit Formel im Inhaltsverzeichnis
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+unboldmath
+\end_layout
+
+\end_inset
+
+In der ersten Überschrift wurde ein Kurztitel verwendet.
+ In der zweiten
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+.
+\end_layout
+
+\begin_layout Standard
+Damit die Formeln so wie der Rest der Überschrift formatiert werden, wurde
+ die komplette Überschrift in eine
+\series bold
+boldmath-Umgebung
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset LatexCommand ref
+reference "sub:Fett-gedruckte-Formeln"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ gesetzt.
+\end_layout
+
+\begin_layout Subsection
+Formeln im mehrspaltigen Text
+\begin_inset LatexCommand index
+name "Formel ! im mehrspaltigen Text"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Formeln im mehrspaltigen Text sind oftmals zu breit für eine Spalte und
+ müssen daher über die gesamte Seitenbreite gesetzt werden.
+ Dazu verwendet man das LaTeX-Paket
+\series bold
+multicol
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+multicol
+\series default
+ ist Teil jeder LaTeX-Standardinstallation.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! multicol"
+
+\end_inset
+
+, das mit der LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{multicol}
+\end_layout
+
+\begin_layout Standard
+geladen wird.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Standard
+Dabei ist zu beachten, dass im Menü
+\family sans
+Dokument\SpecialChar \menuseparator
+Einstellungen
+\family default
+ unter
+\family sans
+Textformat
+\family default
+
+\emph on
+nicht
+\emph default
+
+\family sans
+Zweispaltiges\InsetSpace ~
+Dokument
+\family default
+ ausgewählt sein darf.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Vor den mehrspaltigen Text schreibt man im TeX-Modus den Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+begin{multicols}{Spaltenanzahl}
+\end_layout
+
+\begin_layout Standard
+wobei die Spaltenanzahl eine Zahl im Bereich 2\InsetSpace \thinspace{}
+-\InsetSpace \thinspace{}
+10 ist.
+ Vor der Formel beendet man den mehrspaltigen Text mit dem Befehl
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+end{multicols}
+\end_layout
+
+\begin_layout Standard
+der im TeX-Modus eingegeben wird.
+\end_layout
+
+\begin_layout Standard
+Durch den Befehl wird vor der Formel automatisch etwas Leerraum erstellt.
+ Um dies rückgängig zu machen, fügt man vor der Formel -6\InsetSpace \thinspace{}
+mm vertikalen Leerraum
+ ein.
+ Ist der Formelstil
+\series bold
+Eingerückt
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Formelstile siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ gewählt, fügt man stattdessen -9\InsetSpace \thinspace{}
+mm Leerraum ein.
+\end_layout
+
+\begin_layout Standard
+Als Beispiel ein mehrspaltiger Text mit einer abgesetzten Formel:
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+Das Spektrum wird fouriertransformiert.
+ Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk
+, Lösungsmittel) zu trennen.
+ Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns
+ nun das Aussehen des Ausgangssignals.
+ Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man
+ über alle Phasen integrieren muss.
+ Sei nun
+\begin_inset Formula $S$
+\end_inset
+
+ unser normiertes Ausgangssignal und
+\begin_inset Formula $P$
+\end_inset
+
+ die Phasenverteilungsfunktion, so ergibt sich die Beziehung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\begin_inset VSpace -6mm
+\end_inset
+
+
+\begin_inset Formula \begin{equation}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+begin{multicols}{2}
+\end_layout
+
+\end_inset
+
+wobei
+\begin_inset Formula $S_{0}$
+\end_inset
+
+ das Signal ohne Gradient ist und die Normierungsbedingung
+\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
+\end_inset
+
+ gilt.
+ Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen.
+ Direkt nach dem
+\begin_inset Formula $\nicefrac{\pi}{2}$
+\end_inset
+
+\InsetSpace \thinspace{}
+-rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich
+ das Signal zusätzlich abschwächt.
+ Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten
+
+\begin_inset Formula $T_{2}$
+\end_inset
+
+-Zeit.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+end{multicols}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Formeln mit Beschreibung der Variablen
+\begin_inset LatexCommand index
+name "Formel ! mit Variablenbeschreibung"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Möchte man wie in Formel
+\begin_inset LatexCommand eqref
+reference "eq:innerhalb"
+
+\end_inset
+
+, Variablen innerhalb einer Formel beschreiben, verwendet man eine 2
+\series bold
+×
+\series default
+
+\begin_inset Formula $n$
+\end_inset
+
+\InsetSpace ~
+Matrix mit links ausgerichteten Spalten für die verwendeten
+\begin_inset Formula $n$
+\end_inset
+
+ Variablen.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Matrizen siehe
+\begin_inset LatexCommand ref
+reference "sec:Matrizen"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ Um die Beschreibung kleiner zu setzen, gibt man vor der Matrix z.\InsetSpace \thinspace{}
+B.
+ den Befehl
+\series bold
+
+\backslash
+footnotesize
+\series default
+ ein.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Schriftgrößen siehe
+\begin_inset LatexCommand ref
+reference "sub:Schriftgrößen"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Wird der Formelstil
+\series bold
+Eingerückt
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+Formelstile siehe
+\begin_inset LatexCommand ref
+reference "sec:Formelstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\series default
+ verwendet, fügt man vor und nach der Matrix ein
+\series bold
+
+\backslash
+hfill
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+hfill
+\series default
+ wirkt nur in Formeln mit dem Stil
+\series bold
+Eingerückt
+\series default
+, siehe
+\begin_inset LatexCommand ref
+reference "sub:Variabler-Leerraum"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+ ein, damit der Abstand der Matrix von der Gleichung und vom Seitenrand
+ gleich ist.
+\end_layout
+
+\begin_layout Standard
+Ist der Formelstil
+\series bold
+Zentriert
+\series default
+ gewählt, nutzt man die in
+\begin_inset LatexCommand ref
+reference "sub:Flalign-Umgebung"
+
+\end_inset
+
+ beschriebene Möglichkeit, Formeln einzurücken.
+ Formel
+\begin_inset LatexCommand eqref
+reference "eq:innerhalb"
+
+\end_inset
+
+ besteht aus fünf Spalten, wobei in den ersten beiden die Gleichung, in
+ der dritten die Matrix und in der letzten die leere TeX-Klammer steht.
+\begin_inset Formula \begin{flalign}
+\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
+\rho & \textrm{Dichte}\\
+V & \textrm{Volumen}\\
+g & \textrm{Fallbeschleunigung}\end{array} & & {}\label{eq:innerhalb}\end{flalign}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Aufrechte kleine griechische Buchstaben
+\begin_inset LatexCommand label
+name "sub:Aufrechte-kleine-griechische"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "griechische Buchstaben ! aufrechte"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die meisten Mathe-Schriften stellen nur kursive kleine griechische Buchstaben
+ zur Verfügung.
+ Für Symbole der Elementarteilchen, wie Pionen und Neutrinos werden jedoch
+ aufrechte griechische Buchstaben benötigt.
+ Die Datei
+\series bold
+upgreek.sty
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+upgreek
+\series default
+ ist Teil des LaTeX-Paketes
+\series bold
+was
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! was\\vspace{4mm}"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Pakete ! upgreek"
+
+\end_inset
+
+, die mit der LaTeX-Vorspannzeile
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{upgreek}
+\end_layout
+
+\begin_layout Standard
+geladen wird, stellt diese Buchstaben zur Verfügung.
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+ifupgreek
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Die folgende Tabelle erscheint nur im Ausdruck wenn das LaTeX-Paket
+\series bold
+upgreek
+\series default
+ installiert ist:
+\end_layout
+
+\end_inset
+
+ Sie werden erzeugt, wenn der Befehl für einen griechischen Buchstaben mit
+
+\series bold
+up
+\series default
+ begonnen wird.
+ So erzeugt z.\InsetSpace \thinspace{}
+B.
+ der Befehl
+\series bold
+
+\backslash
+uptau
+\series default
+ dies:
+\begin_inset Formula $\uptau$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Damit kann man Elementarteilchenreaktionen erstellen:
+\begin_inset Formula \[
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Die aufrechten Buchstaben sind fetter und breiter als die kursiven.
+ Sie sollten daher nicht für Einheiten wie
+\begin_inset Quotes gld
+\end_inset
+
+µm
+\begin_inset Quotes grd
+\end_inset
+
+ verwendet werden.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+else
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status open
+
+\begin_layout Standard
+Folgendes erscheint im Ausdruck wenn das LaTeX-Paket
+\series bold
+upgreek
+\series default
+ nicht installiert ist:
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Das LaTeX-Paket
+\series bold
+upgreek
+\series default
+muss installiert sein, um den Rest dieses Abschnitts im Ausdruck zu sehen.
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+fi
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Textzeichen in Formeln
+\begin_inset LatexCommand label
+name "sub:Textzeichen-in-Formeln"
+
+\end_inset
+
+
+\begin_inset LatexCommand index
+name "Text ! in Formeln"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In einigen Fällen möchte man Textzeichen direkt in Formeln eingeben.
+ Benötigt man z.\InsetSpace \thinspace{}
+B.
+ den mittigen Punkt · in Formeln wie
+\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
+\end_inset
+
+, müsste man dafür jedes Mal den Befehl
+\series bold
+
+\backslash
+cdot
+\series default
+ eingeben
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+siehe
+\begin_inset LatexCommand ref
+reference "sub:Binäre-Operatoren"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+, da dieses Zeichen in allen Kodierungen als Textzeichen definiert ist.
+ Man kann jedoch die Kodierung mit folgender LaTeX-Vorspannzeile ändern:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputText{183}{
+\backslash
+ifmmode
+\backslash
+cdot
+\backslash
+else
+\backslash
+textperiodcentered
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+Die Zeichenkodierung (Menü
+\family sans
+Dokument\SpecialChar \menuseparator
+Einstellungen\SpecialChar \menuseparator
+Sprache
+\family default
+) legt fest, welches Zeichen beim Druck einer bestimmten Taste erscheint.
+ Wenn man die Taste für das Zeichen '·' drückt, wird intern der Befehl
+\series bold
+
+\backslash
+textperiodcentered
+\series default
+ verwendet.
+ Dieser Befehl ist in einer Formel jedoch nicht verfügbar, so dass es zu
+ LaTeX-Fehlern kommen würde.
+ Durch die geänderte Kodierung wird hingegen automatisch der richtige Befehl
+ gewählt, je nachdem ob das Zeichen in eine Formel eingegeben wurde oder
+ nicht.
+\end_layout
+
+\begin_layout Standard
+Die Kodierung der einzelnen Zeichen ist in Definitionsdateien abgespeichert.
+ Z.\InsetSpace \thinspace{}
+B.
+ ist die Kodierung
+\series bold
+latin9
+\series default
+ in der Datei
+\series bold
+latin9.def
+\series default
+ definiert, die sich im Installationsverzeichnis von LaTeX befindet.
+ Kodierungen sollten nur über den LaTeX-Vorspann und nicht in den Definitionsdat
+eien geändert werden.
+ Ansonsten können eigene Dokumente von anderen LyX-Nutzern auf anderen Computern
+ nicht ohne Weiteres bearbeitet werden.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+In diesem Dokument wurde außerdem mittigen Punkt noch das Gradzeichen °
+ mit folgenden LaTeX-Vorspannzeilen so definiert, dass sie direkt in eine
+ Formel eingegeben werden können:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+DeclareInputText{176}{
+\backslash
+ifmmode^
+\backslash
+circ
+\backslash
+else
+\backslash
+textdegree
+\backslash
+f\SpecialChar \textcompwordmark{}
+i}
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+\start_of_appendix
+Typographische Hinweise
+\begin_inset LatexCommand index
+name "Typographische Hinweise"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Dieses Kapitel ist eine Zusammenfassung der wichtigsten typographischen
+ Regeln, die teilweise auch im Duden
+\begin_inset LatexCommand cite
+key "Duden"
+
+\end_inset
+
+ unter
+\family typewriter
+Textverarbeitung
+\family default
+ aufgelistet sind.
+\end_layout
+
+\begin_layout Itemize
+Physikalische Einheiten werden
+\emph on
+immer
+\emph default
+ aufrecht gesetzt
+\begin_inset Foot
+status collapsed
+
+\begin_layout Standard
+wird durch Schriftstile erreicht, siehe
+\begin_inset LatexCommand ref
+reference "sub:Schriftstile"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+: 30\InsetSpace \thinspace{}
+km/h
+\newline
+Zwischen Wert und Einheit befindet sich der kleinste Leerraum, siehe
+
+\begin_inset LatexCommand ref
+reference "sub:Vordefinierter-Leerraum"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Prozent- und Promillezeichen werden wie physikalische Einheiten gesetzt:
+\newline
+1,2\InsetSpace \thinspace{}
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+textperthousand
+\end_layout
+
+\end_inset
+
+\InsetSpace ~
+Alkohol im Blut
+\newline
+Sie folgen jedoch direkt auf die Zahl, wenn sie in einer
+ Zusammensetzung oder Ableitung stehen: 3%-ige Rendite, 20%-Grenze
+\end_layout
+
+\begin_layout Itemize
+Das Grad-Symbol folgt immer unmittelbar auf die Zahl: 15°, es sei denn es
+ wird in einer Einheit verwendet: 15\InsetSpace \thinspace{}
+°C
+\end_layout
+
+\begin_layout Itemize
+In Zahlen mit mehr als vier Ziffern wird zur Gruppierung vor jeder dritten
+ Ziffer der kleinste Leerraum eingefügt: 18\InsetSpace \thinspace{}
+473\InsetSpace \thinspace{}
+588
+\end_layout
+
+\begin_layout Itemize
+Für Bemaßungen wie z.\InsetSpace \thinspace{}
+B.
+ 120×90×40\InsetSpace \thinspace{}
+cm, verwendet man das gelegte Kreuz
+\begin_inset Quotes gld
+\end_inset
+
+×
+\begin_inset Quotes grd
+\end_inset
+
+, dass über den LaTeX-Befehl
+\series bold
+
+\backslash
+texttimes
+\series default
+ verfügbar ist, mit einigen Tastaturdefinitionen aber auch direkt eingegeben
+ werden kann.
+\end_layout
+
+\begin_layout Itemize
+Bei Datumsangaben befindet sich zwischen Tag und Monat der kleinste Leerraum,
+ zwischen Monat und Jahr ein geschütztes Leerzeichen: 23.\InsetSpace \thinspace{}
+6.\InsetSpace ~
+1979
+\end_layout
+
+\begin_layout Itemize
+Funktionen, deren Name aus mehreren Buchstaben besteht, werden aufrecht
+ gesetzt um Verwechslungen mit Variablen zu vermeiden, siehe
+\begin_inset LatexCommand ref
+reference "sub:Vordefinierte-Funktionen"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Indizes, die aus mehreren Buchstaben bestehen, werden aufrecht gesetzt:
+
+\begin_inset Formula $E_{\mathrm{kin}}$
+\end_inset
+
+
+\newline
+Komponenten von Matrizen werden kursiv gesetzt:
+\begin_inset Formula $\hat{H}_{kl}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Der Ableitungs-/Integrationsoperator 'd', die Eulersche Zahl 'e' und die
+ Imaginäre Zahl 'i' sollten aufrecht gesetzt werden, um sie nicht mit anderen
+ Variablen zu verwechseln.
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Section
+Synonyme
+\begin_inset LatexCommand index
+name "Synonyme"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Einige Zeichen und Symbole können mit mehreren Befehlen erstellt werden.
+ Hier ist eine Übersicht der Synonymbefehle:
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+äquivalent zu
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ dient nur als Abstandhalter.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ast
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+raisebox{-1.2mm}{
+\end_layout
+
+\end_inset
+
+*
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+choose
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+binom
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+geq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+{
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+[
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+gets
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+leq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+le
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vee
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neq
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+slash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+/
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+vert
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+|
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="12" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0pt">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Befehl
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+äquivalent zu
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+backslash
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+
+\backslash
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dasharrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+dashrightarrow
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+land
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+wedge
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rbrace
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rbracket
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+]
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+rightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+to
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+lnot
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+neg
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ne
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+not=
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+owns
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+ni
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+square
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Box
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+Vert
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\backslash
+|
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\hfill
+
+\end_layout
+
+\begin_layout Standard
+
+\newpage
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "TLC2"
+
+\end_inset
+
+
+\shape smallcaps
+Mittelbach, F.
+ ; Goossens, M.
+\shape default
+:
+\shape italic
+The LaTeX Companion
+\shape default
+.
+ Addison Wesley, 2004
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Mathmode"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
+\end_layout
+
+\end_inset
+
+Beschreibung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ der mathematischen Fähigkeiten von LaTeX
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Voss"
+
+\end_inset
+
+LaTeX Tipps- und Tricks-
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://tug.org/TeXnik/}{
+\end_layout
+
+\end_inset
+
+Seite
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "AMS"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
+\end_layout
+
+\end_inset
+
+Beschreibung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ von
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+AmS
+\end_layout
+
+\end_inset
+
+-LaTeX
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Symbole"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
+\end_layout
+
+\end_inset
+
+Auflistung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ aller über LaTeX-Pakete verfügbare Symbole
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "hyperref"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
+\end_layout
+
+\end_inset
+
+Dokumentation
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ des LaTeX-Pakets
+\series bold
+hyperref
+\series default
+
+\begin_inset LatexCommand index
+name "Pakete ! hyperref"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Mathclap"
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+
+\backslash
+href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
+\end_layout
+
+\end_inset
+
+Beschreibung
+\begin_inset ERT
+status collapsed
+
+\begin_layout Standard
+
+}
+\end_layout
+
+\end_inset
+
+ des in
+\begin_inset LatexCommand ref
+reference "sub:Operatorgrenzen"
+
+\end_inset
+
+ vorgestellten Befehls
+\series bold
+
+\backslash
+mathclap
+\series default
+
+\begin_inset LatexCommand index
+name "Befehle ! M ! \\textbackslash mathclap"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\begin_inset LatexCommand bibitem
+key "Duden"
+
+\end_inset
+
+
+\emph on
+Duden Band 1
+\emph default
+.
+ 22.
+ Auflage, Duden Verlag 2001
+\end_layout
+
+\begin_layout Subsubsection*
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Standard
+Damit der Index den Namen
+\begin_inset Quotes gld
+\end_inset
+
+Stichwortverzeichnis
+\begin_inset Quotes grd
+\end_inset
+
+ erhält, wurde im LaTeX-Vorspann
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage[ngerman]{babel}
+\newline
+
+\backslash
+addto
+\backslash
+captionsngerman{
+\backslash
+renewcommand{
+\backslash
+indexname}{Stichwortverzeichnis}}
+\end_layout
+
+\begin_layout Standard
+eingefügt.
+\end_layout
+
+\begin_layout Standard
+Das Paket
+\series bold
+babel
+\series default
+ sorgt dafür, dass die Beschriftungen in der ausgewählten Sprache erscheinen.
+ Ehe man Beschriftungen ändern kann, muss es geladen werden.
+ Außerdem wird
+\series bold
+babel
+\series default
+ von LyX automatisch nach dem LaTeX-Vorspann geladen.
+ Das ruft aber keine Probleme hervor, solange im LaTeX-Vorspann die Dokumentspra
+che verwendet wurde.
+\end_layout
+
+\begin_layout Standard
+Möchte man andere Beschriftungen ändern, ersetzt man
+\series bold
+
+\backslash
+indexname
+\series default
+ durch
+\series bold
+
+\backslash
+<Beschriftungs>name
+\series default
+.
+ Eine Auflistung der möglichen Namen findet man unter
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+http://www.tex.ac.uk/cgi-bin/texfaq2html?label=fixnam
+\end_layout
+
+\begin_layout Standard
+Möchte man Beschriftungen für andere Sprachen ändern, ersetzt man
+\series bold
+ngerman
+\series default
+ durch die Dokumentsprache und
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+captionsgerman
+\series default
+ durch
+\series bold
+
+\backslash
+captions<Dokumentsprache>
+\series default
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset LatexCommand printindex
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
import re
-possible_documents = ("Intro", "FAQ", "Tutorial", "UserGuide", "EmbeddedObjects", "Extended", "Customization")
+possible_documents = ("Customization", "EmbeddedObjects", "Extended", "FAQ", "Intro", "Math", "Tutorial", "UserGuide")
def documents(srcdir, lang, dir_prefix = None):
'''Return documents for specified language. Translated files are in lang
+++ /dev/null
-#LyX 1.5.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 276
-\begin_document
-\begin_header
-\textclass article
-\begin_preamble
-\usepackage{a4wide}
-\end_preamble
-\language ngerman
-\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-\graphics default
-\float_placement H
-\paperfontsize default
-\spacing single
-\papersize a4paper
-\use_geometry false
-\use_amsmath 1
-\use_esint 0
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\defskip medskip
-\quotes_language german
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-Von und nach mathed konvertieren
-\end_layout
-
-\begin_layout Standard
-Mathematische Formeln können im Hauptteil des Dokuments eingegeben werden
- und in den Mathe-Modus konvertiert werden, indem Sie die Formel markieren,
-
-\family default
-
-\family sans
-Strg+C
-\family default
- für kopieren eingeben, auf
-\begin_inset Formula $$\frac{a+b}{c}$$
-\end_inset
-
- klicken und
-\family default
-
-\family sans
-Strg+V
-\family default
- zum einfügen eingeben.
- Der Text kann von Trennzeichen umgeben sein oder auch nicht.
- Das heißt, wenn Sie eine der folgenden Formeln markieren:
-\end_layout
-
-\begin_layout Standard
-\align center
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="1">
-<features>
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\backslash
-begin{math}
-\backslash
-frac{abc}{xyz}
-\backslash
-end{math}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\backslash
-(
-\backslash
-frac{abc}{xyz}
-\backslash
-)
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-$
-\backslash
-frac{abc}{xyz} $
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\backslash
-begin{displaymath}
-\backslash
-frac{abc}{xyz}
-\backslash
-end{displaymath}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\backslash
-[
-\backslash
-frac{abc}{xyz}
-\backslash
-]
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-wird sie konvertiert nach:
-\end_layout
-
-\begin_layout Standard
-\begin_inset Formula $$\frac{abc}{xyz}$$
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-Zur Zeit können Sie eine mathematische Formel nicht in Text zurückverwandeln.
- Es gibt aber einen kleinen Trick: Markieren Sie den Inhalt der Mathe-Einfügung
- (nicht die Mathe-Einfügung selber, nur den Inhalt), und fügen Sie ihn mit
- dem mittleren Mausknopf ins Dokument ein.
-\end_layout
-
-\begin_layout Section
-LaTeX-Symbole anzeigen
-\end_layout
-
-\begin_layout Standard
-LyX kann die meisten LaTeX-Symbole und
-\emph default
-
-\emph on
-alle
-\emph default
- AMS-Symbole anzeigen.
- Der Vollständigkeit halber werden auch noch die Symboltabellen aus
-\noun on
-Lamport
-\noun default
-s und
-\noun on
-Goosen
-\noun default
-s Bücher angefügt.
-\end_layout
-
-\begin_layout Section
-Einige Beispiele
-\end_layout
-
-\begin_layout Standard
-Die folgenden Tabellen aus
-\noun on
-Goossen
-\noun default
- et al.
-
-\begin_inset Quotes gld
-\end_inset
-
-The LaTeX companion
-\begin_inset Quotes grd
-\end_inset
-
- sollten auf dem Bildschirm zu sehen sein.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status inlined
-
-\begin_layout Standard
-
-\backslash
-setcounter{table}{1}
-\end_layout
-
-\begin_layout Standard
-
-\backslash
-renewcommand{
-\backslash
-thetable}{8.
-\backslash
-arabic{table}}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="2" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\hat{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-hat{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\acute{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-acute{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\bar{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bar{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\dot{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-dot{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\breve{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-breve{a}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\check{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-check{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\grave{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-grave{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\vec{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vec{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\ddot{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ddot{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-\begin_inset Formula $\tilde{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-tilde{a}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Mathe-Modus-Akzente
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="11" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\alpha$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-alpha
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\beta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-beta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gamma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\delta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-delta
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\epsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-epsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varepsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varepsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\zeta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-zeta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\eta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-eta
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\theta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-theta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vartheta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vartheta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\iota$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-iota
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\kappa$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-kappa
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lambda$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lambda
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\mu$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-mu
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nu$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nu
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\xi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-xi
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $o$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-o
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\pi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-pi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varpi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varpi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rho
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varrho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varrho
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sigma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varsigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varsigma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\tau$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-tau
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\upsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-upsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\phi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-phi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varphi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varphi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\chi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-chi
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\psi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-psi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\omega$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-omega
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Gamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Gamma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Delta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Delta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Theta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Theta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Lambda$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Lambda
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Xi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Xi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Pi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Pi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Sigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Sigma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Upsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Upsilon
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Phi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Phi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Psi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Psi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Omega$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Omega
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Griechische Buchstaben
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="9" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\pm$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-pm
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-cap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\diamond$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-diamond
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\oplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-oplus
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\mp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-mp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-cup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigtriangleup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigtriangleup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ominus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ominus
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\times$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-times
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\uplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-uplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigtriangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigtriangledown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\otimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-otimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\div$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-div
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqcap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqcap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\triangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-triangleleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\oslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-oslash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ast$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ast
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqcup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\triangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-triangleright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\odot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-odot
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\star$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-star
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vee
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigcirc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circ$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circ
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\wedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-wedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\dagger$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-dagger
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bullet$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bullet
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\setminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-setminus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\unlhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-unlhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ddagger$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ddagger
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-cdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\wr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-wr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\unrhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-unrhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\amalg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-amalg
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Symbole für binäre Operationen
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leq
-\backslash
-le
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\geq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-geq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\equiv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-equiv
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\models$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-models
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\prec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-prec
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succ$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succ
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\perp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-perp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\preceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-preceq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\simeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-simeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\mid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-mid
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ll$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ll
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gg
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\asymp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-asymp
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\parallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-parallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\subset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-subset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\supset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-supset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\approx$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-approx
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bowtie$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bowtie
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\subseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-subseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\supseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-supseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cong$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-cong
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Join$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Join
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqsubset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqsubset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqsupset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqsupset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\neq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-neq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\smile$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-smile
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqsubseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqsubseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqsupseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqsupseteq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\doteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-doteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\frown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-frown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\in$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-in
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ni$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ni
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\propto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-propto
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $=$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-=
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vdash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\dashv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-dashv
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $<$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-<
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $>$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
->
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Symbole für Relationen
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="10" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\longleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-longleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-uparrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Leftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Leftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Longleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Longleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Uparrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\longrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-longrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-downarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Rightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Rightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Longrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Longrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Downarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\longleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-longleftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-updownarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Leftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Longleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Longleftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Updownarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\mapsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-mapsto
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\longmapsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-longmapsto
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nearrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nearrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\hookleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-hookleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\hookrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-hookrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\searrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-searrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftharpoonup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftharpoonup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightharpoonup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightharpoonup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\swarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-swarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftharpoondown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftharpoondown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightharpoondown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightharpoondown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nwarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nwarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Pfeilsymbole
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="7" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ldots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ldots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cdots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-cdots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vdots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vdots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ddots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ddots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\aleph$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-aleph
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\prime$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-prime
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\forall$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-forall
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\infty$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-infty
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\hbar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-hbar
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\emptyset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-emptyset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\exists$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-exists
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nabla$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nabla
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\surd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-surd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Box$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Box
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\triangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-triangle
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Diamond$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Diamond
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\imath$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-imath
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\jmath$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-jmath
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ell$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ell
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\neg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-neg
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\top$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-top
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\flat$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-flat
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\natural$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-natural
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sharp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sharp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\wp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-wp
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\clubsuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-clubsuit
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\diamondsuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-diamondsuit
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\heartsuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-heartsuit
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\spadesuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-spadesuit
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\mho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-mho
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Re$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Re
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Im$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Im
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\angle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-angle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\partial$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-partial
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Verschiedene Symbole
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sum$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sum
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\prod$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-prod
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\coprod$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-coprod
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\int$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-int
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\oint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-oint
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigcap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigcap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigcup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigsqcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigsqcup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigvee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigvee
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigwedge
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigodot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigodot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigotimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigotimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigoplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigoplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\biguplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-biguplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Symbole mit variabler Größe
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" columns="8">
-<features>
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\arccos$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cos$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\csc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\exp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ker$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\limsup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\min$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sinh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\arcsin$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cosh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\deg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gcd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ln$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Pr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\arctan$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\cot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\det$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\hom$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\log$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\tan$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\arg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\coth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\dim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\inf$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\liminf$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\max$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sin$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\tanh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Funktions-Symbole
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-uparrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Uparrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-downarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Downarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\{$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-{
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-updownarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Updownarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lfloor$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lfloor
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rfloor$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rfloor
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lceil$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lceil
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rceil$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rceil
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\langle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-langle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rangle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $/$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-/
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\backslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-backslash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $|$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-|
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\|$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-|
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Trennsymbole
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="6" columns="4">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\widetilde{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-widetilde{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\widehat{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-widehat{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\overleftarrow{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-overleftarrow{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\overrightarrow{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-overrightarrow{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\overline{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-overline{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\underline{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-underline{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\overbrace{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-overbrace{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\underbrace{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-underbrace{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqrt{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqrt{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqrt[n]{abc}\sqrt[3]{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqrt[n]{abc}
-\backslash
-root3{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $f'$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-f'
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\frac{abc}{xyz}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-frac{abc}{xyz}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Symbole für mathematische Konstrukte
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="1" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\digamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-digamma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varkappa$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varkappa
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\beth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-beth
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\daleth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-daleth
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gimel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gimel
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-AMS-Griechisch und -Hebräisch
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="1" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ulcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ulcorner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\urcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-urcorner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\llcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-llcorner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lrcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lrcorner
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-AMS-Trennsymbole
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="11" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\dashrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-dashrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\dashleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-dashleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftleftarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftleftarrows
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftrightarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftrightarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Lleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Lleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\twoheadleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-twoheadleftarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftarrowtail$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftarrowtail
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\looparrowleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-looparrowleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftrightharpoons$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftrightharpoons
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\curvearrowleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-curvearrowleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circlearrowleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circlearrowleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Lsh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Lsh
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\upuparrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-upuparrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\upharpoonleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-upharpoonleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\downharpoonleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-downharpoonleft
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\multimap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-multimap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftrightsquigarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftrightsquigarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightrightarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightrightarrows
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightleftarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightleftarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightrightarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightrightarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightleftarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightleftarrows
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\twoheadrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-twoheadrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightarrowtail$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightarrowtail
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\looparrowright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-looparrowright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightleftharpoons$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightleftharpoons
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\curvearrowright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-curvearrowright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circlearrowright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circlearrowright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Rsh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Rsh
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\downdownarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-downdownarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\upharpoonright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-upharpoonright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\downharpoonright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-downharpoonright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightsquigarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightsquigarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-AMS-Pfeile
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="2" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nLeftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nLeftarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nRightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nRightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nleftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nLeftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nLeftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Durchgestrichene AMS-Pfeile
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="22" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leqslant
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\eqslantless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-eqslantless
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lesssim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lesssim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lessapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lessapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\approxeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-approxeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lessdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lessdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lll$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lll
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lessgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lessgtr
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lesseqgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lesseqgtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lesseqqgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lesseqqgtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\doteqdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-doteqdot
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\risingdotseq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-risingdotseq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\fallingdotseq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-fallingdotseq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\backsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-backsim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\backsimeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-backsimeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\subseteqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-subseteqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Subset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Subset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqsubset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqsubset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\preccurlyeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-preccurlyeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\curlyeqprec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-curlyeqprec
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\precsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-precsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\precapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-precapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vartriangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vartriangleleft
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\trianglelefteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-trianglelefteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vDash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Vvdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Vvdash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\smallsmile$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-smallsmile
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\smallfrown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-smallfrown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bumpeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bumpeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Bumpeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Bumpeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\geqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-geqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\geqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-geqslant
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\eqslantgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-eqslantgtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gtrsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gtrsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gtrapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gtrapprox
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gtrdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gtrdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ggg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ggg
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gtrless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gtrless
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gtreqless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gtreqless
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gtreqqless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gtreqqless
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\eqcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-eqcirc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\triangleq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-triangleq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\thicksim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-thicksim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\thickapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-thickapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\supseteqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-supseteqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Supset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Supset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sqsupset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sqsupset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succcurlyeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succcurlyeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\curlyeqsucc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-curlyeqsucc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vartriangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vartriangleright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\trianglerighteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-trianglerighteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Vdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Vdash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\shortmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-shortmid
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\shortparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-shortparallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\between$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-between
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\pitchfork$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-pitchfork
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varpropto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varpropto
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\blacktriangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-blacktriangleleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\therefore$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-therefore
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\backepsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-backepsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\blacktriangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-blacktriangleright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\because$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-because
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-AMS-Symbole für binäre Relationen
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="17" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nless
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nleq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nleq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nleqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nleqslant
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nleqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nleqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lneqq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lvertneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lvertneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lnsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lnapprox
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nprec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nprec
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\npreceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-npreceq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\precnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-precnsim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\precnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-precnapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nshortmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nshortmid
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nmid
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nvdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nvdash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nvDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nvDash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ntriangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ntriangleleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ntrianglelefteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ntrianglelefteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nsubseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nsubseteq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\subsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-subsetneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varsubsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varsubsetneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\subsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-subsetneqq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varsubsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varsubsetneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ngtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ngtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ngeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ngeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ngeqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ngeqslant
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ngeqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ngeqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gneq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gvertneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gvertneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gnsim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\gnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-gnapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nsucc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nsucc
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nsucceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nsucceq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succnsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\succnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-succnapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ncong$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ncong
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nshortparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nshortparallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nparallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nvDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nvDash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nVDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nVDash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ntriangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ntriangleright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ntrianglerighteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ntrianglerighteq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nsupseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nsupseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nsupseteqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nsupseteqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\supsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-supsetneq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varsupsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varsupsetneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\supsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-supsetneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varsupsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varsupsetneqq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-AMS-Symbole für negierte binäre Relationen
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\dotplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-dotplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\smallsetminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-smallsetminus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Cap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Cap
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Cup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Cup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\barwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-barwedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\veebar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-veebar
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\doublebarwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-doublebarwedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\boxminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-boxminus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\boxtimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-boxtimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\boxdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-boxdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\boxplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-boxplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\divideontimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-divideontimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\ltimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-ltimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rtimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rtimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\leftthreetimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-leftthreetimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\rightthreetimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-rightthreetimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\curlywedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-curlywedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\curlyvee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-curlyvee
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circleddash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circleddash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circledast$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circledast
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circledcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circledcirc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\centerdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-centerdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\intercal$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-intercal
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-AMS-Symbole für binäre Operationen
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-\begin_inset Tabular
-<lyxtabular version="3" rows="9" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\hbar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-hbar
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\hslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-hslash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\vartriangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-vartriangle
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\triangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-triangledown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\square$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-square
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\lozenge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-lozenge
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\circledS$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-circledS
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\angle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-angle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\measuredangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-measuredangle
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\nexists$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-nexists
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\mho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-mho
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Finv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Finv
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Game$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Game
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\Bbbk$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-Bbbk
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\backprime$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-backprime
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\varnothing$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-varnothing
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\blacktriangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-blacktriangle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\blacktriangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-blacktriangledown
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\blacksquare$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-blacksquare
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\blacklozenge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-blacklozenge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\bigstar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-bigstar
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\sphericalangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-sphericalangle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\complement$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-complement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\eth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-eth
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\diagup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-diagup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-\begin_inset Formula $\diagdown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\family typewriter
-
-\backslash
-diagdown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-Verschiedene AMS-Symbole
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
+++ /dev/null
-#LyX 1.5.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 276
-\begin_document
-\begin_header
-\textclass article
-\begin_preamble
-\usepackage{a4wide}
-\end_preamble
-\language english
-\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
-\font_default_family default
-\font_sc false
-\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
-\graphics default
-\float_placement H
-\paperfontsize default
-\spacing single
-\papersize default
-\use_geometry false
-\use_amsmath 1
-\use_esint 0
-\cite_engine basic
-\use_bibtopic false
-\paperorientation portrait
-\secnumdepth 3
-\tocdepth 3
-\paragraph_separation indent
-\defskip medskip
-\quotes_language english
-\papercolumns 1
-\papersides 1
-\paperpagestyle default
-\tracking_changes false
-\output_changes false
-\end_header
-
-\begin_body
-
-\begin_layout Section
-
-Converting to and from mathed
-\end_layout
-
-\begin_layout Standard
-
-Math can be typed in the body of the document and converted to mathed-mode
- by highlighting it and typing
-\family default
-
-\family sans
-M-c\InsetSpace ~
-m
-\family default
-.
- The text can be bounded with delimiters or not.
- That is, highlighting any of the formulae below:
-\end_layout
-
-\begin_layout Standard
-\align center
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="1">
-<features>
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\backslash
-begin{math}
-\backslash
-frac{abc}{xyz}
-\backslash
-end{math}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\backslash
-(
-\backslash
-frac{abc}{xyz}
-\backslash
-)
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-$
-\backslash
-frac{abc}{xyz} $
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\backslash
-begin{displaymath}
-\backslash
-frac{abc}{xyz}
-\backslash
-end{displaymath}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\backslash
-[
-\backslash
-frac{abc}{xyz}
-\backslash
-]
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-will convert it to:
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Formula \begin{equation}
-\frac{abc}{xyz}\end{equation}
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-At present, no formal way exists to convert the contents of a math inset
- back into plain text.
- It can be done using a
-\begin_inset Quotes eld
-\end_inset
-
-fudge
-\begin_inset Quotes erd
-\end_inset
-
- however.
- Highlight the contents of a math inset (not the math inset itself, just
- the contents), but do
-\emph default
-
-\emph on
-not
-\emph default
- copy it into LyX's buffer.
- It is now stored in the X system buffer and can be pasted back into the
- document using the middle mouse button.
-\end_layout
-
-\begin_layout Section
-
-Displaying LaTeX symbols
-\end_layout
-
-\begin_layout Standard
-
-Historically, LyX has provided visual support for a relatively small subset
- of the math symbols available in LaTeX.
- That changes with version 1.2; we now have visual support for most of the
- symbols defined in basic LaTeX and
-\emph default
-
-\emph on
-all
-\emph default
- the extra ones defined by the AMS.
- For completeness, the tables of symbols in Lamport's and in Goosen's books
- are presented below.
-\end_layout
-
-\begin_layout Section
-
-Some example math tables
-\end_layout
-
-\begin_layout Standard
-
-The following tables from Goossen et al.'s
-\begin_inset Quotes eld
-\end_inset
-
-The LaTeX companion
-\begin_inset Quotes erd
-\end_inset
-
- should appear on the screen in all their glory.
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset ERT
-status collapsed
-
-\begin_layout Standard
-
-\backslash
-setcounter{table}{1}
-\end_layout
-
-\begin_layout Standard
-
-\end_layout
-
-\begin_layout Standard
-
-\backslash
-renewcommand{
-\backslash
-thetable}{8.
-\backslash
-arabic{table}}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="2" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\hat{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-hat{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\acute{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-acute{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\bar{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bar{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\dot{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-dot{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\breve{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-breve{a}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\check{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-check{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\grave{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-grave{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\vec{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vec{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\ddot{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ddot{a}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\begin_inset Formula $\tilde{a}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-tilde{a}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Math mode accents
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="11" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\alpha$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-alpha
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\beta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-beta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gamma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\delta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-delta
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\epsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-epsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varepsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varepsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\zeta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-zeta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\eta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-eta
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\theta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-theta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vartheta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vartheta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\iota$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-iota
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\kappa$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-kappa
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lambda$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lambda
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\mu$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-mu
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nu$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nu
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\xi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-xi
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $o$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-o
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\pi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-pi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varpi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varpi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rho
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varrho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varrho
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sigma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varsigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varsigma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\tau$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-tau
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\upsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-upsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\phi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-phi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varphi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varphi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\chi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-chi
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\psi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-psi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\omega$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-omega
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Gamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Gamma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Delta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Delta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Theta$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Theta
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Lambda$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Lambda
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Xi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Xi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Pi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Pi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Sigma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Sigma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Upsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Upsilon
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Phi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Phi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Psi$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Psi
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Omega$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Omega
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Greek letters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="9" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\pm$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-pm
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-cap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\diamond$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-diamond
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\oplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-oplus
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\mp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-mp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-cup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigtriangleup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigtriangleup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ominus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ominus
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\times$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-times
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\uplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-uplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigtriangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigtriangledown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\otimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-otimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\div$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-div
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqcap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqcap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\triangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-triangleleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\oslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-oslash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ast$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ast
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqcup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\triangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-triangleright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\odot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-odot
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\star$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-star
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vee
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigcirc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circ$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circ
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\wedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-wedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\dagger$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-dagger
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bullet$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bullet
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\setminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-setminus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\unlhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-unlhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ddagger$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ddagger
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-cdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\wr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-wr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\unrhd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-unrhd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\amalg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-amalg
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Binary operation symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leq
-\backslash
-le
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\geq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-geq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\equiv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-equiv
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\models$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-models
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\prec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-prec
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succ$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succ
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\perp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-perp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\preceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-preceq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\simeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-simeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\mid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-mid
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ll$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ll
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gg
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\asymp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-asymp
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\parallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-parallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\subset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-subset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\supset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-supset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\approx$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-approx
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bowtie$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bowtie
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\subseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-subseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\supseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-supseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cong$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-cong
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Join$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Join
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqsubset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqsubset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqsupset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqsupset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\neq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-neq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\smile$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-smile
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqsubseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqsubseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqsupseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqsupseteq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\doteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-doteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\frown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-frown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\in$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-in
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ni$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ni
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\propto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-propto
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $=$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-=
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vdash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\dashv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-dashv
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $<$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-<
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $>$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
->
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Relation symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="10" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\longleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-longleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-uparrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Leftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Leftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Longleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Longleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Uparrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\longrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-longrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-downarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Rightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Rightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Longrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Longrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Downarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\longleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-longleftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-updownarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Leftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Leftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Longleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Longleftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Updownarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\mapsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-mapsto
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\longmapsto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-longmapsto
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nearrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nearrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\hookleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-hookleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\hookrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-hookrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\searrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-searrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftharpoonup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftharpoonup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightharpoonup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightharpoonup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\swarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-swarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftharpoondown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftharpoondown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightharpoondown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightharpoondown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nwarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nwarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Arrow symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="7" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ldots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ldots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cdots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-cdots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vdots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vdots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ddots$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ddots
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\aleph$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-aleph
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\prime$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-prime
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\forall$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-forall
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\infty$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-infty
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\hbar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-hbar
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\emptyset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-emptyset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\exists$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-exists
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nabla$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nabla
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\surd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-surd
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Box$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Box
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\triangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-triangle
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Diamond$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Diamond
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\imath$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-imath
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\jmath$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-jmath
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ell$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ell
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\neg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-neg
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\top$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-top
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\flat$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-flat
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\natural$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-natural
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sharp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sharp
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\wp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-wp
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\clubsuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-clubsuit
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\diamondsuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-diamondsuit
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\heartsuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-heartsuit
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\spadesuit$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-spadesuit
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\mho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-mho
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Re$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Re
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Im$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Im
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\angle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-angle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\partial$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-partial
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Miscellaneous symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sum$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sum
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\prod$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-prod
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\coprod$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-coprod
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\int$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-int
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\oint$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-oint
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigcap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigcap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigcup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigsqcup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigsqcup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigvee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigvee
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigwedge
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigodot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigodot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigotimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigotimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigoplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigoplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\biguplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-biguplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Variable-sized symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="4" columns="8">
-<features>
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\arccos$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cos$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\csc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\exp$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ker$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\limsup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\min$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sinh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\arcsin$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cosh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\deg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gcd$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ln$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Pr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\arctan$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\cot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\det$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\hom$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\log$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\tan$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\arg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\coth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\dim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\inf$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\liminf$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\max$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sin$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\tanh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Log-like symbols
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-uparrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Uparrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Uparrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-downarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Downarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Downarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\{$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-{
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-updownarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Updownarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Updownarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lfloor$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lfloor
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rfloor$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rfloor
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lceil$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lceil
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rceil$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rceil
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\langle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-langle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rangle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $/$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-/
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\backslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-backslash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $|$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-|
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\|$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-|
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-Delimiters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="6" columns="4">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\widetilde{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-widetilde{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\widehat{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-widehat{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\overleftarrow{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-overleftarrow{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\overrightarrow{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-overrightarrow{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\overline{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-overline{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\underline{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-underline{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\overbrace{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-overbrace{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\underbrace{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-underbrace{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqrt{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqrt{abc}
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqrt[n]{abc}\sqrt[3]{abc}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqrt[n]{abc}
-\backslash
-root3{abc}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $f'$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-f'
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\frac{abc}{xyz}$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-frac{abc}{xyz}
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-LaTeX math constructs
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="1" columns="10">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\digamma$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-digamma
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varkappa$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varkappa
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\beth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-beth
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\daleth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-daleth
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gimel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gimel
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS Greek and Hebrew
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="1" columns="8">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ulcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ulcorner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\urcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-urcorner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\llcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-llcorner
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lrcorner$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lrcorner
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS delimiters
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="11" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\dashrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-dashrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\dashleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-dashleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftleftarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftleftarrows
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftrightarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftrightarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Lleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Lleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\twoheadleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-twoheadleftarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftarrowtail$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftarrowtail
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\looparrowleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-looparrowleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftrightharpoons$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftrightharpoons
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\curvearrowleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-curvearrowleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circlearrowleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circlearrowleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Lsh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Lsh
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\upuparrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-upuparrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\upharpoonleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-upharpoonleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\downharpoonleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-downharpoonleft
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\multimap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-multimap
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftrightsquigarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftrightsquigarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightrightarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightrightarrows
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightleftarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightleftarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightrightarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightrightarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightleftarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightleftarrows
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\twoheadrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-twoheadrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightarrowtail$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightarrowtail
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\looparrowright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-looparrowright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightleftharpoons$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightleftharpoons
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\curvearrowright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-curvearrowright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circlearrowright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circlearrowright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Rsh$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Rsh
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\downdownarrows$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-downdownarrows
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\upharpoonright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-upharpoonright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\downharpoonright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-downharpoonright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightsquigarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightsquigarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS arrows
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="2" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nleftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nleftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nLeftarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nLeftarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nRightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nRightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nleftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nleftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nLeftrightarrow$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nLeftrightarrow
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS negated arrows
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="22" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leqslant
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\eqslantless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-eqslantless
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lesssim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lesssim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lessapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lessapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\approxeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-approxeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lessdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lessdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lll$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lll
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lessgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lessgtr
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lesseqgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lesseqgtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lesseqqgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lesseqqgtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\doteqdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-doteqdot
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\risingdotseq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-risingdotseq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\fallingdotseq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-fallingdotseq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\backsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-backsim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\backsimeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-backsimeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\subseteqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-subseteqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Subset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Subset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqsubset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqsubset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\preccurlyeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-preccurlyeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\curlyeqprec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-curlyeqprec
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\precsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-precsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\precapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-precapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vartriangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vartriangleleft
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\trianglelefteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-trianglelefteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vDash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Vvdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Vvdash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\smallsmile$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-smallsmile
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\smallfrown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-smallfrown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bumpeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bumpeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Bumpeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Bumpeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\geqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-geqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\geqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-geqslant
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\eqslantgtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-eqslantgtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gtrsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gtrsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gtrapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gtrapprox
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gtrdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gtrdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ggg$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ggg
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gtrless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gtrless
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gtreqless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gtreqless
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gtreqqless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gtreqqless
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\eqcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-eqcirc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\triangleq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-triangleq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\thicksim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-thicksim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\thickapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-thickapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\supseteqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-supseteqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Supset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Supset
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sqsupset$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sqsupset
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succcurlyeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succcurlyeq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\curlyeqsucc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-curlyeqsucc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vartriangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vartriangleright
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\trianglerighteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-trianglerighteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Vdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Vdash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\shortmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-shortmid
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\shortparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-shortparallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\between$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-between
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\pitchfork$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-pitchfork
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varpropto$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varpropto
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\blacktriangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-blacktriangleleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\therefore$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-therefore
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\backepsilon$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-backepsilon
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\blacktriangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-blacktriangleright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\because$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-because
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS binary relations
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="17" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nless$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nless
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nleq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nleq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nleqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nleqslant
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nleqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nleqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lneqq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lvertneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lvertneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lnsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lnapprox
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nprec$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nprec
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\npreceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-npreceq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\precnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-precnsim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\precnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-precnapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nshortmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nshortmid
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nmid$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nmid
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nvdash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nvdash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nvDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nvDash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ntriangleleft$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ntriangleleft
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ntrianglelefteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ntrianglelefteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nsubseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nsubseteq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\subsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-subsetneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varsubsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varsubsetneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\subsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-subsetneqq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varsubsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varsubsetneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ngtr$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ngtr
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ngeq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ngeq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ngeqslant$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ngeqslant
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ngeqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ngeqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gneq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gvertneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gvertneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gnsim
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\gnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-gnapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nsucc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nsucc
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nsucceq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nsucceq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succnsim$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succnsim
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\succnapprox$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-succnapprox
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ncong$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ncong
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nshortparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nshortparallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nparallel$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nparallel
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nvDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nvDash
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nVDash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nVDash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ntriangleright$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ntriangleright
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ntrianglerighteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ntrianglerighteq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nsupseteq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nsupseteq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nsupseteqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nsupseteqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\supsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-supsetneq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varsupsetneq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varsupsetneq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\supsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-supsetneqq
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varsupsetneqq$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varsupsetneqq
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS negated binary relations
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\dotplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-dotplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\smallsetminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-smallsetminus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Cap$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Cap
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Cup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Cup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\barwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-barwedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\veebar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-veebar
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\doublebarwedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-doublebarwedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\boxminus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-boxminus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\boxtimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-boxtimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\boxdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-boxdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\boxplus$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-boxplus
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\divideontimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-divideontimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\ltimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-ltimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rtimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rtimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\leftthreetimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-leftthreetimes
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\rightthreetimes$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-rightthreetimes
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\curlywedge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-curlywedge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\curlyvee$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-curlyvee
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circleddash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circleddash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circledast$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circledast
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circledcirc$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circledcirc
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\centerdot$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-centerdot
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\intercal$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-intercal
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS binary operators
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-
-
-\begin_inset Float table
-placement H
-wide false
-sideways false
-status open
-
-\begin_layout Standard
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="9" columns="6">
-<features>
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<column alignment="right" valignment="top" width="0pt">
-<column alignment="left" valignment="top" width="0pt">
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\hbar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-hbar
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\hslash$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-hslash
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\vartriangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-vartriangle
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\triangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-triangledown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\square$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-square
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\lozenge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-lozenge
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\circledS$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-circledS
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\angle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-angle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\measuredangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-measuredangle
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\nexists$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-nexists
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\mho$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-mho
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Finv$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Finv
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Game$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Game
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\Bbbk$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-Bbbk
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\backprime$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-backprime
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\varnothing$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-varnothing
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\blacktriangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-blacktriangle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\blacktriangledown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-blacktriangledown
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\blacksquare$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-blacksquare
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\blacklozenge$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-blacklozenge
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\bigstar$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-bigstar
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\sphericalangle$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-sphericalangle
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\complement$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-complement
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\eth$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-eth
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\diagup$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-diagup
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\begin_inset Formula $\diagdown$
-\end_inset
-
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-
-\family typewriter
-
-\backslash
-diagdown
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Standard
-
-\end_layout
-
-\end_inset
-</cell>
-</row>
-</lyxtabular>
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout
-\begin_inset Caption
-
-\begin_layout
-
-AMS miscellaneous
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document
Item "Tutorial|T" "help-open Tutorial"
Item "User's Guide|U" "help-open UserGuide"
Item "Extended Features|E" "help-open Extended"
- Item "Embedded Objects|m" "help-open EmbeddedObjects"
+ Item "Embedded Objects|m" "help-open EmbeddedObjects"
+ Item "Math|h" "help-open Math"
Item "Customization|C" "help-open Customization"
Item "Shortcuts|S" "help-open Shortcuts"
Item "FAQ|F" "help-open FAQ"
projects / features.git / commitdiff