From cfdad9946d1cc98bead1a3fdb543fff201944588 Mon Sep 17 00:00:00 2001 From: =?utf8?q?Uwe=20St=C3=B6hr?= Date: Sun, 27 Jan 2008 20:58:45 +0000 Subject: [PATCH] I wrote a new manual "LyX's detailed math manual". See the announcement on the list. The file examples/mathed.lyx is no longer needed as its content is part of the new manual. git-svn-id: svn://svn.lyx.org/lyx/lyx-devel/trunk@22691 a592a061-630c-0410-9148-cb99ea01b6c8 --- development/scons/build_msvc.bat | 2 +- development/scons/scons_manifest.py | 6 +- lib/Makefile.am | 2 - lib/doc/Formula-numbering.lyx | 374 + lib/doc/Makefile.am | 4 + lib/doc/Makefile.depend | 40 +- lib/doc/Math.lyx | 33322 +++++++++++++++++++++++++ lib/doc/de/Formelnummerierung.lyx | 376 + lib/doc/de/Math.lyx | 33674 ++++++++++++++++++++++++++ lib/doc/depend.py | 2 +- lib/examples/de/mathed.lyx | 13075 ---------- lib/examples/mathed.lyx | 14594 ----------- lib/ui/stdmenus.inc | 3 +- 13 files changed, 67778 insertions(+), 27696 deletions(-) create mode 100644 lib/doc/Formula-numbering.lyx create mode 100644 lib/doc/Math.lyx create mode 100644 lib/doc/de/Formelnummerierung.lyx create mode 100644 lib/doc/de/Math.lyx delete mode 100644 lib/examples/de/mathed.lyx delete mode 100644 lib/examples/mathed.lyx diff --git a/development/scons/build_msvc.bat b/development/scons/build_msvc.bat index 85df663410..d76a67994f 100644 --- a/development/scons/build_msvc.bat +++ b/development/scons/build_msvc.bat @@ -1 +1 @@ -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 diff --git a/development/scons/scons_manifest.py b/development/scons/scons_manifest.py index 2ae6fbe851..0ca4fa4ab1 100644 --- a/development/scons/scons_manifest.py +++ b/development/scons/scons_manifest.py @@ -2024,8 +2024,10 @@ lib_doc_files = Split(''' EmbeddedObjects.lyx Extended.lyx FAQ.lyx + Formula-numbering.lyx Intro.lyx LaTeXConfig.lyx + Math.lyx Reference.lyx Shortcuts.lyx Tutorial.lyx @@ -2095,7 +2097,9 @@ lib_doc_de_files = Split(''' EmbeddedObjects.lyx Extended.lyx FAQ.lyx + Formelnummerierung.lyx Intro.lyx + Math.lyx Tutorial.lyx UserGuide.lyx ''') @@ -2308,7 +2312,6 @@ lib_examples_files = Split(''' linguistics.lyx listerrors.lyx listings.lyx - mathed.lyx modernCV.lyx multicol.lyx noweb2lyx.lyx @@ -2341,7 +2344,6 @@ lib_examples_de_files = Split(''' Minipage.lyx beispiel_gelyxt.lyx beispiel_roh.lyx - mathed.lyx multicol.lyx splash.lyx ''') diff --git a/lib/Makefile.am b/lib/Makefile.am index 34df22eddc..ece1cd7e36 100644 --- a/lib/Makefile.am +++ b/lib/Makefile.am @@ -90,7 +90,6 @@ dist_deexamples_DATA = \ 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 @@ -221,7 +220,6 @@ dist_examples_DATA = \ examples/linguistics.lyx \ examples/listerrors.lyx \ examples/listings.lyx \ - examples/mathed.lyx \ examples/modernCV.lyx \ examples/multicol.lyx \ examples/noweb2lyx.lyx \ diff --git a/lib/doc/Formula-numbering.lyx b/lib/doc/Formula-numbering.lyx new file mode 100644 index 0000000000..62b96a1601 --- /dev/null +++ b/lib/doc/Formula-numbering.lyx @@ -0,0 +1,374 @@ +#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 diff --git a/lib/doc/Makefile.am b/lib/doc/Makefile.am index 7309b865d8..0b4e9a1d97 100644 --- a/lib/doc/Makefile.am +++ b/lib/doc/Makefile.am @@ -59,7 +59,9 @@ dist_dedoc_DATA = \ de/EmbeddedObjects.lyx \ de/Extended.lyx \ de/FAQ.lyx \ + de/Formelnummerierung.lyx \ de/Intro.lyx \ + de/Math.lyx \ de/Tutorial.lyx \ de/UserGuide.lyx @@ -217,8 +219,10 @@ dist_doc_DATA = \ EmbeddedObjects.lyx \ Extended.lyx \ FAQ.lyx \ + Formula-numbering.lyx \ Intro.lyx \ LaTeXConfig.lyx \ + Math.lyx \ Reference.lyx \ Shortcuts.lyx \ Tutorial.lyx \ diff --git a/lib/doc/Makefile.depend b/lib/doc/Makefile.depend index de564d3ec1..9a8088f14f 100644 --- a/lib/doc/Makefile.depend +++ b/lib/doc/Makefile.depend @@ -4,64 +4,64 @@ # 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 diff --git a/lib/doc/Math.lyx b/lib/doc/Math.lyx new file mode 100644 index 0000000000..8c60a905fc --- /dev/null +++ b/lib/doc/Math.lyx @@ -0,0 +1,33322 @@ +#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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Unit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Name / Description +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +mm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Millimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +cm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Centimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Inch (1\InsetSpace \thinspace{} +in = 2,54\InsetSpace \thinspace{} +cm) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +pt +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Point (72.27\InsetSpace \thinspace{} +pt = 1\InsetSpace \thinspace{} +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +pc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Pica (1\InsetSpace \thinspace{} +pc = 12\InsetSpace \thinspace{} +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +sp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +scaled point (65536\InsetSpace \thinspace{} +sp = 1\InsetSpace \thinspace{} +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +bp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +big point (72\InsetSpace \thinspace{} +bp = 1\InsetSpace \thinspace{} +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +dd +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +cc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Cicero (1\InsetSpace \thinspace{} +cc = 12\InsetSpace \thinspace{} +dd) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +ex +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +em +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +mu +\end_layout + +\end_inset + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +B_V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $B_{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +B^V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}B^{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}B^{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dbinom{A +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\begin{cases} +A & B>0\end{cases}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Indices created with sub- and superscripts: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +correct indices: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1},\dots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1}+\dots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1},\ldots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1}+\cdots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vdots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vdots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ddots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +3×3\InsetSpace \thinspace{} +matrix with the different dots +\end_layout + +\end_inset + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $($ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +{ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\{$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +[ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $[$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +langle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\langle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +/ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $/$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $)$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +] +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $]$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash + +\backslash + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\backslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +all brackets in the same size: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +this looks better: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigl) +\backslash +ln(3x) +\backslash +bigr( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\overbrace{A+B}^{3}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\underbrace{A+B}_{5}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gets +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gets$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Leftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leftharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leftharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hookleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hookleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +to +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\to$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Rightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rightharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rightharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hookrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hookrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\end_layout + +\begin_layout Standard + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightleftharpoons +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rightleftharpoons$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +hspace{25pt} +\end_layout + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longmapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longmapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leadsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leadsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dasharrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nearrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nearrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +searrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\searrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +swarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\swarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nwarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nwarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\dot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddddot{A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\vec{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\bar{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\hat{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\check{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\acute{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\grave{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\breve{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\lang ngerman +\begin_inset Quotes grd +\end_inset + +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\lang ngerman +\begin_inset Formula $"i$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +, +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +; +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +quad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +qquad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +! +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Number of +\family sans +Space +\family default + keystrokes after inserting the protected space +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +4 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +5 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\, B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\: B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\; B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\quad B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\qquad B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\! B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +negmedspace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +negthickspace +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Number of +\family sans +Space +\family default + keystrokes after inserting the protected space +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +6 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +7 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\negmedspace B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\negthickspace B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +normal equation +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A{=}B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +24 kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +space between value and unit +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +24\InsetSpace \thinspace{} +kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +smallest space between value and unit +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A=B\hspace{3cm}A\not=C$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +A +\backslash +hspace{-1mm +\begin_inset Formula $\to$ +\end_inset + +A +\backslash +not=A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\hspace{-1mm}A\not=A$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A=A\hfill B=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\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 + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{} + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $H\raisebox{2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $H\raisebox{-2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +colorbox{yellow +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sum +\begin_inset LatexCommand index +name "Commands ! S ! \\textbackslash sum" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sum$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +int +\begin_inset LatexCommand index +name "Commands ! I ! \\textbackslash int" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\int$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +intop +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\intop$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\oint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ointop +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ointop$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ointctrclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ointctrclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ointclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ointclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +prod +\begin_inset LatexCommand index +name "Commands ! P ! \\textbackslash prod" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\prod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +coprod +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\coprod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigodot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigodot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigotimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigotimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigoplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigoplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigwedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigwedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigvee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigvee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigsqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigsqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +biguplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\biguplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iiiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dotsint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard ++ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $+$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $-$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +pm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\pm$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cdot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cdot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +times +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\times$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +div +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\div$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $*$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +star +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\star$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +circ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\circ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nabla +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nabla$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigtriangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigtriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigtriangleup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigtriangleup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Box +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Box$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ddagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\wr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigcirc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigcirc$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\wedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\oplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ominus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ominus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +otimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\otimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\oslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +odot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\odot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +amalg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\amalg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +uplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\uplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +setminus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\setminus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +triangleleft +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\triangleleft$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +triangleright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\triangleright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +shortcut +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathbb{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z k +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathbf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z f +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\boldsymbol{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathcal{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z h +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathfrak{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +shortcut +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathit{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathrm{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z r +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathsf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z s +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathtt{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +alpha +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\alpha$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +beta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\beta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +epsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\epsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varepsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varepsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +zeta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\zeta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +eta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\eta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vartheta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vartheta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iota +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\iota$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +kappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\kappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varkappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varkappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $o$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varpi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varpi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varrho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varrho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varsigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varsigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +tau +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\tau$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varphi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varphi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +chi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\chi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Upsilon +\backslash +boldsymbol +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +theta +\backslash +boldsymbol +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\theta\boldsymbol{\theta}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +neg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\neg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Im +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Im$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Re +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Re$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +aleph +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\aleph$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +partial +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\partial$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +infty +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\infty$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\wp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +imath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\imath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +jmath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\jmath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +forall +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\forall$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +exists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\exists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nexists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nexists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +emptyset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\emptyset$ +\end_inset + + +\end_layout + +\end_inset + + + + 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+ +\begin_inset ERT +status collapsed + +\begin_layout Standard + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Bbbk +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Bbbk$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +prime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\prime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +backprime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\backprime$ 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Standard + +\backslash +sphericalangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sphericalangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +top +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\top$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 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+\begin_layout Standard +\begin_inset Formula $\surd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +checkmark +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\checkmark$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +yen +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\yen$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +pounds +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\pounds$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +$ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\$$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +§ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $§$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hbar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hbar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +clubsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\clubsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +spadesuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\spadesuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigstar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigstar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +blacklozenge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\blacklozenge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +blacktriangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\blacktriangle$ +\end_inset + + 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+\begin_layout Standard + +\backslash +Diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +heartsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\heartsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +P +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\P$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +copyright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\copyright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +circledR +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\circledR$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +maltese +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\maltese$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diagup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diagup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diagdown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diagdown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + +\begin_inset Text + +\begin_layout Standard + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +formula +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +euro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\euro$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +mathematical text +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +€ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mbox{€}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +TeX-mode +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +officialeuro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +officialeuro +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 +eurosym +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the package +\series bold +eurosym +\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 Section +Relations +\begin_inset LatexCommand label +name "sec:Relations" + +\end_inset + + +\begin_inset LatexCommand index +name "Relations" + +\end_inset + + +\begin_inset LatexCommand index +name "Comparisons|see{Relations}" + +\end_inset + + +\end_layout + +\begin_layout Standard +All relations can also be inserted via the toolbar button +\begin_inset Graphics + filename ../images/math/leq.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +< +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $<$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ll +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ll$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +prec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\prec$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +preceq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\preceq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +subset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\subset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +subseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\subseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqsubseteq +\end_layout + +\end_inset + + +\begin_inset Text + 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+\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\notin$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +perp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\perp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +propto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\propto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +asymp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\asymp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +doteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\doteq$ +\end_inset + + +\end_layout 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+ +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $>$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +succ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\succ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +succeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\succeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +supset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\supset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +supseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\supseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqsupseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqsupseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ni +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ni$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dashv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dashv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +frown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\frown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +unrhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\unrhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lessgtr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lessgtr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nparallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nparallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Asin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $Asin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +A +\backslash +sin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\sin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sinh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arcsin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cosh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arccos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +inf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +tan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +tanh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arctan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lim +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +coth +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +liminf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +min +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +deg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +limsup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +csc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +max +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +det +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Pr +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ln +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +exp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +log +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ker +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gcd +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +A +\backslash +sgn(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\sgn(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\,\textrm{sgn}(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varliminf +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varliminf$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varlimsup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varlimsup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varprojlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varprojlim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varinjlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varinjlim$ +\end_inset + + +\begin_inset Formula $\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oe +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\oe}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +OE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\OE}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ae +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\ae}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +AE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\AE}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +aa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\aa}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +AA +\begin_inset LatexCommand index +name "\\@\\textrm{\\AA}" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\AA}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\i}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\o}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +O +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\O}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +l +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\l}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +L +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\L}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{!`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{?`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +j +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\j}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash + +\begin_inset Quotes grd +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +"e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +`e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +`e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +^e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +=e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +=e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +'e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +'e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +~e +\begin_inset LatexCommand index +name "Tilde" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +~e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +.e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +.e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +textcircled{w} +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Large +\backslash +textcircled{ +\backslash +normalsize +\backslash +protect +\backslash +raisebox{-1.5pt}{W}} +\end_layout + +\end_inset + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathcircumflex$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +_ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\_$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $^{\circ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 +() +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\gr B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +us{ABcd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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@<<>> +\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 \[ +\begin{CD}A@>j>>B@>>k>C@=F\\ +@AmAA@.@VV{V}V@|\\ +D@<k>>F@=C\end{CD}\] + +\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@<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 + + + + + + +\begin_inset Text + +\begin_layout Standard +normal text: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +x = -2 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +formula: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $x=-2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +solution: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $x=\textrm{-}2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Bra{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Bra{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Ket{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Ket{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Braket{ +\backslash +psi| +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Braket{\psi|\phi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Number +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Style (Size) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +display style formula +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +inline formula +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +small +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +tiny +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ast +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +choose +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +binom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +geq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +{ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +[ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gets +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +le +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vee +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +neq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +slash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +/ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +| +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +equivalent to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +backslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash + +\backslash + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dashrightarrow +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +land +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wedge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +} +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +] +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lnot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +neg +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ne +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +owns +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ni +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +square +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Box +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +| +\end_layout + +\end_inset + + + + +\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 + +Description +\begin_inset ERT +status collapsed + +\begin_layout Standard + +} +\end_layout + +\end_inset + + of LaTeX's math abilities +\end_layout + +\begin_layout Bibliography +\begin_inset LatexCommand bibitem +key "Voss" + +\end_inset + +LaTeX tips and tricks- +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +href{http://tug.org/TeXnik/}{ +\end_layout + +\end_inset + +page +\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 + +Description +\begin_inset ERT +status collapsed + +\begin_layout Standard + +} +\end_layout + +\end_inset + + of +\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 + +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 + +\begin_layout Standard + + +\backslash +href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{ +\end_layout + +\end_inset + +Documentation +\begin_inset ERT +status collapsed + +\begin_layout Standard + +} +\end_layout + +\end_inset + + of the LaTeX-package +\series bold +hyperref +\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 diff --git a/lib/doc/de/Formelnummerierung.lyx b/lib/doc/de/Formelnummerierung.lyx new file mode 100644 index 0000000000..a1a6d47643 --- /dev/null +++ b/lib/doc/de/Formelnummerierung.lyx @@ -0,0 +1,376 @@ +#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-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 +\options fleqn +\language ngerman +\inputencoding auto +\font_roman ae +\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 german +\papercolumns 1 +\papersides 1 +\paperpagestyle empty +\tracking_changes false +\output_changes false +\author "" +\end_header + +\begin_body + +\begin_layout Standard +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} + +\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 +setroem +\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 +setroem +\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 +Querverweise: +\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 + +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 + +\series bold + +\backslash +newcounter{roem} +\newline + +\backslash +renewcommand{ +\backslash +theroem}{ +\backslash +roman{roem}} +\end_layout + +\begin_layout Standard + +\newpage +Damit sich LaTeX den Zählerstand des arabischen Zählers +\series bold +equation +\series default + merkt, gibt man im Vorspann +\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 +ein. + Um im Dokument zwischen den beiden Nummerierungen umschalten zu können, + werden folgende beiden Befehle im Vorspann definiert: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +newcommand{ +\backslash +setroem}{ +\backslash +let +\backslash +c@equation +\backslash +c@roem +\backslash +let +\backslash +theequation +\backslash +theroem} +\end_layout + +\begin_layout Standard +für römische Nummerierung und +\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 +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 diff --git a/lib/doc/de/Math.lyx b/lib/doc/de/Math.lyx new file mode 100644 index 0000000000..f0acc22f63 --- /dev/null +++ b/lib/doc/de/Math.lyx @@ -0,0 +1,33674 @@ +#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 +\family sans +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 +Option +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Einheit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Name / Beschreibung +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +mm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Millimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +cm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Zentimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Inch / Zoll (1\InsetSpace \thinspace{} +in = 2,54\InsetSpace \thinspace{} +cm) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +pt +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Punkt (72,27\InsetSpace \thinspace{} +pt = 1\InsetSpace \thinspace{} +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +pc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Pica (1\InsetSpace \thinspace{} +pc = 12\InsetSpace \thinspace{} +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +sp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +scaled point (65536\InsetSpace \thinspace{} +sp = 1\InsetSpace \thinspace{} +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +bp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +big point (72\InsetSpace \thinspace{} +bp = 1\InsetSpace \thinspace{} +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +dd +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +cc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Cicero (1\InsetSpace \thinspace{} +cc = 12\InsetSpace \thinspace{} +dd) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +ex +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Höhe des Buchstabens +\emph on +x +\emph default + in der aktuellen Schrift +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +em +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Breite des Buchstabens +\emph on +M +\emph default + in der aktuellen Schrift +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +mu +\end_layout + +\end_inset + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +B_V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $B_{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +B^V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}B^{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}B^{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dbinom{A +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\begin{cases} +A & B>0\end{cases}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +durch Hoch- und Tiefstellen erzeugte Indizes: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +korrekte Indizes: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1},\dots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1}+\dots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1},\ldots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A_{1}+\cdots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vdots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vdots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ddots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +3 +\series bold +× +\series default +3\InsetSpace \thinspace{} +Matrix mit obigen Befehlen +\end_layout + +\end_inset + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $($ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +{ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\{$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +[ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $[$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +langle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\langle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +/ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $/$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $)$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +] +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $]$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash + +\backslash + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\backslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +einheitliche Klammergröße: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +besser sieht das so aus: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigl) +\backslash +ln(3x) +\backslash +bigr( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\overbrace{A+B}^{3}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\underbrace{A+B}_{5}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gets +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gets$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Leftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leftharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leftharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hookleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hookleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +to +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\to$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Rightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rightharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rightharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hookrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hookrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\end_layout + +\begin_layout Standard + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightleftharpoons +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rightleftharpoons$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +hspace{25pt} +\end_layout + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +longmapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\longmapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leadsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\leadsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dasharrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nearrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nearrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +searrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\searrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +swarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\swarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nwarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nwarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\dot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddddot{A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\vec{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\bar{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\hat{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\check{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\acute{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\grave{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\breve{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Quotes grd +\end_inset + +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $"i$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +, +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +; +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +quad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +qquad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +! +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Anzahl der Leertastendrücke nach Eingabe des geschützten Leerzeichens +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +4 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +5 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\, B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\: B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\; B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\quad B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\qquad B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\! B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +negmedspace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +negthickspace +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Anzahl der Leertastendrücke nach Eingabe des geschützten Leerzeichens +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +6 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +7 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\negmedspace B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\negthickspace B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +normale Gleichung +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A{=}B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +24 kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Leerzeichen zwischen Wert und Einheit +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +24\InsetSpace \thinspace{} +kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +kleinster Leerraum zwischen Wert und Einheit +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A=B\hspace{3cm}A\not=C$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +A +\backslash +hspace{-1mm +\begin_inset Formula $\to$ +\end_inset + +A +\backslash +not=A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\hspace{-1mm}A\not=A$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A=A\hfill B=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\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 + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{} + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $H\raisebox{2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $H\raisebox{-2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +colorbox{yellow +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sum +\begin_inset LatexCommand index +name "Befehle ! S ! \\textbackslash sum" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sum$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +int +\begin_inset LatexCommand index +name "Befehle ! I ! \\textbackslash int" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\int$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +intop +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\intop$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\oint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ointop +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ointop$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ointctrclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ointctrclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ointclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ointclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +prod +\begin_inset LatexCommand index +name "Befehle ! P ! \\textbackslash prod" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\prod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +coprod +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\coprod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigodot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigodot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigotimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigotimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigoplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigoplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigwedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigwedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigvee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigvee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigsqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigsqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +biguplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\biguplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iiiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dotsint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard ++ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $+$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $-$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +pm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\pm$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cdot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cdot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +times +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\times$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +div +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\div$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $*$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +star +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\star$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +circ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\circ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nabla +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nabla$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigtriangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigtriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigtriangleup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigtriangleup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Box +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Box$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ddagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\wr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigcirc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigcirc$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\wedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\oplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ominus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ominus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +otimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\otimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\oslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +odot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\odot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +amalg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\amalg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +uplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\uplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +setminus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\setminus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +triangleleft +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\triangleleft$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +triangleright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\triangleright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Tastenkürzel +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathbb{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z k +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathbf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z f +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\boldsymbol{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathcal{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z h +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathfrak{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Tastenkürzel +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathit{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathrm{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z r +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathsf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Alt-z s +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathtt{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +- +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +alpha +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\alpha$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +beta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\beta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +epsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\epsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varepsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varepsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +zeta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\zeta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +eta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\eta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vartheta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vartheta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +iota +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\iota$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +kappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\kappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varkappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varkappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $o$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varpi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varpi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varrho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varrho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varsigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varsigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +tau +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\tau$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varphi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varphi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +chi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\chi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Upsilon +\backslash +boldsymbol +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +theta +\backslash +boldsymbol +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\theta\boldsymbol{\theta}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +neg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\neg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Im +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Im$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Re +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Re$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +aleph +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\aleph$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +partial +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\partial$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +infty +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\infty$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\wp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +imath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\imath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +jmath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\jmath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +forall +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\forall$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +exists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\exists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nexists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nexists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +emptyset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\emptyset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varnothing +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varnothing$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dag +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dag$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ddag +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ddag$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +complement +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Bbbk +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Bbbk$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +prime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\prime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +backprime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\backprime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +triangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\triangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +angle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\angle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +measuredangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\measuredangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sphericalangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sphericalangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +top +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\top$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +flat +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\flat$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +natural +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\natural$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sharp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sharp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +surd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\surd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +checkmark +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\checkmark$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +yen +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\yen$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +pounds +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\pounds$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +$ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\$$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +§ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $§$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hbar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hbar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\hslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +clubsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\clubsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +spadesuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\spadesuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bigstar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bigstar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +blacklozenge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\blacklozenge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +blacktriangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\blacktriangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +blacktiangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\blacktriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diamondsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diamondsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +heartsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\heartsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +P +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\P$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +copyright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\copyright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +circledR +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\circledR$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +maltese +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\maltese$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diagup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diagup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +diagdown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\diagdown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + +\begin_inset Text + +\begin_layout Standard + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Formel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +euro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\euro$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +mathematischer Text +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +€ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mbox{€}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +TeX-Modus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +officialeuro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +officialeuro +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +< +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $<$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ll +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ll$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +prec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\prec$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +preceq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\preceq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +subset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\subset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +subseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\subseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqsubseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqsubseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\in$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vdash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\vdash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +smile +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\smile$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +unlhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\unlhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gtrless +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gtrless$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +mid +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mid$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nmid +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nmid$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard += +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +equiv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\equiv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +simeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\simeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +approx +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\approx$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cong +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\cong$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +bowtie +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\bowtie$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +notin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\notin$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +perp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\perp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +propto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\propto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +asymp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\asymp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +doteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\doteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +circeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\circeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +models +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\models$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +widehat= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\widehat{=}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +> +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $>$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\gg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +succ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\succ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +succeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\succeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +supset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\supset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +supseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\supseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sqsupseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\sqsupseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ni +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\ni$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dashv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\dashv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +frown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\frown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\rhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +unrhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\unrhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lessgtr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\lessgtr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +nparallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\nparallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Asin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $Asin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +A +\backslash +sin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\sin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sinh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arcsin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cosh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arccos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +inf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +tan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +tanh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arctan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lim +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +cot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +coth +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +arg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +liminf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +sec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +min +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +deg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +limsup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +csc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +max +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +det +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Pr +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ln +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +exp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +hom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +log +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ker +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gcd +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +A +\backslash +sgn(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\sgn(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\,\textrm{sgn}(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varliminf +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varliminf$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varlimsup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varlimsup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varprojlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varprojlim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +varinjlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\varinjlim$ +\end_inset + + +\begin_inset Formula $\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +oe +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\oe}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +OE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\OE}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ae +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\ae}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +AE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\AE}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +aa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\aa}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +AA +\begin_inset LatexCommand index +name "\\@\\textrm{\\AA}" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\AA}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\i}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\o}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +O +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\O}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +l +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\l}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +L +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\L}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{!`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{?`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +j +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\textrm{\j}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash + +\begin_inset Quotes grd +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +"e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +`e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +`e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +^e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +=e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +=e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +u +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +leer +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +t +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +leer +\end_layout + +\end_inset + +ee +\end_layout + +\end_inset + + +\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 + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +H +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +leer +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +'e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +'e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +~e +\begin_inset LatexCommand index +name "Tilde" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +~e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +.e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Standard + + +\backslash +.e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +textcircled{w} +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Large +\backslash +textcircled{ +\backslash +normalsize +\backslash +protect +\backslash +raisebox{-1.5pt}{W}} +\end_layout + +\end_inset + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\mathcircumflex$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +_ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\_$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $^{\circ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 +() +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $A\gr B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +us{ABcd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + +\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 + + + + +\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@<<>> +\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 \[ +\begin{CD}A@>j>>B@>>k>C@=F\\ +@AmAA@.@VV{V}V@|\\ +D@<k>>F@=C\end{CD}\] + +\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@<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 + + + + + + +\begin_inset Text + +\begin_layout Standard +normaler Text: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +x = -2 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Formelmodus: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $x=-2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +Lösung: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $x=\textrm{-}2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ergebnis +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Bra{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Bra{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Ket{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Ket{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Braket{ +\backslash +psi| +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +\begin_inset Formula $\Braket{\psi|\phi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Nummer +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +Ansichtsstil +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +abgesetzte Formel +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +eingebettete Formel +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +klein +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +winzig +\end_layout + +\end_inset + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + +\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 + + + + +\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 + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ast +\end_layout + +\end_inset + + +\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 + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +choose +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +binom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +geq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +{ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +[ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +gets +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +leq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +le +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vee +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +neq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +slash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +/ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +| +\end_layout + +\end_inset + + + + +\end_inset + + +\hfill + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Standard +Befehl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +äquivalent zu +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +backslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash + +\backslash + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +dashrightarrow +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +land +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +wedge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +} +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard +] +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +lnot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +neg +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ne +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +owns +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +ni +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +square +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Box +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Standard + +\backslash +Vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Standard + +\backslash +| +\end_layout + +\end_inset + + + + +\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 +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 +\series default +. +\end_layout + +\end_inset + + +\begin_inset LatexCommand printindex + +\end_inset + + +\end_layout + +\end_body +\end_document diff --git a/lib/doc/depend.py b/lib/doc/depend.py index 4a5b585f66..deeb067afc 100644 --- a/lib/doc/depend.py +++ b/lib/doc/depend.py @@ -30,7 +30,7 @@ import os 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 diff --git a/lib/examples/de/mathed.lyx b/lib/examples/de/mathed.lyx deleted file mode 100644 index 0dba718ed4..0000000000 --- a/lib/examples/de/mathed.lyx +++ /dev/null @@ -1,13075 +0,0 @@ -#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 - - - - - -\begin_inset Text - -\begin_layout Standard - -\backslash -begin{math} -\backslash -frac{abc}{xyz} -\backslash -end{math} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - -\backslash -( -\backslash -frac{abc}{xyz} -\backslash -) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -$ -\backslash -frac{abc}{xyz} $ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - -\backslash -begin{displaymath} -\backslash -frac{abc}{xyz} -\backslash -end{displaymath} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - -\backslash -[ -\backslash -frac{abc}{xyz} -\backslash -] -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\hat{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -hat{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\acute{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -acute{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\bar{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bar{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\dot{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -dot{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\breve{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -breve{a} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\check{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -check{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\grave{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -grave{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\vec{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -vec{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\ddot{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -ddot{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter -\begin_inset Formula $\tilde{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -tilde{a} -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\alpha$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -alpha -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\beta$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -beta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\gamma$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -gamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\delta$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -delta -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\epsilon$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -epsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\varepsilon$ -\end_inset - 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- - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\uparrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -uparrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Leftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Uparrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Uparrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\downarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -downarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Rightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Downarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Downarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -updownarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Updownarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\mapsto$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -mapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\longmapsto$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -longmapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nearrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -nearrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\hookleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -hookleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\hookrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -hookrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\searrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -searrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leftharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leftharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rightharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -rightharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\swarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -swarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leftharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leftharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rightharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -rightharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nwarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -nwarrow -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\ldots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -ldots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\cdots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -cdots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\vdots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -vdots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\ddots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -ddots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\aleph$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -aleph -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\prime$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -prime -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\forall$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -forall -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\infty$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -infty -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\hbar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -hbar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\emptyset$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -emptyset -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\exists$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -exists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nabla$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -nabla -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\surd$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -surd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Box$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Box -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\triangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -triangle -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Diamond$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Diamond -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\imath$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -imath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\jmath$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -jmath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\ell$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -ell -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\neg$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -neg -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\top$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -top -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\flat$ -\end_inset - 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-\begin_layout Standard - -\family typewriter - -\backslash -bot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\clubsuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -clubsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\diamondsuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -diamondsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\heartsuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -heartsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\spadesuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -spadesuit -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\mho$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -mho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Re$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Re -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Im$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Im -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\angle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -angle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\partial$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -partial -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\sum$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -sum -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\prod$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -prod -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\coprod$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -coprod -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\int$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -int -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\oint$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -oint -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigcap$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigcap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigcup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigsqcup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigsqcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigvee$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigvee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigwedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigwedge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigodot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigodot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigotimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigotimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigoplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigoplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\biguplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -biguplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\arccos$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\cos$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\csc$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\exp$ -\end_inset - - -\end_layout - 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-\begin_layout Standard - -\family typewriter - -\backslash -rfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\lceil$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -lceil -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rceil$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -rceil -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\langle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -langle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - 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-\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\widetilde{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -widetilde{abc} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\widehat{abc}$ -\end_inset - - -\end_layout - 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-\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -nleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -nrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nLeftarrow$ -\end_inset - 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-\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leqq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leqq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leqslant$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leqslant -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\eqslantless$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -eqslantless -\end_layout - 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-\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\supsetneqq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -supsetneqq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\varsupsetneqq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -varsupsetneqq -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\dotplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -dotplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\smallsetminus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -smallsetminus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Cap$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Cap -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Cup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Cup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\barwedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -barwedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\veebar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -veebar -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\doublebarwedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -doublebarwedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\boxminus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -boxminus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\boxtimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -boxtimes -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\boxdot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -boxdot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\boxplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -boxplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\divideontimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -divideontimes -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\ltimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -ltimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rtimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -rtimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\leftthreetimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -leftthreetimes -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\rightthreetimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -rightthreetimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\curlywedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -curlywedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\curlyvee$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -curlyvee -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\circleddash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -circleddash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\circledast$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -circledast -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\circledcirc$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -circledcirc -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\centerdot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -centerdot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\intercal$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -intercal -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\hbar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -hbar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\hslash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -hslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\vartriangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -vartriangle -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\triangledown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -triangledown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\square$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -square -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\lozenge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -lozenge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\circledS$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -circledS -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\angle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -angle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\measuredangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -measuredangle -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\nexists$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -nexists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\mho$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -mho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Finv$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Finv -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Game$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Game -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\Bbbk$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -Bbbk -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\backprime$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -backprime -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\varnothing$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -varnothing -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\blacktriangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -blacktriangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\blacktriangledown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -blacktriangledown -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\blacksquare$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -blacksquare -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\blacklozenge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -blacklozenge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\bigstar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -bigstar -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\sphericalangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -sphericalangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\complement$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -complement -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\eth$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -eth -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\diagup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -diagup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard -\begin_inset Formula $\diagdown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\family typewriter - -\backslash -diagdown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 diff --git a/lib/examples/mathed.lyx b/lib/examples/mathed.lyx deleted file mode 100644 index 63c23fd7fc..0000000000 --- a/lib/examples/mathed.lyx +++ /dev/null @@ -1,14594 +0,0 @@ -#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 - - - - - -\begin_inset Text - -\begin_layout Standard - - -\backslash -begin{math} -\backslash -frac{abc}{xyz} -\backslash -end{math} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\backslash -( -\backslash -frac{abc}{xyz} -\backslash -) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - -$ -\backslash -frac{abc}{xyz} $ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\backslash -begin{displaymath} -\backslash -frac{abc}{xyz} -\backslash -end{displaymath} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\backslash -[ -\backslash -frac{abc}{xyz} -\backslash -] -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\hat{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -hat{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\acute{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -acute{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\bar{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bar{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\dot{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -dot{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\breve{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -breve{a} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\check{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -check{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\grave{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -grave{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\vec{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -vec{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\ddot{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ddot{a} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\begin_inset Formula $\tilde{a}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -tilde{a} -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\alpha$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -alpha -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\beta$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -beta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\gamma$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -gamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\delta$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -delta -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\epsilon$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -epsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\varepsilon$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -varepsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\zeta$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -zeta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\eta$ -\end_inset - - -\end_layout - 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- -\begin_inset Formula $=$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter -= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\vdash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -vdash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\dashv$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -dashv -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $<$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter -< -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $>$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter -> -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\uparrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -uparrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Leftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Uparrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Uparrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\downarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -downarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Rightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Downarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Downarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -updownarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Updownarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\mapsto$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -mapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\longmapsto$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -longmapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nearrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nearrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\hookleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -hookleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\hookrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -hookrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\searrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -searrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\swarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -swarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nwarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nwarrow -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ldots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ldots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\cdots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -cdots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\vdots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -vdots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ddots$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ddots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\aleph$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -aleph -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\prime$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -prime -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\forall$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -forall -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\infty$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -infty -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\hbar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -hbar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\emptyset$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -emptyset -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\exists$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -exists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nabla$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nabla -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\surd$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -surd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Box$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Box -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\triangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -triangle -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Diamond$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Diamond -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\imath$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -imath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\jmath$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -jmath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ell$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ell -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\neg$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -neg -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\top$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -top -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\flat$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -flat -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\natural$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -natural -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sharp$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -sharp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\wp$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -wp -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\clubsuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -clubsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\diamondsuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -diamondsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\heartsuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -heartsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\spadesuit$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -spadesuit -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\mho$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -mho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Re$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Re -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Im$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Im -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\angle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -angle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\partial$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -partial -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sum$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -sum -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\prod$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -prod -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\coprod$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -coprod -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\int$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -int -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\oint$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -oint -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigcap$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigcap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigcup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigsqcup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigsqcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigvee$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigvee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigwedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigwedge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigodot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigodot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigotimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigotimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigoplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigoplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\biguplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -biguplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\arccos$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\cos$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\csc$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\exp$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ker$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\limsup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\min$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sinh$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\arcsin$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\cosh$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\deg$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\gcd$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\lg$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ln$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Pr$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\arctan$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\cot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\det$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\hom$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\lim$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\log$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sec$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\tan$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\arg$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\coth$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\dim$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\inf$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\liminf$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\max$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sin$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\tanh$ -\end_inset - - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\uparrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -uparrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Uparrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Uparrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\downarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -downarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Downarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Downarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\{$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -{ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -updownarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Updownarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\lfloor$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -lfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rfloor$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\lceil$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -lceil -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rceil$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rceil -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\langle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -langle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $/$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter -/ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\backslash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -backslash -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $|$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter -| -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\|$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -| -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\widetilde{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -widetilde{abc} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\widehat{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -widehat{abc} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\overleftarrow{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -overleftarrow{abc} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\overrightarrow{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -overrightarrow{abc} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\overline{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -overline{abc} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\underline{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -underline{abc} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\overbrace{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -overbrace{abc} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\underbrace{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -underbrace{abc} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sqrt{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -sqrt{abc} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sqrt[n]{abc}\sqrt[3]{abc}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -sqrt[n]{abc} -\backslash -root3{abc} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $f'$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter -f' -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\frac{abc}{xyz}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -frac{abc}{xyz} -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\digamma$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -digamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\varkappa$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -varkappa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\beth$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -beth -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\daleth$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -daleth -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\gimel$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -gimel -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ulcorner$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ulcorner -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\urcorner$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -urcorner -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\llcorner$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -llcorner -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\lrcorner$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -lrcorner -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\dashrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -dashrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\dashleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -dashleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftleftarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftleftarrows -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftrightarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftrightarrows -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Lleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Lleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\twoheadleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -twoheadleftarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftarrowtail$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftarrowtail -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\looparrowleft$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -looparrowleft -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftrightharpoons$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftrightharpoons -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\curvearrowleft$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -curvearrowleft -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\circlearrowleft$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -circlearrowleft -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Lsh$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Lsh -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\upuparrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -upuparrows -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\upharpoonleft$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -upharpoonleft -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\downharpoonleft$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -downharpoonleft -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\multimap$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -multimap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftrightsquigarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftrightsquigarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightrightarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightrightarrows -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightleftarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightleftarrows -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightrightarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightrightarrows -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightleftarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightleftarrows -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\twoheadrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -twoheadrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightarrowtail$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightarrowtail -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\looparrowright$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -looparrowright -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightleftharpoons$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightleftharpoons -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\curvearrowright$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -curvearrowright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\circlearrowright$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -circlearrowright -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Rsh$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Rsh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\downdownarrows$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -downdownarrows -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\upharpoonright$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -upharpoonright -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\downharpoonright$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -downharpoonright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightsquigarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightsquigarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nLeftarrow$ -\end_inset - - -\end_layout - 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- -\family typewriter - -\backslash -nsucc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nsucceq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nsucceq -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\succnsim$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -succnsim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\succnapprox$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -succnapprox -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ncong$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ncong -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nshortparallel$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nshortparallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nparallel$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nparallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nvDash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nvDash -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nVDash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nVDash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ntriangleright$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ntriangleright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ntrianglerighteq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ntrianglerighteq -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nsupseteq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nsupseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nsupseteqq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nsupseteqq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\supsetneq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -supsetneq -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\varsupsetneq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -varsupsetneq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\supsetneqq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -supsetneqq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\varsupsetneqq$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -varsupsetneqq -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\dotplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -dotplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\smallsetminus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -smallsetminus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Cap$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Cap -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Cup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Cup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\barwedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -barwedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\veebar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -veebar -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\doublebarwedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -doublebarwedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\boxminus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -boxminus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\boxtimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -boxtimes -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\boxdot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -boxdot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\boxplus$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -boxplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\divideontimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -divideontimes -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\ltimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -ltimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rtimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rtimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\leftthreetimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -leftthreetimes -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\rightthreetimes$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -rightthreetimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\curlywedge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -curlywedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\curlyvee$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -curlyvee -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\circleddash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -circleddash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\circledast$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -circledast -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\circledcirc$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -circledcirc -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\centerdot$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -centerdot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\intercal$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -intercal -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 - - - - - - - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\hbar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -hbar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\hslash$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -hslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\vartriangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -vartriangle -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\triangledown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -triangledown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\square$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -square -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\lozenge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -lozenge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\circledS$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -circledS -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\angle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -angle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\measuredangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -measuredangle -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\nexists$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -nexists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\mho$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -mho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Finv$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Finv -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Game$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Game -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\Bbbk$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -Bbbk -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\backprime$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -backprime -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\varnothing$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -varnothing -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\blacktriangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -blacktriangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\blacktriangledown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -blacktriangledown -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\blacksquare$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -blacksquare -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\blacklozenge$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -blacklozenge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\bigstar$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -bigstar -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\sphericalangle$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -sphericalangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\complement$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -complement -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\eth$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -eth -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\diagup$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -diagup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\begin_inset Formula $\diagdown$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - - -\family typewriter - -\backslash -diagdown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Standard - -\end_layout - -\end_inset - - - - -\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 diff --git a/lib/ui/stdmenus.inc b/lib/ui/stdmenus.inc index d53acd653c..95050737b9 100644 --- a/lib/ui/stdmenus.inc +++ b/lib/ui/stdmenus.inc @@ -510,7 +510,8 @@ Menuset 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" -- 2.39.5