X-Git-Url: https://git.lyx.org/gitweb/?a=blobdiff_plain;f=lib%2Fdoc%2FMath.lyx;h=e023438bbaf0ed6570c86d798af456df60635a58;hb=6f04bfaf9601268ac8019d19024b335da3bcdf0a;hp=5ac17d57428bb7c74a53e0df4876a99db6161c22;hpb=4f043fba4dc71647d560babdcaa24dc565f38243;p=lyx.git diff --git a/lib/doc/Math.lyx b/lib/doc/Math.lyx index 5ac17d5742..e023438bba 100644 --- a/lib/doc/Math.lyx +++ b/lib/doc/Math.lyx @@ -1,38459 +1,38413 @@ -#LyX 2.1 created this file. For more info see http://www.lyx.org/ -\lyxformat 474 -\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}}{} - -\fi % end if pdflatex is used - -% solves the following problem: -% If the dection number consits of too many numerals the section heading -% will be printed in the TOC without a space between it and the section number. -% As solution more space between the number and the heading is inserted: -\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, -\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}} -\@ifundefined{extrasenglish}{\usepackage[english]{babel}}{} -\addto\extrasenglish{% - \renewcommand*{\equationautorefname}[1]{}% - \renewcommand{\sectionautorefname}{sec.\negthinspace}% - \renewcommand{\subsectionautorefname}{sec.\negthinspace}% - \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}% -} - -% 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]{\contentsname}{} - \myTOC - \cleardoublepage - \pagenumbering{arabic}} - -% insert additional vertical space of 1.5 mm between footnotes, -\let\myFoot\footnote -\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}} - -% provides caption formatting -\setkomafont{captionlabel}{\bfseries} - -% used in sec. 24.5 -\usepackage[samesize]{cancel} - -% enables calculation of values -\usepackage{calc} - -% for multiple columns used in sec. 24.7 -\usepackage{multicol} - -% needed in sec. 19.4 -\usepackage{remreset} - -% for the Fourier transformation symbol -\usepackage{mathrsfs} - -% 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{$\mathsurround =0pt #1{#2}$}} - - -% ------------------------------------ -% used to check for needed LaTeX packages -\usepackage{ifthen} - -% check for package eurosym -% used for the Euro symbol -\newboolean{eurosym} -\IfFileExists{eurosym.sty} - {\usepackage[gennarrow]{eurosym} - \setboolean{eurosym}{true}} - {\setboolean{eurosym}{false}} - -% check for package braket -% used for physical vectors -\newboolean{braket} -\IfFileExists{braket.sty} - {\usepackage{braket} - \setboolean{braket}{true}} - {\setboolean{braket}{false}} - -% check for package cancel -\newboolean{cancel} -\IfFileExists{cancel.sty} - {\usepackage{cancel} - \setboolean{cancel}{true}} - {\setboolean{cancel}{false}} - -% check for package upgreek -\newboolean{upgreek} -\IfFileExists{upgreek.sty} - {\usepackage{upgreek} - \setboolean{upgreek}{true}} - {\setboolean{upgreek}{false}} -\end_preamble -\options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading -\use_default_options false -\maintain_unincluded_children false -\language english -\language_package default -\inputencoding auto -\fontencoding global -\font_roman default -\font_sans default -\font_typewriter default -\font_math auto -\font_default_family default -\use_non_tex_fonts false -\font_sc false -\font_osf false -\font_sf_scale 100 -\font_tt_scale 100 -\graphics default -\default_output_format default -\output_sync 0 -\bibtex_command default -\index_command default -\paperfontsize 12 -\spacing single -\use_hyperref true -\pdf_title "LyX's Math Manual" -\pdf_author "LyX Team, Uwe Stöhr" -\pdf_subject "LyX-documentation about math" -\pdf_keywords "LyX, Mathed" -\pdf_bookmarks true -\pdf_bookmarksnumbered true -\pdf_bookmarksopen true -\pdf_bookmarksopenlevel 1 -\pdf_breaklinks false -\pdf_pdfborder false -\pdf_colorlinks true -\pdf_backref false -\pdf_pdfusetitle false -\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false" -\papersize a4paper -\use_geometry false -\use_package amsmath 2 -\use_package amssymb 2 -\use_package cancel 0 -\use_package esint 1 -\use_package mathdots 1 -\use_package mathtools 0 -\use_package mhchem 1 -\use_package stackrel 0 -\use_package stmaryrd 0 -\use_package undertilde 0 -\cite_engine basic -\cite_engine_type default -\biblio_style plain -\use_bibtopic false -\use_indices false -\paperorientation portrait -\suppress_date false -\justification true -\use_refstyle 0 -\notefontcolor #0000ff -\index Index -\shortcut idx -\color #008000 -\end_index -\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 -\html_math_output 0 -\html_css_as_file 0 -\html_be_strict false -\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 Plain Layout -\noindent -If you have comments or error corrections, please send them to the LyX Documenta -tion mailing list: -\family typewriter - -\begin_inset CommandInset href -LatexCommand href -name "lyx-docs@lists.lyx.org" -target "lyx-docs@lists.lyx.org?subject=LyX's Math manual" -type "mailto:" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -author: Uwe Stöhr -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\family sans -Version 2.0.x -\end_layout - -\begin_layout Standard -\begin_inset CommandInset toc -LatexCommand tableofcontents - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Note -status open - -\begin_layout Plain Layout -To export this document to PDF, PS or DVI the LaTeX-packages -\series bold -braket, cancel, eurosym, mathdots, mhchem -\series default - and -\series bold -was -\series default - should be installed. - If they are not installed the document can be exported anyway but the sections - where the packages are required will not appear in the output. - An exception is -\series bold -mhchem -\series default -; if it is not installed, this file cannot be exported. -\end_layout - -\begin_layout Plain Layout -The latest PDF-version of this document can be found here: -\begin_inset Newline newline -\end_inset - - -\series bold -http://wiki.lyx.org/LyX/DocumentationDevelopment#Math -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Introduction -\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 -\begin_inset space ~ -\end_inset - -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 checked in the document settings (menu -\family sans -Document\SpecialChar \menuseparator -Settings\SpecialChar \menuseparator -Math -\begin_inset space ~ -\end_inset - -Options -\family default -). -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -The option -\family sans -Use AMS math package automatically -\family default - only uses -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --math commands -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -A list with all -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --math commands is in the file -\family sans - -\begin_inset CommandInset href -LatexCommand href -name "amsguide.ps" -target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf" - -\end_inset - - -\family default -, which is part of every LaTeX standard installation. -\end_layout - -\end_inset - - for lucidity reasons. -\end_layout - -\begin_layout Section -General Instructions -\end_layout - -\begin_layout Standard -To create an inline formula -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! inline -\end_layout - -\end_inset - - that is embedded into a text line, use one of the shortcuts -\begin_inset Info -type "shortcuts" -arg "math-mode" -\end_inset - - or the toolbar button -\begin_inset Graphics - filename ../images/math-mode.png - scale 85 - -\end_inset - -. -\begin_inset Newline newline -\end_inset - -To create a display style formula -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! display style -\end_layout - -\end_inset - - which will appear bigger, has a different format, and will be in a separate - paragraph, use one of these shortcuts: -\begin_inset Info -type "shortcuts" -arg "math-display" -\end_inset - -. -\end_layout - -\begin_layout Standard -To change a display style formula to an inline formula, set the cursor into - the formula and use one of the shortcuts -\begin_inset Info -type "shortcuts" -arg "math-mode" -\end_inset - - or 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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -displaystyle -\end_layout - -\end_inset - - 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 -\begin_inset space ~ -\end_inset - -(auto) -\begin_inset Quotes erd -\end_inset - -. -\end_layout - -\begin_layout Standard -The TeX-mode -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -T@TeX-mode -\end_layout - -\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 -Te -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{} -\end_layout - -\end_inset - -X Code -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "ert-insert" -\end_inset - -). -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -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 Plain Layout -To avoid that these names are recognized as proper names, a TeX-brace pair - is inserted. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To change the LaTeX-preamble -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -L@LaTeX-preamble -\end_layout - -\end_inset - -, use the menu -\family sans -Document\SpecialChar \menuseparator -Settings\SpecialChar \menuseparator -LaT -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{} -\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, - use the menus -\family sans -Edit\SpecialChar \menuseparator -Math -\family default - and -\family sans -Edit\SpecialChar \menuseparator -Rows -\begin_inset space \thinspace{} -\end_inset - -& -\begin_inset space \thinspace{} -\end_inset - -Columns, -\family default - or the -\family sans -table toolbar -\family default -. - 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 Plain Layout -For multiline formulas the command -\series bold - -\backslash -intertext -\series default - is used, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Text-in-multiline" - -\end_inset - -. -\end_layout - -\end_inset - - -\emph on -mathematical text -\emph default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! in formulas -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Mathematical text -\end_layout - -\end_inset - - is used. - This mode is invoked with the shortcut -\begin_inset Info -type "shortcut" -arg "font-default" -\end_inset - - or by the insertion of the command -\series bold - -\backslash -text -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -text -\end_layout - -\end_inset - -. - The text appears black in LyX and can therefore be distinguished from the - other formula parts which 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 always starts 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 Index idx -status collapsed - -\begin_layout Plain Layout -T@TeX-braces -\end_layout - -\end_inset - -. - If you add in a formula a left brace to a command name, LyX automatically - creates 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 which 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 -\begin_inset Info -type "shortcuts" -arg "command-alternatives space-insert protected ; math-space" -\end_inset - -. -\end_layout - -\begin_layout Subsection* -\begin_inset Newpage newpage -\end_inset - -Syntax Explanation -\end_layout - -\begin_layout Itemize -The symbol -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -This visible space character can be created with the command -\series bold - -\backslash -textvisiblespace -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textvisiblespace -\end_layout - -\end_inset - -, inserted in TeX-mode. -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset space ~ -\end_inset - -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. - The -\family sans -Tab -\family default - key can often be used instead of -\begin_inset Formula $\to$ -\end_inset - - and -\begin_inset Formula $\downarrow$ -\end_inset - -, and -\family sans -Shift+Tab -\family default - instead of -\begin_inset Formula $\leftarrow$ -\end_inset - - and -\begin_inset Formula $\uparrow$ -\end_inset - -. -\end_layout - -\begin_layout Subsection* -Available units -\end_layout - -\begin_layout Standard -\align center -\begin_inset Float table -placement H -wide false -sideways false -status open - -\begin_layout Plain Layout -\align center -\begin_inset Caption Standard - -\begin_layout Plain Layout -\begin_inset CommandInset label -LatexCommand label -name "tab:Available-units" - -\end_inset - -Available units -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Plain Layout -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Unit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Name / Description -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -mm -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Millimeter -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -cm -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Centimeter -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -in -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Inch (1 -\begin_inset space \thinspace{} -\end_inset - -in = 2,54 -\begin_inset space \thinspace{} -\end_inset - -cm) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -pt -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Point (72.27 -\begin_inset space \thinspace{} -\end_inset - -pt = 1 -\begin_inset space \thinspace{} -\end_inset - -in) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -pc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Pica (1 -\begin_inset space \thinspace{} -\end_inset - -pc = 12 -\begin_inset space \thinspace{} -\end_inset - -pt) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -sp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -scaled point (65536 -\begin_inset space \thinspace{} -\end_inset - -sp = 1 -\begin_inset space \thinspace{} -\end_inset - -pt) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -bp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -big point (72 -\begin_inset space \thinspace{} -\end_inset - -bp = 1 -\begin_inset space \thinspace{} -\end_inset - -in) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -dd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Didot (1 -\begin_inset space \thinspace{} -\end_inset - -dd -\begin_inset Formula $\approx$ -\end_inset - - 0.376 -\begin_inset space \thinspace{} -\end_inset - -mm) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -cc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Cicero (1 -\begin_inset space \thinspace{} -\end_inset - -cc = 12 -\begin_inset space \thinspace{} -\end_inset - -dd) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -ex -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -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 Plain Layout -em -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -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 Plain Layout -mu -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -math unit (1 -\begin_inset space \thinspace{} -\end_inset - -mu = -\begin_inset Formula $\nicefrac{1}{18}$ -\end_inset - - -\begin_inset space \thinspace{} -\end_inset - -em) -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Basic Functions -\end_layout - -\begin_layout Subsection -Exponents -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Exponents -\end_layout - -\end_inset - - and Indices -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Indices -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Superscripts|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Exponents -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Subscripts|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Indices -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\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 Plain Layout -command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -B_V -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $B_{V}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -B^V -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}B^{V}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -B^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout -Depending on the used keyboard settings this can also happen for characters - other than vowels. -\end_layout - -\end_inset - -. - To get exponents in this case, press -\family sans -Space -\family default - after the caret as in the last example. -\end_layout - -\begin_layout Subsection -Fractions -\begin_inset CommandInset label -LatexCommand label -name "sub:Fractions" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Fractions -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Fractions are generated with the command -\series bold - -\backslash -frac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -frac -\end_layout - -\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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dfrac -\end_layout - -\end_inset - - a fraction can be created that always has the size of a display style formula. - With -\series bold - -\backslash -tfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -tfrac -\end_layout - -\end_inset - - 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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e^ -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout -\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 - - -\begin_inset Newpage newpage -\end_inset - -For nested fractions the command -\series bold - -\backslash -cfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cfrac -\end_layout - -\end_inset - - can be used. - Here is 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 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B+ -\backslash -cfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C+ -\backslash -cfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -E -\begin_inset Formula $\downarrow$ -\end_inset - -F -\begin_inset Formula $\downarrow$ -\end_inset - -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. -\end_layout - -\begin_layout Standard -It is possible to specify the alignment of the numerator. - The command -\series bold - -\backslash -cfracleft -\series default - is used to left align it, the command -\series bold - -\backslash -cfracright -\series default - to right-align it. - -\series bold - -\backslash -cfrac -\series default - centers the numerator. - These fractions demonstrate the different alignments: -\end_layout - -\begin_layout Standard - -\series bold -\begin_inset Formula -\[ -\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - -\series bold - -\backslash -cfracleft -\series default - and -\series bold - -\backslash -cfracright -\series default - are no real LaTeX commands but represent the command -\series bold - -\backslash -cfrac[alignment]{numerator}{denominator} -\series default - . - Therefore you cannot use them in TeX code. -\end_layout - -\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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -nicefrac -\end_layout - -\end_inset - -: -\begin_inset Formula $\nicefrac{5}{31}$ -\end_inset - - or -\series bold - -\backslash -unitfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -unitfrac -\end_layout - -\end_inset - -: -\begin_inset Formula $\unitfrac{5}{31}$ -\end_inset - - There is furthermore the command -\series bold - -\backslash -unitfracthree -\series default - that offers to write a fraction in combination with a number: -\begin_inset Formula $\unitfrac[2]{1}{3}$ -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - -\series bold - -\backslash -unitfracthree -\series default - is not a real LaTeX command but the command -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -unitfrac[number]{numerator}{denominator} -\series default - . - Therefore you cannot use it in TeX code. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -How to define own fractions where the fraction stroke can be changed, is - explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Self-defined-Fractions" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Subsection -Roots -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Roots -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Square roots are created with -\series bold - -\backslash -sqrt -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -sqrt -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -root -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqrt -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A-B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -root -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -3 -\begin_inset Formula $\downarrow$ -\end_inset - -A-B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 - - -\begin_inset Newline newline -\end_inset - -The -\begin_inset Formula $\beta$ -\end_inset - - touches the root. - To avoid this, the commands -\series bold - -\backslash -leftroot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -leftroot -\end_layout - -\end_inset - - and -\series bold - -\backslash -uproot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -uproot -\end_layout - -\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 -\begin_inset Newline newline -\end_inset - - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -B -\begin_inset Newline newline -\end_inset - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Binomial coefficients -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Binomial coefficients are inserted with the command -\series bold - -\backslash -binom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -binom -\end_layout - -\end_inset - - or with the submenu of the math toolbar button -\begin_inset Graphics - filename ../images/math/frac-square.png - scale 85 - -\end_inset - -. - As with fractions ( -\series bold - -\backslash -frac -\series default -) in addition to -\series bold - -\backslash -binom -\series default - there are the commands -\series bold - -\backslash -dbinom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dbinom -\end_layout - -\end_inset - - and -\series bold - -\backslash -tbinom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -tbinom -\end_layout - -\end_inset - -. - For other brackets around binomial coeficients there are the commands -\series bold - -\backslash -brace -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -brace -\end_layout - -\end_inset - - and -\series bold - -\backslash -brack -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -brack -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -binom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dbinom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tbinom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -brack -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -brace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsection -Case Differentiations -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Case differentiations -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cases -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\to$ -\end_inset - -B>0 -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cases -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\begin{cases} -A & B>0\end{cases}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cases -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\begin{cases} -A & \textrm{for }x>0\\ -B & \textrm{for }x=0 -\end{cases}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -After inserting -\series bold - -\backslash -cases -\series default - or pressing the math toolbar button -\begin_inset Graphics - filename ../images/math/cases.png - scale 85 - -\end_inset - - you can create new lines with the shortcut -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - or the table toolbar button -\begin_inset Graphics - filename ../images/tabular-feature_append-row.png - scale 85 - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Negations -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -By inserting -\series bold - -\backslash -not -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -not -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not=$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not -\backslash -le -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not\le$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not -\backslash -parallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 special commands for some negations (see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Mathematical-Symbols" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Relations" - -\end_inset - -). -\end_layout - -\begin_layout Subsection -Placeholders -\begin_inset CommandInset label -LatexCommand label -name "sub:Placeholders" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Placeholders -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Chemical characters ! Isotopes -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Isotopes|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Chemical characters -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -When displaying e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -isotopes -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -Typesetting isotopes and chemical symbols is described in -\begin_inset CommandInset ref -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 Plain Layout -Indices created with sub- and superscripts: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -correct indices: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! P ! -\backslash -phantom -\end_layout - -\end_inset - - or the math toolbar button -\begin_inset space \thinspace{} -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -can be found in the submenu of the toolbar button -\begin_inset Graphics - filename ../images/math/space.png - scale 85 - -\end_inset - - -\end_layout - -\end_inset - - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -^19 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_ -\backslash -phantom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -1 -\begin_inset Formula $\to$ -\end_inset - -9 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -F -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout -^235 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_ -\backslash -phantom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -23 -\begin_inset Formula $\to$ -\end_inset - -9 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -F -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -Lambda^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -phantom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -ii -\begin_inset Formula $\to$ -\end_inset - -t -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_MMt -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! V ! -\backslash -vphantom -\end_layout - -\end_inset - - (toolbar button -\begin_inset space ~ -\end_inset - - -\begin_inset Graphics - filename ../images/math/vphantom.png - scale 85 - -\end_inset - -) and -\series bold - -\backslash -hphantom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hphantom -\end_layout - -\end_inset - - (toolbar button -\begin_inset space ~ -\end_inset - - -\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 the command -\series bold - -\backslash -vphantom -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold -a -\backslash -int -\series default - creates space for the height of the integral sign, -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -The command -\series bold - -\backslash -int -\series default - creates an integral sign, see -\begin_inset CommandInset ref -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 CommandInset ref -LatexCommand ref -reference "sub:Multiline-Brackets" - -\end_inset - -. -\end_layout - -\begin_layout Standard -Placeholders can also be used for text when they are inserted via the menu - -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Phantom -\family default -: -\end_layout - -\begin_layout Standard -This is a sentence. -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom Phantom -status open - -\begin_layout Plain Layout -This -\end_layout - -\end_inset - - is a sentence. -\end_layout - -\begin_layout Subsection -Lines -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Lines -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! underlined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -overline -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -underline -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -underline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 use -\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 Standard -\begin_inset VSpace bigskip -\end_inset - -Custom lines can be created using the command -\series bold - -\backslash -rule -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -rule -\end_layout - -\end_inset - - which has the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -rule[vertical offset]{length}{thickness} -\end_layout - -\begin_layout Standard -The optional vertical offset shifts the line upwards (or downwards, when - the value is negative). - The units listed in -\begin_inset CommandInset ref -LatexCommand ref -reference "tab:Available-units" - -\end_inset - - can be used for the values. - Here are two example lines created with the commands -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -rule[-2ex]{3cm}{2pt} -\series default - and -\series bold - -\backslash -rule{2cm}{1pt} -\series default -: -\end_layout - -\begin_layout Standard -This is a sentence -\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$ -\end_inset - - with two lines. -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -rule -\series default - can also be used for text when a line is inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Horizontal -\begin_inset space ~ -\end_inset - -Line -\family default -: -\end_layout - -\begin_layout Standard -This is a sentence -\begin_inset CommandInset line -LatexCommand rule -offset "0.5ex" -width "3cm" -height "1pt" - -\end_inset - - with one line. -\end_layout - -\begin_layout Subsection -Ellipses -\begin_inset CommandInset label -LatexCommand label -name "sub:Ellipses" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Ellipses -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -There are different types of ellipses available. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -ldots -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cdots -\end_layout - -\end_inset - -). - When using the command -\series bold - -\backslash -dots -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dots -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -, -\backslash -dots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -,A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1},\dots,A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\backslash -dots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1}+\dots+A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -, -\backslash -ldots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -,A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1},\ldots,A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\backslash -cdots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1}+\cdots+A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vdots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vdots$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ddots$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iddots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\iddots$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -3×3 -\begin_inset space \thinspace{} -\end_inset - -matrix with the different dots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 -\begin_inset space ~ -\end_inset - -Character -\family default - are -\series bold - -\backslash -ldots -\series default -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -To use -\series bold - -\backslash -iddots -\series default -, one of the options -\family sans -Use mathdots package (automatically) -\family default - must be set in the document settings under -\family sans -Math -\begin_inset space ~ -\end_inset - -Options -\family default -. -\begin_inset Newline newline -\end_inset - -Using the option -\family sans -Use mathdots package -\family default - will improve the appearance of all dots in the documents if their font - style or size is not the 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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hdotsfor -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dotfill -\end_layout - -\end_inset - - the rest of a line with dots. - The effect of these commands is the same as with -\series bold - -\backslash -hfill -\series default -, see -\begin_inset CommandInset ref -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 Plain Layout - - -\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 -Similar to -\series bold - -\backslash -dotfill -\series default - there is for a line the command -\series bold - -\backslash -hrulefill -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hrulefill -\end_layout - -\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 CommandInset label -LatexCommand label -name "sec:Matrices" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Matrices -\end_layout - -\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 -. - In the matrix dialog you can specify the number of columns and rows, the - alignment and the decoration. - The vertical alignment is 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 -\begin_inset space ~ -\end_inset - -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 in a matrix all columns are centered, therefore the default for - every column is a -\series bold -c -\series default -. -\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. -\begin_inset space \thinspace{} -\end_inset - -, or the menu -\family sans -Edit\SpecialChar \menuseparator -Rows & Columns -\family default - can be used. - New rows can also be created with -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -The -\family sans -Decoration -\family default - adds parentheses in the selected style around the matrix. - Alternatively, parentheses can can either be created with the commands - -\series bold - -\backslash -left -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -left -\end_layout - -\end_inset - - and -\series bold - -\backslash -right -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -right -\end_layout - -\end_inset - - (shortcut -\family sans -Alt+M -\begin_inset space ~ -\end_inset - -Parenthesis -\family default -), see -\begin_inset CommandInset ref -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 -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -Bmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -pmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -Vmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -matrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -When e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - - -\series bold - -\backslash -vmatrix -\series default - is inserted, a blue box appears between two vertical lines where the matrix - is inserted. -\begin_inset Newline newline -\end_inset - -Note that decorated matrices ignore the vertical alignment. -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arraycolsep -\end_layout - -\end_inset - - that is described in -\begin_inset CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arraystretch -\end_layout - -\end_inset - - is used. - It is used as follows: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -arraystretch}{stretch factor} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -renewcommand -\end_layout - -\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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -smallmatrix -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Brackets -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Delimiters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Vertical Brackets and Delimiters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets ! vertical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -( -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $($ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -{ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\{$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -[ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $[$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -langle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\langle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lceil -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lceil$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lfloor$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -/ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $/$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -| -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $|$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $)$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -] -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $]$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rceil -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rceil$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rfloor$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash - -\backslash - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\backslash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -| -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\|$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard - -\series medium -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - In TeX-mode the command -\series bold - -\backslash -textbackslash -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textbackslash -\end_layout - -\end_inset - - must be used for the backslash, because the command -\series bold - -\backslash - -\backslash - -\series default - produces a line break there. -\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 CommandInset label -LatexCommand label -name "sub:Manual-Bracket-Size" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Bracket size ! manual -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -big -\end_layout - -\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 Plain Layout -all brackets in the same size: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -this looks better: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\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 Plain Layout - - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -sin(x) -\backslash -Big]^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 -Besides the -\series bold - -\backslash -big -\series default --commands there is the variant -\series bold - -\backslash -bigm -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -bigm -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -bigl - -\backslash -bigr -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bigm( -\backslash -bigm( -\backslash -ln(3x) -\backslash -bigm)^2 -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default - -\backslash -Bigm) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -Big( -\backslash -big( -\backslash -ln(3x) -\backslash -big)^2 -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default - -\backslash -Big) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -Bigl( -\backslash -bigl( -\backslash -ln(3x) -\backslash -bigr)^2 -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default - -\backslash -Bigr) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - -\backslash -bigl) -\backslash -ln(3x) -\backslash -bigr( -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 CommandInset label -LatexCommand label -name "sub:Automatic-Bracket-Size" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Bracket size ! automatic -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -left -\end_layout - -\end_inset - - and -\series bold - -\backslash -right -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -right -\end_layout - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 -\begin_inset space ~ -\end_inset - -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. -\begin_inset Newline newline -\end_inset - -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 Plain Layout - - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -middle -\end_layout - -\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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -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 CommandInset ref -LatexCommand ref -reference "sub:Physical-Vectors" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Horizontal Brackets -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets ! horizontal -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{2.3mm}{ -\end_layout - -\end_inset - - -\backslash -overbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -3 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -overbrace -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\overbrace{A+B}^{3}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-2.2mm}{ -\end_layout - -\end_inset - - -\backslash -underbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_5 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -underbrace -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\underbrace{A+B}_{5}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -underbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B_w -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_7 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 CommandInset ref -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 Plain Layout -Space commands are explained in -\begin_inset CommandInset ref -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 Plain Layout -because a bracket is not handled as a character, see -\begin_inset CommandInset ref -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 Plain Layout -more about -\series bold - -\backslash -hphantom -\series default - see -\begin_inset CommandInset ref -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 Plain Layout - - -\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 Plain Layout - - -\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 needs to be reduced. - This is not easily possible due to a bug in LyX -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #1505" -target "http://www.lyx.org/trac/ticket/1505" - -\end_inset - - -\end_layout - -\end_inset - -. - As a solution for the problem, the global formula row separation -\series bold - -\backslash -jot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! J ! -\backslash -jot -\end_layout - -\end_inset - - must be changed to -6 -\begin_inset space \thinspace{} -\end_inset - -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 -\begin_inset space \thinspace{} -\end_inset - -pt using the same command. - More about the row separation in formulas is explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Line-Separation" - -\end_inset - -. -\end_layout - -\begin_layout Section -Arrows -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! horizontal -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gets -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gets$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Leftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leftharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leftharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hookleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hookleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -to -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\to$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Rightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rightharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rightharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hookrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hookrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightleftharpoons -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rightleftharpoons$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hspace{} -\length 25pt -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mapsto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longmapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longmapsto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leadsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leadsto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dasharrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dasharrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Arrows used as accents like e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -vector arrows are listed in -\begin_inset CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! labeled -\end_layout - -\end_inset - - -\series bold - -\backslash -xleftarrow -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! X ! -\backslash -xleftarrow -\end_layout - -\end_inset - - and -\series bold - -\backslash -xrightarrow -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! X ! -\backslash -xrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -F(a) -\backslash -xleftarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout -\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 Plain Layout -F(x) -\backslash -xrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! diagonal -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! vertical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -uparrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\uparrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Uparrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Uparrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -updownarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Updownarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Downarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Downarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -downarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\downarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nearrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nearrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -searrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\searrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -swarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\swarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nwarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nwarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Vertical arrows can be used also as delimiters together with the commands - described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Manual-Bracket-Size" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - -. -\end_layout - -\begin_layout Section -Accents -\begin_inset CommandInset label -LatexCommand label -name "sec:Accents" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents -\end_layout - -\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 Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -accents in text see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Accents-in-Text" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -texorpdfstring -\series default - is used to avoid that the footnote appears in the PDF-bookmark. -\end_layout - -\begin_layout Plain Layout -More about -\series bold - -\backslash -texorpdfstring -\series default - is in section -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Formulas-in-Section" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset CommandInset label -LatexCommand label -name "sub:Accents-for-one" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents ! for one character -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\dot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vec -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Vectors -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\vec{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bar -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\bar{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathring -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tilde -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hat -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\hat{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -check -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\check{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -acute -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\acute{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -grave -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\grave{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -breve -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\breve{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - - -\end_layout - -\begin_layout Standard -You can directly insert accents like é to formulas. - LyX will transform them to the corresponding accent command. - For umlauts -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Umlauts -\end_layout - -\end_inset - - it is better to insert a quotation mark 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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - and the 0 -\begin_inset space \thinspace{} -\end_inset - -pt space are only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\lang ngerman -\begin_inset Quotes grd -\end_inset - -i -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset space \hspace{} -\length 0pt -\end_inset - - -\lang ngerman - -\begin_inset Formula $"i$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -i -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -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 several Characters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents ! for several characters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overleftarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underleftarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overleftrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underleftrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -widetilde -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -widehat -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -overset -\end_layout - -\end_inset - - and -\series bold - -\backslash -underset -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -underset -\end_layout - -\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 Plain Layout - - -\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 Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Space -\begin_inset CommandInset label -LatexCommand label -name "sub:Space" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! horizontal -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Predefined Space -\begin_inset CommandInset label -LatexCommand label -name "sub:Predefined-Space" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! horizontal ! predefined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Sometimes it is necessary to insert horizontal space into a formula. - This is done by inserting a protected space (shortcut -\begin_inset Info -type "shortcut" -arg "command-alternatives space-insert protected ; math-space" -\end_inset - -). - A -\begin_inset Quotes eld -\end_inset - - -\color blue - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -, -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -; -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -quad -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -qquad -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -! -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Number of -\family sans -Space -\family default - keystrokes after inserting the protected space -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -0 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -1 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -2 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -4 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -5 -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\, B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\: B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\; B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\quad B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\qquad B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -negmedspace -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -negthickspace -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Number of -\family sans -Space -\family default - keystrokes after inserting the protected space -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -6 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -7 -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\negmedspace B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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, which are e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -useful for summation operators: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sum -\backslash -sum -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -f_kl -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sum -\backslash -negmedspace -\backslash -sum -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -f_kl -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout -normal equation -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\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 Plain Layout -\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 -\begin_inset space ~ -\end_inset - -Space -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "space-insert thin" -\end_inset - -). -\end_layout - -\begin_layout Standard -An example to visualize the difference: -\end_layout - -\begin_layout Standard -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -24 kW -\begin_inset Formula $\cdot$ -\end_inset - -h -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -space between value and unit -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -24 -\begin_inset space \thinspace{} -\end_inset - -kW -\begin_inset Formula $\cdot$ -\end_inset - -h -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -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 Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -for vertical space in formulas see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Line-Separation" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\backslash -texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. -\end_layout - -\begin_layout Plain Layout -More about -\backslash -texorpdfstring is in section -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Formulas-in-Section" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset CommandInset label -LatexCommand label -name "sub:Variable-Space" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! horizontal ! variable -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Space with a defined length can be inserted with the command -\series bold - -\backslash -hspace -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hspace -\end_layout - -\end_inset - -. - Then a long -\begin_inset Quotes eld -\end_inset - - -\color blue - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\color inherit - -\begin_inset Quotes erd -\end_inset - - appears. - The length can be specified by left-clicking on the -\begin_inset Quotes eld -\end_inset - - -\color blue - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\color inherit - -\begin_inset Quotes erd -\end_inset - -. - The length may also be negative. - To insert as much space as is available, the command -\series bold - -\backslash -hfill -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hfill -\end_layout - -\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 Plain Layout -Command ( -\backslash -hspace length) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A=B -\backslash -hspace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -A -\backslash -not=C (3 -\begin_inset space \thinspace{} -\end_inset - -cm) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=B\hspace{3cm}A\not=C$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -hspace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -A -\backslash -not=A (-1 -\begin_inset space \thinspace{} -\end_inset - -mm) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\hspace{-1mm}A\not=A$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A=A -\backslash -hfill -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 - only has an effect on displayed formulas when the formula style -\series bold -Indented -\series default - is used. - (Formula styles are explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - -.) -\end_layout - -\begin_layout Standard -Besides -\series bold - -\backslash -hfill -\series default -, there are the commands -\series bold - -\backslash -dotfill -\series default - and -\series bold - -\backslash -hrulefill -\series default - that fill the space with a pattern, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Ellipses" - -\end_inset - - for an example. -\end_layout - -\begin_layout Standard -For text, variable space can be inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Horizontal -\begin_inset space ~ -\end_inset - -Space -\family default -: -\end_layout - -\begin_layout Standard -This is a line with -\begin_inset space \hspace{} -\length 2cm -\end_inset - -2 -\begin_inset space \thinspace{} -\end_inset - -cm space. -\end_layout - -\begin_layout Standard -This is a line with -\begin_inset space \hfill{} -\end_inset - -maximum space. -\end_layout - -\begin_layout Subsection -Space besides inline Formulas -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! besides inline formulas -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The space that surrounds inline formulas can be adjusted with the length - -\series bold - -\backslash -mathsurround -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathsurround -\end_layout - -\end_inset - -. - The value of a length is set with the command -\series bold - -\backslash -setlength -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -setlength -\end_layout - -\end_inset - - which 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 -\begin_inset space \thinspace{} -\end_inset - -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 -\begin_inset space \thinspace{} -\end_inset - -mm space will now be set around all inline formulas: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 -\begin_inset space \thinspace{} -\end_inset - -mm surrounding space. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Section -Boxes and Frames -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Frames | see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Boxes -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Boxes for text are described in chapter -\family typewriter -Boxes -\family default - in the -\family typewriter -Embedded -\begin_inset space ~ -\end_inset - -Objects -\family default - manual. -\end_layout - -\begin_layout Subsection -Boxes with Frame -\begin_inset CommandInset label -LatexCommand label -name "sub:Boxes-with-Frame" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! with frame -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -It is possible to frame a formula or part of one with the commands -\series bold - -\backslash -fbox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -fbox -\end_layout - -\end_inset - - and -\series bold - -\backslash -boxed -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -boxed -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -When one of these commands is inserted in 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, because the box content will otherwise be treated as mathemati -cal 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 -An extension to -\series bold - -\backslash -fbox -\series default - is the command -\series bold - -\backslash -framebox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -framebox -\end_layout - -\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. -\begin_inset Newline newline -\end_inset - -If no width is 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. - 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 -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\family sans -Ctrl+M -\family default - -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -boxed -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A+ -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -framebox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}$ -\end_inset - - -\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$ -\end_inset - - -\begin_inset Formula $\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\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 Plain Layout - - -\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 Plain Layout - - -\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 CommandInset label -LatexCommand label -name "sub:Boxes-without-Frame" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! without frame -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mbox -\end_layout - -\end_inset - -, -\series bold - -\backslash -makebox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -makebox -\end_layout - -\end_inset - - and -\series bold - -\backslash -raisebox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -raisebox -\end_layout - -\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 -. - -\series medium - -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - For -\series bold - -\backslash -raisebox -\series default - this extra formula is created by pressing -\family sans -Ctrl+M -\family default - twice instead of once because LyX doesn't yet support -\series bold - -\backslash -raisebox -\series default - directly. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -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 Plain Layout -\begin_inset Formula $H\raisebox{2mm}{al}lo$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -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 Plain Layout -\begin_inset Formula $H\raisebox{-2mm}{al}lo$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A= -\backslash -raisebox{-2mm -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\family sans -Ctrl+M -\family default - -\family sans -Ctrl+M -\family default - -\backslash -sqrt -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\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 CommandInset label -LatexCommand label -name "sub:Colored-Boxes" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! colored -\end_layout - -\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 Plain Layout -The LaTeX-package -\series bold -color -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! color -\end_layout - -\end_inset - - has to be loaded in the LaTeX-preamble with the line -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -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 does not - cause problems. -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -colorbox -\end_layout - -\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 way as for -\series bold - -\backslash -raisebox -\series default -. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -This also applies for the command -\series bold - -\backslash -fcolorbox -\series default -. -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -colorbox{yellow -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -colorbox{green -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -colorbox{green -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\family sans -Ctrl+M -\family default - -\family sans -Ctrl+M -\family default - -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C=D -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$ -\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 desired - color is chosen in the -\family sans -Text -\begin_inset space ~ -\end_inset - -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 -\begin_inset space ~ -\end_inset - -Style\SpecialChar \menuseparator -Customized -\family default -. - The formula number then has 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 CommandInset ref -LatexCommand eqref -reference "eq:red" - -\end_inset - - is completely colored red. -\begin_inset Newline newline -\end_inset - -Formula -\begin_inset CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -fcolorbox -\end_layout - -\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 Plain Layout - - -\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 Plain Layout - - -\backslash -fboxrule 0.4pt -\backslash -fboxsep 3pt -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This formula was created with the command -\begin_inset Newline newline -\end_inset - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -definecolor -\end_layout - -\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 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -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 used for text with the help of the command - -\series bold - -\backslash -textcolor -\series default -: -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! colored -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -textcolor -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textcolor -\end_layout - -\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 CommandInset label -LatexCommand label -name "sub:Paragraph-Boxes" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! as paragraph -\end_layout - -\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 -use_makebox 0 -width "5cm" -special "none" -height "1in" -height_special "totalheight" -status open - -\begin_layout Plain Layout -This is a paragraph box. - It is exactly 5 -\begin_inset space \thinspace{} -\end_inset - -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 -: Rectangular box, -\emph on -Inner Box -\emph default -: Parbox, -\emph on -Width -\emph default -: 5 -\begin_inset space \thinspace{} -\end_inset - -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! P ! -\backslash -parbox -\end_layout - -\end_inset - - which 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 -\begin_inset Quotes eld -\end_inset - -bottom -\begin_inset Quotes erd -\end_inset - - means that the box is aligned within the surrounding text with its last - line. - With -\emph on -t -\emph default - for -\begin_inset Quotes eld -\end_inset - -top -\begin_inset Quotes erd -\end_inset - - 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 -\begin_inset space ~ -\end_inset - -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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -linewidth -\end_layout - -\end_inset - - is hereby the line width set for the document. - Because the frame is outside the parbox, 2 -\begin_inset space \thinspace{} -\end_inset - -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 Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #4483" -target "http://www.lyx.org/trac/ticket/4483" - -\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 Plain Layout - -\series bold -calc -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! calc -\end_layout - -\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 Plain Layout - - -\backslash -fboxsep 5mm -\backslash -fboxrule 5mm -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - -}} -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 the 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 CommandInset ref -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 Plain Layout - - -\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 Plain Layout - -}} -\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 Plain Layout -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 CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Operators -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Big Operators -\begin_inset CommandInset label -LatexCommand label -name "sub:Big-Operators" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators ! big -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Sums -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Integrals -\end_layout - -\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 -\begin_inset space ~ -\end_inset - -Options -\family default -. -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -int -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! I ! -\backslash -int -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\int$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\oint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ointctrclockwise -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ointctrclockwise$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ointclockwise -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ointclockwise$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\begin_inset Formula $\fint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -landupint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\begin_inset Formula $\landupint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -landdownint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\begin_inset Formula $\landdownint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigcap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigcap$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigcup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sum -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -sum -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sum$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prod -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! P ! -\backslash -prod -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\prod$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -coprod -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\coprod$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigodot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigodot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigotimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigotimes$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigoplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigoplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigwedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigwedge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigvee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigvee$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigsqcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigsqcup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -biguplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\biguplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 -For all integral operators there is a second version available, ending in - -\series bold -op -\series default -: -\series bold - -\backslash -intop -\series default -, -\series bold - -\backslash -ointop -\series default - etc.. - These operators are different from -\series bold - -\backslash -int -\series default - etc. -\begin_inset space \space{} -\end_inset - -in the style the operator limits are displayed, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Operator-Limits" - -\end_inset - -. - -\end_layout - -\begin_layout Subsubsection* -Advice 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 -\begin_inset Info -type "shortcut" -arg "font-roman" -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -Font styles -\series bold - -\series default -see -\begin_inset CommandInset ref -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 - - -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout -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 -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iiiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dotsint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Subsection -Operator Limits -\begin_inset CommandInset label -LatexCommand label -name "sub:Operator-Limits" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators ! Limits -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prod^ -\backslash -infty -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout -\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 - for 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 -\begin_inset Info -type "shortcut" -arg "math-limits" -\end_inset - -). - 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 those ending with -\series bold -op -\series default - like -\series bold - -\backslash -intop -\series default -, -\series bold - -\backslash -ointop -\series default - etc., 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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -subarray -\end_layout - -\end_inset - - and -\series bold - -\backslash -substack -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -substack -\end_layout - -\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 Plain Layout -Command -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -+ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $+$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $-$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pm -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\pm$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cdot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cdot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -times -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\times$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -div -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\div$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-1.2mm}{ -\end_layout - -\end_inset - -* -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $*$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -star -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\star$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -circ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\circ$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diamond -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diamond$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bullet -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bullet$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nabla -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nabla$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigtriangledown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigtriangledown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigtriangleup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigtriangleup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Box -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Box$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cap$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dagger -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dagger$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddagger -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ddagger$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wr -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\wr$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigcirc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigcirc$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\wedge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vee$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\oplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ominus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ominus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -otimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\otimes$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\oslash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -odot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\odot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -amalg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\amalg$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -uplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\uplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -setminus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\setminus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqcap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqcap$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqcup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -triangleleft -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\triangleleft$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -triangleright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\triangleright$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 CommandInset label -LatexCommand label -name "sub:Self-defined-Operators" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators ! self-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With the help of the command -\series bold - -\backslash -DeclareMathOperator -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dbinom@ -\backslash -DeclareMathOperator -\end_layout - -\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 CommandInset ref -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 CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathop -\end_layout - -\end_inset - - and -\series bold - -\backslash -mathbin -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathbin -\end_layout - -\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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -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: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -mathop{ -\backslash -sum -\backslash -negmedspace -\backslash -sum -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\begin_inset Formula $\to$ -\end_inset - -^N -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold -_i,j=1 -\end_layout - -\begin_layout Section -Fonts -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Fonts -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Font Styles -\begin_inset CommandInset label -LatexCommand label -name "sub:Font-Styles" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Font ! style -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -shortcut -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathbb -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -ABC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathbb{ABC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-noun" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathbf -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathbf{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-bold" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -boldsymbol -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\boldsymbol{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-boldsymbol" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathcal -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -ABC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathcal{ABC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-emph" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathfrak -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathfrak{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathscr -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathscr{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -shortcut -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathit -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathit{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathrm -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathrm{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-roman" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathsf -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathsf{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-sans" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathtt -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathtt{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-typewriter" -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\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 Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #4629" -target "http://www.lyx.org/trac/ticket/4629" - -\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 CommandInset label -LatexCommand label -name "sub:Bold-Formulas" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! bold -\end_layout - -\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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -boldmath -\end_layout - -\end_inset - - in TeX-mode. - To end the environment, the command -\series bold - -\backslash -unboldmath -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -unboldmath -\end_layout - -\end_inset - - is inserted in TeX-mode. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\backslash -unboldmath -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Colored Formulas -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! colored -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Formulas can be colored like normal text: Highlight a formula or a formula - part and use the -\family sans -Text Style -\family default - dialog. - Here is a formula in magenta: -\begin_inset Formula -\[ -{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -You can also define your own colors as described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Colored-Boxes" - -\end_inset - -. - They can be used with the TeX code command -\series bold - -\backslash -textcolor -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textcolor -\end_layout - -\end_inset - - in the scheme -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -textcolor{color}{characters or formula} -\end_layout - -\begin_layout Standard -The following example was colored completely dark green and partly red: -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textcolor{darkgreen}{ -\end_layout - -\end_inset - - -\begin_inset Formula -\[ -\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)} -\] - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Due to a bug in LyX only complete formulas can be colored with self-defined - colors. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #5269" -target "http://www.lyx.org/trac/ticket/5269" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Font Sizes -\begin_inset CommandInset label -LatexCommand label -name "sub:Font-Sizes" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Font ! size -\end_layout - -\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 -, -\begin_inset Newline newline -\end_inset - - -\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, which - corresponds to 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 -\begin_inset space \thinspace{} -\end_inset - -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 be changed using the following size commands: -\end_layout - -\begin_layout Standard -\noindent -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -displaystyle -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -displaystyle -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -textstyle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -scriptstyle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -scriptscriptstyle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -After entering these commands, a blue box appears in which the formula parts - are inserted. -\end_layout - -\begin_layout Standard -There is a further method to change the font size, that though only works - for symbols or letters in mathematical text. - To use it, one of the above text size commands 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 Plain Layout - - -\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 Plain Layout - - -\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: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -maltese -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A Alt+M M -\backslash -Large -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -maltese -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -textit -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\to$ -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset space \hspace*{} -\length 1cm -\end_inset - -Alt+M -\series default - -\series bold -M -\backslash -tiny -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -maltese -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -textit -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Greek letters can also be inserted via the toolbar button -\begin_inset Graphics - filename ../images/math/alpha.png - scale 85 - -\end_inset - -. - All international typesetting norms purport that Greek letters in math - have to be typeset italic/slanted. - In some languages, like French or Russian, they are nevertheless sometimes - typeset upright. -\end_layout - -\begin_layout Subsection -Small Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! small -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -alpha -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\alpha$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -beta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\beta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gamma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -delta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\delta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -epsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\epsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varepsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varepsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -zeta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\zeta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -eta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\eta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -theta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\theta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vartheta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vartheta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iota -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\iota$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -kappa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\kappa$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varkappa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varkappa$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lambda -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lambda$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mu -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mu$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nu -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nu$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -xi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\xi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -o -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $o$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\pi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varpi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varpi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rho$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varrho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varrho$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sigma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varsigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varsigma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tau -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\tau$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -upsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\upsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -phi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\phi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varphi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varphi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -chi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\chi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\psi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -omega -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\omega$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - - -\end_layout - -\begin_layout Standard -How to create special upright Greek letters is explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Upright-small-Greek" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Big Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! big -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Gamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Gamma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Delta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Delta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Theta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Theta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Lambda -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Lambda$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Xi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Xi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Pi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Pi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Sigma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Upsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Upsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Phi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Phi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Psi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Omega -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Omega$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 - -. - Another way is to load the package -\series bold -fixmath -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -fixmath -\series default - is part of the LaTeX-package -\series bold -was -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! was -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! fixmath -\end_layout - -\end_inset - - with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{fixmath} -\end_layout - -\begin_layout Standard -Then all big Greek letters in a document will automatically be typeset italic. -\end_layout - -\begin_layout Subsection -Bold Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! bold -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -boldsymbol -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Upsilon -\backslash -boldsymbol -\backslash -Upsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -theta -\backslash -boldsymbol -\backslash -theta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -A list with all symbols of most of the LaTeX-packages can be found in -\begin_inset CommandInset citation -LatexCommand cite -key "Symbols" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\backslash -texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. -\end_layout - -\begin_layout Plain Layout -More about -\backslash -texorpdfstring is in section -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Formulas-in-Section" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols -\end_layout - -\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 CommandInset label -LatexCommand label -name "sub:Mathematical-Symbols" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! mathematical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -neg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\neg$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Im -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Im$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Re -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Re$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -aleph -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\aleph$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -partial -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\partial$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -infty -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\infty$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\wp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -imath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\imath$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -jmath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\jmath$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -forall -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\forall$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -exists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\exists$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nexists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nexists$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -emptyset -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\emptyset$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varnothing -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varnothing$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dag -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dag$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddag -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ddag$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -complement -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-0.8mm}{ -\end_layout - -\end_inset - - -\begin_inset Formula $\complement$ -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bbbk -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Bbbk$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prime -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\prime$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -backprime -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\backprime$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mho$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -triangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\triangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -angle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\angle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -measuredangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\measuredangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sphericalangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sphericalangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -top -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\top$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Subsection -Miscellaneous Symbols -\begin_inset CommandInset label -LatexCommand label -name "sub:Miscellaneous-Symbols" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! miscellaneous -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\noindent -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -flat -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\flat$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -natural -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\natural$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sharp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sharp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -surd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\surd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -checkmark -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\checkmark$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -yen -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\yen$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pounds -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\pounds$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -$ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\$$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -§ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $§$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hbar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hbar$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hslash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -clubsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\clubsuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -spadesuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\spadesuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigstar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigstar$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -blacklozenge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\blacklozenge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -blacktriangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\blacktriangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -blacktiangledown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\blacktriangledown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bullet -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bullet$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diamondsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diamondsuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Diamond -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Diamond$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -heartsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\heartsuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -P -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\P$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -copyright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\copyright$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -circledR -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\circledR$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -maltese -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\maltese$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diagup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diagup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diagdown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 CommandInset ref -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 CommandInset ref -LatexCommand ref -reference "sub:Font-Sizes" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -The Euro-Symbol € -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! Euro-symbol -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout - -\backslash -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -officialeuro -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To use the Euro symbol in formulas, the LaTeX-package -\series bold -eurosym -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! eurosym -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! E ! -\backslash -euro -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -officialeuro -\end_layout - -\end_inset - -, that is only available in TeX-mode. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifeurosym -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -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 Plain Layout - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -formula -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -euro -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\euro$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -mathematical text -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -€ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mbox{€}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -TeX-mode -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -officialeuro -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -officialeuro -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -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 LaTeX-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 Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Section -Relations -\begin_inset CommandInset label -LatexCommand label -name "sec:Relations" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Relations -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Comparisons|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Relations -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\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 -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -< -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $<$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -le -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\le$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ll -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ll$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prec -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\prec$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -preceq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\preceq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -subset -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\subset$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -subseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\subseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqsubseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqsubseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -in -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\in$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vdash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vdash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -smile -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\smile$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -unlhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\unlhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gtrless -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gtrless$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mid -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mid$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nmid -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nmid$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $=$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not=$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -equiv -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\equiv$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sim$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -simeq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\simeq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -approx -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\approx$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cong -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cong$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bowtie -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bowtie$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -notin -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\notin$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -perp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\perp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -propto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\propto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -asymp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\asymp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -doteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\doteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -circeq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\circeq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -models -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\models$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -widehat= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\widehat{=}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -> -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $>$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gg$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -succ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\succ$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -succeq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\succeq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -supset -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\supset$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -supseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\supseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqsupseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqsupseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ni -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ni$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dashv -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dashv$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -frown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\frown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -unrhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\unrhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lessgtr -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lessgtr$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -parallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\parallel$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nparallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nparallel$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -stackrel -\end_layout - -\end_inset - -: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A(r) -\backslash -stackrel -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -r -\backslash -to -\backslash -infty -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\downarrow$ -\end_inset - - -\backslash -approx -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 CommandInset label -LatexCommand label -name "sub:Predefined-Functions" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Functions ! predefined -\end_layout - -\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 functionswhich 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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Asin(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $Asin(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -sin(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\sin(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sin -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sinh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arcsin -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sup -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cos -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cosh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arccos -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -inf -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tan -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tanh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arctan -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lim -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -coth -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -liminf -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sec -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -min -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -deg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -limsup -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -csc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -max -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -det -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Pr -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ln -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -exp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hom -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -log -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ker -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Functions ! self-defined -\end_layout - -\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 Plain Layout -For more about -\series bold - -\backslash -DeclareMathOperator -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Self-defined-Operators" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset VSpace -3mm -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -DeclareMathOperator{ -\backslash -sgn}{sgn} -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dbinom@ -\backslash -DeclareMathOperator -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset VSpace -2mm -\end_inset - - -\begin_inset Newline newline -\end_inset - -Now the new defined function can be called with the command -\series bold - -\backslash -sgn -\series default -. -\end_layout - -\begin_layout Itemize -Write the formula as usual, mark the formula name, in our example the letters - -\emph on -sgn -\emph default -, and change it to mathematical text. - Finally, 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 Plain Layout -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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -sgn(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\sgn(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -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 Plain Layout -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Limits -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For limits, in addition to the commands -\series bold - -\backslash -lim -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -lim -\end_layout - -\end_inset - -, -\series bold - -\backslash -liminf -\series default - and -\series bold - -\backslash -limsup -\series default - the following functions are defined: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varliminf -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varliminf$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varlimsup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varlimsup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varprojlim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varprojlim$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varinjlim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset space \hspace{} -\length 1cm -\end_inset - -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -The space 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 Plain Layout - -\backslash -lim_x -\backslash -to -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -x=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Functions ! modulo- -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The modulo-function is special, because it exists in four variants. - The variants in a displayed formula are: -\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. - By default the modulo-functions take only the first following character - into account. - To use more than one character, one has to put them into TeX-braces: -\begin_inset Formula -\begin{align*} -\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ -\mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\ -\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d -\end{align*} - -\end_inset - - -\end_layout - -\begin_layout Section -Special Characters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Special characters -\end_layout - -\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 -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oe -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{œ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -OE -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Œ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ae -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{æ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -AE -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Æ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -aa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{\aa}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -AA -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout - -\backslash -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textrm{ -\backslash -AA} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Å}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -i -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ı}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -command -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -The space of 0 -\begin_inset space \thinspace{} -\end_inset - -mm is used for separation, because otherwise the output will be ¡ and ¿ - respectively. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -o -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ø}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -O -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Ø}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -l -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ł}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -L -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Ł}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -! -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{!`}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -? -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{?`}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -j -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ȷ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 space \hspace{} -\length 0mm -\end_inset - -` -\series default - and -\series bold -? -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\series default -, because they can be inserted in LyX directly to text. -\end_layout - -\begin_layout Subsection -Accents in Text -\begin_inset CommandInset label -LatexCommand label -name "sub:Accents-in-Text" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents ! in text -\end_layout - -\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 -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash - -\begin_inset Quotes grd -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -"e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -`e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -`e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -^e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -=e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -=e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -u -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -u e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -b -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -b e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -t -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -ee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -t ee -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -H -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -H e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -'e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -'e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -~e -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Tilde -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -~e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -.e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -.e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -v -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -v e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -d -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -d e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -c -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -c e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -sz -\series default - creates: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout -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 that are 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 CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textcircled -\end_layout - -\end_inset - - all numbers and letters can be set into a circle, quasi accented with a - circle, similar to the copyright symbol. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -textcircled{w} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textcircled{w} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Large -\backslash -textcircled{ -\backslash -normalsize -\backslash -protect -\backslash -raisebox{-1.5pt}{W}} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}$ -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout -see -\begin_inset CommandInset ref -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 Plain Layout -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Boxes-without-Frame" - -\end_inset - - -\end_layout - -\end_inset - - the character can be centered. -\end_layout - -\begin_layout Subsection -Old-style Figures -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Old-style Figures -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Old-style figures (also known as old-style numerals) are created with the - command -\series bold - -\backslash -oldstylenums -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -oldstylenums -\end_layout - -\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 CommandInset label -LatexCommand label -name "sub:Miscellaneous-special-Characters" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Special characters ! miscellaneous -\end_layout - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathcircumflex$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -_ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\_$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -circ -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout - -\backslash -@° -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Plain Layout -More about this is described in -\begin_inset CommandInset ref -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 -fi} -\end_layout - -\begin_layout Section -Formula Styles -\begin_inset CommandInset label -LatexCommand label -name "sec:Formula-Styles" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! styles -\end_layout - -\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 -\begin_inset space ~ -\end_inset - -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathindent -\end_layout - -\end_inset - -. - Should the distance be 15 -\begin_inset space \thinspace{} -\end_inset - -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 -\begin_inset space \thinspace{} -\end_inset - -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 -\begin_inset space ~ -\end_inset - -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 CommandInset ref -LatexCommand ref -reference "sub:Flalign-Environment" - -\end_inset - -. -\end_layout - -\begin_layout Section -Multiline Formulas -\begin_inset CommandInset label -LatexCommand label -name "sec:Multiline-Formulas" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -General -\end_layout - -\begin_layout Standard -In LyX multiline formulas are created by pressing -\series bold - -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - -\series default - inside a formula. - This creates either an -\series bold -eqnarray environment -\series default - that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Eqnarray-Environment" - -\end_inset - - or, when the option -\family sans -Use AMS math package -\family default - in the document settings is selected, an -\series bold -align environment -\series default - that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Standard-align-Environment" - -\end_inset - -. - The align environment is recommended because it provides in any case a - typographically correct output. -\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 - -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - -. - 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 CommandInset label -LatexCommand label -name "sub:Line-Separation" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! Line separation -\end_layout - -\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 Plain Layout -see -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #1505" -target "http://www.lyx.org/trac/ticket/1505" - -\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 Plain Layout - - -\backslash -begin{eqnarray*} -\end_layout - -\begin_layout Plain Layout - -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 Plain Layout - -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 Plain Layout - - -\backslash -end{eqnarray*} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -To set the line separation for all lines in a formula, the length -\series bold - -\backslash -jot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! J ! -\backslash -jot -\end_layout - -\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 -\begin_inset space \thinspace{} -\end_inset - -pt. - To create 3 -\begin_inset space \thinspace{} -\end_inset - -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 Plain Layout - -\series bold -calc -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! calc -\end_layout - -\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 Plain Layout - - -\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 Plain Layout - - -\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 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Subsubsection -Column Separation -\begin_inset CommandInset label -LatexCommand label -name "sub:Column-Separation" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! Column separation -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arraycolsep -\end_layout - -\end_inset - - according to: -\begin_inset Newline newline -\end_inset - -column separation = 2 -\begin_inset space \thinspace{} -\end_inset - - -\series bold - -\backslash -arraycolsep -\series default - -\begin_inset Newline newline -\end_inset - -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 -\begin_inset space \thinspace{} -\end_inset - -cm. - To get back to the predefined distance, -\series bold - -\backslash -arraycolsep -\series default - is set to 5 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Standard -A formula with 2 -\begin_inset space \thinspace{} -\end_inset - -cm column separation: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 -\begin_inset space \thinspace{} -\end_inset - -pt: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! long -\end_layout - -\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 shorter than the line width, this - one is chosen for the left side and the right side is typeset over two - lines: -\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:shortlong} -\end{eqnarray} - -\end_inset - -The minus sign at the beginning of the second line does normally not appear - as an 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, 3 -\begin_inset space \thinspace{} -\end_inset - -pt space was inserted behind the minus sign with the command -\series bold - -\backslash -hspace -\series default -. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -for more about -\series bold - -\backslash -hspace -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Variable-Space" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hspace -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -lefteqn -\end_layout - -\end_inset - - is used. - It is inserted in the first column of the first line and causes all further - insertions to overwrite the following columns: -\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 - -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 Newline newline -\end_inset - -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 VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout -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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -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 Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #1429" -target "http://www.lyx.org/trac/ticket/1429" - -\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 CommandInset ref -LatexCommand ref -reference "sub:Multline-Environment" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Multiline-Formula-Parts" - -\end_inset - -. -\end_layout - -\begin_layout Subsubsection -Multiline Brackets -\begin_inset CommandInset label -LatexCommand label -name "sub:Multiline-Brackets" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets ! for multiline expressions -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -right -\end_layout - -\end_inset - - and the second line with -\series bold - -\backslash -left. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -for more about -\series bold - -\backslash -left -\series default - and -\series bold - -\backslash -right -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -left -\end_layout - -\end_inset - -. - After -\series bold - -\backslash -left. - -\series default - the command -\series bold - -\backslash -vphantom -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\backslash -prod -\series default -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\backslash -infty -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\begin_inset Formula $\downarrow$ -\end_inset - -_R=1} -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! V ! -\backslash -vphantom -\end_layout - -\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 especially 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 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 CommandInset label -LatexCommand label -name "sub:Standard-align-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! align environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This Align environment is created by pressing -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - 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 Plain Layout -more about -\series bold - -\backslash -hfill -\series default - see -\begin_inset CommandInset ref -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 Plain Layout -formula styles see -\begin_inset CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! alignat environment -\end_layout - -\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 CommandInset ref -LatexCommand ref -reference "sub:Space" - -\end_inset - -. -\end_layout - -\begin_layout Standard -The above example in the alignat environment where 1 -\begin_inset space \thinspace{} -\end_inset - -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 CommandInset label -LatexCommand label -name "sub:Flalign-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! flalign environment -\end_layout - -\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 CommandInset ref -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 -\begin_inset space \thinspace{} -\end_inset - -pt space was inserted at the beginning of the first column. -\end_layout - -\begin_layout Subsection -Eqnarray Environment -\begin_inset CommandInset label -LatexCommand label -name "sub:Eqnarray-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! eqnarray environment -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! gather environment -\end_layout - -\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 CommandInset label -LatexCommand label -name "sub:Multline-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! multline environment -\end_layout - -\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 CommandInset ref -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 last (first) line of a multline environment appears - numbered when the document numbering is right (left). -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -numbering styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With the commands -\series bold - -\backslash -shoveright -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -shoveright -\end_layout - -\end_inset - - and -\series bold - -\backslash -shoveleft -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -shoveleft -\end_layout - -\end_inset - - 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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -multlinegap -\end_layout - -\end_inset - - specifies the distance of the first line from the left page margin. - Predefined is the length 0 -\begin_inset space \thinspace{} -\end_inset - -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 Plain Layout - - -\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 Plain Layout - - -\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 CommandInset label -LatexCommand label -name "sub:Multiline-Formula-Parts" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! formula parts -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To display only parts of a formula with multiple lines, one of the following - environments is 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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -aligned -\end_layout - -\end_inset - - 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 CommandInset ref -LatexCommand eqref -reference "eq:shortlong" - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -alignedat -\end_layout - -\end_inset - - -\series bold - -\backslash -gathered -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! G ! -\backslash -gathered -\end_layout - -\end_inset - -, or -\series bold - -\backslash -split -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -split -\end_layout - -\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 CommandInset label -LatexCommand label -name "sub:Text-in-multiline" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! in formulas -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! text -\end_layout - -\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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! I ! -\backslash -intertext -\end_layout - -\end_inset - - 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 \ensuremath{\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 Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! numbering|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Formula numbering -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\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 -\begin_inset space ~ -\end_inset - -Formula -\family default - (shortcut -\family sans -Ctrl+Alt -\begin_inset space ~ -\end_inset - -N -\family default -). - Existing formulas can be numbered with the menu -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Toggle -\begin_inset space ~ -\end_inset - -Numbering -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "math-number-toggle" -\end_inset - -). - The formula number is displayed in LyX behind the formula as a 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 -\begin_inset space ~ -\end_inset - -Numbering -\begin_inset space ~ -\end_inset - -of -\begin_inset space ~ -\end_inset - -Line -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "math-number-line-toggle" -\end_inset - -) for every line. -\end_layout - -\begin_layout Standard -Except for inline formulas, all formulas can be numbered with two different - styles, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Cross-References -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Cross-references ! to formulas -\end_layout - -\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. - Alternatively you can right-click on the formula and choose -\family sans -Equation Label -\family default -. - 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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -section labels. - To change a label, the menu -\family sans -Insert\SpecialChar \menuseparator -Label -\family default - is used again or you right-click on a formula and then on -\family sans -Equation Label -\family default -. -\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. -\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. -\begin_inset Newline newline -\end_inset - -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 Plain Layout -Note the different cross-reference types. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The equations -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:tag" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:c" - -\end_inset - - are equivalent. - In ( -\begin_inset CommandInset ref -LatexCommand ref -reference "eq:Lat" - -\end_inset - -) big Latin letters are used for the numbering in contrary to ( -\begin_inset CommandInset ref -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 Plain Layout - -\series bold - -\backslash -tag -\series default - is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:User-defined-Numbering" - -\end_inset - -. -\end_layout - -\end_inset - - -\series default - contains a box like in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Paragraph-Boxes" - -\end_inset - -, the formula cannot be referenced. -\end_layout - -\begin_layout Subsection -Subnumbering -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! subnumbering -\end_layout - -\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 Plain Layout - - -\backslash -addtocounter{equation}{-1} -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -addtocounter -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\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 Newline linebreak -\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 CommandInset ref -LatexCommand eqref -reference "eq:a" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:b" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:c" - -\end_inset - - would be numbered as -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:a" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:d" - -\end_inset - -, -\begin_inset CommandInset ref -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 -\begin_inset space \thinspace{} -\end_inset - -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 Plain Layout -formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - is used, -7 -\begin_inset space \thinspace{} -\end_inset - -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 Plain Layout - - -\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 Plain Layout - - -\backslash -end{subequations} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -User-defined Numbering -\begin_inset CommandInset label -LatexCommand label -name "sub:User-defined-Numbering" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! user-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! self-defined delimiters -\end_layout - -\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 Plain Layout -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 -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -tag -\end_layout - -\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 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -something -\series default - was inserted in the formula. -\end_layout - -\begin_layout Standard -When the command -\series bold - -\backslash -tag* -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - - ! -\backslash - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -addtoreset -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - -resp. -\begin_inset Newline newline -\end_inset - - -\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 -\begin_inset Newline newline -\end_inset - - -\backslash -@addtoreset{equation}{section} -\begin_inset Newline newline -\end_inset - - -\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 Plain Layout - -\series bold -remreset -\series default - is part of the LaTeX-package -\series bold -carlisle -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! carlisle -\end_layout - -\end_inset - - that is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! remreset -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - - ! -\backslash - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -removefromreset -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -numberwithin -\end_layout - -\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 TeX code 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 Plain Layout - - -\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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -tables so that the number of the part is the sectioning, -\begin_inset Newline newline -\end_inset - - -\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 TeX code or to the LaTeX-preamble: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arabic -\end_layout - -\end_inset - - -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\end_layout - -\end_inset - - -\series bold - -\begin_inset Newline newline -\end_inset - - -\series default -or -\series bold - -\begin_inset Newline newline -\end_inset - - -\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 Plain Layout - - -\backslash -makeatletter -\end_layout - -\begin_layout Plain Layout - - -\backslash -@removefromreset{equation}{section} -\end_layout - -\begin_layout Plain Layout - - -\backslash -makeatother -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Numbering with Roman Numbers and Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! with letters -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! with Roman numbers -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -renewcommand -\end_layout - -\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 Plain Layout -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 CommandInset ref -LatexCommand ref -reference "sub:The-Command-newcommand" - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -roman -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -roman@ -\backslash -Roman -\end_layout - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -alph -\end_layout - -\end_inset - -, for big ones there is the command -\series bold - -\backslash -Alph -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -alph@ -\backslash -Alph -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -\color none -Note: -\series default - Only maximal 26 -\begin_inset space ~ -\end_inset - -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 Plain Layout - - -\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} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -alph{equation}} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -C=\textrm{small Latin} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arabic -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -E=\textrm{Arabic} -\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 CommandInset href -LatexCommand href -name "Formula-numbering.lyx" -target "run:Formula-numbering.lyx" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Chemical Symbols and Equations -\begin_inset CommandInset label -LatexCommand label -name "sub:Chemical-Symbols-and" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Chemical characters ! Symbols -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Chemical equations -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! chemical -\end_layout - -\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 -\begin{equation} -\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction} -\end{equation} - -\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 -\begin_inset Info -type "shortcut" -arg "font-roman" -\end_inset - - to the upright font style. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -font styles -\series bold - -\series default -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -A more convenient way to typeset chemical formulas is to use the command - -\series bold - -\backslash -ce -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -ce -\end_layout - -\end_inset - - that is available when the LaTeX-package -\series bold -mhchem -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! mhchem -\end_layout - -\end_inset - - is installed. - After inserting -\series bold - -\backslash -ce -\series default - to a formula a new blue box appears where chemical formulas can be inserted - in an intuitive way. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -H2CO3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -SO4^2- -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -(NH4)2S -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -KCr(SO4)2.12H2O -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A-B -\backslash -dbond -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\backslash -tbond -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -D -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -^227 -\begin_inset Formula $\downarrow$ -\end_inset - -_90 -\begin_inset Formula $\to$ -\end_inset - -Th+ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -CO2 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -<=> -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2CO -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -CO2 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -->[ -\backslash -alpha][ -\backslash -beta] -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2CO} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -\color none -Note: -\series default - Inserting a formula to a -\series bold - -\backslash -ce -\series default - box will lead to LaTeX errors due to a LyX bug. -\color inherit - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #8566" -target "http://www.lyx.org/trac/ticket/8566" - -\end_inset - - -\end_layout - -\end_inset - - -\color none - In this case TeX code has to be used like for -\series bold - -\backslash -ce{$ -\backslash -mu -\backslash -hyphen$Cl} -\series default -: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ce{$ -\backslash -mu -\backslash -hyphen$Cl} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -\color none -Note: -\series default - It is not possible in LyX to use the character ^ to get an up-arrow as - described in the -\series bold -mhchem -\series default - manual. - One instead uses a negative thin space followed by the command -\series bold - -\backslash -uparrow -\series default -: -\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$ -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Using -\series bold - -\backslash -ce -\series default - the command for equation -\begin_inset space ~ -\end_inset - - -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:chem-reaction" - -\end_inset - - is: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2Na+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -SO4^2- -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - --> -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -Na2SO4 -\end_layout - -\begin_layout Standard -To create multiline chemical equations first a multiline formula is created - as described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Multiline-Formulas" - -\end_inset - -. - Afterwards the command -\series bold - -\backslash -ce -\series default - is used in every small blue box of the formula. - -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:TEOS-reaction-1" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:TEOS-reaction-2" - -\end_inset - - are an example of a multi-stage chemical reaction where every equation - has its own number. -\begin_inset Formula -\begin{eqnarray} -\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\ -\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2} -\end{eqnarray} - -\end_inset - - -\end_layout - -\begin_layout Standard -Besides -\series bold - -\backslash -ce -\series default - the -\series bold -mhchem -\series default - package provides the command -\series bold - -\backslash -cf -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cf -\end_layout - -\end_inset - - that has to be used for special cases. - For more information about -\series bold - -\backslash -cf -\series default - and more examples have a look at the documentation of -\series bold -mhchem -\series default -, -\begin_inset CommandInset citation -LatexCommand cite -key "mhchem" - -\end_inset - -. -\end_layout - -\begin_layout Section -Diagrams -\end_layout - -\begin_layout Standard -LyX supports two types of commutative diagrams: -\series bold -amscd -\series default - and -\series bold -xymatrix -\series default - that are explained in the following. -\end_layout - -\begin_layout Subsection -Amscd Diagrams -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Diagrams ! amscd -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Diagrams of this type visualize relations by vertical and horizontal lines - or arrows: -\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 - a 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 -If 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: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -CD -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A@>j>>B@>>k>C@=F Ctrl+Return -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -CD -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -@AmAA@.@VV -\backslash -{V -\series default - -\begin_inset Formula $\to$ -\end_inset - - -\series bold -V@| Ctrl+Return -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -CD -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -D@<k>>F@=C -\end_layout - -\begin_layout Subsection -Xymatrix Diagrams -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Diagrams ! xymatrix -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To be able to use xymatrices, the LaTeX-package -\series bold -xypic -\series default - must be installed. - A xymatrix is created by inserting the command -\series bold - -\backslash -xymatrix -\series default - in a formula. - Then you are able to add new matrix columns and rows like for normal matrices, - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Matrices" - -\end_inset - -. -\end_layout - -\begin_layout Standard -In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows, - and much more. - All possibilities to create commutative diagrams and decorations are explained - in detail in the -\emph on -XY-pic manual -\emph default - that you find in the menu -\family sans -Help\SpecialChar \menuseparator -Specific -\begin_inset space ~ -\end_inset - -Manuals -\family default -. -\end_layout - -\begin_layout Subsection - -\noun on -Feynman -\noun default - Diagrams -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Diagrams ! Feynman -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To be able to use -\noun on -Feynman -\noun default --diagrams, the LaTeX-package -\series bold -feyn -\series default - must be installed. - A -\noun on -Feynman -\noun default --diagram is created by inserting the command -\series bold - -\backslash -Diagram -\series default - in a formula. - Then you are able to add new matrix columns and rows like for normal matrices, - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Matrices" - -\end_inset - -. -\end_layout - -\begin_layout Standard -Examples how to create -\noun on -Feynman- -\noun default -diagrams in LyX is given in the -\emph on -Feynman-diagram manual -\emph default - that you find in the menu -\family sans -Help\SpecialChar \menuseparator -Specific -\begin_inset space ~ -\end_inset - -Manuals -\family default -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -User-defined Commands -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -User-defined commands -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - The names of user-defined commands and macros may only consist of Latin - letters. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -The Command -\backslash -newcommand -\begin_inset CommandInset label -LatexCommand label -name "sub:The-Command-newcommand" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -User-defined commands ! -\backslash -newcommand -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -newcommand -\end_layout - -\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 - 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] -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -newcommand -\end_layout - -\end_inset - -{command definition} -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\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 -The number of arguments is an integer in the range 0 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -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 VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\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 VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -us}[1]{ -\backslash -underline{#1}} -\series default - -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - -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. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -define the command -\series bold - -\backslash -fb -\series default -: -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -fb}[3]{ -\backslash -framebox#1#2{$#3$}} -\series default - -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - -The two Dollar signs creates the extra formula needed for -\series bold - -\backslash -framebox -\series default -, see -\begin_inset CommandInset ref -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 need not be specified, the argument for the - color is defined optional: -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -cb}[3][white]{ -\backslash -fcolorbox{#2}{#1}{$#3$}} -\series default - -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - -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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -gr -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\gr B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -us{ABcd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\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 Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cb{red -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cb[green] -\backslash -{red -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Subsection -Math Macros -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -User-defined commands! Math macros -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Macros -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -User-defined commands are especially convenient for complex expressions. - When you are for example dealing with a document that has quadratic equations, - the same solution type occurs several times. - The general form of a quadratic equation is -\begin_inset Formula -\[ -0=\lambda^{2}+p\lambda+q -\] - -\end_inset - -The general form of the solution is -\begin_inset Formula -\[ -\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -To define a command for the solution formula where only the three parameters - -\begin_inset Formula $\lambda$ -\end_inset - -, -\begin_inset Formula $p$ -\end_inset - - and -\begin_inset Formula $q$ -\end_inset - - need to be specified and the index of -\begin_inset Formula $\lambda$ -\end_inset - - can be given optionally, the LaTeX-preamble line is -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -qG}[4][1, -\backslash -,2]{#2_{#1}=- -\backslash -frac{#3}{2} -\backslash -pm -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -newcommand -\end_layout - -\end_inset - - -\backslash -sqrt{ -\backslash -frac{#3^{2}}{4}-#4}} -\end_layout - -\begin_layout Standard -To create with this the solution formula, the command -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -qG{ -\backslash -lambda -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{p -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{q -\series default - is inserted to a formula -\series bold -. -\end_layout - -\begin_layout Standard -The definition of the new command is unintuitive because one has to know - the schemes of all used LaTeX commands, e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -that a fraction is inserted in LaTeX as -\series bold - -\backslash -frac{numerator}{denominator} -\series default -. - Furthermore one can easily forget a brace in the definition and cannot - see in LyX what the new command is doing. - To avoid these problems LyX offers the possibility to use math macros instead - of the command -\series bold - -\backslash -newcommand -\series default -. -\end_layout - -\begin_layout Standard -A math macro is created by using the menu -\family sans -Insert\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\family default - or the toolbar button -\begin_inset Graphics - filename ../images/math-macro_newmacroname_newcommand.png - scale 85 - -\end_inset - -. - The math macro toolbar appears together with the following box where the - macro is defined: -\begin_inset Newline newline -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Graphics - filename clipart/macrobox.png - -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset FormulaMacro -\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}} -\end_inset - - -\backslash -newmacroname is the default name of the macro that should be changed to - something sensible. - The wanted formula is inserted in the first blue box. - An argument placeholder is inserted with the command -\series bold - -\backslash -#argumentnumber -\series default -, e. -\begin_inset space \thinspace{} -\end_inset - -g -\begin_inset space \space{} -\end_inset - - -\series bold - -\backslash -#1 -\series default - or by using the macro toolbar button -\begin_inset Graphics - filename ../images/math-macro-add-param.png - scale 85 - -\end_inset - -. - Argument placeholders are displayed red. - A maximum of 9 -\begin_inset space ~ -\end_inset - -arguments are possible. - Optional arguments are created with the toolbar button -\begin_inset Graphics - filename ../images/math-macro-add-optional-param.png - scale 85 - -\end_inset - -. - The first non-optional argument can be transformed to an optional one with - the toolbar button -\begin_inset Graphics - filename ../images/math-macro-make-optional.png - scale 85 - -\end_inset - -. - In the second blue box the appearance of the macro in LyX can be defined. - Normally you want to see it as it is defined, so the box is kept empty. - But when you have created a macro that needs lot of space on the screen, - you can insert in the box for example -\begin_inset Newline newline -\end_inset - - -\series bold -qG: -\backslash -#1 -\series default - -\series bold -, -\series default - -\series bold - -\backslash -#2 -\series default - -\series bold -, -\series default - -\series bold - -\backslash -#3, -\backslash -#4 -\begin_inset Newline newline -\end_inset - - -\series default -For the macro only the arguments with the macro name in front of them will - then be displayed in LyX, leading to a better overview. - The formula appears in the output as defined in the first box. -\begin_inset Newline newline -\end_inset - -The appearance of macros in formulas can furthermore be changed for single - macros by setting the cursor in the macro and using the menu -\family sans -View\SpecialChar \menuseparator -(Un)fold -\begin_inset space ~ -\end_inset - -Math -\begin_inset space ~ -\end_inset - -Macro -\family default -. -\end_layout - -\begin_layout Standard -To use a macro, the macro name is inserted as command to a formula, in our - case -\series bold - -\backslash -qG -\series default -. - Our macro looks in LyX like this: -\begin_inset Newline newline -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Graphics - filename clipart/macrouse.png - -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Newline newline -\end_inset - -Here is our macro example with the arguments -\begin_inset Formula $x$ -\end_inset - -, -\begin_inset Formula $\ln(x)$ -\end_inset - - and -\begin_inset Formula $B$ -\end_inset - -: -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -\qG x{\ln(x)}B -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -LyX offers in the menu -\family sans -Tools\SpecialChar \menuseparator -Preferences\SpecialChar \menuseparator -Editing\SpecialChar \menuseparator -Control -\family default - different styles to edit macros. - To find the style that suits you the most, choose a style and set the cursor - in a macro formula to see the difference. -\end_layout - -\begin_layout Standard -A math macro is transformed internally to a -\series bold - -\backslash -newcommand -\series default - command when exporting the document. - The created -\series bold - -\backslash -newcommand -\series default - command is not placed in the LaTeX-preamble, therefore macros can only - be used in formulas that are in the document below the macro definition - box. -\end_layout - -\begin_layout Standard -Math macros can also be directly created from a -\series bold - -\backslash -newcommand -\series default - command. - When writing for example the command -\series bold - -\begin_inset Newline newline -\end_inset - - -\backslash -newcommand{ -\backslash -larrow}[2]{ -\backslash -xleftarrow[#2]{#1}} -\begin_inset Newline newline -\end_inset - - -\series default -in LyX as normal text, highlighting it completely and using then the shortcut - -\family sans -Ctrl+M -\family default -, the command will be transformed to a math macro. - Using this method you need to be careful that the -\series bold - -\backslash -newcommand -\series default - command is typed correctly, otherwise you get a faulty macro leading to - LaTeX errors. -\end_layout - -\begin_layout Standard -Math macros currently have the problem that further formulas in macro definition -s are handled wrongly. - Therefore the example -\series bold - -\backslash -fb -\series default - from -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:The-Command-newcommand" - -\end_inset - - cannot be created as macro. -\end_layout - -\begin_layout Standard -When the cursor is in a macro definition box, you will see the macro toolbar - in LyX: -\end_layout - -\begin_layout Standard -\begin_inset VSpace defskip -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Graphics - filename clipart/MacroToolbar.png - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Macros ! Toolbar -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace defskip -\end_inset - - -\end_layout - -\begin_layout Standard -The macro toolbar contains from left to right the following buttons: -\end_layout - -\begin_layout Standard -\begin_inset VSpace defskip -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-remove-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Remove Last Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-add-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Append Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-make-optional.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Make First Non-Optional into -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-make-nonoptional.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Make Last Optional into -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Non-Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-remove-optional-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Remove Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-add-optional-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Insert Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-remove-greedy-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Remove Last Argument -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Spitting Out To The Right -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-append-greedy-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Append Argument -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Eating From The Right -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-add-greedy-optional-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Append Optional Argument -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Eating From The Right -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Section -Computer Algebra Systems -\end_layout - -\begin_layout Standard -LyX offers the exchange between mathematical expressions written in LyX's - math editor and external applications or user defined scripts. - Currently supported applications are -\family sans -Maple -\family default -, -\family sans -Mathematica -\family default -, -\family sans -Maxima -\family default - and -\family sans -Octave -\family default -. - Note that the set of supported mathematical constructs is limited only - to very simple cases. -\end_layout - -\begin_layout Subsection -Usage -\end_layout - -\begin_layout Standard -Write some expression in a formula, go to the -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Use Computer Algebra System -\family default - menu and choose the application you have installed on the computer. - After that the result of computation should show on the right side of the - expression together with the -\begin_inset Quotes eld -\end_inset - -= -\begin_inset Quotes erd -\end_inset - - operator. -\end_layout - -\begin_layout Standard -Here are few simple examples (with results from -\family typewriter -Maxima -\family default -) to show what kind of computations can be performed: -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\det\left[\begin{array}{ccc} -1 & 6 & 7\\ -2 & 5 & 8\\ -3 & 4 & 17 -\end{array}\right]=-56$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$ -\end_inset - - -\end_layout - -\begin_layout Subsection -Keyboard shortcut -\end_layout - -\begin_layout Standard -Currently there is no keyboard shortcut for calling the algebra applications. - One can easily bind a shortcut to the -\family sans -math-extern -\family default - LyX function (see the -\family sans -\emph on -LyX Functions -\family default -\emph default - manual). - One could e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -bind the -\family sans -Return -\family default - key inside the math editor. - To bind it to -\family typewriter -Maxima -\family default - one would use this shortcut definition command: -\end_layout - -\begin_layout Standard - -\series bold -command-alternatives break-paragraph;math-extern maxima -\end_layout - -\begin_layout Section -Miscellaneous -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Miscellaneous -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Negative Numbers -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Numbers ! negative -\end_layout - -\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 Plain Layout -normal text: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -x = -2 -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -formula: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $x=-2$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -solution: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Index idx -status collapsed - -\begin_layout Plain Layout -Comma -\end_layout - -\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 -\begin_inset Info -type "shortcut" -arg "math-mode" -\end_inset - -). -\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 Plain Layout - -\series bold -icomma -\series default - is part of the LaTeX-package -\series bold -was -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! was -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! icomma -\end_layout - -\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 CommandInset label -LatexCommand label -name "sub:Physical-Vectors" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Vectors ! physical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Predefined vectors are offered by the LaTeX-package -\series bold -braket -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! braket -\end_layout - -\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 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifbraket -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following table will only be displayed when the LaTeX-package -\series bold -braket -\series default - is installed. -\end_layout - -\end_inset - - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bra{ -\backslash -psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Bra{\psi}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Ket{ -\backslash -psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Ket{\psi}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Braket{ -\backslash -psi| -\backslash -phi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following will be displayed when the LaTeX-package -\series bold -braket -\series default - is not installed: -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -You need to install the LaTeX-package -\series bold -braket -\series default - to see the rest of this subsection in the output. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fi -\end_layout - -\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 CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Self-defined Fractions -\begin_inset CommandInset label -LatexCommand label -name "sub:Self-defined-Fractions" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Fractions ! self-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To define custom commands for fractions, the command -\series bold - -\backslash -genfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! G ! -\backslash -genfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\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} -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -genfrac -\end_layout - -\end_inset - -{numerator}{denominator} -\end_layout - -\begin_layout Standard -The style is a number in the range of 0 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -3. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Number -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Style (Size) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -0 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -display style formula -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -1 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -inline formula -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -2 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -small -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -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 -\begin_inset space \thinspace{} -\end_inset - -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 CommandInset ref -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 Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! canceled -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To cancel formulas or formula parts, the LaTeX-package -\series bold -cancel -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! cancel -\end_layout - -\end_inset - - has to be loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{cancel} -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifcancel -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following table will only be displayed when the LaTeX-package -\series bold -cancel -\series default - is installed. -\end_layout - -\end_inset - - -\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 Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -The space 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 Plain Layout - -\backslash -cancel{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bcancel{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -xcancel{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cancelto{1 -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\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 Standard -To change the size of -\series bold - -\backslash -cancelto -\series default -'s -\begin_inset Quotes eld -\end_inset - -subscript -\begin_inset Quotes erd -\end_inset - - value one can load the package -\series bold -cancel -\series default - with either the option -\series bold -samesize -\series default - which leads to the same size as for the canceled value or with the option - -\series bold -Smaller -\series default - which makes is it a bit smaller than the size one gets without using a - package option. - In this document -\series bold -cancel -\series default - was loaded with this line: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage[samesize]{cancel} -\end_layout - -\begin_layout Standard -To color the cancellation bar one adds this command as TeX code: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -CancelColor}{ -\backslash -color{red}} -\end_layout - -\begin_layout Standard - -\series bold -red -\series default - can be replaced by a color of your choice. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -CancelColor}{ -\backslash -color{red}} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\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 Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -CancelColor}{ -\backslash -color{black}} -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -reset the color -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For further customizations, see the documentation of the package -\series bold -cancel -\series default -, -\begin_inset CommandInset citation -LatexCommand cite -key "cancel" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following will be displayed when the LaTeX-package -\series bold -cancel -\series default - is not installed: -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -You need to install the LaTeX-package -\series bold -cancel -\series default - to see the rest of this subsection in the output. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Subsection -Formulas in Section Headings -\begin_inset CommandInset label -LatexCommand label -name "sub:Formulas-in-Section" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! in section headings -\end_layout - -\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 Plain Layout -When -\series bold -hyperref -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! hyperref -\end_layout - -\end_inset - - support is enabled in the document settings dialog under -\family sans -PDF -\begin_inset space ~ -\end_inset - -Properties -\family default -, PDF-bookmarks are 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 -\begin_inset space ~ -\end_inset - -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 Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -texorpdfstring -\end_layout - -\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 Plain Layout - - -\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 Argument 1 -status collapsed - -\begin_layout Plain Layout -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 Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Formula $\sqrt{-1}=\mathrm{i}$ -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 -\series default - environment -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Bold-Formulas" - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Formulas in multi-column Text -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! in multi-column text -\end_layout - -\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 Plain Layout - -\series bold -multicol -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! multicol -\end_layout - -\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 Plain Layout -Note that in this case the setting -\family sans -Two-column -\begin_inset space ~ -\end_inset - -document -\family default - in the menu -\family sans -Document\SpecialChar \menuseparator -Settings -\family default - under -\family sans -Text -\begin_inset space ~ -\end_inset - -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 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -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 -\begin_inset space \thinspace{} -\end_inset - -mm vertical space is inserted before the formula. - When the formula style -\series bold -Indented -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - is used, -9 -\begin_inset space \thinspace{} -\end_inset - -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 - -\lang german -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 Plain Layout - - -\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 -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\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 - - -\begin_inset space \thinspace{} -\end_inset - --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 - -\lang german -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -end{multicols} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Formulas with Description of Variables -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! with description of variables -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To describe variables within a formula, like in formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:within" - -\end_inset - -, a 2 -\series bold -× -\series default - -\begin_inset Formula $n$ -\end_inset - - -\begin_inset space ~ -\end_inset - -matrix is used with left aligned columns for the -\begin_inset Formula $n$ -\end_inset - - used variables. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -matrices see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Matrices" - -\end_inset - - -\end_layout - -\end_inset - - To set the description in a smaller size, before the matrix e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -the command -\series bold - -\backslash -footnotesize -\series default - is inserted. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -font sizes see -\begin_inset CommandInset ref -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 Plain Layout -formula styles see -\begin_inset CommandInset ref -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 Plain Layout - -\series bold - -\backslash -hfill -\series default - only works in formulas with the style -\series bold -Indented -\series default -, see -\begin_inset CommandInset ref -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 CommandInset ref -LatexCommand ref -reference "sub:Flalign-Environment" - -\end_inset - - is used to indent formulas. - Formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:within" - -\end_inset - - consists of five columns where 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 CommandInset label -LatexCommand label -name "sub:Upright-small-Greek" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! upright -\end_layout - -\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 Plain Layout - -\series bold -upgreek -\series default - is part of the LaTeX-package -\series bold -was -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! was -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! upgreek -\end_layout - -\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 Plain Layout - - -\backslash -ifupgreek -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -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 letter 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 Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -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 LaTeX-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 Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Text Characters in Formulas -\begin_inset CommandInset label -LatexCommand label -name "sub:Text-Characters-in" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! in formulas -\end_layout - -\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 Plain Layout -see -\begin_inset CommandInset ref -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. - For example the encoding -\series bold -latin9 -\series default - is defined in the file -\series bold -latin9.def -\series default - which is in the installation folder of LaTeX. - Encodings should only be changed via the LaTeX-preamble and not in the - definition files. - Otherwise 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 be directly inserted - into 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 -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -\start_of_appendix -Typographic Advice -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Typographic advice -\end_layout - -\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 Plain Layout -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 CommandInset citation -LatexCommand cite -key "Duden" - -\end_inset - - that lists some of the ISO rules. - More rules are listed in -\begin_inset CommandInset citation -LatexCommand cite -key "Checklist" - -\end_inset - -. -\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 Plain Layout -done with font styles, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Styles" - -\end_inset - - -\end_layout - -\end_inset - -, no matter if they appear in italic text: 30 -\begin_inset space \thinspace{} -\end_inset - -km/h -\begin_inset Newline newline -\end_inset - -Between the value and the unit is the smallest space, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Predefined-Space" - -\end_inset - -. -\begin_inset Newline newline -\end_inset - -This convention is automatically fulfilled when the command -\series bold - -\backslash -unittwo -\series default - is used. - When it is entered to a formula, two boxes appear. - In the first one the value is inserted, in the second one the unit, and - one gets as above: -\begin_inset Formula $\unit[30]{km/h}$ -\end_inset - - -\begin_inset space \thinspace{} -\end_inset - -. - Note that -\series bold - -\backslash -unittwo -\series default - is not a real LaTeX command but the command -\series bold - -\backslash -unit[value]{unit} -\series default -, therefore you cannot use it in TeX code. -\end_layout - -\begin_layout Itemize -Percent and perthousand signs are set like physical units: -\begin_inset Newline newline -\end_inset - -1.2 -\begin_inset space \thinspace{} -\end_inset - -‰ 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 -\begin_inset space \thinspace{} -\end_inset - -°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 -\begin_inset space \thinspace{} -\end_inset - -473 -\begin_inset space \thinspace{} -\end_inset - -588 -\end_layout - -\begin_layout Itemize -For dimensions like 120×90×40 -\begin_inset space \thinspace{} -\end_inset - -cm the multiplication sign -\begin_inset Quotes eld -\end_inset - -× -\begin_inset Quotes erd -\end_inset - - is used. - It is available either via the command -\series bold - -\backslash -times -\series default - or via the menu -\family sans -Insert\SpecialChar \menuseparator -Special Character\SpecialChar \menuseparator -Symbols -\family default -. -\end_layout - -\begin_layout Itemize -Functions with names consisting of several letters are set upright to avoid - confusions, see -\begin_inset CommandInset ref -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 - - -\begin_inset Newline newline -\end_inset - -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 Itemize -The character that denotes a -\noun on -Fourier -\noun default - transformation is inserted either by the command -\series bold - -\backslash -mathscr -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -F -\series default - or via the menu -\family sans -Insert\SpecialChar \menuseparator -Special Character\SpecialChar \menuseparator -Symbols\SpecialChar \menuseparator -Letterlike -\begin_inset space ~ -\end_inset - -Symbols -\family default -: -\begin_inset Formula $\mathscr{F}$ -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Synonyms -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Synonyms -\end_layout - -\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 - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -equivalent to -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ast -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-1.2mm}{ -\end_layout - -\end_inset - -* -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -choose -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -binom -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -geq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lbrace -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -{ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lbracket -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -[ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gets -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -le -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vee -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -neq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -slash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -/ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vert -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -| -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -equivalent to -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -backslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash - -\backslash - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dasharrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dashrightarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -land -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wedge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rbrace -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rbracket -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -] -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -to -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lnot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -neg -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ne -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -owns -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ni -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -square -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Box -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Vert -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -| -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -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 CommandInset bibitem -LatexCommand bibitem -key "Mathmode" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Description" -target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf" - -\end_inset - - of LaTeX's math abilities -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "AMS" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Description" -target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf" - -\end_inset - - of -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --LaTeX -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Symbols" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "List" -target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf" - -\end_inset - - of all symbols available with LaTeX-packages -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "cancel" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Documentation" -target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf" - -\end_inset - - of the LaTeX-package -\series bold -cancel -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! cancel -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "hyperref" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Documentation" -target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf" - -\end_inset - - of the LaTeX-package -\series bold -hyperref -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! hyperref -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "mhchem" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Documentation" -target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf" - -\end_inset - - of the LaTeX-package -\series bold -mhchem -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! mhchem -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Mathclap" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Description" -target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf" - -\end_inset - - of the command -\series bold - -\backslash -mathclap -\series default -, described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Operator-Limits" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathclap -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Duden" - -\end_inset - - -\emph on -Duden Band 1 -\emph default -. - 22. - Auflage, Duden 2001 -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Checklist" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Check list" -target "http://physics.nist.gov/Document/checklist.pdf" - -\end_inset - - for reviewing manuscripts -\end_layout - -\begin_layout Standard -\begin_inset CommandInset index_print -LatexCommand printindex -type "idx" - -\end_inset - - -\end_layout - -\end_body -\end_document +#LyX 2.1 created this file. For more info see http://www.lyx.org/ +\lyxformat 474 +\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}}{} + +\fi % end if pdflatex is used + +% solves the following problem: +% If the dection number consits of too many numerals the section heading +% will be printed in the TOC without a space between it and the section number. +% As solution more space between the number and the heading is inserted: +\renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}} +\renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}} + +% increase link area for cross-references and autoname them, +\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}} +\@ifundefined{extrasenglish}{\usepackage[english]{babel}}{} +\addto\extrasenglish{% + \renewcommand*{\equationautorefname}[1]{}% + \renewcommand{\sectionautorefname}{sec.\negthinspace}% + \renewcommand{\subsectionautorefname}{sec.\negthinspace}% + \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}% +} + +% 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]{\contentsname}{} + \myTOC + \cleardoublepage + \pagenumbering{arabic}} + +% insert additional vertical space of 1.5 mm between footnotes, +\let\myFoot\footnote +\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}} + +% provides caption formatting +\setkomafont{captionlabel}{\bfseries} + +% enables calculation of values +\usepackage{calc} + +% for multiple columns used in sec. 24.7 +\usepackage{multicol} + +% needed in sec. 19.4 +\usepackage{remreset} + +% for the Fourier transformation symbol +\usepackage{mathrsfs} + +% 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} + +% 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|}} + + +% ------------------------------------ +% used to check for needed LaTeX packages +\usepackage{ifthen} + +% check for package undertilde +% used for the command \utilde +\newboolean{undertilde} +\IfFileExists{undertilde.sty} + {\usepackage{undertilde} + \setboolean{undertilde}{true}} + {\setboolean{undertilde}{false}} + +% check for package eurosym +% used for the Euro symbol +\newboolean{eurosym} +\IfFileExists{eurosym.sty} + {\usepackage[gennarrow]{eurosym} + \setboolean{eurosym}{true}} + {\setboolean{eurosym}{false}} + +% check for package braket +% used for physical vectors +\newboolean{braket} +\IfFileExists{braket.sty} + {\usepackage{braket} + \setboolean{braket}{true}} + {\setboolean{braket}{false}} + +% check for package cancel +\newboolean{cancel} +\IfFileExists{cancel.sty} + {\usepackage{cancel} + \setboolean{cancel}{true}} + {\setboolean{cancel}{false}} + +% check for package upgreek +\newboolean{upgreek} +\IfFileExists{upgreek.sty} + {\usepackage{upgreek} + \setboolean{upgreek}{true}} + {\setboolean{upgreek}{false}} +\end_preamble +\options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading +\use_default_options false +\maintain_unincluded_children false +\language english +\language_package default +\inputencoding auto +\fontencoding global +\font_roman default +\font_sans default +\font_typewriter default +\font_math auto +\font_default_family default +\use_non_tex_fonts false +\font_sc false +\font_osf false +\font_sf_scale 100 +\font_tt_scale 100 +\graphics default +\default_output_format default +\output_sync 0 +\bibtex_command default +\index_command default +\paperfontsize 12 +\spacing single +\use_hyperref true +\pdf_title "LyX's Math Manual" +\pdf_author "LyX Team, Uwe Stöhr" +\pdf_subject "LyX-documentation about math" +\pdf_keywords "LyX, Mathed" +\pdf_bookmarks true +\pdf_bookmarksnumbered true +\pdf_bookmarksopen true +\pdf_bookmarksopenlevel 1 +\pdf_breaklinks false +\pdf_pdfborder false +\pdf_colorlinks true +\pdf_backref false +\pdf_pdfusetitle false +\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false" +\papersize a4paper +\use_geometry false +\use_package amsmath 2 +\use_package amssymb 2 +\use_package cancel 0 +\use_package esint 1 +\use_package mathdots 1 +\use_package mathtools 2 +\use_package mhchem 1 +\use_package stackrel 0 +\use_package stmaryrd 0 +\use_package undertilde 0 +\cite_engine basic +\cite_engine_type default +\biblio_style plain +\use_bibtopic false +\use_indices false +\paperorientation portrait +\suppress_date false +\justification true +\use_refstyle 0 +\notefontcolor #0000ff +\index Index +\shortcut idx +\color #008000 +\end_index +\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 +\html_math_output 0 +\html_css_as_file 0 +\html_be_strict false +\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 Plain Layout +\noindent +If you have comments or error corrections, please send them to the LyX Documenta +tion mailing list: +\family typewriter + +\begin_inset CommandInset href +LatexCommand href +name "lyx-docs@lists.lyx.org" +target "lyx-docs@lists.lyx.org?subject=LyX's Math manual" +type "mailto:" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +author: Uwe Stöhr +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\family sans +Version 2.1.x +\end_layout + +\begin_layout Standard +\begin_inset CommandInset toc +LatexCommand tableofcontents + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Note +status open + +\begin_layout Plain Layout +To export this document to PDF, PS or DVI the LaTeX-packages +\series bold +braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde +\series default + and +\series bold +was +\series default + should be installed. + If they are not installed the document can be exported anyway but the sections + where the packages are required will not appear in the output. + An exception is +\series bold +mhchem +\series default +; if it is not installed, this file cannot be exported. +\end_layout + +\begin_layout Plain Layout +The latest PDF-version of this document can be found here: +\begin_inset Newline newline +\end_inset + + +\series bold +http://wiki.lyx.org/LyX/DocumentationDevelopment#Math +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Introduction +\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 +\begin_inset space ~ +\end_inset + +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 checked in the document settings (menu +\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator +Math +\begin_inset space ~ +\end_inset + +Options +\family default +). +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +The option +\family sans +Use AMS math package automatically +\family default + only uses +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-math commands +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +A list with all +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-math commands is in the file +\family sans + +\begin_inset CommandInset href +LatexCommand href +name "amsguide.ps" +target "ftp://ftp.ams.org/pub/tex/doc/amstex/amsguide.pdf" + +\end_inset + + +\family default +, which is part of every LaTeX standard installation. +\end_layout + +\end_inset + + for lucidity reasons. +\end_layout + +\begin_layout Section +General Instructions +\end_layout + +\begin_layout Standard +To create an inline formula +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! inline +\end_layout + +\end_inset + + that is embedded into a text line, use one of the shortcuts +\begin_inset Info +type "shortcuts" +arg "math-mode" +\end_inset + + or the toolbar button +\begin_inset Info +type "icon" +arg "math-mode" +\end_inset + +. +\begin_inset Newline newline +\end_inset + +To create a display style formula +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! display style +\end_layout + +\end_inset + + which will appear bigger, has a different format, and will be in a separate + paragraph, use one of these shortcuts: +\begin_inset Info +type "shortcuts" +arg "math-display" +\end_inset + +. +\end_layout + +\begin_layout Standard +To change a display style formula to an inline formula, set the cursor into + the formula and use one of the shortcuts +\begin_inset Info +type "shortcuts" +arg "math-mode" +\end_inset + + or 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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +displaystyle +\end_layout + +\end_inset + + 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 +\begin_inset space ~ +\end_inset + +(auto) +\begin_inset Quotes erd +\end_inset + +. +\end_layout + +\begin_layout Standard +The TeX-mode +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +T@TeX-mode +\end_layout + +\end_inset + + is invoked by pressing the toolbar button +\begin_inset Info +type "icon" +arg "ert-insert" +\end_inset + + or by using the menu +\family sans +Insert\SpecialChar \menuseparator +Te +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +X Code +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "ert-insert" +\end_inset + +). +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +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 Plain Layout +To avoid that these names are recognized as proper names, a TeX-brace pair + is inserted. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To change the LaTeX-preamble +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +L@LaTeX-preamble +\end_layout + +\end_inset + +, use the menu +\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator +LaT +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\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, + use the menus +\family sans +Edit\SpecialChar \menuseparator +Math +\family default + and +\family sans +Edit\SpecialChar \menuseparator +Rows +\begin_inset space \thinspace{} +\end_inset + +& +\begin_inset space \thinspace{} +\end_inset + +Columns, +\family default + or the +\family sans +table toolbar +\family default +. + 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 Plain Layout +For multiline formulas the command +\series bold + +\backslash +intertext +\series default + is used, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Text-in-multiline" + +\end_inset + +. +\end_layout + +\end_inset + + +\emph on +mathematical text +\emph default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! in formulas +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Mathematical text +\end_layout + +\end_inset + + is used. + This mode is invoked with the shortcut +\begin_inset Info +type "shortcut" +arg "font-default" +\end_inset + + or by the insertion of the command +\series bold + +\backslash +text +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +text +\end_layout + +\end_inset + +. + The text appears black in LyX and can therefore be distinguished from the + other formula parts which 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 always starts 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 Index idx +status collapsed + +\begin_layout Plain Layout +T@TeX-braces +\end_layout + +\end_inset + +. + If you add in a formula a left brace to a command name, LyX automatically + creates 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 which 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 +\begin_inset Info +type "shortcuts" +arg "command-alternatives space-insert protected ; math-space" +\end_inset + +. +\end_layout + +\begin_layout Subsection* +\begin_inset Newpage newpage +\end_inset + +Syntax Explanation +\end_layout + +\begin_layout Itemize +The symbol +\begin_inset space \textvisiblespace{} +\end_inset + + 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. + The +\family sans +Tab +\family default + key can often be used instead of +\begin_inset Formula $\to$ +\end_inset + + and +\begin_inset Formula $\downarrow$ +\end_inset + +, and +\family sans +Shift+Tab +\family default + instead of +\begin_inset Formula $\leftarrow$ +\end_inset + + and +\begin_inset Formula $\uparrow$ +\end_inset + +. +\end_layout + +\begin_layout Subsection* +Available units +\end_layout + +\begin_layout Standard +\align center +\begin_inset Float table +placement H +wide false +sideways false +status open + +\begin_layout Plain Layout +\align center +\begin_inset Caption Standard + +\begin_layout Plain Layout +\begin_inset CommandInset label +LatexCommand label +name "tab:Available-units" + +\end_inset + +Available units +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Plain Layout +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Unit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Name / Description +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +mm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Millimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +cm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Centimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Inch (1 +\begin_inset space \thinspace{} +\end_inset + +in = 2,54 +\begin_inset space \thinspace{} +\end_inset + +cm) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +pt +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Point (72.27 +\begin_inset space \thinspace{} +\end_inset + +pt = 1 +\begin_inset space \thinspace{} +\end_inset + +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +pc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Pica (1 +\begin_inset space \thinspace{} +\end_inset + +pc = 12 +\begin_inset space \thinspace{} +\end_inset + +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +sp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +scaled point (65536 +\begin_inset space \thinspace{} +\end_inset + +sp = 1 +\begin_inset space \thinspace{} +\end_inset + +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +bp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +big point (72 +\begin_inset space \thinspace{} +\end_inset + +bp = 1 +\begin_inset space \thinspace{} +\end_inset + +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +dd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Didot (1 +\begin_inset space \thinspace{} +\end_inset + +dd +\begin_inset Formula $\approx$ +\end_inset + + 0.376 +\begin_inset space \thinspace{} +\end_inset + +mm) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +cc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Cicero (1 +\begin_inset space \thinspace{} +\end_inset + +cc = 12 +\begin_inset space \thinspace{} +\end_inset + +dd) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +ex +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +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 Plain Layout +em +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +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 Plain Layout +mu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +math unit (1 +\begin_inset space \thinspace{} +\end_inset + +mu = +\begin_inset Formula $\nicefrac{1}{18}$ +\end_inset + + +\begin_inset space \thinspace{} +\end_inset + +em) +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Basic Functions +\end_layout + +\begin_layout Subsection +Exponents +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Exponents +\end_layout + +\end_inset + + and Indices +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Indices +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Superscripts|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Exponents +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Subscripts|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Indices +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\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 Info +type "icon" +arg "math-subscript" +\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 Info +type "icon" +arg "math-superscript" +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +B_V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $B_{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +B^V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}B^{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +B^ +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout +Depending on the used keyboard settings this can also happen for characters + other than vowels. +\end_layout + +\end_inset + +. + To get exponents in this case, press +\family sans +Space +\family default + after the caret as in the last example. +\end_layout + +\begin_layout Subsection +Fractions +\begin_inset CommandInset label +LatexCommand label +name "sub:Fractions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fractions +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Fractions are generated with the command +\series bold + +\backslash +frac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +frac +\end_layout + +\end_inset + + or via the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\frac" +\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 Info +type "icon" +arg "math-insert \\frac-square" +\end_inset + + you can select different fraction types. +\end_layout + +\begin_layout Standard +With the command +\series bold + +\backslash +dfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dfrac +\end_layout + +\end_inset + + a fraction can be created that always has the size of a display style formula. + With +\series bold + +\backslash +tfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +tfrac +\end_layout + +\end_inset + + 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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +frac +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dfrac +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dfrac +\begin_inset space \textvisiblespace{} +\end_inset + +e^ +\backslash +frac +\begin_inset space \textvisiblespace{} +\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 Plain Layout +\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 + + +\begin_inset Newpage newpage +\end_inset + +For nested fractions the command +\series bold + +\backslash +cfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cfrac +\end_layout + +\end_inset + + can be used. + Here is 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 +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B+ +\backslash +cfrac +\begin_inset space \textvisiblespace{} +\end_inset + +C+ +\backslash +cfrac +\begin_inset space \textvisiblespace{} +\end_inset + +E +\begin_inset Formula $\downarrow$ +\end_inset + +F +\begin_inset Formula $\downarrow$ +\end_inset + +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. +\end_layout + +\begin_layout Standard +It is possible to specify the alignment of the numerator. + The command +\series bold + +\backslash +cfracleft +\series default + is used to left align it, the command +\series bold + +\backslash +cfracright +\series default + to right-align it. + +\series bold + +\backslash +cfrac +\series default + centers the numerator. + These fractions demonstrate the different alignments: +\end_layout + +\begin_layout Standard + +\series bold +\begin_inset Formula +\[ +\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + +\series bold + +\backslash +cfracleft +\series default + and +\series bold + +\backslash +cfracright +\series default + are no real LaTeX commands but represent the command +\series bold + +\backslash +cfrac[alignment]{numerator}{denominator} +\series default + . + Therefore you cannot use them in TeX code. +\end_layout + +\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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +nicefrac +\end_layout + +\end_inset + +: +\begin_inset Formula $\nicefrac{5}{31}$ +\end_inset + + or +\series bold + +\backslash +unitfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +unitfrac +\end_layout + +\end_inset + +: +\begin_inset Formula $\unitfrac{5}{31}$ +\end_inset + + There is furthermore the command +\series bold + +\backslash +unitfracthree +\series default + that offers to write a fraction in combination with a number: +\begin_inset Formula $\unitfrac[2]{1}{3}$ +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + +\series bold + +\backslash +unitfracthree +\series default + is not a real LaTeX command but the command +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +unitfrac[number]{numerator}{denominator} +\series default + . + Therefore you cannot use it in TeX code. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +How to define own fractions where the fraction stroke can be changed, is + explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Self-defined-Fractions" + +\end_inset + +. +\end_layout + +\begin_layout Standard +Multiline fractions are explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Multiline-Fractions" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Roots +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Roots +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Square roots are created with +\series bold + +\backslash +sqrt +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +sqrt +\end_layout + +\end_inset + + or the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\sqrt" +\end_inset + +, all other roots with the command +\series bold + +\backslash +root +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +root +\end_layout + +\end_inset + + or with the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\root" +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqrt +\begin_inset space \textvisiblespace{} +\end_inset + +A-B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +root +\begin_inset space \textvisiblespace{} +\end_inset + +3 +\begin_inset Formula $\downarrow$ +\end_inset + +A-B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 + + +\begin_inset Newline newline +\end_inset + +The +\begin_inset Formula $\beta$ +\end_inset + + touches the root. + To avoid this, the commands +\series bold + +\backslash +leftroot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +leftroot +\end_layout + +\end_inset + + and +\series bold + +\backslash +uproot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +uproot +\end_layout + +\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 +\begin_inset Newline newline +\end_inset + + +\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 space \textvisiblespace{} +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + +B +\begin_inset Newline newline +\end_inset + + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Binomial coefficients +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Binomial coefficients are inserted with the command +\series bold + +\backslash +binom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +binom +\end_layout + +\end_inset + + or with the submenu of the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\frac-square" +\end_inset + +. + As with fractions ( +\series bold + +\backslash +frac +\series default +) in addition to +\series bold + +\backslash +binom +\series default + there are the commands +\series bold + +\backslash +dbinom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dbinom +\end_layout + +\end_inset + + and +\series bold + +\backslash +tbinom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +tbinom +\end_layout + +\end_inset + +. + For other brackets around binomial coeficients there are the commands +\series bold + +\backslash +brace +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +brace +\end_layout + +\end_inset + + and +\series bold + +\backslash +brack +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +brack +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +binom +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dbinom +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tbinom +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +brack +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +brace +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Case Differentiations +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Case differentiations +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cases +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\to$ +\end_inset + +B>0 +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cases +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\begin{cases} +A & B>0\end{cases}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cases +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\begin{cases} +A & \textrm{for }x>0\\ +B & \textrm{for }x=0 +\end{cases}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +After inserting +\series bold + +\backslash +cases +\series default + or pressing the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\cases" +\end_inset + + you can create new lines with the shortcut +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + or the table toolbar button +\begin_inset Info +type "icon" +arg "inset-modify tabular append-row" +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Negations +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +By inserting +\series bold + +\backslash +not +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +not +\end_layout + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 special commands for some negations (see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Mathematical-Symbols" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Relations" + +\end_inset + +). +\end_layout + +\begin_layout Subsection +Placeholders +\begin_inset CommandInset label +LatexCommand label +name "sub:Placeholders" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Placeholders +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Chemical characters ! Isotopes +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Isotopes|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Chemical characters +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +When displaying e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +isotopes +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +Typesetting isotopes and chemical symbols is described in +\begin_inset CommandInset ref +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 Plain Layout +Indices created with sub- and superscripts: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +correct indices: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! P ! +\backslash +phantom +\end_layout + +\end_inset + + or the math toolbar button +\begin_inset space \thinspace{} +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +can be found in the submenu of the toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\space" +\end_inset + + +\end_layout + +\end_inset + + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +^19 +\begin_inset space \textvisiblespace{} +\end_inset + +_ +\backslash +phantom +\begin_inset space \textvisiblespace{} +\end_inset + +1 +\begin_inset Formula $\to$ +\end_inset + +9 +\begin_inset space \textvisiblespace{} +\end_inset + +F +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout +^235 +\begin_inset space \textvisiblespace{} +\end_inset + +_ +\backslash +phantom +\begin_inset space \textvisiblespace{} +\end_inset + +23 +\begin_inset Formula $\to$ +\end_inset + +9 +\begin_inset space \textvisiblespace{} +\end_inset + +F +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +Lambda^ +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +phantom +\begin_inset space \textvisiblespace{} +\end_inset + +ii +\begin_inset Formula $\to$ +\end_inset + +t +\begin_inset space \textvisiblespace{} +\end_inset + +_MMt +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! V ! +\backslash +vphantom +\end_layout + +\end_inset + + (toolbar button +\begin_inset space ~ +\end_inset + + +\begin_inset Graphics + filename ../images/math/vphantom.png + scale 85 + +\end_inset + +) and +\series bold + +\backslash +hphantom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hphantom +\end_layout + +\end_inset + + (toolbar button +\begin_inset space ~ +\end_inset + + +\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 the command +\series bold + +\backslash +vphantom +\begin_inset space \textvisiblespace{} +\end_inset + +a +\backslash +int +\series default + creates space for the height of the integral sign, +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +The command +\series bold + +\backslash +int +\series default + creates an integral sign, see +\begin_inset CommandInset ref +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 CommandInset ref +LatexCommand ref +reference "sub:Multiline-Brackets" + +\end_inset + +. +\end_layout + +\begin_layout Standard +Placeholders can also be used for text when they are inserted via the menu + +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Phantom +\family default +: +\end_layout + +\begin_layout Standard +This is a sentence. +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom Phantom +status open + +\begin_layout Plain Layout +This +\end_layout + +\end_inset + + is a sentence. +\end_layout + +\begin_layout Subsection +Lines +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Lines +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! underlined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overline +\begin_inset space \textvisiblespace{} +\end_inset + +A+B +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overline +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underline +\begin_inset space \textvisiblespace{} +\end_inset + +A+B +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +underline +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overline +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +underline +\begin_inset space \textvisiblespace{} +\end_inset + +A+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 use +\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 Standard +\begin_inset VSpace bigskip +\end_inset + +Custom lines can be created using the command +\series bold + +\backslash +rule +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +rule +\end_layout + +\end_inset + + which has the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +rule[vertical offset]{length}{thickness} +\end_layout + +\begin_layout Standard +The optional vertical offset shifts the line upwards (or downwards, when + the value is negative). + The units listed in +\begin_inset CommandInset ref +LatexCommand ref +reference "tab:Available-units" + +\end_inset + + can be used for the values. + Here are two example lines created with the commands +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +rule[-2ex]{3cm}{2pt} +\series default + and +\series bold + +\backslash +rule{2cm}{1pt} +\series default +: +\end_layout + +\begin_layout Standard +This is a sentence +\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$ +\end_inset + + with two lines. +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +rule +\series default + can also be used for text when a line is inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Horizontal +\begin_inset space ~ +\end_inset + +Line +\family default +: +\end_layout + +\begin_layout Standard +This is a sentence +\begin_inset CommandInset line +LatexCommand rule +offset "0.5ex" +width "3cm" +height "1pt" + +\end_inset + + with one line. +\end_layout + +\begin_layout Subsection +Ellipses +\begin_inset CommandInset label +LatexCommand label +name "sub:Ellipses" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Ellipses +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +There are different types of ellipses available. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +In the math toolbar in the submenu of the button +\begin_inset Info +type "icon" +arg "math-insert \\ldots" +\end_inset + + +\end_layout + +\end_inset + + For listings dots at the baseline are used ( +\series bold + +\backslash +ldots +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +ldots +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cdots +\end_layout + +\end_inset + +). + When using the command +\series bold + +\backslash +dots +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dots +\end_layout + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset space \textvisiblespace{} +\end_inset + +, +\backslash +dots +\begin_inset space \textvisiblespace{} +\end_inset + +,A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1},\dots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset space \textvisiblespace{} +\end_inset + ++ +\backslash +dots +\begin_inset space \textvisiblespace{} +\end_inset + ++A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1}+\dots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset space \textvisiblespace{} +\end_inset + +, +\backslash +ldots +\begin_inset space \textvisiblespace{} +\end_inset + +,A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1},\ldots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset space \textvisiblespace{} +\end_inset + ++ +\backslash +cdots +\begin_inset space \textvisiblespace{} +\end_inset + ++A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1}+\cdots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vdots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vdots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ddots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iddots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\iddots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +3×3 +\begin_inset space \thinspace{} +\end_inset + +matrix with the different dots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 +\begin_inset space ~ +\end_inset + +Character +\family default + are +\series bold + +\backslash +ldots +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +To use +\series bold + +\backslash +iddots +\series default +, one of the options +\family sans +Use mathdots package (automatically) +\family default + must be set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default +. +\begin_inset Newline newline +\end_inset + +Using the option +\family sans +Use mathdots package +\family default + will improve the appearance of all dots in the documents if their font + style or size is not the 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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hdotsfor +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dotfill +\end_layout + +\end_inset + + the rest of a line with dots. + The effect of these commands is the same as with +\series bold + +\backslash +hfill +\series default +, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + +. +\end_layout + +\begin_layout Standard +For example the command +\series bold +A +\backslash +dotfill +\begin_inset space \textvisiblespace{} +\end_inset + +B +\series default + produces +\end_layout + +\begin_layout Standard +\begin_inset Formula $A\dotfill B$ +\end_inset + + +\end_layout + +\begin_layout Standard +Similar to +\series bold + +\backslash +dotfill +\series default + there is for a line the command +\series bold + +\backslash +hrulefill +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hrulefill +\end_layout + +\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 CommandInset label +LatexCommand label +name "sec:Matrices" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Matrices +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Matrices can be inserted via the math toolbar button +\begin_inset Info +type "icon" +arg "dialog-show mathmatrix" +\end_inset + + or the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Matrix +\family default +. + In the matrix dialog you can specify the number of columns and rows, the + alignment and the decoration. + The vertical alignment is 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 +\begin_inset space ~ +\end_inset + +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 in a matrix all columns are centered, therefore the default for + every column is a +\series bold +c +\series default +. +\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 Info +type "icon" +arg "inset-modify tabular append-row" +\end_inset + +, +\begin_inset Info +type "icon" +arg "inset-modify tabular delete-row" +\end_inset + +, etc. +\begin_inset space \thinspace{} +\end_inset + +, or the menu +\family sans +Edit\SpecialChar \menuseparator +Rows & Columns +\family default + can be used. + New rows can also be created with +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +The +\family sans +Decoration +\family default + adds parentheses in the selected style around the matrix. + Alternatively, parentheses can can either be created with the commands + +\series bold + +\backslash +left +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +left +\end_layout + +\end_inset + + and +\series bold + +\backslash +right +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +right +\end_layout + +\end_inset + + (shortcut +\family sans +Alt+M +\begin_inset space ~ +\end_inset + +Parenthesis +\family default +), see +\begin_inset CommandInset ref +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 +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bmatrix +\begin_inset space \textvisiblespace{} +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +Bmatrix +\begin_inset space \textvisiblespace{} +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +pmatrix +\begin_inset space \textvisiblespace{} +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vmatrix +\begin_inset space \textvisiblespace{} +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +Vmatrix +\begin_inset space \textvisiblespace{} +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +matrix +\begin_inset space \textvisiblespace{} +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +When e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + + +\series bold + +\backslash +vmatrix +\series default + is inserted, a blue box appears between two vertical lines where the matrix + is inserted. +\begin_inset Newline newline +\end_inset + +Note that decorated matrices ignore the vertical alignment. +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arraycolsep +\end_layout + +\end_inset + + that is described in +\begin_inset CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arraystretch +\end_layout + +\end_inset + + is used. + It is used as follows: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +arraystretch}{stretch factor} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +renewcommand +\end_layout + +\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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +smallmatrix +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Brackets +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Delimiters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Vertical Brackets and Delimiters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets ! vertical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $($ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +{ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\{$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +[ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $[$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +langle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\langle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +/ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $/$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $)$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +] +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $]$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\backslash + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\backslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard + +\series medium +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + In TeX-mode the command +\series bold + +\backslash +textbackslash +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textbackslash +\end_layout + +\end_inset + + must be used for the backslash, because the command +\series bold + +\backslash + +\backslash + +\series default + produces a line break there. +\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 CommandInset label +LatexCommand label +name "sub:Manual-Bracket-Size" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Bracket size ! manual +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +big +\end_layout + +\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 Plain Layout +all brackets in the same size: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +this looks better: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\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 space \textvisiblespace{} +\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 space \textvisiblespace{} +\end_inset + + +\backslash +sin(x) +\backslash +Big]^ +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset space \textvisiblespace{} +\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 +Besides the +\series bold + +\backslash +big +\series default +-commands there is the variant +\series bold + +\backslash +bigm +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +bigm +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +bigl - +\backslash +bigr +\end_layout + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bigm( +\backslash +bigm( +\backslash +ln(3x) +\backslash +bigm)^2 +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +Bigm) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +Big( +\backslash +big( +\backslash +ln(3x) +\backslash +big)^2 +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +Big) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +Bigl( +\backslash +bigl( +\backslash +ln(3x) +\backslash +bigr)^2 +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +Bigr) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + +\backslash +bigl) +\backslash +ln(3x) +\backslash +bigr( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 CommandInset label +LatexCommand label +name "sub:Automatic-Bracket-Size" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Bracket size ! automatic +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +left +\end_layout + +\end_inset + + and +\series bold + +\backslash +right +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +right +\end_layout + +\end_inset + + or via the math toolbar button +\begin_inset Info +type "icon" +arg "dialog-show mathdelimiter" +\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 space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +C +\begin_inset space \textvisiblespace{} +\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 space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +C +\begin_inset space \textvisiblespace{} +\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 +\begin_inset space ~ +\end_inset + +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. +\begin_inset Newline newline +\end_inset + +The command for the last example would then be: +\series bold + +\backslash +ln Alt+M +\series default + +\series bold +( +\backslash +frac +\begin_inset space \textvisiblespace{} +\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 space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\begin_inset space \textvisiblespace{} +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +middle +\end_layout + +\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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +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 CommandInset ref +LatexCommand ref +reference "sub:Physical-Vectors" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Horizontal Brackets +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets ! horizontal +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{2.3mm}{ +\end_layout + +\end_inset + + +\backslash +overbrace +\begin_inset space \textvisiblespace{} +\end_inset + +A+B +\begin_inset space \textvisiblespace{} +\end_inset + +^3 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overbrace +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\overbrace{A+B}^{3}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-2.2mm}{ +\end_layout + +\end_inset + + +\backslash +underbrace +\begin_inset space \textvisiblespace{} +\end_inset + +A+B +\begin_inset space \textvisiblespace{} +\end_inset + +_5 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +underbrace +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\underbrace{A+B}_{5}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overbrace +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +underbrace +\begin_inset space \textvisiblespace{} +\end_inset + +A+B_w +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset space \textvisiblespace{} +\end_inset + +_7 +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset space \textvisiblespace{} +\end_inset + +^ +\begin_inset space \textvisiblespace{} +\end_inset + +C +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 medskip +\end_inset + + +\end_layout + +\begin_layout Standard +If you set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default + for the package +\series bold +mathtools +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mathtools +\end_layout + +\end_inset + + the option +\family sans +Load +\begin_inset space ~ +\end_inset + +always +\family default +, you have access to square backets: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{2.3mm}{ +\end_layout + +\end_inset + + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +overbracket +\family default +\series default +\shape default +\size default +\emph default +\bar default +\strikeout default +\uuline default +\uwave default +\noun default +\color inherit +{A+B +\begin_inset space \textvisiblespace{} +\end_inset + +^3 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overbracket +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\overbracket{A+B}^{3}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-2.2mm}{ +\end_layout + +\end_inset + + +\backslash +under +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +bracket +\family default +\series default +\shape default +\size default +\emph default +\bar default +\strikeout default +\uuline default +\uwave default +\noun default +\color inherit +{A+B +\begin_inset space \textvisiblespace{} +\end_inset + +_5 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +under +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +bracket +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\underbracket{A+B}_{5}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overbracket{ +\backslash +underbracket{A+B_w +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset space \textvisiblespace{} +\end_inset + +_7 +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset space \textvisiblespace{} +\end_inset + +^ +\begin_inset space \textvisiblespace{} +\end_inset + +C +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +For +\series bold + +\backslash +overbracket +\series default + and +\series bold + +\backslash +underbracket +\series default + you can change the thickness of the bracket's stroke by specifying the + desired thickness in square brackets behind the command: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{2.3mm}{ +\end_layout + +\end_inset + + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +overbracket +\family default +\series default +\shape default +\size default +\emph default +\bar default +\strikeout default +\uuline default +\uwave default +\noun default +\color inherit +[3pt] +\backslash +{A+B +\begin_inset space \textvisiblespace{} +\end_inset + +^3 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\overbracket[3pt]{A+B}^{3}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-2.2mm}{ +\end_layout + +\end_inset + + +\backslash +under +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +bracket +\family default +\series default +\shape default +\size default +\emph default +\bar default +\strikeout default +\uuline default +\uwave default +\noun default +\color inherit +[1pt] +\backslash +{A+B +\begin_inset space \textvisiblespace{} +\end_inset + +_5 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\underbracket[1pt]{A+B}_{5}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +When brackets should overlap each other, multiline formulas, as described + in +\begin_inset CommandInset ref +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 Plain Layout +Space commands are explained in +\begin_inset CommandInset ref +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 Plain Layout +because a bracket is not handled as a character, see +\begin_inset CommandInset ref +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 Plain Layout +more about +\series bold + +\backslash +hphantom +\series default + see +\begin_inset CommandInset ref +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 above and under + the formula, like in the following example: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + + +\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 needs to be reduced. + This is not easily possible due to a bug in LyX. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #1505" +target "http://www.lyx.org/trac/ticket/1505" + +\end_inset + + +\end_layout + +\end_inset + + As a solution for the problem, the global formula row separation +\series bold + +\backslash +jot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! J ! +\backslash +jot +\end_layout + +\end_inset + + must be changed to -6 +\begin_inset space \thinspace{} +\end_inset + +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 +\begin_inset space \thinspace{} +\end_inset + +pt using the same command. + More about the row separation in formulas is explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Line-Separation" + +\end_inset + +. +\end_layout + +\begin_layout Section +Arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Arrows can be inserted via the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\leftarrow" +\end_inset + + or the commands listed in the following subsections. +\end_layout + +\begin_layout Subsection +Horizontal Arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! horizontal +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gets +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gets$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Leftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leftharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leftharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hookleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hookleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +to +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\to$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Rightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rightharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rightharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hookrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hookrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightleftharpoons +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rightleftharpoons$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hspace{} +\length 25pt +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longmapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longmapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leadsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leadsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dasharrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Arrows used as accents like e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +vector arrows are listed in +\begin_inset CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! labeled +\end_layout + +\end_inset + + +\series bold + +\backslash +xleftarrow +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! X ! +\backslash +xleftarrow +\end_layout + +\end_inset + + and +\series bold + +\backslash +xrightarrow +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! X ! +\backslash +xrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +F(a) +\backslash +xleftarrow +\begin_inset space \textvisiblespace{} +\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 Plain Layout +\begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +F(x) +\backslash +xrightarrow +\begin_inset space \textvisiblespace{} +\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 Plain Layout +\begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +If you set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default + for the package +\series bold +mathtools +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mathtools +\end_layout + +\end_inset + + the option +\family sans +Load +\begin_inset space ~ +\end_inset + +always +\family default +, you have access to the following labeled arrows: +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Example +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none + +\backslash +xleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none + +\backslash +xLeftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xRightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xLeftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none + +\backslash +xhookleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none + +\backslash +xhookrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Example +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xleftharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xleftharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xrightharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xrightharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xleftrightharpoons +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\strikeout off +\uuline off +\uwave off +\noun off +\color none +xrightleftharpoons +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\end_layout + +\begin_layout Standard +The command scheme is for all these arrows: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +F(a) +\backslash +xleftrightarrow[x=a] +\backslash +{x>0 +\begin_inset Formula $\to$ +\end_inset + +F(x) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Vertical and diagonal Arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! diagonal +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! vertical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nearrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nearrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +searrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\searrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +swarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\swarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nwarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nwarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Vertical arrows can be used also as delimiters together with the commands + described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Manual-Bracket-Size" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + +. +\end_layout + +\begin_layout Section +Accents +\begin_inset CommandInset label +LatexCommand label +name "sec:Accents" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Accents can be inserted via the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\hat" +\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 Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +accents in text see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Accents-in-Text" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +texorpdfstring +\series default + is used to avoid that the footnote appears in the PDF-bookmark. +\end_layout + +\begin_layout Plain Layout +More about +\series bold + +\backslash +texorpdfstring +\series default + is in section +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Formulas-in-Section" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset CommandInset label +LatexCommand label +name "sub:Accents-for-one" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents ! for one character +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dot +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\dot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddot +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dddot +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddddot +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vec +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Vectors +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\vec{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bar +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\bar{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathring +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tilde +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hat +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\hat{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +check +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\check{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +acute +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\acute{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +grave +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\grave{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +breve +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\breve{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + + +\end_layout + +\begin_layout Standard +You can directly insert accents like é to formulas. + LyX will transform them to the corresponding accent command. + For umlauts +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Umlauts +\end_layout + +\end_inset + + it is better to insert a quotation mark 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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + and the 0 +\begin_inset space \thinspace{} +\end_inset + +pt space are only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\lang ngerman +\begin_inset Quotes grd +\end_inset + +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset space \hspace{} +\length 0pt +\end_inset + + +\lang ngerman + +\begin_inset Formula $"i$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddot +\begin_inset space \textvisiblespace{} +\end_inset + +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +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 Standard +\begin_inset VSpace bigskip +\end_inset + + +\end_layout + +\begin_layout Standard +LyX also supports a tilde under the character if the LaTeX-package +\series bold +undertilde +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! undertilde +\end_layout + +\end_inset + + is installed on your system: +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifundertilde +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +undertilde +\series default + is installed. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +utilde +\begin_inset space \textvisiblespace{} +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\utilde{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +undertilde +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +undertilde +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Subsection +Accents for several Characters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents ! for several characters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overleftarrow +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underleftarrow +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overleftrightarrow +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underleftrightarrow +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overrightarrow +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underrightarrow +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +widetilde +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +widehat +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overset +\end_layout + +\end_inset + + and +\series bold + +\backslash +underset +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +underset +\end_layout + +\end_inset + + described in the previous subsection it is also possible to accent several + characters. + The command +\series bold + +\backslash +underset +\begin_inset space \textvisiblespace{} +\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 CommandInset label +LatexCommand label +name "sub:Space" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! horizontal +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Predefined Space +\begin_inset CommandInset label +LatexCommand label +name "sub:Predefined-Space" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! horizontal ! predefined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Sometimes it is necessary to insert horizontal space into a formula. + This is done by inserting a protected space (shortcut +\begin_inset Info +type "shortcut" +arg "command-alternatives space-insert protected ; math-space" +\end_inset + +). + A +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset space \textvisiblespace{} +\end_inset + + +\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 Info +type "icon" +arg "math-insert \\space" +\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 Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Number of +\family sans +Space +\family default + keystrokes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +, +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\, B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\: B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +; +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\; B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +quad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\quad B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +qquad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +4 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\qquad B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Number of +\family sans +Space +\family default + keystrokes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hfill +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +5 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\hfill B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hspace*{1em} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +6 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\hspace*{1em}B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hspace{1em} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +7 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\hspace{1em}B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\begin_inset space \textvisiblespace{} +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +8 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\ B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +! +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +9 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\! B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +Space +\begin_inset space ~ +\end_inset + +5 +\begin_inset space \thinspace{} +\end_inset + +-- +\begin_inset space \thinspace{} +\end_inset + +7 are variable spaces which are explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + +. + Space +\begin_inset space ~ +\end_inset + +9 seems 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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +negmedspace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +negthickspace +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Number of +\family sans +Space +\family default + keystrokes after inserting the protected space +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +10 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +11 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\negmedspace B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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, which are e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +useful for summation operators: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sum +\backslash +sum +\begin_inset space \textvisiblespace{} +\end_inset + +f_kl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sum +\backslash +negmedspace +\backslash +sum +\begin_inset space \textvisiblespace{} +\end_inset + +f_kl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 +\noindent +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +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 Plain Layout +normal equation +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\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 Plain Layout +\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 + + +\end_layout + +\begin_layout Standard +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 +\begin_inset space ~ +\end_inset + +Space +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "space-insert thin" +\end_inset + +). +\end_layout + +\begin_layout Standard +An example to visualize the difference: +\end_layout + +\begin_layout Standard +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +24 kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +space between value and unit +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +24 +\begin_inset space \thinspace{} +\end_inset + +kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +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 Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +for vertical space in formulas see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Line-Separation" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\backslash +texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. +\end_layout + +\begin_layout Plain Layout +More about +\backslash +texorpdfstring is in section +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Formulas-in-Section" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset CommandInset label +LatexCommand label +name "sub:Variable-Space" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! horizontal ! variable +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Space with a defined length can be inserted with the command +\series bold + +\backslash +hspace +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hspace +\end_layout + +\end_inset + +. + Then a long +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset space \textvisiblespace{} +\end_inset + + +\color inherit + +\begin_inset Quotes erd +\end_inset + + appears. + The length can be specified by left-clicking on the +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset space \textvisiblespace{} +\end_inset + + +\color inherit + +\begin_inset Quotes erd +\end_inset + +. + The length may also be negative. + When a space would be the first character in a line it would be omitted. + To force its output use the command +\series bold + +\backslash +hspace* +\series default + instead of +\series bold + +\backslash +hspace +\series default + or left-click on the +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset space \textvisiblespace{} +\end_inset + + +\color inherit + +\begin_inset Quotes erd +\end_inset + + and check the option +\family sans +Protect +\family default +. +\begin_inset Newline newline +\end_inset + +To insert as much space as is available, the command +\series bold + +\backslash +hfill +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hfill +\end_layout + +\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 Plain Layout +Command ( +\backslash +hspace length) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A=B +\backslash +hspace +\begin_inset space \textvisiblespace{} +\end_inset + +A +\backslash +not=C (3 +\begin_inset space \thinspace{} +\end_inset + +cm) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=B\hspace{3cm}A\not=C$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +hspace +\begin_inset space \textvisiblespace{} +\end_inset + +A +\backslash +not=A (-1 +\begin_inset space \thinspace{} +\end_inset + +mm) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\hspace{-1mm}A\not=A$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A=A +\backslash +hfill +\begin_inset space \textvisiblespace{} +\end_inset + +B=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 + only has an effect on displayed formulas when the formula style +\series bold +Indented +\series default + is used. + (Formula styles are explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + +.) +\end_layout + +\begin_layout Standard +Besides +\series bold + +\backslash +hfill +\series default +, there are the commands +\series bold + +\backslash +dotfill +\series default + and +\series bold + +\backslash +hrulefill +\series default + that fill the space with a pattern, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Ellipses" + +\end_inset + + for an example. +\end_layout + +\begin_layout Standard +For text, variable space can be inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Horizontal +\begin_inset space ~ +\end_inset + +Space +\family default +: +\end_layout + +\begin_layout Standard +This is a line with +\begin_inset space \hspace{} +\length 2cm +\end_inset + +2 +\begin_inset space \thinspace{} +\end_inset + +cm space. +\end_layout + +\begin_layout Standard +This is a line with +\begin_inset space \hfill{} +\end_inset + +maximum space. +\end_layout + +\begin_layout Subsection +Space besides inline Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! besides inline formulas +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The space that surrounds inline formulas can be adjusted with the length + +\series bold + +\backslash +mathsurround +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathsurround +\end_layout + +\end_inset + +. + The value of a length is set with the command +\series bold + +\backslash +setlength +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +setlength +\end_layout + +\end_inset + + which 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 +\begin_inset space \thinspace{} +\end_inset + +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 +\begin_inset space \thinspace{} +\end_inset + +mm space will now be set around all inline formulas: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 +\begin_inset space \thinspace{} +\end_inset + +mm surrounding space. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Section +Boxes and Frames +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Frames | see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Boxes +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Boxes for text are described in chapter +\family typewriter +Boxes +\family default + in the +\family typewriter +Embedded +\begin_inset space ~ +\end_inset + +Objects +\family default + manual. +\end_layout + +\begin_layout Subsection +Boxes with Frame +\begin_inset CommandInset label +LatexCommand label +name "sub:Boxes-with-Frame" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! with frame +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +It is possible to frame a formula or part of one with the commands +\series bold + +\backslash +fbox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +fbox +\end_layout + +\end_inset + + and +\series bold + +\backslash +boxed +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +boxed +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +When one of these commands is inserted in 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, because the box content will otherwise be treated as mathemati +cal 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 +An extension to +\series bold + +\backslash +fbox +\series default + is the command +\series bold + +\backslash +framebox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +framebox +\end_layout + +\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. +\begin_inset Newline newline +\end_inset + +If no width is 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. + 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 Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fbox +\begin_inset space \textvisiblespace{} +\end_inset + + +\family sans +Ctrl+M +\family default + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +boxed +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A+ +\backslash +fbox +\begin_inset space \textvisiblespace{} +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +framebox +\begin_inset space \textvisiblespace{} +\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 space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}$ +\end_inset + + +\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$ +\end_inset + + +\begin_inset Formula $\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 Plain Layout + + +\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 Plain Layout + + +\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 CommandInset label +LatexCommand label +name "sub:Boxes-without-Frame" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! without frame +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mbox +\end_layout + +\end_inset + +, +\series bold + +\backslash +makebox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +makebox +\end_layout + +\end_inset + + and +\series bold + +\backslash +raisebox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +raisebox +\end_layout + +\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 +. + +\series medium + +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + For +\series bold + +\backslash +raisebox +\series default + this extra formula is created by pressing +\family sans +Ctrl+M +\family default + twice instead of once because LyX doesn't yet support +\series bold + +\backslash +raisebox +\series default + directly. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +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 Plain Layout +\begin_inset Formula $H\raisebox{2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +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 Plain Layout +\begin_inset Formula $H\raisebox{-2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A= +\backslash +raisebox{-2mm +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\family sans +Ctrl+M +\family default + +\family sans +Ctrl+M +\family default + +\backslash +sqrt +\begin_inset space \textvisiblespace{} +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 CommandInset label +LatexCommand label +name "sub:Colored-Boxes" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! colored +\end_layout + +\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 Plain Layout +The LaTeX-package +\series bold +color +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! color +\end_layout + +\end_inset + + has to be loaded in the LaTeX-preamble with the line +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +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 does not + cause problems. +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +colorbox +\end_layout + +\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 way as for +\series bold + +\backslash +raisebox +\series default +. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +This also applies for the command +\series bold + +\backslash +fcolorbox +\series default +. +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +colorbox{yellow +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +colorbox{green +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +fbox +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fbox +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +colorbox{green +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\family sans +Ctrl+M +\family default + +\family sans +Ctrl+M +\family default + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +C=D +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$ +\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 desired + color is chosen in the +\family sans +Text +\begin_inset space ~ +\end_inset + +Style +\family default + dialog. + The dialog can be called with the toolbar button +\begin_inset Info +type "icon" +arg "dialog-show character" +\end_inset + + or the menu +\family sans +Edit\SpecialChar \menuseparator +Text +\begin_inset space ~ +\end_inset + +Style\SpecialChar \menuseparator +Customized +\family default +. + The formula number then has 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 CommandInset ref +LatexCommand eqref +reference "eq:red" + +\end_inset + + is completely colored red. +\begin_inset Newline newline +\end_inset + +Formula +\begin_inset CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +fcolorbox +\end_layout + +\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 Plain Layout + + +\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 Plain Layout + + +\backslash +fboxrule 0.4pt +\backslash +fboxsep 3pt +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This formula was created with the command +\begin_inset Newline newline +\end_inset + + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +definecolor +\end_layout + +\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 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +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 used for text with the help of the command + +\series bold + +\backslash +textcolor +\series default +: +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! colored +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +textcolor +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textcolor +\end_layout + +\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 CommandInset label +LatexCommand label +name "sub:Paragraph-Boxes" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! as paragraph +\end_layout + +\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 Info +type "icon" +arg "box-insert" +\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 +use_makebox 0 +width "5cm" +special "none" +height "1in" +height_special "totalheight" +status open + +\begin_layout Plain Layout +This is a paragraph box. + It is exactly 5 +\begin_inset space \thinspace{} +\end_inset + +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 +: Rectangular box, +\emph on +Inner Box +\emph default +: Parbox, +\emph on +Width +\emph default +: 5 +\begin_inset space \thinspace{} +\end_inset + +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! P ! +\backslash +parbox +\end_layout + +\end_inset + + which 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 +\begin_inset Quotes eld +\end_inset + +bottom +\begin_inset Quotes erd +\end_inset + + means that the box is aligned within the surrounding text with its last + line. + With +\emph on +t +\emph default + for +\begin_inset Quotes eld +\end_inset + +top +\begin_inset Quotes erd +\end_inset + + 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 +\begin_inset space ~ +\end_inset + +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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +linewidth +\end_layout + +\end_inset + + is hereby the line width set for the document. + Because the frame is outside the parbox, 2 +\begin_inset space \thinspace{} +\end_inset + +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 Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #4483" +target "http://www.lyx.org/trac/ticket/4483" + +\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 Plain Layout + +\series bold +calc +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! calc +\end_layout + +\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 Plain Layout + + +\backslash +fboxsep 5mm +\backslash +fboxrule 5mm +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + +}} +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 the 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 CommandInset ref +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 Plain Layout + + +\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 Plain Layout + +}} +\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 Plain Layout +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 CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Operators +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Big Operators +\begin_inset CommandInset label +LatexCommand label +name "sub:Big-Operators" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators ! big +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Sums +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Integrals +\end_layout + +\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 +\begin_inset space ~ +\end_inset + +Options +\family default +. +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +int +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! I ! +\backslash +int +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\int$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\oint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ointctrclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ointctrclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ointclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ointclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\begin_inset Formula $\fint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +landupint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\begin_inset Formula $\landupint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +landdownint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\begin_inset Formula $\landdownint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sum +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +sum +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sum$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prod +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! P ! +\backslash +prod +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\prod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +coprod +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\coprod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigodot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigodot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigotimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigotimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigoplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigoplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigwedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigwedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigvee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigvee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigsqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigsqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +biguplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\biguplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +All big operators can also be inserted via the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\intop" +\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 +For all integral operators there is a second version available, ending in + +\series bold +op +\series default +: +\series bold + +\backslash +intop +\series default +, +\series bold + +\backslash +ointop +\series default + etc.. + These operators are different from +\series bold + +\backslash +int +\series default + etc. +\begin_inset space \space{} +\end_inset + +in the style the operator limits are displayed, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Operator-Limits" + +\end_inset + +. + +\end_layout + +\begin_layout Subsubsection* +Advice 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 +\begin_inset Info +type "shortcut" +arg "font-roman" +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +Font styles +\series bold + +\series default +see +\begin_inset CommandInset ref +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 + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout +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 +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iiiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dotsint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Subsection +Operator Limits +\begin_inset CommandInset label +LatexCommand label +name "sub:Operator-Limits" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators ! Limits +\end_layout + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prod^ +\backslash +infty +\begin_inset space \textvisiblespace{} +\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 Plain Layout +\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 + for 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 +\begin_inset Info +type "shortcut" +arg "math-limits" +\end_inset + +). + 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 those ending with +\series bold +op +\series default + like +\series bold + +\backslash +intop +\series default +, +\series bold + +\backslash +ointop +\series default + etc., 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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +subarray +\end_layout + +\end_inset + + and +\series bold + +\backslash +substack +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +substack +\end_layout + +\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 Plain Layout +Command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout ++ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $+$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $-$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\pm$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cdot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cdot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +times +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\times$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +div +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\div$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-1.2mm}{ +\end_layout + +\end_inset + +* +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $*$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +star +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\star$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +circ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\circ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nabla +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nabla$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigtriangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigtriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigtriangleup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigtriangleup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Box +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Box$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ddagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\wr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigcirc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigcirc$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\wedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\oplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ominus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ominus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +otimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\otimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\oslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +odot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\odot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +amalg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\amalg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +uplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\uplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +setminus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\setminus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +triangleleft +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\triangleleft$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +triangleright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\triangleright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +All binary operators can also be inserted via the math toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\pm" +\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 CommandInset label +LatexCommand label +name "sub:Self-defined-Operators" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators ! self-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With the help of the command +\series bold + +\backslash +DeclareMathOperator +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dbinom@ +\backslash +DeclareMathOperator +\end_layout + +\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 CommandInset ref +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 CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathop +\end_layout + +\end_inset + + and +\series bold + +\backslash +mathbin +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathbin +\end_layout + +\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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +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: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +mathop{ +\backslash +sum +\backslash +negmedspace +\backslash +sum +\series default + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series bold + +\begin_inset Formula $\to$ +\end_inset + +^N +\series default + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series bold +_i,j=1 +\end_layout + +\begin_layout Section +Fonts +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fonts +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Font Styles +\begin_inset CommandInset label +LatexCommand label +name "sub:Font-Styles" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Font ! style +\end_layout + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +shortcut +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathbb +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +ABC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathbb{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-noun" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathbf +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathbf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-bold" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +boldsymbol +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\boldsymbol{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-boldsymbol" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathcal +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +ABC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathcal{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-emph" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathfrak +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathfrak{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathscr +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathscr{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +shortcut +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathit +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathit{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathrm +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathrm{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-roman" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathsf +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathsf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-sans" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathtt +\series bold + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathtt{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-typewriter" +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\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 Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #4629" +target "http://www.lyx.org/trac/ticket/4629" + +\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 Info +type "icon" +arg "math-insert \\font" +\end_inset + + can be used. +\end_layout + +\begin_layout Subsection +Bold Formulas +\begin_inset CommandInset label +LatexCommand label +name "sub:Bold-Formulas" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! bold +\end_layout + +\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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +boldmath +\end_layout + +\end_inset + + in TeX-mode. + To end the environment, the command +\series bold + +\backslash +unboldmath +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +unboldmath +\end_layout + +\end_inset + + is inserted in TeX-mode. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + + +\backslash +unboldmath +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Colored Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! colored +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Formulas can be colored like normal text: Highlight a formula or a formula + part and use the +\family sans +Text Style +\family default + dialog. + Here is a formula in magenta: +\begin_inset Formula +\[ +{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +You can also define your own colors as described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Colored-Boxes" + +\end_inset + +. + They can be used with the TeX code command +\series bold + +\backslash +textcolor +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textcolor +\end_layout + +\end_inset + + in the scheme +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +textcolor{color}{characters or formula} +\end_layout + +\begin_layout Standard +The following example was colored completely dark green and partly red: +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textcolor{darkgreen}{ +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)} +\] + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Due to a bug in LyX only complete formulas can be colored with self-defined + colors. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #5269" +target "http://www.lyx.org/trac/ticket/5269" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Font Sizes +\begin_inset CommandInset label +LatexCommand label +name "sub:Font-Sizes" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Font ! size +\end_layout + +\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 +, +\begin_inset Newline newline +\end_inset + + +\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, which + corresponds to 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 +\begin_inset space \thinspace{} +\end_inset + +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 be changed using the following size commands + or the toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\style" +\end_inset + +: +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +displaystyle +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +displaystyle +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +textstyle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +scriptstyle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +scriptscriptstyle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +After entering these commands, a blue box appears in which the formula parts + are inserted. +\end_layout + +\begin_layout Standard +There is a further method to change the font size, that though only works + for symbols or letters in mathematical text. + To use it, one of the above text size commands 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 Plain Layout + + +\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 Plain Layout + + +\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: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +maltese +\begin_inset space \textvisiblespace{} +\end_inset + +A Alt+M M +\backslash +Large +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +maltese +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +textit +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset Formula $\to$ +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset space \hspace*{} +\length 1cm +\end_inset + +Alt+M +\series default + +\series bold +M +\backslash +tiny +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +maltese +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +textit +\begin_inset space \textvisiblespace{} +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Greek letters can also be inserted via the toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\alpha" +\end_inset + +. + All international typesetting norms purport that Greek letters in math + have to be typeset italic/slanted. + In some languages, like French or Russian, they are nevertheless sometimes + typeset upright. +\end_layout + +\begin_layout Subsection +Small Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! small +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +alpha +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\alpha$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +beta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\beta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +epsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\epsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varepsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varepsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +zeta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\zeta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +eta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\eta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vartheta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vartheta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iota +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\iota$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +kappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\kappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varkappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varkappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $o$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varpi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varpi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varrho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varrho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varsigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varsigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tau +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\tau$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varphi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varphi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +chi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\chi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +How to create special upright Greek letters is explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Upright-small-Greek" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Big Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! big +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\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 + +. + Another way is to load the package +\series bold +fixmath +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +fixmath +\series default + is part of the LaTeX-package +\series bold +was +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! was +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! fixmath +\end_layout + +\end_inset + + with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{fixmath} +\end_layout + +\begin_layout Standard +Then all big Greek letters in a document will automatically be typeset italic. +\end_layout + +\begin_layout Subsection +Bold Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! bold +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +boldsymbol +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Upsilon +\backslash +boldsymbol +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +theta +\backslash +boldsymbol +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +A list with all symbols of most of the LaTeX-packages can be found in +\begin_inset CommandInset citation +LatexCommand cite +key "Symbols" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\backslash +texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. +\end_layout + +\begin_layout Plain Layout +More about +\backslash +texorpdfstring is in section +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Formulas-in-Section" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols +\end_layout + +\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 Info +type "icon" +arg "math-insert \\nabla" +\end_inset + + and +\begin_inset Info +type "icon" +arg "math-insert \\digamma" +\end_inset + +. +\end_layout + +\begin_layout Subsection +Mathematical Symbols +\begin_inset CommandInset label +LatexCommand label +name "sub:Mathematical-Symbols" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! mathematical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +neg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\neg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Im +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Im$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Re +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Re$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +aleph +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\aleph$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +partial +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\partial$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +infty +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\infty$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\wp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +imath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\imath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +jmath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\jmath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +forall +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\forall$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +exists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\exists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nexists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nexists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +emptyset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\emptyset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varnothing +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varnothing$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dag +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dag$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddag +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ddag$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +complement +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-0.8mm}{ +\end_layout + +\end_inset + + +\begin_inset Formula $\complement$ +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bbbk +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Bbbk$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\prime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +backprime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\backprime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +triangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\triangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +angle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\angle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +measuredangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\measuredangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sphericalangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sphericalangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +top +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\top$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Subsection +Miscellaneous Symbols +\begin_inset CommandInset label +LatexCommand label +name "sub:Miscellaneous-Symbols" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! miscellaneous +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +flat +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\flat$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +natural +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\natural$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sharp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sharp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +surd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\surd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +checkmark +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\checkmark$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +yen +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\yen$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pounds +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\pounds$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +$ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\$$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +§ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $§$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hbar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hbar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +clubsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\clubsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +spadesuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\spadesuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigstar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigstar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +blacklozenge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\blacklozenge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +blacktriangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\blacktriangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +blacktiangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\blacktriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diamondsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diamondsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +heartsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\heartsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +P +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\P$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +copyright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\copyright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +circledR +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\circledR$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +maltese +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\maltese$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diagup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diagup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diagdown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diagdown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +Some symbols can be displayed in different sizes, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Sizes" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +The Euro-Symbol € +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! Euro-symbol +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout + +\backslash +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +officialeuro +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To use the Euro symbol in formulas, the LaTeX-package +\series bold +eurosym +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! eurosym +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! E ! +\backslash +euro +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +officialeuro +\end_layout + +\end_inset + +, that is only available in TeX-mode. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifeurosym +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +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 Plain Layout + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +formula +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +euro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\euro$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +mathematical text +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +€ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mbox{€}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +TeX-mode +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +officialeuro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +officialeuro +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +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 LaTeX-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 Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Section +Relations +\begin_inset CommandInset label +LatexCommand label +name "sec:Relations" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Relations +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Comparisons|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Relations +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +All following relations can also be inserted via the toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\leq" +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +< +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $<$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ll +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ll$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\prec$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +preceq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\preceq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +subset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\subset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +subseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\subseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqsubseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqsubseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\in$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vdash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vdash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +smile +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\smile$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +unlhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\unlhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gtrless +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gtrless$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mid +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mid$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nmid +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nmid$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout += +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +equiv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\equiv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +simeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\simeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +approx +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\approx$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cong +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cong$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bowtie +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bowtie$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +notin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\notin$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +perp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\perp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +propto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\propto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +asymp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\asymp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +doteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\doteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +circeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\circeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +models +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\models$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +widehat= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\widehat{=}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +> +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $>$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +succ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\succ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +succeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\succeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +supset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\supset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +supseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\supseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqsupseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqsupseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ni +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ni$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dashv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dashv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +frown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\frown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +unrhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\unrhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lessgtr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lessgtr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nparallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nparallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\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 +LyX supports also many special relations. + Use the toolbar button +\begin_inset Info +type "icon" +arg "math-insert \\leqq" +\end_inset + + to see a list of these relations. +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +stackrel +\end_layout + +\end_inset + +: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A(r) +\backslash +stackrel +\begin_inset space \textvisiblespace{} +\end_inset + +r +\backslash +to +\backslash +infty +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset Formula $\downarrow$ +\end_inset + + +\backslash +approx +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset space \textvisiblespace{} +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 CommandInset label +LatexCommand label +name "sub:Predefined-Functions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Functions ! predefined +\end_layout + +\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 functionswhich 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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Asin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $Asin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +sin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\sin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sinh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arcsin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cosh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arccos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +inf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tanh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arctan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lim +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +coth +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +liminf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +min +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +deg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +limsup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +csc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +max +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +det +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Pr +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ln +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +exp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +log +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ker +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\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 Info +type "icon" +arg "math-insert \\functions" +\end_inset + +. +\end_layout + +\begin_layout Subsection +Self-defined Functions +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Functions ! self-defined +\end_layout + +\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 Plain Layout +For more about +\series bold + +\backslash +DeclareMathOperator +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Self-defined-Operators" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset VSpace -3mm +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +DeclareMathOperator{ +\backslash +sgn}{sgn} +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dbinom@ +\backslash +DeclareMathOperator +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset VSpace -2mm +\end_inset + + +\begin_inset Newline newline +\end_inset + +Now the new defined function can be called with the command +\series bold + +\backslash +sgn +\series default +. +\end_layout + +\begin_layout Itemize +Write the formula as usual, mark the formula name, in our example the letters + +\emph on +sgn +\emph default +, and change it to mathematical text. + Finally, 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 Plain Layout +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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +sgn(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\sgn(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +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 Plain Layout +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Limits +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For limits, in addition to the commands +\series bold + +\backslash +lim +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +lim +\end_layout + +\end_inset + +, +\series bold + +\backslash +liminf +\series default + and +\series bold + +\backslash +limsup +\series default + the following functions are defined: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varliminf +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varliminf$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varlimsup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varlimsup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varprojlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varprojlim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varinjlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset space \hspace{} +\length 1cm +\end_inset + +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +The space 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 Plain Layout + +\backslash +lim_x +\backslash +to +\begin_inset space \textvisiblespace{} +\end_inset + +A +\begin_inset space \textvisiblespace{} +\end_inset + +x=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +How to adjust the typesetting of the limits see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Operator-Limits" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Modulo-Functions +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Functions ! modulo- +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The modulo-function is special, because it exists in four variants. + The variants in a displayed formula are: +\begin_inset Formula +\begin{align*} +\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ +\mathrm{a\backslash mod\textrm{␣}b} & & a\mod b\\ +\mathrm{a\backslash pmod\textrm{␣}b} & & a\pmod b\\ +\mathrm{a\backslash bmod\textrm{␣}b} & & a\bmod b\\ +\mathrm{a\backslash pod\textrm{␣}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. + By default the modulo-functions take only the first following character + into account. + To use more than one character, one has to put them into TeX-braces: +\begin_inset Formula +\begin{align*} +\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ +\mathrm{a\backslash pod\textrm{␣}bcd} & & a\pod bcd\\ +\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d +\end{align*} + +\end_inset + + +\end_layout + +\begin_layout Section +Special Characters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Special characters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The characters ^ and _ would normally create a superscript and subscript, + respectively. + To get these characters you have to insert them with a leading +\backslash +: +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +^ +\begin_inset space \textvisiblespace{} +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathcircumflex$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +_ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\_$ +\end_inset + + +\end_layout + +\end_inset + + + + +\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 +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oe +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{œ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +OE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Œ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ae +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{æ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +AE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Æ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +aa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{\aa}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +AA +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout + +\backslash +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textrm{ +\backslash +AA} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Å}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ı}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +The space of 0 +\begin_inset space \thinspace{} +\end_inset + +mm is used for separation, because otherwise the output will be ¡ and ¿ + respectively. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ø}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +O +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Ø}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +l +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ł}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +L +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Ł}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +! +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\begin_inset space \textvisiblespace{} +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{!`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +? +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\begin_inset space \textvisiblespace{} +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{?`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +j +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ȷ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\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 Info +type "icon" +arg "math-insert \\digamma" +\end_inset + +. +\end_layout + +\begin_layout Standard +An exception are the commands +\series bold +! +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\series default + and +\series bold +? +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\series default +, because they can be inserted in LyX directly to text. +\end_layout + +\begin_layout Subsection +Accents in Text +\begin_inset CommandInset label +LatexCommand label +name "sub:Accents-in-Text" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents ! in text +\end_layout + +\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 +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\begin_inset Quotes grd +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +"e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +`e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +`e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +^ +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +^e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +=e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +=e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +u +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +u e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +b +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +b e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +t +\begin_inset space \textvisiblespace{} +\end_inset + +ee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +t ee +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +H +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +H e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +'e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +'e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +~e +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Tilde +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +~e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +.e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +.e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +v +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +v e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +d +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +d e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +c +\begin_inset space \textvisiblespace{} +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +c e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\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 space \textvisiblespace{} +\end_inset + +sz +\series default + creates: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout +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 that are 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 CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textcircled +\end_layout + +\end_inset + + all numbers and letters can be set into a circle, quasi accented with a + circle, similar to the copyright symbol. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +textcircled{w} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textcircled{w} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Large +\backslash +textcircled{ +\backslash +normalsize +\backslash +protect +\backslash +raisebox{-1.5pt}{W}} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}$ +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout +see +\begin_inset CommandInset ref +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 Plain Layout +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Boxes-without-Frame" + +\end_inset + + +\end_layout + +\end_inset + + the character can be centered. +\end_layout + +\begin_layout Subsection +Old-style Figures +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Old-style Figures +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Old-style figures (also known as old-style numerals) are created with the + command +\series bold + +\backslash +oldstylenums +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +oldstylenums +\end_layout + +\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 Section +Formula Styles +\begin_inset CommandInset label +LatexCommand label +name "sec:Formula-Styles" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! styles +\end_layout + +\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 +\begin_inset space ~ +\end_inset + +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathindent +\end_layout + +\end_inset + +. + Should the distance be 15 +\begin_inset space \thinspace{} +\end_inset + +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 +\begin_inset space \thinspace{} +\end_inset + +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 +\begin_inset space ~ +\end_inset + +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 CommandInset ref +LatexCommand ref +reference "sub:Flalign-Environment" + +\end_inset + +. +\end_layout + +\begin_layout Section +Multiline Formulas +\begin_inset CommandInset label +LatexCommand label +name "sec:Multiline-Formulas" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +General +\end_layout + +\begin_layout Standard +In LyX multiline formulas are created by pressing +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + inside a formula. + This creates either an +\series bold +eqnarray environment +\series default + that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Eqnarray-Environment" + +\end_inset + + or, when the option +\family sans +Use AMS math package +\family default + in the document settings is selected, an +\series bold +align environment +\series default + that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Standard-align-Environment" + +\end_inset + +. + The align environment is recommended because it provides in any case a + typographically correct output. +\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 + +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + +. + To add or delete lines, the math toolbar buttons +\begin_inset Info +type "icon" +arg "inset-modify tabular append-row" +\end_inset + + or +\begin_inset Info +type "icon" +arg "inset-modify tabular delete-row" +\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 CommandInset label +LatexCommand label +name "sub:Line-Separation" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! Line separation +\end_layout + +\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 Plain Layout +see +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #1505" +target "http://www.lyx.org/trac/ticket/1505" + +\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 Plain Layout + + +\backslash +begin{eqnarray*} +\end_layout + +\begin_layout Plain Layout + +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 Plain Layout + +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 Plain Layout + + +\backslash +end{eqnarray*} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +To set the line separation for all lines in a formula, the length +\series bold + +\backslash +jot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! J ! +\backslash +jot +\end_layout + +\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 +\begin_inset space \thinspace{} +\end_inset + +pt. + To create 3 +\begin_inset space \thinspace{} +\end_inset + +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 Plain Layout + +\series bold +calc +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! calc +\end_layout + +\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 Plain Layout + + +\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 Plain Layout + + +\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 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Subsubsection +Column Separation +\begin_inset CommandInset label +LatexCommand label +name "sub:Column-Separation" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! Column separation +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arraycolsep +\end_layout + +\end_inset + + according to: +\begin_inset Newline newline +\end_inset + +column separation = 2 +\begin_inset space \thinspace{} +\end_inset + + +\series bold + +\backslash +arraycolsep +\series default + +\begin_inset Newline newline +\end_inset + +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 +\begin_inset space \thinspace{} +\end_inset + +cm. + To get back to the predefined distance, +\series bold + +\backslash +arraycolsep +\series default + is set to 5 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Standard +A formula with 2 +\begin_inset space \thinspace{} +\end_inset + +cm column separation: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 +\begin_inset space \thinspace{} +\end_inset + +pt: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! long +\end_layout + +\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 shorter than the line width, this + one is chosen for the left side and the right side is typeset over two + lines: +\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:shortlong} +\end{eqnarray} + +\end_inset + +The minus sign at the beginning of the second line does normally not appear + as an 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, 3 +\begin_inset space \thinspace{} +\end_inset + +pt space was inserted behind the minus sign with the command +\series bold + +\backslash +hspace +\series default +. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +for more about +\series bold + +\backslash +hspace +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hspace +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +lefteqn +\end_layout + +\end_inset + + is used. + It is inserted in the first column of the first line and causes all further + insertions to overwrite the following columns: +\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 + +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 Newline newline +\end_inset + +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 VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout +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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +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 Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #1429" +target "http://www.lyx.org/trac/ticket/1429" + +\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 CommandInset ref +LatexCommand ref +reference "sub:Multline-Environment" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Multiline-Formula-Parts" + +\end_inset + +. +\end_layout + +\begin_layout Subsubsection +Multiline Fractions +\begin_inset CommandInset label +LatexCommand label +name "sub:Multiline-Fractions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fractions ! multiline +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +There are cases where the denominator and/or the numerator of a fraction + is so long that the fraction does not fit into one line. + It is then necessary to add a line break within the fraction. + This can be done using the command +\series bold + +\backslash +splitfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +splitfrac +\end_layout + +\end_inset + +. + To activate it, set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default + for the package +\series bold +mathtools +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mathtools +\end_layout + +\end_inset + + the option +\family sans +Load +\begin_inset space ~ +\end_inset + +always +\family default +. + +\series bold + +\backslash +splitfrac +\series default + has the scheme +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +splitfrac{first line}{second line} +\end_layout + +\begin_layout Standard +and is used as denominator and/or numerator: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z} +\] + +\end_inset + +The command for the first numerator above is: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +splitfrac{xy+xy+xy+xy+xy +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +{+wy+wy+wy+wy +\end_layout + +\begin_layout Subsubsection +Multiline Brackets +\begin_inset CommandInset label +LatexCommand label +name "sub:Multiline-Brackets" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets ! for multiline expressions +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +right +\end_layout + +\end_inset + + and the second line with +\series bold + +\backslash +left. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +for more about +\series bold + +\backslash +left +\series default + and +\series bold + +\backslash +right +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +left +\end_layout + +\end_inset + +. + After +\series bold + +\backslash +left. + +\series default + the command +\series bold + +\backslash +vphantom +\series default + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series bold + +\backslash +prod +\series default +^ +\begin_inset space \textvisiblespace{} +\end_inset + + +\series bold + +\backslash +infty +\series default + +\begin_inset space \textvisiblespace{} +\end_inset + + +\series bold + +\begin_inset Formula $\downarrow$ +\end_inset + +_R=1} +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! V ! +\backslash +vphantom +\end_layout + +\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 especially 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 formulas can be converted to Align environments. +\end_layout + +\begin_layout Standard +To add or delete columns, the math toolbar buttons +\begin_inset Info +type "icon" +arg "inset-modify tabular append-column" +\end_inset + + or +\begin_inset Info +type "icon" +arg "inset-modify tabular delete-column" +\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 CommandInset label +LatexCommand label +name "sub:Standard-align-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! align environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This Align environment is created by pressing +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + 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 Plain Layout +more about +\series bold + +\backslash +hfill +\series default + see +\begin_inset CommandInset ref +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 Plain Layout +formula styles see +\begin_inset CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! alignat environment +\end_layout + +\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 CommandInset ref +LatexCommand ref +reference "sub:Space" + +\end_inset + +. +\end_layout + +\begin_layout Standard +The above example in the alignat environment where 1 +\begin_inset space \thinspace{} +\end_inset + +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 CommandInset label +LatexCommand label +name "sub:Flalign-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! flalign environment +\end_layout + +\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 CommandInset ref +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 +\begin_inset space \thinspace{} +\end_inset + +pt space was inserted at the beginning of the first column. +\end_layout + +\begin_layout Subsection +Eqnarray Environment +\begin_inset CommandInset label +LatexCommand label +name "sub:Eqnarray-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! eqnarray environment +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! gather environment +\end_layout + +\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 CommandInset label +LatexCommand label +name "sub:Multline-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! multline environment +\end_layout + +\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 CommandInset ref +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 last (first) line of a multline environment appears + numbered when the document numbering is right (left). +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +numbering styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With the commands +\series bold + +\backslash +shoveright +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +shoveright +\end_layout + +\end_inset + + and +\series bold + +\backslash +shoveleft +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +shoveleft +\end_layout + +\end_inset + + 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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +multlinegap +\end_layout + +\end_inset + + specifies the distance of the first line from the left page margin. + Predefined is the length 0 +\begin_inset space \thinspace{} +\end_inset + +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 Plain Layout + + +\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 Plain Layout + + +\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 CommandInset label +LatexCommand label +name "sub:Multiline-Formula-Parts" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! formula parts +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To display only parts of a formula with multiple lines, one of the following + environments is 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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +aligned +\end_layout + +\end_inset + + 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 CommandInset ref +LatexCommand eqref +reference "eq:shortlong" + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +alignedat +\end_layout + +\end_inset + + +\series bold + +\backslash +gathered +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! G ! +\backslash +gathered +\end_layout + +\end_inset + +, or +\series bold + +\backslash +split +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +split +\end_layout + +\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 CommandInset label +LatexCommand label +name "sub:Text-in-multiline" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! in formulas +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! text +\end_layout + +\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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! I ! +\backslash +intertext +\end_layout + +\end_inset + + 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 \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi +\end{align} + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +intertext +\series default + always creates some vertical space between the text and the formula lines. + To avoid this space, set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default + for the package +\series bold +mathtools +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mathtools +\end_layout + +\end_inset + + the option +\family sans +Load +\begin_inset space ~ +\end_inset + +always +\family default +. + Then you can use the command +\series bold + +\backslash +shortintertext +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +shortintertext +\end_layout + +\end_inset + + instead of +\series bold + +\backslash +intertext +\series default +: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{align} +I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\ +\shortintertext{\text{integrand is symmetric to \ensuremath{\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 Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! numbering|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Formula numbering +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\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 +\begin_inset space ~ +\end_inset + +Formula +\family default + (shortcut +\family sans +Ctrl+Alt +\begin_inset space ~ +\end_inset + +N +\family default +). + Existing formulas can be numbered with the menu +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Toggle +\begin_inset space ~ +\end_inset + +Numbering +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "math-number-toggle" +\end_inset + +). + The formula number is displayed in LyX behind the formula as a 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 +\begin_inset space ~ +\end_inset + +Numbering +\begin_inset space ~ +\end_inset + +of +\begin_inset space ~ +\end_inset + +Line +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "math-number-line-toggle" +\end_inset + +) for every line. +\end_layout + +\begin_layout Standard +Except for inline formulas, all formulas can be numbered with two different + styles, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Cross-References +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Cross-references ! to formulas +\end_layout + +\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 Info +type "icon" +arg "label-insert" +\end_inset + +. + The cursor must hereby be inside a displayed formula. + Alternatively you can right-click on the formula and choose +\family sans +Equation Label +\family default +. + 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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +section labels. + To change a label, the menu +\family sans +Insert\SpecialChar \menuseparator +Label +\family default + is used again or you right-click on a formula and then on +\family sans +Equation Label +\family default +. +\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. +\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 Info +type "icon" +arg "dialog-show-new-inset ref" +\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. +\begin_inset Newline newline +\end_inset + +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 Plain Layout +Note the different cross-reference types. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The equations +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:tag" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:c" + +\end_inset + + are equivalent. + In ( +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:Lat" + +\end_inset + +) big Latin letters are used for the numbering in contrary to ( +\begin_inset CommandInset ref +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 Plain Layout + +\series bold + +\backslash +tag +\series default + is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:User-defined-Numbering" + +\end_inset + +. +\end_layout + +\end_inset + + +\series default + contains a box like in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Paragraph-Boxes" + +\end_inset + +, the formula cannot be referenced. +\end_layout + +\begin_layout Subsection +Subnumbering +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! subnumbering +\end_layout + +\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 Plain Layout + + +\backslash +addtocounter{equation}{-1} +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +addtocounter +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\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 Newline linebreak +\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 CommandInset ref +LatexCommand eqref +reference "eq:a" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:b" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:c" + +\end_inset + + would be numbered as +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:a" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:d" + +\end_inset + +, +\begin_inset CommandInset ref +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 +\begin_inset space \thinspace{} +\end_inset + +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 Plain Layout +formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + is used, -7 +\begin_inset space \thinspace{} +\end_inset + +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 Plain Layout + + +\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 Plain Layout + + +\backslash +end{subequations} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +User-defined Numbering +\begin_inset CommandInset label +LatexCommand label +name "sub:User-defined-Numbering" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! user-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! self-defined delimiters +\end_layout + +\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 Plain Layout +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 +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +tag +\end_layout + +\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 +\begin_inset space \textvisiblespace{} +\end_inset + +something +\series default + was inserted in the formula. +\end_layout + +\begin_layout Standard +When the command +\series bold + +\backslash +tag* +\begin_inset space \textvisiblespace{} +\end_inset + +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + + ! +\backslash + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +addtoreset +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + +resp. +\begin_inset Newline newline +\end_inset + + +\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 +\begin_inset Newline newline +\end_inset + + +\backslash +@addtoreset{equation}{section} +\begin_inset Newline newline +\end_inset + + +\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 Plain Layout + +\series bold +remreset +\series default + is part of the LaTeX-package +\series bold +carlisle +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! carlisle +\end_layout + +\end_inset + + that is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! remreset +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + + ! +\backslash + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +removefromreset +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +numberwithin +\end_layout + +\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 TeX code 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 Plain Layout + + +\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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +tables so that the number of the part is the sectioning, +\begin_inset Newline newline +\end_inset + + +\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 TeX code or to the LaTeX-preamble: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arabic +\end_layout + +\end_inset + + +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\end_layout + +\end_inset + + +\series bold + +\begin_inset Newline newline +\end_inset + + +\series default +or +\series bold + +\begin_inset Newline newline +\end_inset + + +\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 Plain Layout + + +\backslash +makeatletter +\end_layout + +\begin_layout Plain Layout + + +\backslash +@removefromreset{equation}{section} +\end_layout + +\begin_layout Plain Layout + + +\backslash +makeatother +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Numbering with Roman Numbers and Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! with letters +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! with Roman numbers +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +renewcommand +\end_layout + +\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 Plain Layout +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 CommandInset ref +LatexCommand ref +reference "sub:The-Command-newcommand" + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +roman +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +roman@ +\backslash +Roman +\end_layout + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +alph +\end_layout + +\end_inset + +, for big ones there is the command +\series bold + +\backslash +Alph +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +alph@ +\backslash +Alph +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\color none +Note: +\series default + Only maximal 26 +\begin_inset space ~ +\end_inset + +formulas can be numbered with Latin letters in one document. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +alph{equation}} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +C=\textrm{small Latin} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arabic +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +E=\textrm{Arabic} +\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 CommandInset href +LatexCommand href +name "Formula-numbering.lyx" +target "run:Formula-numbering.lyx" + +\end_inset + +. +\end_layout + +\begin_layout Section +Chemical Symbols and Equations +\begin_inset CommandInset label +LatexCommand label +name "sub:Chemical-Symbols-and" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Chemical characters ! Symbols +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Chemical equations +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! chemical +\end_layout + +\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 +\begin{equation} +\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction} +\end{equation} + +\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 +\begin_inset Info +type "shortcut" +arg "font-roman" +\end_inset + + to the upright font style. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +font styles +\series bold + +\series default +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +A more convenient way to typeset chemical formulas is to use the command + +\series bold + +\backslash +ce +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +ce +\end_layout + +\end_inset + + that is available when the LaTeX-package +\series bold +mhchem +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mhchem +\end_layout + +\end_inset + + is installed. + After inserting +\series bold + +\backslash +ce +\series default + to a formula a new blue box appears where chemical formulas can be inserted + in an intuitive way. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +H2CO3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +SO4^2- +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +(NH4)2S +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +KCr(SO4)2.12H2O +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +A-B +\backslash +dbond +\begin_inset space \textvisiblespace{} +\end_inset + +C +\backslash +tbond +\begin_inset space \textvisiblespace{} +\end_inset + +D +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +^227 +\begin_inset Formula $\downarrow$ +\end_inset + +_90 +\begin_inset Formula $\to$ +\end_inset + +Th+ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +CO2 +\begin_inset space \textvisiblespace{} +\end_inset + ++ +\begin_inset space \textvisiblespace{} +\end_inset + +C +\begin_inset space \textvisiblespace{} +\end_inset + +<=> +\begin_inset space \textvisiblespace{} +\end_inset + +2CO +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +CO2 +\begin_inset space \textvisiblespace{} +\end_inset + ++ +\begin_inset space \textvisiblespace{} +\end_inset + +C +\begin_inset space \textvisiblespace{} +\end_inset + +->[ +\backslash +alpha][ +\backslash +beta] +\begin_inset space \textvisiblespace{} +\end_inset + +2CO} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\color none +Note: +\series default + Inserting a formula to a +\series bold + +\backslash +ce +\series default + box will lead to LaTeX errors due to a LyX bug. +\color inherit + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #8566" +target "http://www.lyx.org/trac/ticket/8566" + +\end_inset + + +\end_layout + +\end_inset + + +\color none + In this case TeX code has to be used like for +\series bold + +\backslash +ce{$ +\backslash +mu +\backslash +hyphen$Cl} +\series default +: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ce{$ +\backslash +mu +\backslash +hyphen$Cl} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\color none +Note: +\series default + It is not possible in LyX to use the character ^ to get an up-arrow as + described in the +\series bold +mhchem +\series default + manual. + One instead uses a negative thin space followed by the command +\series bold + +\backslash +uparrow +\series default +: +\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$ +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Using +\series bold + +\backslash +ce +\series default + the command for equation +\begin_inset space ~ +\end_inset + + +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:chem-reaction" + +\end_inset + + is: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +ce +\begin_inset space \textvisiblespace{} +\end_inset + +2Na+ +\begin_inset space \textvisiblespace{} +\end_inset + ++ +\begin_inset space \textvisiblespace{} +\end_inset + +SO4^2- +\begin_inset space \textvisiblespace{} +\end_inset + + +\begin_inset space \textvisiblespace{} +\end_inset + +-> +\begin_inset space \textvisiblespace{} +\end_inset + +Na2SO4 +\end_layout + +\begin_layout Standard +To create multiline chemical equations first a multiline formula is created + as described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Multiline-Formulas" + +\end_inset + +. + Afterwards the command +\series bold + +\backslash +ce +\series default + is used in every small blue box of the formula. + +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:TEOS-reaction-1" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:TEOS-reaction-2" + +\end_inset + + are an example of a multi-stage chemical reaction where every equation + has its own number. +\begin_inset Formula +\begin{eqnarray} +\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\ +\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2} +\end{eqnarray} + +\end_inset + + +\end_layout + +\begin_layout Standard +Besides +\series bold + +\backslash +ce +\series default + the +\series bold +mhchem +\series default + package provides the command +\series bold + +\backslash +cf +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cf +\end_layout + +\end_inset + + that has to be used for special cases. + For more information about +\series bold + +\backslash +cf +\series default + and more examples have a look at the documentation of +\series bold +mhchem +\series default +, +\begin_inset CommandInset citation +LatexCommand cite +key "mhchem" + +\end_inset + +. +\end_layout + +\begin_layout Section +Diagrams +\end_layout + +\begin_layout Standard +LyX supports two types of commutative diagrams: +\series bold +amscd +\series default + and +\series bold +xymatrix +\series default + that are explained in the following. +\end_layout + +\begin_layout Subsection +Amscd Diagrams +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Diagrams ! amscd +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Diagrams of this type visualize relations by vertical and horizontal lines + or arrows: +\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 + a 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 +If 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: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +CD +\begin_inset space \textvisiblespace{} +\end_inset + +A@>j>>B@>>k>C@=F Ctrl+Return +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +CD +\begin_inset space \textvisiblespace{} +\end_inset + + +\end_layout + +\end_inset + +@AmAA@.@VV +\backslash +{V +\series default + +\begin_inset Formula $\to$ +\end_inset + + +\series bold +V@| Ctrl+Return +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +CD +\begin_inset space \textvisiblespace{} +\end_inset + + +\end_layout + +\end_inset + +D@<k>>F@=C +\end_layout + +\begin_layout Subsection +Xymatrix Diagrams +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Diagrams ! xymatrix +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To be able to use xymatrices, the LaTeX-package +\series bold +xypic +\series default + must be installed. + A xymatrix is created by inserting the command +\series bold + +\backslash +xymatrix +\series default + in a formula. + Then you are able to add new matrix columns and rows like for normal matrices, + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Matrices" + +\end_inset + +. +\end_layout + +\begin_layout Standard +In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows, + and much more. + All possibilities to create commutative diagrams and decorations are explained + in detail in the +\emph on +XY-pic manual +\emph default + that you find in the menu +\family sans +Help\SpecialChar \menuseparator +Specific +\begin_inset space ~ +\end_inset + +Manuals +\family default +. +\end_layout + +\begin_layout Subsection + +\noun on +Feynman +\noun default + Diagrams +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Diagrams ! Feynman +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To be able to use +\noun on +Feynman +\noun default +-diagrams, the LaTeX-package +\series bold +feyn +\series default + must be installed. + A +\noun on +Feynman +\noun default +-diagram is created by inserting the command +\series bold + +\backslash +Diagram +\series default + in a formula. + Then you are able to add new matrix columns and rows like for normal matrices, + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Matrices" + +\end_inset + +. +\end_layout + +\begin_layout Standard +Examples how to create +\noun on +Feynman- +\noun default +diagrams in LyX is given in the +\emph on +Feynman-diagram manual +\emph default + that you find in the menu +\family sans +Help\SpecialChar \menuseparator +Specific +\begin_inset space ~ +\end_inset + +Manuals +\family default +. +\end_layout + +\begin_layout Section +User-defined Commands +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +User-defined commands +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + The names of user-defined commands and macros may only consist of Latin + letters. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +The Command +\backslash +newcommand +\begin_inset CommandInset label +LatexCommand label +name "sub:The-Command-newcommand" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +User-defined commands ! +\backslash +newcommand +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +newcommand +\end_layout + +\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 + 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] +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +newcommand +\end_layout + +\end_inset + +{command definition} +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\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 +The number of arguments is an integer in the range 0 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +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 VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\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 VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +us}[1]{ +\backslash +underline{#1}} +\series default + +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + +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. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +define the command +\series bold + +\backslash +fb +\series default +: +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +fb}[3]{ +\backslash +framebox#1#2{$#3$}} +\series default + +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + +The two Dollar signs creates the extra formula needed for +\series bold + +\backslash +framebox +\series default +, see +\begin_inset CommandInset ref +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 need not be specified, the argument for the + color is defined optional: +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +cb}[3][white]{ +\backslash +fcolorbox{#2}{#1}{$#3$}} +\series default + +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + +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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +gr +\begin_inset space \textvisiblespace{} +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\gr B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +us{ABcd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fb{[2cm] +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cb{red +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cb[green] +\backslash +{red +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Subsection +Math Macros +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +User-defined commands! Math macros +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Macros +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +User-defined commands are especially convenient for complex expressions. + When you are for example dealing with a document that has quadratic equations, + the same solution type occurs several times. + The general form of a quadratic equation is +\begin_inset Formula +\[ +0=\lambda^{2}+p\lambda+q +\] + +\end_inset + +The general form of the solution is +\begin_inset Formula +\[ +\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +To define a command for the solution formula where only the three parameters + +\begin_inset Formula $\lambda$ +\end_inset + +, +\begin_inset Formula $p$ +\end_inset + + and +\begin_inset Formula $q$ +\end_inset + + need to be specified and the index of +\begin_inset Formula $\lambda$ +\end_inset + + can be given optionally, the LaTeX-preamble line is +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +qG}[4][1, +\backslash +,2]{#2_{#1}=- +\backslash +frac{#3}{2} +\backslash +pm +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +newcommand +\end_layout + +\end_inset + + +\backslash +sqrt{ +\backslash +frac{#3^{2}}{4}-#4}} +\end_layout + +\begin_layout Standard +To create with this the solution formula, the command +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +qG{ +\backslash +lambda +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{p +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{q +\series default + is inserted to a formula +\series bold +. +\end_layout + +\begin_layout Standard +The definition of the new command is unintuitive because one has to know + the schemes of all used LaTeX commands, e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +that a fraction is inserted in LaTeX as +\series bold + +\backslash +frac{numerator}{denominator} +\series default +. + Furthermore one can easily forget a brace in the definition and cannot + see in LyX what the new command is doing. + To avoid these problems LyX offers the possibility to use math macros instead + of the command +\series bold + +\backslash +newcommand +\series default +. +\end_layout + +\begin_layout Standard +A math macro is created by using the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\family default + or the toolbar button +\begin_inset Info +type "icon" +arg "math-macro newmacroname_newcommand" +\end_inset + +. + The math macro toolbar appears together with the following box where the + macro is defined: +\begin_inset Newline newline +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Graphics + filename clipart/macrobox.png + +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset FormulaMacro +\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}} +\end_inset + + +\backslash +newmacroname is the default name of the macro that should be changed to + something sensible. + The wanted formula is inserted in the first blue box. + An argument placeholder is inserted with the command +\series bold + +\backslash +#argumentnumber +\series default +, e. +\begin_inset space \thinspace{} +\end_inset + +g +\begin_inset space \space{} +\end_inset + + +\series bold + +\backslash +#1 +\series default + or by using the macro toolbar button +\begin_inset Info +type "icon" +arg "math-macro-add-param" +\end_inset + +. + Argument placeholders are displayed red. + A maximum of 9 +\begin_inset space ~ +\end_inset + +arguments are possible. + Optional arguments are created with the toolbar button +\begin_inset Info +type "icon" +arg "math-macro-add-optional-param" +\end_inset + +. + The first non-optional argument can be transformed to an optional one with + the toolbar button +\begin_inset Info +type "icon" +arg "math-macro-make-optional" +\end_inset + +. + In the second blue box the appearance of the macro in LyX can be defined. + Normally you want to see it as it is defined, so the box is kept empty. + But when you have created a macro that needs lot of space on the screen, + you can insert in the box for example +\begin_inset Newline newline +\end_inset + + +\series bold +qG: +\backslash +#1 +\series default + +\series bold +, +\series default + +\series bold + +\backslash +#2 +\series default + +\series bold +, +\series default + +\series bold + +\backslash +#3, +\backslash +#4 +\begin_inset Newline newline +\end_inset + + +\series default +For the macro only the arguments with the macro name in front of them will + then be displayed in LyX, leading to a better overview. + The formula appears in the output as defined in the first box. +\begin_inset Newline newline +\end_inset + +The appearance of macros in formulas can furthermore be changed for single + macros by setting the cursor in the macro and using the menu +\family sans +View\SpecialChar \menuseparator +(Un)fold +\begin_inset space ~ +\end_inset + +Math +\begin_inset space ~ +\end_inset + +Macro +\family default +. +\end_layout + +\begin_layout Standard +To use a macro, the macro name is inserted as command to a formula, in our + case +\series bold + +\backslash +qG +\series default +. + Our macro looks in LyX like this: +\begin_inset Newline newline +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Graphics + filename clipart/macrouse.png + +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Newline newline +\end_inset + +Here is our macro example with the arguments +\begin_inset Formula $x$ +\end_inset + +, +\begin_inset Formula $\ln(x)$ +\end_inset + + and +\begin_inset Formula $B$ +\end_inset + +: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\qG x{\ln(x)}B +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +LyX offers in the menu +\family sans +Tools\SpecialChar \menuseparator +Preferences\SpecialChar \menuseparator +Editing\SpecialChar \menuseparator +Control +\family default + different styles to edit macros. + To find the style that suits you the most, choose a style and set the cursor + in a macro formula to see the difference. +\end_layout + +\begin_layout Standard +A math macro is transformed internally to a +\series bold + +\backslash +newcommand +\series default + command when exporting the document. + The created +\series bold + +\backslash +newcommand +\series default + command is not placed in the LaTeX-preamble, therefore macros can only + be used in formulas that are in the document below the macro definition + box. +\end_layout + +\begin_layout Standard +Math macros can also be directly created from a +\series bold + +\backslash +newcommand +\series default + command. + When writing for example the command +\series bold + +\begin_inset Newline newline +\end_inset + + +\backslash +newcommand{ +\backslash +larrow}[2]{ +\backslash +xleftarrow[#2]{#1}} +\begin_inset Newline newline +\end_inset + + +\series default +in LyX as normal text, highlighting it completely and using then the shortcut + +\family sans +Ctrl+M +\family default +, the command will be transformed to a math macro. + Using this method you need to be careful that the +\series bold + +\backslash +newcommand +\series default + command is typed correctly, otherwise you get a faulty macro leading to + LaTeX errors. +\end_layout + +\begin_layout Standard +Math macros currently have the problem that further formulas in macro definition +s are handled wrongly. + Therefore the example +\series bold + +\backslash +fb +\series default + from +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:The-Command-newcommand" + +\end_inset + + cannot be created as macro. +\end_layout + +\begin_layout Standard +When the cursor is in a macro definition box, you will see the macro toolbar + in LyX: +\end_layout + +\begin_layout Standard +\begin_inset VSpace defskip +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Graphics + filename clipart/MacroToolbar.png + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Macros ! Toolbar +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace defskip +\end_inset + + +\end_layout + +\begin_layout Standard +The macro toolbar contains from left to right the following buttons: +\end_layout + +\begin_layout Standard +\begin_inset VSpace defskip +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-remove-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Remove Last Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-add-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Append Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-make-optional" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Transform First Non-Optional to +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-make-nonoptional" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Transform Last Optional to +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Non-Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-remove-optional-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Remove Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-add-optional-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Insert Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-remove-greedy-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Remove Last Argument +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Spitting Out To The Right +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-append-greedy-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Append Argument +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Eating From The Right +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "icon" +arg "math-macro-add-greedy-optional-param" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Append Optional Argument +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Eating From The Right +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Section +Computer Algebra Systems +\end_layout + +\begin_layout Standard +LyX offers the exchange between mathematical expressions written in LyX's + math editor and external applications or user defined scripts. + Currently supported applications are +\family sans +Maple +\family default +, +\family sans +Mathematica +\family default +, +\family sans +Maxima +\family default + and +\family sans +Octave +\family default +. + Note that the set of supported mathematical constructs is limited only + to very simple cases. +\end_layout + +\begin_layout Subsection +Usage +\end_layout + +\begin_layout Standard +Write some expression in a formula, go to the +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Use Computer Algebra System +\family default + menu and choose the application you have installed on the computer. + After that the result of computation should show on the right side of the + expression together with the +\begin_inset Quotes eld +\end_inset + += +\begin_inset Quotes erd +\end_inset + + operator. +\end_layout + +\begin_layout Standard +Here are few simple examples (with results from +\family typewriter +Maxima +\family default +) to show what kind of computations can be performed: +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\det\left[\begin{array}{ccc} +1 & 6 & 7\\ +2 & 5 & 8\\ +3 & 4 & 17 +\end{array}\right]=-56$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$ +\end_inset + + +\end_layout + +\begin_layout Subsection +Keyboard shortcut +\end_layout + +\begin_layout Standard +Currently there is no keyboard shortcut for calling the algebra applications. + One can easily bind a shortcut to the +\family sans +math-extern +\family default + LyX function (see the +\family sans +\emph on +LyX Functions +\family default +\emph default + manual). + One could e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +bind the +\family sans +Return +\family default + key inside the math editor. + To bind it to +\family typewriter +Maxima +\family default + one would use this shortcut definition command: +\end_layout + +\begin_layout Standard + +\series bold +command-alternatives paragraph-break;math-extern maxima +\end_layout + +\begin_layout Section +Miscellaneous +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Miscellaneous +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Negative Numbers +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Numbers ! negative +\end_layout + +\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 Plain Layout +normal text: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +x = -2 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +formula: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $x=-2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +solution: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Index idx +status collapsed + +\begin_layout Plain Layout +Comma +\end_layout + +\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 +\begin_inset Info +type "shortcut" +arg "math-mode" +\end_inset + +). +\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 Plain Layout + +\series bold +icomma +\series default + is part of the LaTeX-package +\series bold +was +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! was +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! icomma +\end_layout + +\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 CommandInset label +LatexCommand label +name "sub:Physical-Vectors" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Vectors ! physical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Predefined vectors are offered by the LaTeX-package +\series bold +braket +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! braket +\end_layout + +\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 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifbraket +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +braket +\series default + is installed. +\end_layout + +\end_inset + + +\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 Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bra{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Bra{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Ket{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Ket{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Braket{ +\backslash +psi| +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +braket +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +braket +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\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 CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Self-defined Fractions +\begin_inset CommandInset label +LatexCommand label +name "sub:Self-defined-Fractions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fractions ! self-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To define custom commands for fractions, the command +\series bold + +\backslash +genfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! G ! +\backslash +genfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\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} +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +genfrac +\end_layout + +\end_inset + +{numerator}{denominator} +\end_layout + +\begin_layout Standard +The style is a number in the range of 0 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +3. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Number +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Style (Size) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +display style formula +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +inline formula +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +small +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +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 +\begin_inset space \thinspace{} +\end_inset + +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 CommandInset ref +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 Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! canceled +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +There are four ways to cancel formulas or parts of formulas: +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifcancel +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +cancel +\series default + is installed. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +The space 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 Plain Layout + +\backslash +cancel +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bcancel +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +xcancel +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cancelto +\begin_inset space \textvisiblespace{} +\end_inset + + +\backslash +int +\begin_inset space \textvisiblespace{} +\end_inset + +A=B +\begin_inset Formula $\to$ +\end_inset + +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\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 Standard +To change the size of +\series bold + +\backslash +cancelto +\series default +'s +\begin_inset Quotes eld +\end_inset + +subscript +\begin_inset Quotes erd +\end_inset + + value one can add the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +PassOptionsToPackage{option}{cancel} +\end_layout + +\begin_layout Standard +where +\series bold +option +\series default + is either +\series bold +samesize +\series default + which leads to the same size as for the canceled value, or +\series bold +Smaller +\series default + which makes is it a bit smaller than normal. +\end_layout + +\begin_layout Standard +To color the cancellation bar one adds this command as TeX code: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +CancelColor}{ +\backslash +color{red}} +\end_layout + +\begin_layout Standard + +\series bold +red +\series default + can be replaced by a color of your choice. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +CancelColor}{ +\backslash +color{red}} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\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 Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +CancelColor}{ +\backslash +color{black}} +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +reset the color +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For further customizations, see the documentation of the package +\series bold +cancel +\series default +, +\begin_inset CommandInset citation +LatexCommand cite +key "cancel" + +\end_inset + +. +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! cancel +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +cancel +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +cancel +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Formulas in Section Headings +\begin_inset CommandInset label +LatexCommand label +name "sub:Formulas-in-Section" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! in section headings +\end_layout + +\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 Plain Layout +When +\series bold +hyperref +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! hyperref +\end_layout + +\end_inset + + support is enabled in the document settings dialog under +\family sans +PDF +\begin_inset space ~ +\end_inset + +Properties +\family default +, PDF-bookmarks are 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 +\begin_inset space ~ +\end_inset + +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 Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +texorpdfstring +\end_layout + +\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 Plain Layout + + +\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 Argument 1 +status collapsed + +\begin_layout Plain Layout +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 Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Formula $\sqrt{-1}=\mathrm{i}$ +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 +\series default + environment +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Bold-Formulas" + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Formulas in multi-column Text +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! in multi-column text +\end_layout + +\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 Plain Layout + +\series bold +multicol +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! multicol +\end_layout + +\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 Plain Layout +Note that in this case the setting +\family sans +Two-column +\begin_inset space ~ +\end_inset + +document +\family default + in the menu +\family sans +Document\SpecialChar \menuseparator +Settings +\family default + under +\family sans +Text +\begin_inset space ~ +\end_inset + +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 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +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 +\begin_inset space \thinspace{} +\end_inset + +mm vertical space is inserted before the formula. + When the formula style +\series bold +Indented +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + is used, -9 +\begin_inset space \thinspace{} +\end_inset + +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 + +\lang german +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 Plain Layout + + +\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 +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\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 + + +\begin_inset space \thinspace{} +\end_inset + +-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 + +\lang german +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +end{multicols} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Formulas with Description of Variables +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! with description of variables +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To describe variables within a formula, like in formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:within" + +\end_inset + +, a 2 +\series bold +× +\series default + +\begin_inset Formula $n$ +\end_inset + + +\begin_inset space ~ +\end_inset + +matrix is used with left aligned columns for the +\begin_inset Formula $n$ +\end_inset + + used variables. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +matrices see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Matrices" + +\end_inset + + +\end_layout + +\end_inset + + To set the description in a smaller size, before the matrix e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +the command +\series bold + +\backslash +footnotesize +\series default + is inserted. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +font sizes see +\begin_inset CommandInset ref +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 Plain Layout +formula styles see +\begin_inset CommandInset ref +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 Plain Layout + +\series bold + +\backslash +hfill +\series default + only works in formulas with the style +\series bold +Indented +\series default +, see +\begin_inset CommandInset ref +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 CommandInset ref +LatexCommand ref +reference "sub:Flalign-Environment" + +\end_inset + + is used to indent formulas. + Formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:within" + +\end_inset + + consists of five columns where 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 CommandInset label +LatexCommand label +name "sub:Upright-small-Greek" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! upright +\end_layout + +\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 Plain Layout + +\series bold +upgreek +\series default + is part of the LaTeX-package +\series bold +was +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! was +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! upgreek +\end_layout + +\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 Plain Layout + + +\backslash +ifupgreek +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +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 letter 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 Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +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 LaTeX-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 Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Text Characters in Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! in formulas +\end_layout + +\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 Plain Layout +see +\begin_inset CommandInset ref +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. + For example the encoding +\series bold +latin9 +\series default + is defined in the file +\series bold +latin9.def +\series default + which is in the installation folder of LaTeX. + Encodings should only be changed via the LaTeX-preamble and not in the + definition files. + Otherwise 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 be directly inserted + into 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 Subsection +LaTeX-comments in formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +LaTeX-comments +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +In text you can insert a comment that will only be visible in the LaTeX + source code of your file with the menu +\family sans +Insert\SpecialChar \menuseparator +Note\SpecialChar \menuseparator +Comment +\family default +. + This is not possible in a formula but you can insert LaTeX-comments with + the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +% +\end_layout + +\begin_layout Standard +This creates a box in which you can write your comment. + Due to a bug in LyX +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #9002" +target "http://www.lyx.org/trac/ticket/9002" + +\end_inset + + +\end_layout + +\end_inset + + you cannot write normal text inside the comment, even when you use mathematical + text, you will see its LaTeX-commands in the LaTeX-output. +\begin_inset Newline newline +\end_inset + +This a formula with a LaTeX-comment: +\begin_inset Formula +\[ +A=B%\text{This is the comment} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +\start_of_appendix +Typographic Advice +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Typographic advice +\end_layout + +\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 Plain Layout +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 CommandInset citation +LatexCommand cite +key "Duden" + +\end_inset + + that lists some of the ISO rules. + More rules are listed in +\begin_inset CommandInset citation +LatexCommand cite +key "Checklist" + +\end_inset + +. +\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 Plain Layout +done with font styles, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Styles" + +\end_inset + + +\end_layout + +\end_inset + +, no matter if they appear in italic text: 30 +\begin_inset space \thinspace{} +\end_inset + +km/h +\begin_inset Newline newline +\end_inset + +Between the value and the unit is the smallest space, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Predefined-Space" + +\end_inset + +. +\begin_inset Newline newline +\end_inset + +This convention is automatically fulfilled when the command +\series bold + +\backslash +unittwo +\series default + is used. + When it is entered to a formula, two boxes appear. + In the first one the value is inserted, in the second one the unit, and + one gets as above: +\begin_inset Formula $\unit[30]{km/h}$ +\end_inset + + +\begin_inset space \thinspace{} +\end_inset + +. + Note that +\series bold + +\backslash +unittwo +\series default + is not a real LaTeX command but the command +\series bold + +\backslash +unit[value]{unit} +\series default +, therefore you cannot use it in TeX code. +\end_layout + +\begin_layout Itemize +Percent and perthousand signs are set like physical units: +\begin_inset Newline newline +\end_inset + +1.2 +\begin_inset space \thinspace{} +\end_inset + +‰ 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 +\begin_inset space \thinspace{} +\end_inset + +°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 +\begin_inset space \thinspace{} +\end_inset + +473 +\begin_inset space \thinspace{} +\end_inset + +588 +\end_layout + +\begin_layout Itemize +For dimensions like 120×90×40 +\begin_inset space \thinspace{} +\end_inset + +cm the multiplication sign +\begin_inset Quotes eld +\end_inset + +× +\begin_inset Quotes erd +\end_inset + + is used. + It is available either via the command +\series bold + +\backslash +times +\series default + or via the menu +\family sans +Insert\SpecialChar \menuseparator +Special Character\SpecialChar \menuseparator +Symbols +\family default +. +\end_layout + +\begin_layout Itemize +Functions with names consisting of several letters are set upright to avoid + confusions, see +\begin_inset CommandInset ref +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 + + +\begin_inset Newline newline +\end_inset + +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 Itemize +The character that denotes a +\noun on +Fourier +\noun default + transformation is inserted either by the command +\series bold + +\backslash +mathscr +\begin_inset space \textvisiblespace{} +\end_inset + +F +\series default + or via the menu +\family sans +Insert\SpecialChar \menuseparator +Special Character\SpecialChar \menuseparator +Symbols\SpecialChar \menuseparator +Letterlike +\begin_inset space ~ +\end_inset + +Symbols +\family default +: +\begin_inset Formula $\mathscr{F}$ +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Synonyms +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Synonyms +\end_layout + +\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 + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +equivalent to +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ast +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-1.2mm}{ +\end_layout + +\end_inset + +* +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +choose +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +binom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +geq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +{ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +[ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gets +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +le +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vee +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +neq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +slash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +/ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +| +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +equivalent to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +backslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\backslash + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dashrightarrow +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +land +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wedge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +} +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +] +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lnot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +neg +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ne +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +owns +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ni +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +square +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Box +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +| +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +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 CommandInset bibitem +LatexCommand bibitem +key "Mathmode" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Description" +target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf" + +\end_inset + + of LaTeX's math abilities +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "AMS" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Description" +target "http://mirrors.ctan.org/macros/latex/required/amslatex/math/amsldoc.pdf" + +\end_inset + + of +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-LaTeX +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Symbols" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "List" +target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf" + +\end_inset + + of all symbols available with LaTeX-packages +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "cancel" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Documentation" +target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf" + +\end_inset + + of the LaTeX-package +\series bold +cancel +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! cancel +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "hyperref" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Documentation" +target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf" + +\end_inset + + of the LaTeX-package +\series bold +hyperref +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! hyperref +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "mhchem" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Documentation" +target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf" + +\end_inset + + of the LaTeX-package +\series bold +mhchem +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mhchem +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Duden" + +\end_inset + + +\emph on +Duden Band 1 +\emph default +. + 22. + Auflage, Duden 2001 +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Checklist" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Check list" +target "http://physics.nist.gov/Document/checklist.pdf" + +\end_inset + + for reviewing manuscripts +\end_layout + +\begin_layout Standard +\begin_inset CommandInset index_print +LatexCommand printindex +type "idx" + +\end_inset + + +\end_layout + +\end_body +\end_document