diff options
Diffstat (limited to 'Master/texmf-doc/doc/english/mathmode/Mathmode.tex')
| -rw-r--r-- | Master/texmf-doc/doc/english/mathmode/Mathmode.tex | 8271 |
1 files changed, 0 insertions, 8271 deletions
diff --git a/Master/texmf-doc/doc/english/mathmode/Mathmode.tex b/Master/texmf-doc/doc/english/mathmode/Mathmode.tex deleted file mode 100644 index e0c5c314cec..00000000000 --- a/Master/texmf-doc/doc/english/mathmode/Mathmode.tex +++ /dev/null @@ -1,8271 +0,0 @@ -%% -%% This is file `Mathmode.tex', -%% -%% IMPORTANT NOTICE: -%% -%% Herbert Voss <hvoss at tug dot org> -%% 2009-04-08 -%% -%% This program can be redistributed and/or modified under the terms -%% of the LaTeX Project Public License Distributed from CTAN archives -%% in directory macros/latex/base/lppl.txt. -%% -%% DESCRIPTION: -%% `Mathmode' is a document how the math mode works inside LaTeX -%% - \ifpdf\title{Math mode - v.\MathmodeVersion}\else - \title{\logo Math mode - v.\MathmodeVersion}\fi%\fi -% -\author{Herbert Vo\ss\footnote{\sloppy Thanks for the feedback to: - Hendri Adriaens; Juan Mari Alberdi; - Luciano Battaia; - Heiko Bauke; Neal Becker; Andrea Blomenhofer; Alexander Boronka; Walter Brown; - Alexander Buchner; - Christian Faulhammer; Jos\'e{} Luis G\'omez Dans; - Zongbao Fang; - Sabine Glaser; Sven Gleich; - Azzam Hassam; Gernot Hassenpflug; Henning Heinze; Martin Hensel; Mathias Hoffmann; - Jon Kirwan; - Morten H\o{}gholm; M. Kalidoss; Dan Lasley; - Angus Leeming; Vladimir Lomov; Tim Love; Ladislav Lukas; Dan Luecking; - Hendrik Maryns; Heinz Mezera; - David Neuway; - Luis Trucco Passadore; Joachim Punter; - Carl Riehm; Will Robertson; Christoph Rumsm\"uller; - Jos\'e{} Carlos Santos; Arnaud Schmittbuhl; - Rainer Sch\"opf; Jens Schwaiger; Uwe Siart; Martin Sievers; Heiko Stamer; - G. Stengert; Uwe St\"ohr; - Carsten Thiel; - Juan Luis Varona; - David Weenink; - Philipp Wook; - Michael Zedler; - Zou Yuan-Chuan; - and last but not least a special thanks to Monika Hattenbach for her - excellent job of proofreading. -}} -\date{\today} - -\maketitle - -\begin{abstract} -It is often said that \TeX{} was designed for mathematical or technical purposes. -This may be true when we remember the reasons why Donald Knuth created \TeX{}. But nowadays -there are many examples in which \TeX\ is - used for publications with no mathematical or technical background content. However, -writing publications with such -material is one of the important advantages of \TeX{}. Because it -seems impossible to -know all existing macros and options of \AllTeX{} and the several additional packages, -especially of \AmSmath. This is the reason why I have attempted to gather -all the relevant -facts in this paper. An advanced german version of this paper is available as a book~\cite{voss09}, -for members of DANTE, the german \TeX\ users group, for a special price! - -\vspace{3cm} -\noindent Please report typos or any other comments to this documentation to -\href{mailto:voss@perce.de}{voss@perce.de}. -%\noindent This document was written with the \LaTeX{} editor \verb+Kile 1.8+ -%\verb+(Qt 3.3+ \verb+KDE 3.4)+ -%\href{http://sourceforge.net/projects/kile/}{http://sourceforge.net/projects/kile/} -%and the PDF output was built with the Linux version of \texttt{V\TeX/Free}, Version 8.46 -%(\href{http://www.micropress-inc.com/linux/}{http://www.micropress-inc.com/linux/}) - -This file can be redistributed and/or modified under the terms -of the \LaTeX\ Project Public License Distributed from \verb+CTAN+ archives -in directory \url{CTAN://macros/latex/base/lppl.txt}. - -\end{abstract} - - - -\clearpage -%\fancypagestyle{plain} -\tableofcontents{} - -\clearpage -\pagestyle{fancy} -\part{Standard \protect\LaTeX{} math mode} - -\section{Introduction} -The following sections describe all the math commands which are available -without any additional package. Most of them also work with special -packages and some of them are redefined. -At first some important facts for typesetting math expressions. - -\section{The Inlinemode}\label{sec:The-Inlinemode} -As the name says there are always math expressions which are in a standard -textline, like this one: $f(x)=\int_{a}^{b}\frac{\sin x}{x}\,\mathrm{d}x$. There -are no limitations for the height of the math expressions, so that -the layout may be very lousy if you insert a big matrix in an inline mode -like this: -$\underline{A}=\left[\begin{array}{ccc} -a & b & c\\ -d & e & f\\ -g & h & i\end{array}\right]$. In this case it is better to use the \verb|\smallmatrix| environment -$\underline{A}=\left[\begin{smallmatrix}% -a & b & c\cr -d & e & f\cr -g & h & i\end{smallmatrix}\right]$ from the \AmSmath{} package (see section \vref{sec:ams-matrix}) or the -displaymath mode\index{Display math mode} (section~\vref{display}). - -This inline mode is possible with three different commands: - -\bigskip -\begin{minipage}{0.35\fullwidth} -\(\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)\)\\[10pt] -$\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)$\\[10pt] -\begin{math} - \sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1) -\end{math} -\end{minipage}\hfill -\begin{minipage}{0.62\fullwidth} -\begin{lstlisting} -\(\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)\)\\[10pt] -$\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)$\\[10pt] -\begin{math} - \sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1) -\end{math} -\end{lstlisting} -\end{minipage} - -\begin{enumerate} -\item \CMD{( ... }\CMD{)} \mPar{\CMD{(}...\CMD{)}}, the problem is that \verb+\(+ is -not a robust macro (see section~\vref{subsec:mathInTitles}). -\item \verb+$ ... $+ \mPar{\$...\$} -\item \CMD{begin\{math\}} ... \CMD{end\{math\}}, also not robust% -\mPar{\CMD{begin\{math\}}\\...\\\CMD{end\{math\}}} -\end{enumerate} - -\index{*@\texttt{\textbackslash\char040}}\index{*@\texttt{\textbackslash\char041}} -In general \verb+$...$+ is the best choice, but this does not work in environments like \verb+verbatim+ -or \verb+alltt+. In this case \verb+\(...\)+ works.\index{$@\texttt{\$}} - - -\subsection{Limits}\label{sub:Limits-Inline} - -In the inline mode the \Index{limits} are by default only in -super\index{Superscript} or subscript mode\index{Subscript} and -the fractions\index{Fraction} are always in the \Index{scriptstyle}% -\footnote{See section \vref{sec:Styles}.}\index{scriptstyle} -font size. For -example: $\int_{1}^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1$, which is not too -big for the textline. You % -\mPar{\CMD{limits}}can change this with the command \CIndex{limits}, -which must follow a math operator\footnote{To define a new operator see -page~\pageref{OperatorNames}}\index{Math operator} like % -\mPar{\CMD{int}\\\CMD{lim}\\\CMD{prod}\\\CMD{sum}} - an integral (\CIndex{int}), a sum (\CIndex{sum}), -a product (\CIndex{prod}) or a limes -(\CIndex{lim}). But this $\int\limits_{1}^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1$ -(\lstinline|$\int\limits_{1}^...|) %$ -does not look very nice in a text line when it appears between two lines, -especially when there are multiline limits.\footnote{For more -information about limits see section~\vref{sub:Multiple-Limits} or section~\vref{sec:limit-AMS}.} - - -\subsection{Fraction command}\label{sub:fraction command} - -For inlined formulas the fractions\index{Fraction} are by default -in the scriptstyle\index{scriptstyle@\textbackslash scriptstyle} (see tabular~\vref{cap:Mathstyles}), -which is good for typesetting $y=\frac{a}{b+1}$, because the -linespacing % -\mPar{\CMD{frac}}is nearly the same, but not optimal, when the formula shows some important -facts. There are two solutions to get a better reading: - -\begin{enumerate} -\item choose the display mode instead of the inline mode, which is the better -one; -\item set the fontstyle to \CIndex{displaystyle}, which makes -the fraction $y={\displaystyle\frac{a}{b+1}}$ more readable but -the linespacing increases which is always a bad solution and should -only be used when the first solution makes no sense.\footnote{For an abbreviation see -section~\vref{sec:ams-fraction}, there is a special \CIndex{dfrac} macro.} - -\bigskip -\begin{minipage}{0.25\fullwidth} -$y=\frac{a}{b+1}={\displaystyle\frac{a}{b+1}}$ -\end{minipage}\hfill -\begin{minipage}{0.72\fullwidth} -\begin{lstlisting} -$y=\frac{a}{b+1}={\displaystyle\frac{a}{b+1}}$ -\end{lstlisting} -\end{minipage} -\end{enumerate} - - -\subsection[Math in Chapter/Section Titles]{\label{inline-chapter}Math in \CIndex{part}, -\CIndex{chapter}, \CIndex{section}, -... titles like $f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}\label{subsec:mathInTitles} - -All commands which appear in positions like contents, index, header, -... must be robust\footnote{% -\texttt{robust} means that the macro is not expanded before it is moved -into for example the tableofcontents file (\texttt{*.toc}). No robustness is -often a problem, when a macro is part of another macro.} -which is the case for \verb+$...$+ but not for \verb+\(...\)+. -The latest package \PIndex{fixltx2e} defines an macro for declaring -existing commands to be robust. The package itself does this already for: - -\begin{lstlisting} -\MakeRobust\( -\MakeRobust\) -\MakeRobust\[ -\MakeRobust\] -\MakeRobust\makebox -\MakeRobust\savebox -\MakeRobust\framebox -\MakeRobust\parbox -\MakeRobust\rule -\MakeRobust\raisebox -\end{lstlisting} - - -If you do not have any contents, index, a.s.o. -you can write the mathstuff in \CIndex{chapter}, \CIndex{section}, -a.s.o without any restriction. Otherwise use \verb+\protect\(+ and \verb+\protect\)+ or the -\verb+$...$+ version.\index{$@\texttt{\$}} - -The whole math expression appears in the default font shape and not -in bold like the other text. Section~\vref{sec:titleItem} describes how the math -expressions can be printed also in bold. - -\mPar{\CMD{texorpdfstring}}% -There are problems with the \PIndex{hyperref} package when there is no -text part in a title. It is possible with the command \CIndex{texorpdfstring} -to tell \verb+hyperref+ to use different -commands, one for the title and another one for the bookmarks: - -\begin{verbatim} -\texorpdfstring{<TeX part>}{<hyperref part>} -\end{verbatim} - - -\begin{minipage}{\fullwidth} -\begin{lstlisting} -\texorpdfstring{$\int f(x)\,\mathrm{d}x$}{Integral function} -\end{lstlisting} -\end{minipage} - - - -\subsection{Equation numbering} - -It is obvious that the numbering of inline mathstuff makes no sense! - -\subsection{Framed math} -With the \CIndex{fbox} macro everything of inline math can be framed\index{Framed inline -math}\index{boxed inline math}, like the following one: - -\bigskip -\begin{minipage}{0.325\fullwidth} -\fbox{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} -\end{minipage}\hfill -\begin{minipage}{0.67\fullwidth} -\begin{lstlisting} -\fbox{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} -\end{lstlisting} -\end{minipage} - -%$ - -Parameters are the width of \LIndex{fboxsep} and \LIndex{fboxrule}, the predefined values -from the file \verb|latex.ltx| are: - -\bigskip -\begin{minipage}{\fullwidth} -\begin{lstlisting} -\fboxsep = 3pt -\fboxrule = .4pt -\end{lstlisting} -\end{minipage} - -The same is possible with the \CIndex{colorbox} -\colorbox{yellow}{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} -from the color package. - -\bigskip -\begin{minipage}{\fullwidth} -\begin{lstlisting} -\colorbox{yellow}{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$} -\end{lstlisting} -\end{minipage} - -%$ - -\subsection{Linebreak}\label{subsec:linebreak} - -\LaTeX{} can break an inline formula only when a relation symbol ($=, <, >, \ldots$) or a -binary operation symbol ($+,-, \ldots$) exists and at least one of these symbols appears at -the outer level of a formula. -Thus \verb|$a+b+c$| can be broken across lines, but \verb|${a+b+c}$| not.\index{$@\texttt{\$}} - -\begin{itemize} -\item The default: \hspace{1cm} -$f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\ldots - +a_ix^i +a_2x^2 +a_1x^1 +a_0$ -\item The same inside a group \{...\}: -${f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\ldots - +a_ix^i +a_2x^2 +a_1x^1 +a_0}$ - -\item Without any symbol: \hspace{4cm} -$f(x)=a_n\left(a_{n-1}\left(a_{n-2}\left(\ldots\right)\ldots\right)\ldots\right)$ -\end{itemize} - -If it is not possible to have any mathsymbol, then split the inline formula in two -or more pieces (\verb|$...$ $...$|). If you do not want a linebreak for the whole -document, you can set in the preamble: -\begin{verbatim} -\relpenalty=9999 -\binoppenalty=9999 -\end{verbatim} - -\noindent -which is the extreme case of grudgingly allowing breaks in extreme cases, or -% -\begin{verbatim} -\relpenalty=10000 -\binoppenalty=10000 -\end{verbatim} -% -for absolutely no breaks. - -\subsection{Whitespace}\label{subsec:whitespace} -\LaTeX{} defines the length \LIndex{mathsurround} with the default value of -\verb|0pt|. This length is added before and after an inlined math expression -(see table~\vref{tab:whitespace}). - -\begin{table}[htb] -\hspace*{-0.1\linewidth}% -\begin{tabular}{@{}cc@{}} -foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar & -\begin{minipage}{0.7\linewidth} -\begin{lstlisting} -foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar -\end{lstlisting} -\end{minipage}\tabularnewline -% -foo \rule{20pt}{\ht\strutbox}\fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $}\rule{20pt}{\ht\strutbox} bar & -\begin{minipage}{0.7\linewidth} -\begin{lstlisting} -foo \rule{20pt}{\ht\strutbox}\fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $}\rule{20pt}{\ht\strutbox} bar -\end{lstlisting} -\end{minipage}\tabularnewline -\setlength{\mathsurround}{20pt}foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar & -\begin{minipage}{0.7\linewidth} -\begin{lstlisting} -\setlength{\mathsurround}{20pt} -foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar -\end{lstlisting} -\end{minipage} -\end{tabular} -% -\caption{Meaning of \CMD{mathsurround}}\label{tab:whitespace} -\end{table} - -%$ - -\subsection{\AmSmath for the inline mode} - -None of the \AmSmath-functions are available in inline mode. - -\section{Displaymath mode}\label{display} -This means, that every formula gets its own paragraph (line). There are -some differences in the layout to the one from the title -of \ref{inline-chapter}. - - -\subsection{\texttt{equation} environment} - -For example: - -\bigskip\noindent -\begin{tabular}{cc} -\begin{minipage}{0.35\linewidth} -\begin{equation} - f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) -\end{equation} -\end{minipage} & -\begin{minipage}{0.63\linewidth} -\begin{lstlisting} -\begin{equation} - f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) -\end{equation} -\end{lstlisting} -\end{minipage} -\end{tabular} - -\bigskip -The delimiters\index{Delimiter} -\CMD{begin\{equation\} ... }\CMD{end\{equation\}} are the only difference to the inline version. -There are some equivalent commands for the display-math mode: - -\begin{enumerate} -\mPar{\CMD{begin\{displaymath\}}\\ -\ldots\\ -\CMD{end\{displaymath\}}}% -\item \CMD{begin\{displaymath\}}\ldots\CMD{end\{displaymath\}}, same as -\CMD{[} \ldots \CMD{]} -% -\item \CMD{[\ldots}\CMD{]}. (see above) the short form of a displayed formula, no number% -\mPar{\texttt{\textbackslash[\ldots\textbackslash{}]}} -\[ -f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) -\] -% -displayed, no number. Same as 1. -% -\item \CMD{begin\{equation\}\ldots}\CMD{end\{equation\}}% -\mPar{\CMD{begin\{equation\}}\\ -\ldots\\ -\CMD{end\{equation\}}}% -% -\begin{equation} -f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right) -\end{equation} -% -displayed, a sequential equation number, which may be reset when -starting a new chapter or section. - - -\begin{enumerate} -\item There is only \textbf{one} equation number for the whole environment. -\item \mPar{\CMD{nonumber}}There exists no star-version of the equation environment -because \CIndex{[}\ldots\CIndex{]} is the equivalent. With the tag -\CIndex{nonumber} it is possible to suppress the equation number: - -\begin{minipage}{0.5\linewidth} -\begin{equation} - f(x)= [...] \nonumber -\end{equation} -\end{minipage}% -\begin{minipage}{0.6\linewidth} -\begin{lstlisting} -\begin{equation} - f(x)= [...] \nonumber -\end{equation} -\end{lstlisting} -\end{minipage} -% -\end{enumerate} -\end{enumerate} - - -\subsection{\texttt{eqnarray} environment}\label{display:eqnarray} - -This is by default an array with three columns and as many rows as -you like. \mPar{\CMD{begin\{eqnarray\}}\\ -...\\ -\CMD{end\{eqnarray\}}} It is nearly the same as an array with a \verb|rcl| column definition. - -It is \textbf{not possible} to change the internal behaviour of the \verb|eqnarray| environment without -rewriting the environment. -It is always an impli\-cit array with \textbf{three} columns and the horizontal -alignment \verb|right-center-left (rcl)| and small \textbf{symbol} sizes for the -middle column. All this can not be changed by the user without rewriting -the whole environment in \verb|latex.ltx|. - -\bigskip\noindent -\begin{tabular}{cc} -\begin{minipage}{0.35\linewidth} -\begin{eqnarray*} -\mathrm{left} & \mathrm{middle} & \mathrm{right}\\ -\frac{1}{\sqrt{n}}= & \frac{\sqrt{n}}{n}= & \frac{n}{n\sqrt{n}} -\end{eqnarray*} -\end{minipage} & -\begin{minipage}{0.63\linewidth} -\begin{lstlisting} -\begin{eqnarray*} -\mathrm{left} & \mathrm{middle} & \mathrm{right}\\ -\frac{1}{\sqrt{n}}= & \frac{\sqrt{n}}{n}= & \frac{n}{n\sqrt{n}} -\end{eqnarray*} -\end{lstlisting} -\end{minipage} -\end{tabular} - -\bigskip -The \UIndex{eqnarray} should not be used as an array. As seen in the above -example the typesetting is wrong for the middle column. The numbering of eqnarray -environments is always for every row, means, -that four lines get four different equation numbers (for the labels see -section~\vref{sec:Labels}): - -\bigskip -\begin{minipage}{0.5\columnwidth} -\begin{eqnarray} -y & = & d\label{eq:2}\\ -y & = & cx+d\\ -y & = & bx^{2}+cx+d\\ -y & = & ax^{3}+bx^{2}+cx+d\label{eq:5} -\end{eqnarray} -\end{minipage}\hfill -\begin{minipage}{0.43\columnwidth} -\begin{lstlisting} -\begin{eqnarray} -y & = & d\label{eq:2}\\ -y & = & cx+d\\ -y & = & bx^{2}+cx+d\\ -y & = & ax^{3}+bx^{2}+cx+d\label{eq:5} -\end{eqnarray} -\end{lstlisting} -\end{minipage} - - -\medskip -Toggling numbering off/on for \textbf{all} rows is possible -with the starred version of eqnarray. - -\medskip -\begin{minipage}{0.45\columnwidth} -\begin{eqnarray*} -y & = & d\label{eq:3}\\ -y & = & cx+d\\ -y & = & bx^{2}+cx+d\\ -y & = & ax^{3}+bx^{2}+cx+d\label{eq:4} -\end{eqnarray*} -\end{minipage} -\begin{minipage}{0.53\columnwidth} -\begin{lstlisting} -\begin{eqnarray*} -y & = & d\label{eq:3}\\ -y & = & cx+d\\ -y & = & bx^{2}+cx+d\\ -y & = & ax^{3}+bx^{2}+cx+d\label{eq:4} -\end{eqnarray*} -\end{lstlisting} -\end{minipage} - -\medskip -Toggling off/on for \textbf{single} rows is possible with the above -mentioned \CIndex{nonumber} tag at the end of a row -(before the newline command). For example: - -\medskip -\begin{minipage}{0.45\columnwidth} -\begin{eqnarray} - y & = & d\nonumber \\ - y & = & cx+d\nonumber \\ - y & = & bx^{2}+cx+d\nonumber \\ - y & = & ax^{3}+bx^{2}+cx+d -\end{eqnarray} -\end{minipage} -\begin{minipage}{0.53\columnwidth} -\begin{lstlisting} -\begin{eqnarray} - y & = & d\nonumber \\ - y & = & cx+d\nonumber \\ - y & = & bx^{2}+cx+d\nonumber \\ - y & = & ax^{3}+bx^{2}+cx+d -\end{eqnarray} -\end{lstlisting} -\end{minipage} - - -\subsubsection{Short commands}\label{subsec:shortcommand} -It is possible to define short commands for the \UIndex{eqnarray} -% -\begin{lstlisting} -\makeatletter -\newcommand{\be}{% - \begingroup -% \setlength{\arraycolsep}{2pt} - \eqnarray% - \@ifstar{\nonumber}{}% -} -\newcommand{\ee}{\endeqnarray\endgroup} -\makeatother -\end{lstlisting} - -\makeatletter -\newcommand{\be}{% - \begingroup -% \setlength{\arraycolsep}{2pt} - \eqnarray% - \@ifstar{\nonumber}{}% -} -\newcommand{\ee}{\endeqnarray\endgroup} -\makeatother - -Now you can write the whole equation as - - -\begin{LTXexample}[width=0.5\columnwidth,wide] -\be - f(x) &=& \int\frac{\sin x}{x}\,\mathrm{d}x -\ee -\end{LTXexample} - -\medskip -\noindent or, if you do not want to have a numbered equation as - -\begin{LTXexample}[width=0.5\columnwidth,wide] -\be* - f(x) &=& \int\frac{\sin x}{x}\,\mathrm{d}x -\ee -\end{LTXexample} - - -\subsection{Equation numbering}\label{sub:Equationnumbering} - -For all equations which can have one or % -\mPar{\CMD{nonumber}}more equation numbers (for every line/row) the numbering -for the whole equation can be disabled with switching from the unstarred to the star -version. This is still for the whole formula and doesn't work for single rows. -In this case use the \CIndex{nonumber} tag. - -\begin{itemize} -\item This doc is written with the article-class, which counts the equations -continuously over all parts/sections. You can change this behaviour -in different ways (see the following subsections). -\item In standard \LaTeX{} it is a problem with too long equations and the -equation number, which may be printed with the equation one upon the other. In this case -use the \AmSmath package, where the number is set above or below -of a too long equation (see equation~\vref{eq:braces}). -\item For counting subequations see section~\vref{ams:subeqn}. -\end{itemize} - -\subsubsection{Changing the style} - -\mPar{\CMD{theequation}}% -With the beginning of Section \vref{sec:alignat environment} the -counting changes from ``\ref{eq:IntoSection}{}'' into the new style -``\ref{eq:newCounting}''. The command sequence is - -\begin{lstlisting} -\renewcommand\theequation{\thepart-\arabic{equation}} -\end{lstlisting} - -See section~\vref{sec:Equation-numbering} for the \AmSmath command. - - -\subsubsection{Resetting a counter style} - -Removing a given reset is possible with the \PIndex{remreset}.% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/supported/carlisle/remreset.sty}{CTAN://macros/latex/contrib/supported/carlisle/remreset.sty}} Write into the % -\mPar{\CMD{@removefromreset}} preamble - -\begin{lstlisting} -\makeatletter -\@removefromreset{equation}{section} -\makeatother -\end{lstlisting} -or anywhere in the text. - -Now the equation counter is no longer reset when a new section starts. -You can see this after section~\vref{split}. - - -\subsubsection{Equation numbers on the left side} - -Choose package \PIndex{leqno}% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/unpacked/leqno.sty}{CTAN://macros/latex/unpacked/leqno.sty}} -or have a look at your document class, if such an option exists. - -\subsubsection{Changing the equation number style} -The number style can be changed with a redefinition of - -\begin{verbatim} -\def\@eqnnum{{\normalfont \normalcolor (\theequation)}} -\end{verbatim} - -For example: if you want the numbers not in parentheses write - -\begin{lstlisting} -\makeatletter -\def\@eqnnum{{\normalfont \normalcolor \theequation}} -\makeatother -\end{lstlisting} - -For \AmSmath there is another macro, see section~\ref{sec:Equation-numbering} on -page~\pageref{sec:Equation-numbering}. - -\subsubsection{More than one equation counter} -You can have more than the default equation counter. With the following code you -can easily toggle between roman and arabic equation counting. -\makeatletter -%Roman counter -\newcounter{roem} -\renewcommand{\theroem}{\roman{roem}} - -% save the original counter -\newcommand{\c@org@eq}{} -\let\c@org@eq\c@equation -\newcommand{\org@theeq}{} -\let\org@theeq\theequation - -%\setroem sets roman counting -\newcommand{\setroem}{ - \let\c@equation\c@roem - \let\theequation\theroem} - -%\setarab the arabic counting -\newcommand{\setarab}{ - \let\c@equation\c@org@eq - \let\theequation\org@theeq} -\makeatother - -\begin{lstlisting} -%code by Heiko Oberdiek -\makeatletter -%Roman counter -\newcounter{roem} -\renewcommand{\theroem}{\roman{roem}} - -% save the original counter -\newcommand{\c@org@eq}{} -\let\c@org@eq\c@equation -\newcommand{\org@theeq}{} -\let\org@theeq\theequation - -%\setroem sets roman counting -\newcommand{\setroem}{ - \let\c@equation\c@roem - \let\theequation\theroem} - -%\setarab the arabic counting -\newcommand{\setarab}{ - \let\c@equation\c@org@eq - \let\theequation\org@theeq} -\makeatother -\end{lstlisting} - -The following examples show how it works: - -\noindent -\begin{minipage}{1.2\linewidth} -\begin{minipage}{0.38\linewidth} -\begin{align} -f(x) &= \int\sin x\,\mathrm{d}x\label{eq:arab1}\\ -g(x) &= \int\frac{1}{x}\,\mathrm{d}x -\end{align} -% -\setroem -% -\begin{align} -F(x) &=-\cos x\\ -G(x) &=\ln x\label{eq:rom1} -\end{align} -% -\setarab -% -\begin{align} -f^{\prime} (x) &= \sin x\\ -g^{\prime} (x) &= \frac{1}{x}\label{eq:arab2} -\end{align} -\end{minipage}\hfill -\begin{minipage}{0.58\linewidth} -\begin{lstlisting} -\begin{align} -f(x) &= \int\sin x\,\mathrm{d}x\label{eq:arab1}\\ -g(x) &= \int\frac{1}{x}\,\mathrm{d}x -\end{align} -% -\setroem -% -\begin{align} -F(x) &=-\cos x\\ -G(x) &=\ln x\label{eq:rom1} -\end{align} -% -\setarab -% -\begin{align} -f^{\prime} (x) &= \sin x\\ -g^{\prime} (x) &= \frac{1}{x}\label{eq:arab2} -\end{align} -\end{lstlisting} -\end{minipage} -\end{minipage} - -\medskip -There can be references to these equations in the usual way, like eq.\ref{eq:arab1}, -\ref{eq:arab2} and for the roman one eq.\ref{eq:rom1}. - - -\subsection{Labels}\label{sec:Labels} - -Every numbered equation can have a label\index{Label} to which a -reference\index{Reference} is possible. - -\begin{itemize} -\item There is one restriction for the label names, they cannot include -one of \LaTeX{}'s command characters.\footnote{\$ \_ \^{} \textbackslash{} \& \% \{ \}} -\item The label names are replaced by the equation number. -\end{itemize} -% -\mPar{\CMD{tag}}If you do not want a reference to the equation number but to a self -defined name then use the \AmS{}math command \CMD{tag{...}}, -which is described in section \vref{sec:Labels-and-Tags}\index{tag@\textbackslash tag}. - -\subsection{Frames}\label{sec:Frames} -Similiar to the inline mode, displayed equations can also be framed with -the \CIndex{fbox} command, like equation \ref{eq:frame0}. -The only difference is -the fact, that the equation must be packed into a parbox or minipage. It is -nearly the same for a colored box, where the \verb|\fbox{...}| has to be -replaced with \verb|\colorbox{yellow}{...}|. The package \verb|color.sty| must -be loaded and --important -- the \PIndex{calc} package to get a correct boxwidth. - -\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{% -\begin{equation}\label{eq:frame0} -f(x)=\int_1^{\infty}\dfrac{1}{x^2}\,\mathrm{d}x=1 -\end{equation}% -}} - -\medskip -\begin{lstlisting} -\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{% -\begin{equation}\label{eq:frame0} - f(x)=\int_1^{\infty}\dfrac{1}{x^2}\,\mathrm{d}x=1 -\end{equation}% -}} -\end{lstlisting} - - -If the equation number should not be part of the frame, then it is a bit -complicated. There is one tricky solution, which puts an unnumbered equation -just beside an empty numbered equation. The \verb|\hfill| is only useful for -placing the equation number right aligned, which is not the default. The -following four equations \ref{eq:frame2}-\ref{eq:frame5} are the same, -only the second one written with the \verb|\myMathBox| macro which has the -border and background color as optional arguments with the defaults -\verb|white| for background and \verb|black| for the frame. If there is only -one optional argument, then it is still the one for the frame color (\ref{eq:frame3}). - -\makeatletter -\def\myMathBox{\@ifnextchar[{\my@MBoxi}{\my@MBoxi[black]}} -\def\my@MBoxi[#1]{\@ifnextchar[{\my@MBoxii[#1]}{\my@MBoxii[#1][white]}} -\def\my@MBoxii[#1][#2]#3#4{% - \par\noindent% - \fcolorbox{#1}{#2}{% - \parbox{\linewidth-\labelwidth-2\fboxrule-2\fboxsep}{#3}% - }% - \parbox{\labelwidth}{% - \begin{eqnarray}\label{#4}\end{eqnarray}% - }% - \par% -} -\makeatother - -\begin{lstlisting} -\makeatletter -\def\myMathBox{\@ifnextchar[{\my@MBoxi}{\my@MBoxi[black]}} -\def\my@MBoxi[#1]{\@ifnextchar[{\my@MBoxii[#1]}{\my@MBoxii[#1][white]}} -\def\my@MBoxii[#1][#2]#3#4{% - \par\noindent% - \fcolorbox{#1}{#2}{% - \parbox{\linewidth-\labelwidth-2\fboxrule-2\fboxsep}{#3}% - }% - \parbox{\labelwidth}{% - \begin{eqnarray}\label{#4}\end{eqnarray}% - }% - \par% -} -\makeatother -\end{lstlisting} - -\begin{equation}\label{eq:frame2} - f(x)=x^2 +x -\end{equation} -\myMathBox[red]{\[f(x)=x^2 +x\]}{eq:frame3} -\myMathBox[red][yellow]{\[f(x)=x^2 +x\]}{eq:frame4} -\myMathBox{\[f(x)=x^2 +x\]}{eq:frame5} - -\medskip -\begin{lstlisting} -\begin{equation}\label{eq:frame2} - f(x)=x^2 +x -\end{equation} -\myMathBox[red]{\[f(x)=x^2 +x\]}{eq:frame3} -\myMathBox[red][yellow]{\[f(x)=x^2 +x\]}{eq:frame4} -\myMathBox{\[f(x)=x^2 +x\]}{eq:frame5} -\end{lstlisting} - -If you are using the \AmSmath package, then try the solutions from section -\vref{sec:ams-frames}. - -\section{\texttt{array} environment} -\mPar{\CMD{begin\{array\}}\\...\\\CMD{end\{array\}}} -This is simply the same as the \UIndex{eqnarray} only with the -possibility of variable rows \textbf{and} columns and the fact, that -the whole formula has only \textbf{one} equation number and that the -\verb|array| environment can only be part of another math environment, -like the \UIndex{equation} or the \UIndex{displaymath}. With \verb+@{}+ before the -first and after the last column the additional space \LIndex{arraycolsep} -is not used, which maybe important when using left aligned equations. - -\begin{equation} -\left.% -\begin{array}{@{}r@{\quad}ccrr@{}} - \textrm{a}) & y & = & c & (constant)\\ - \textrm{b}) & y & = & cx+d & (linear)\\ - \textrm{c}) & y & = & bx^{2}+cx+d & (square)\\ - \textrm{d}) & y & = & ax^{3}+bx^{2}+cx+d & (cubic) -\end{array}% -\right\} \textrm{Polynomes} -\end{equation} - - -\begin{lstlisting} -\begin{equation} -\left.% -\begin{array}{@{}r@{\quad}ccrr@{}} - \textrm{a}) & y & = & c & (constant)\\ - \textrm{b}) & y & = & cx+d & (linear)\\ - \textrm{c}) & y & = & bx^{2}+cx+d & (square)\\ - \textrm{d}) & y & = & ax^{3}+bx^{2}+cx+d & (cubic) -\end{array}% -\right\} \textrm{Polynomes} -\end{equation} -\end{lstlisting} - - -The horizontal alignment of the columns is the same as the one from the -\UIndex{tabular}. - -For arrays with delimiters see section~\vref{delarray}. - -\subsection{Cases structure} - -If you do not want to use the \AmSmath package then write your own -cases structure\index{cases@\textbackslash cases} with the \verb|array| environment: - -\begin{LTXexample}[pos=b] -\begin{equation} -x=\left\{ \begin{array}{cl} -0 & \textrm{if }A=\ldots\\ -1 & \textrm{if }B=\ldots\\ -x & \textrm{this runs with as much text as you like, but without an raggeright text.}\end{array}\right. -\end{equation} -\end{LTXexample} - - -It is obvious, that we need a \CMD{parbox} if the text is longer than the possible linewidth. - -\begin{LTXexample}[pos=b] -\begin{equation} -x = \left\{% - \begin{array}{l>{\raggedright}p{.5\textwidth}}% - 0 & if $A=\ldots$\tabularnewline - 1 & if $B=\ldots$\tabularnewline - x & \parbox{0.5\columnwidth}{this runs with as much text as you like, % - because an automatic linebreak is given with % - a raggedright text. Without this % - \raggedright command, you'll get a formatted % - text like the following one ... but with a parbox ... it works} - \end{array}% - \right. % -\end{equation} -\end{LTXexample} - - - -\subsection{\texttt{arraycolsep}}\label{sec:arraycolsep} -\mPar{\CMD{arraycolsep}}% -All the foregoing math environments use the array to typeset the math -expression. The predefined separation between two columns is the length -\LIndex{arraycolsep}|, which is set by nearly all document classes to \verb|5pt|, -which seems to be too big. The following equation is typeset with the -default value and the second one with \verb|\arraycolsep=1.4pt| - - -\bgroup -\fboxsep=0pt -\def\xstrut{\vphantom{\int\frac{\sin x}{x}}} -\begin{eqnarray*} -\boxed{f(x)\xstrut} & \boxed{=\xstrut} & \boxed{\int\frac{\sin x}{x}\,\mathrm{d}x} -\end{eqnarray*} - -\vspace{-2ex} -\arraycolsep=1.4pt -\begin{eqnarray*} -\boxed{f(x)\xstrut} & \boxed{=\xstrut} & \boxed{\int\frac{\sin x}{x}\,\mathrm{d}x} -\end{eqnarray*} -\egroup - -If this modification should be valid for all arrays/equations, then write it into the -preamble, otherwise put it into a group or define your own environment as done -in section~\vref{subsec:shortcommand}. - -\begin{lstlisting} -\bgroup -\arraycolsep=1.4pt -\begin{eqnarray} -f(x) & = & \int\frac{\sin x}{x}\,\mathrm{d}x -\end{eqnarray} -\egroup -\end{lstlisting} - -\begin{lstlisting} -\makeatletter -\newcommand{\be}{% - \begingroup - \setlength{\arraycolsep}{1.4pt} -[ ... ] -\end{lstlisting} - -\section{Matrix}\label{sec:matrix} -\mPar{\CMD{begin\{matrix\}}\\\ldots\\\CMD{end\{matrix\}}\\\CMD{bordermatrix}}% -\TeX{} knows two macros and \LaTeX{} one more for typesetting a -matrix\index{bordermatrix@\textbackslash bordermatrix}: - -\begin{LTXexample} -$\begin{matrix} - A & B & C \\ - d & e & f \\ - 1 & 2 & 3 \\ -\end{matrix}$ -\end{LTXexample} -\vspace{-10pt} -\begin{LTXexample} -$\bordermatrix{% - & 0 & 1 & 2 \cr - 0 & A & B & C \cr - 1 & d & e & f \cr - 2 & 1 & 2 & 3 \cr -}$ -\end{LTXexample} - -\iffalse % smallmatrix belongs to amsmath -\begin{minipage}{0.4\textwidth} -\begin{center} -$ -\begin{smallmatrix}% - A & B & C \\ - d & e & f \\ - 1 & 2 & 3 -\end{smallmatrix} -$ -\end{center} -\end{minipage}\hfill -\begin{minipage}{0.4\textwidth} -\begin{lstlisting} -\begin{smallmatrix}% - A & B & C \\ - d & e & f \\ - 1 & 2 & 3 -\end{smallmatrix} -\end{lstlisting} -\end{minipage} -\fi - -The first two macros are listed here for some historical reason, because the -\UIndex{array} or especially the -\AmSmath package offers the same or better macros/environments. Nevertheless it is -possible to redefine the \CIndex{bordermatrix} macro to get other parentheses and a star -version which takes the left top part as matrix: - -\makeatletter -\newif\if@borderstar -\def\bordermatrix{\@ifnextchar*{% - \@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}% -} -\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}} -\def\@bordermatrix@ii[#1]#2{% -\begingroup - \m@th\@tempdima8.75\p@\setbox\z@\vbox{% - \def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}% - \ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace % - \hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut % - \hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit % - \strut\cr}}% - \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}% - \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}% - \setbox\tw@\hbox{% - $\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1% - \if@borderstar\kern2pt\else\kern -\wd\@ne\fi% - \global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}% - \vcenter{\if@borderstar\else\kern -\ht\@ne\fi% - \unvbox\z@\kern-\if@borderstar2\fi\baselineskip}% - \if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $% - }\null \;\vbox{\kern\ht\@ne\box\tw@}% -\endgroup -} -\makeatother - -\begin{LTXexample} -$\bordermatrix{% - & 1 & 2 \cr -1 & x1 & x2 \cr -2 & x3 & x4 \cr -3 & x5 & x6 -}$ -\end{LTXexample} -\vspace{-10pt} -\begin{LTXexample} -$\bordermatrix[{[]}]{% - & 1 & 2 \cr -1 & x1 & x2 \cr -2 & x3 & x4 \cr -3 & x5 & x6 -}$ -\end{LTXexample} -\vspace{-10pt} -\begin{LTXexample} -$\bordermatrix[\{\}]{% - & 1 & 2 \cr -1 & x1 & x2 \cr -2 & x3 & x4 \cr -3 & x5 & x6 -}$ -\end{LTXexample} -\vspace{-10pt} -\begin{LTXexample} -$\bordermatrix*{% - x1 & x2 & 1 \cr - x3 & x4 & 2 \cr - x5 & x6 & 3 \cr - 1 & 2 -}$ -\end{LTXexample} -\vspace{-10pt} -\begin{LTXexample} -$\bordermatrix*[{[]}]{% - x1 & x2 & 1 \cr - x3 & x4 & 2 \cr - x5 & x6 & 3 \cr - 1 & 2 -}$ -\end{LTXexample} -\vspace{-10pt} -\begin{LTXexample} -$\bordermatrix*[\{\}]{% - x1 & x2 & 1 \cr - x3 & x4 & 2 \cr - x5 & x6 & 3 \cr - 1 & 2 -}$ -\end{LTXexample} - - -There is now an optional argument for the parenthesis with \verb|()| as the -default one. To get such a behaviour, write into the preamble: - -\begin{lstlisting}[xleftmargin=-0.75cm,xrightmargin=-0.75cm] -\makeatletter -\newif\if@borderstar -\def\bordermatrix{\@ifnextchar*{% - \@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}% -} -\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}} -\def\@bordermatrix@ii[#1]#2{% -\begingroup - \m@th\@tempdima8.75\p@\setbox\z@\vbox{% - \def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}% - \ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace % - \hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut % - \hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit % - \strut\cr}}% - \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}% - \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}% - \setbox\tw@\hbox{% - $\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1% - \if@borderstar\kern2pt\else\kern -\wd\@ne\fi% - \global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}% - \vcenter{\if@borderstar\else\kern -\ht\@ne\fi% - \unvbox\z@\kern-\if@borderstar2\fi\baselineskip}% - \if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $% - }\null \;\vbox{\kern\ht\@ne\box\tw@}% -\endgroup -} -\makeatother -\end{lstlisting} - -The \UIndex{matrix} macro cannot be used together with the \AmSmath package, it redefines -this environment (see section~\vref{sec:ams-matrix}). - -\section{Super/Subscript and limits}\label{sec:limits} -Writing $a_{min}$ and $a_{max}$ gives the same depth for the \Index{subscript}, but -writing them in \Index{upright mode} with \verb+\mbox+ gives a different -depth: $a_{\mbox{min}}$ and $a_{\mbox{max}}$. -The problem is the different height, which can be modified in several ways -\begin{itemize} -\item \verb+$a_{\mbox{\vphantom{i}max}}+: $a_{\mbox{min}}$ and $a_{\mbox{\vphantom{i}max}}$; -\item \verb+$a_{\mathrm{max}}+: $a_{\mathrm{min}}$ and $a_{\mathrm{max}}$; -\item \verb+$a_{\max}+: $a_{\min}$ and $a_{\max}$. Both are predefined - operators (see section~\vref{sec:ltxOperators}). -\end{itemize} -%$ - -\subsection{Multiple limits}\label{sub:Multiple-Limits} - -\mPar{\CMD{atop}}% -For general information about limits\index{Limits} read section -\vref{sub:Limits-Inline}. With the \TeX\ command \CIndex{atop} -multiple limits for a \CIndex{sum} or \CIndex{prod} are possible. The syntax is: - -\begin{LTXexample}[width=0.4\linewidth] -\[ {above \atop below} \] -\end{LTXexample} - -\noindent which is nearly the same as a fraction without a rule. This can -be enhanced to \verb|a\atop b\atop c| and so on. For equation \ref{eq:atop} do the following steps: - -\begin{LTXexample}[width=0.4\linewidth] -\begin{equation}\label{eq:atop} -\sum_{{1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}% -}a_{ij}b_{jk}c_{ki} -\end{equation} -\end{LTXexample} - - -\bigskip -\mPar{\CMD{shortstack}}% -which is not the best solution because the space between the lines -is too big. -The \AmSmath package provides several commands for -limits (section~\vref{sec:limit-AMS}) and the \CIndex{underset} and \CIndex{overset} -commands (see section~\vref{sec:misc-AMS}). - -\subsection{Problems} - -\begin{equation}\label{eq:disp-limits} -\fboxsep=0pt\fboxrule=0.1pt -\boxed{\sum_{ - {{1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}% - }}% -}\boxed{a_{ij}b_{jk}c_{ki}} -\end{equation} - -The equation \ref{eq:disp-limits} shows that the horizontal alignment -is not optimal, because the math expression on the right follows at the -end of the limits which are a unit together with the sum symbol. There -is an elegant solution with \AmSmath, described in subsection -\vref{subsec:ams-limits}. If you do not want to use \AmSmath, -then use \CIndex{makebox}. But there is a problem when the general fontsize -is increased, \CMD{makebox} knows nothing about the actual math font -size. Equation \ref{eq:disp-limits2} shows the effect and equation -\ref{eq:disp-limits3} the view without the boxes. - -\vspace{\abovedisplayskip} -\begin{subequations} -\begin{minipage}{0.45\textwidth} -\begin{equation}\label{eq:disp-limits2} -\fboxsep=0pt\fboxrule=0.1pt -\boxed{\sum_{% - \makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}% - }% -}\boxed{a_{ij}b_{jk}c_{ki}} -\end{equation} -\end{minipage}\hfill -\begin{minipage}{0.45\textwidth} -\begin{equation}\label{eq:disp-limits3} -\sum_{% - \makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}}a_{ij}b_{jk}c_{ki} -\end{equation} -\end{minipage} -\end{subequations} - -\medskip -\begin{lstlisting} -\begin{equation} -\sum_{\makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}}a_{ij}b_{jk}c_{ki} -\end{equation} -\end{lstlisting} - - - -\section{Roots}\label{sec:Roots} - -The square root\index{Root} \CIndex{sqrt} is the default -for \LaTeX{} and the $n$-th root can be inserted with the optional -parameter \CMD{sqrt[n]\{\ldots\}}. -\mPar{\CMD{sqrt}}. - -\begin{center} -\begin{tabular}{cc} - \verb|\sqrt{x}| & $\sqrt{x}$\\ - \verb|\sqrt[3]{x}| & $\sqrt[3]{x}$ -\end{tabular} -\end{center} - -There is a different typesetting in roots. Equation~\vref{eq:root1} -has different heights for the roots, whereas equation~\vref{eq:root2} -has the same one. This is possible with the % -\mPar{\CMD{vphantom}}% -\CIndex{vphantom} command, -which reserves the vertical space (without a horizontal one) of the -parameter height. - -\begin{LTXexample}[width=0.35\linewidth,wide] -\begin{equation} - \sqrt{a}\,% - \sqrt{T}\,% - \sqrt{2\alpha k_{B_1}T^i}\label{eq:root1} -\end{equation} -\end{LTXexample} - - -\vspace{-10pt} -\begin{LTXexample}[width=0.35\linewidth,wide] -\begin{equation}\label{eq:root2} - \sqrt{a\vphantom{k_{B_1}T^i}}\,% - \sqrt{T\vphantom{k_{B_1}T^i}}\,% - \sqrt{2\alpha k_{B_1}T^i} -\end{equation} -\end{LTXexample} - - -The typesetting looks much better, especially when the formula -has different roots in a row, like equation~\vref{eq:root1}. Using -\AmSmath with the \CIndex{smash} command% -\footnote{The \CMD{smash} command exists also in \LaTeX{} -but without an optional argument, which makes the use for roots possible.} -gives some more possibilities for the typesetting of roots (see section~\vref{sec:Roots-ams}). - - -\section[Brackets, braces \ldots]{Brackets, braces and parentheses}\label{sec:Brackets,-Braces-and} - -This is one of the major problems inside the math mode, because there is often a need for different -brackets, braces and parentheses in different size. At first we had to admit, that -there is a difference between the characters ``\verb|()[]/\| -$\lbrace\rbrace$ -| -$\Vert$ -$\lfloor\rfloor$ -$\lceil\rceil$ -$\langle\rangle$ -$\uparrow\Uparrow$ -$\downarrow\Downarrow$ -$\updownarrow\Updownarrow${}'' -and their use as an argument % -\mPar{\CMD{leftX}\\\CMD{rightX}} of the \CIndex{left} and \CIndex{right} -command, where \LaTeX{} stretches the size in a way that everything between -the pair of left and right parentheses is smaller than the parentheses themselves. In some cases% -\footnote{See section \vref{cap:Use-of-the-vphantom} for example.} -it may be useful to choose a fixed height, which is possible with -the \CMD{big}-series. Instead of writing \CMD{leftX} -or \CMD{rightX} one of the following commands can -be chosen: - -\medskip -\mPar{\CMD{bigX}\\\CMD{BigX}\\\CMD{biggX}\\\CMD{BiggX}} -\index{big@\textbackslash big}\index{Big@\textbackslash Big}% -\index{bigg@\textbackslash bigg}\index{Bigg@\textbackslash Bigg} -\begin{tabular}{rl} -default & ()[]/\textbackslash$\lbrace\rbrace$|$\Vert$ $\lfloor\rfloor$ -$\lceil\rceil$ $\langle\rangle$ $\uparrow\Uparrow$ $\downarrow\Downarrow$% -$\updownarrow\Updownarrow$\\[2pt] -\CMD{bigX} & $\big(\big)$ $\big[\big]$ -$\bigl/\big\backslash\big\{\big\}$ -$\big|$ $\big\Vert$ $\big\lfloor\big\rfloor$ $\big\lceil\big\rceil$ -$\big\langle\big\rangle$ $\big\uparrow\big\Uparrow$ $\big\downarrow\big\Downarrow$ -$\big\updownarrow\big\Updownarrow$\\[2pt] -\CMD{BigX} & $\Big(\Big)$ -$\Big[\Big]$ $\Bigl/\Big\backslash\Big\{\Big\}$ -$\Big|$ $\Big\Vert$ $\Big\lfloor\Big\rfloor$ -$\Big\lceil\Big\rceil$ $\Big\langle\Big\rangle$ -$\Big\uparrow\Big\Uparrow$ $\Big\downarrow\Big\Downarrow$ -$\Big\updownarrow\Big\Updownarrow$\\[4pt] -\CMD{biggX} & $\bigg(\bigg)$ -$\bigg[\bigg]$ $\biggl/\bigg\backslash\bigg\{\bigg\}$% -$\bigg|$ $\bigg\Vert$ $\bigg\lfloor\bigg\rfloor$ $\bigg\lceil\bigg\rceil$ -$\bigg\langle\bigg\rangle$ $\bigg\uparrow\bigg\Uparrow$ -$\bigg\downarrow\bigg\Downarrow$ $\bigg\updownarrow\bigg\Updownarrow$\\[8pt] -\CMD{BiggX} & $\Bigg(\Bigg)$ -$\Bigg[\Bigg]$ $\Biggl/\Bigg\backslash\Bigg\{\Bigg\}$ -$\Bigg|$ $\Bigg\Vert$ $\Bigg\lfloor\Bigg\rfloor$ -$\Bigg\lceil\Bigg\rceil$ $\Bigg\langle\Bigg\rangle$ -$\Bigg\uparrow\Bigg\Uparrow$ $\Bigg\downarrow\Bigg\Downarrow$% -$\Bigg\updownarrow\Bigg\Updownarrow$ -\end{tabular} - -\medskip{} -Only a few commands can be written in a short form like \CMD{big(}. -The ``X{}'' has to be replaced with one of the following characters -or commands from table~\vref{tab:big}, which shows the parentheses -character, its code for the use with one of the ``big{}'' commands -and an example with the code for that. - -\mPar{\CMD{biglX}\\\CMD{bigrX}}% -For all commands there exists a left/right version \CIndex{bigl}, -\CIndex{bigr}, \CIndex{Bigl} and so on, which only makes sense when writing things like: - -\begin{LTXexample}[width=0.3\linewidth,wide] -\begin{align} - \biggl)\times \frac{a}{b} \times\biggr( -\end{align} -\begin{align} - \bigg)\times \frac{a}{b} \times\bigg( -\end{align} -\end{LTXexample} - -\LaTeX{} takes the \verb|\biggl)| as a \Index{mathopen symbol}, which has by default -another horizontal spacing. - -In addition to the above commands there exist some more: -\CIndex{bigm}, \CIndex{Bigm}, \CIndex{biggm} and \CIndex{Biggm}, -which work as the standard ones (without the addtional ``m{}'') -but add some more horizontal space% -\mPar{\CMD{bigmX}\\\CMD{bigmX}} % -between the delimiter and the formula before and after (see -table~\vref{cap:Difference-between-the-bigg}). - - - -%$3\bigg|a^2-b^2-c^2\bigg|+2$ -%$3\biggm|a^2-b^2-c^2\biggm|+2$ - -\begin{table}[!htb] -\caption{Difference between the default -\CMD{bigg} and the \CMD{biggm} command}\label{cap:Difference-between-the-bigg} -\begin{LTXexample} -$\bigg(\displaystyle\frac{1}{3}\bigg|\frac{3}{4}\bigg)$ -\end{LTXexample} -\vspace{-15pt} -\begin{LTXexample} -$\bigg(\displaystyle\frac{1}{3}\biggm|\frac{3}{4}\bigg)$ -\end{LTXexample} -\end{table} - - -\newcommand{\xstrut}{\rule{0pt}{0.55cm}} -{\setlength{\hangindent}{-\marginparwidth} -\def\arraystretch{1.5} -\begin{longtable}{@{}l>{\raggedright}p{2.4cm}l>{\raggedright}p{5.7cm}@{}} -\caption{Use of the different parentheses for the ``big{}'' commands} \label{tab:big}\tabularnewline -Char & Code & Example & Code\tabularnewline\hline -\endfirsthead -Char & Code & Example & Code\tabularnewline -\hline -\endhead -\xstrut$(\ )$ & ( ) & % - $3\Big(a^{2}+b^{c^{2}}\Big)$ & % - \texttt{3\CMD{Big}( a\^{}2+b\^{}\{c\^{}2\}\CMD{Big})}\tabularnewline -% -\xstrut$[\ ]$ & {[} {]}& -$3\Big[a^{2}+b^{c^{2}}\Big]$& -\texttt{3\CMD{Big}{[} a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}{]}}\tabularnewline -% -\xstrut$/\ \backslash$ & \texttt{/}\CMD{backslash} & $3\Big/a^{2}+b^{c^{2}}\Big\backslash$ & -\texttt{3\CMD{Big}/ a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{backslash}}\tabularnewline -% -\xstrut$\{\ \}$ & \CMD{\{}\CMD{\}}\\ - & $3\Big\{ a^{2}+b^{c^{2}}\Big\}$ & -\texttt{3\CMD{Big}\CMD{\{} a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{\}}}\tabularnewline -% -\xstrut$\vert\ \Vert$ & | \CMD{Vert} & $3\Big|a^{2}+b^{c^{2}}\Big\Vert$ & \texttt{3\CMD{Big}|a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{Vert}}\tabularnewline -% -\xstrut$\lfloor\ \rfloor$ & \CMD{lfloor} \CMD{rfloor} & % - $3\Big\lfloor a^{2}+b^{c^{2}}\Big\rfloor$ & % - \texttt{3\CMD{Big}\CMD{lfloor} a\^{}2+b\^{}\{c\^{}2\} - \CMD{Big}\CMD{rfloor}}\tabularnewline -% -\xstrut$\lceil\ \rceil$ & \CMD{lceil}\CMD{rceil} & - $3\Big\lceil a^{2}+b^{c^{2}}\Big\rceil$ & - \texttt{3\CMD{Big}\CMD{lceil} a\^{}2+b\^{}\{c\^{}2\} \CMD{Big}% - \CMD{rceil}}\tabularnewline -% -\xstrut$\langle\ \rangle$ & \CMD{langle}\CMD{rangle} & - $3\Big\langle a^{2}+b^{c^{2}}\Big\rangle$ & - \texttt{3\CMD{Big}\CMD{langle} a\^{}2+b\^{}\{c\^{}2\}% - \CMD{Big}\CMD{rangle}}\tabularnewline -% -\xstrut$\uparrow\ \Uparrow$ & - \CMD{uparrow} \CMD{Uparrow} & - $3\Big\uparrow a^{2}+b^{c^{2}}\Big\Uparrow$ & - \texttt{3\CMD{Big}\CMD{uparrow} a\^{}2+b\^{}\{c\^{}2\}% - \CMD{Big}\CMD{Uparrow}}\tabularnewline -% -\xstrut$\downarrow\ \Downarrow$ & \CMD{downarrow} \CMD{Downarrow} & - $3\Big\downarrow a^{2}+b^{c^{2}}\Big\Downarrow$ & - \texttt{3\CMD{Big}\CMD{downarrow} a\^{}2+b\^{}\{c\^{}2\} - \CMD{Big}\CMD{Downarrow}}\tabularnewline -% -\xstrut$\updownarrow\ \Updownarrow$ & \CMD{updownarrow} \CMD{Updownarrow} & - $3\Big\updownarrow a^{2}+b^{c^{2}}\Big\Updownarrow$ & - \texttt{3\CMD{Big}\CMD{updownarrow} a\^{}2+b\^{}\{c\^{}2\} - \CMD{Big}\CMD{Updownarrow}}\tabularnewline -\end{longtable}} - - - -\clearpage - - -\subsection{Examples} -\subsubsection{Braces over several lines}\label{cap:Use-of-the-vphantom} -The following equation in the single line mode looks like -% -\begin{equation} -\frac{1}{2}\Delta(f_{ij}f^{ij})=2\left(\sum_{i<j}\chi_{ij} - (\sigma_{i}-\sigma_{j})^{2}+f^{ij}\nabla_{j}\nabla_{i}(\Delta f) - +\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2\nabla_{i}R_{jk} - -\nabla_{k}R_{ij}]\right)\label{eq:braces} -\end{equation} -% -and is too long for the text width and the equation number has to be placed -under the equation.\footnote{In standard \LaTeX{} the equation and the number are -printed one over the other for too long -formulas. Only \AmSmath puts it one line over (left numbers) or under (right -numbers) the formula.} With the array environment the formula can be split in two smaller -pieces: - -{\arraycolsep=2pt -\begin{equation} -\begin{array}{rcl} - \frac{1}{2}\Delta(f_{ij}f^{ij}) & = & 2\left({\displaystyle - \sum_{i<j}}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}+f^{ij}% - \nabla_{j}\nabla_{i}(\Delta f)+\right.\\ -& & \left.+\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2 - \nabla_{i}R_{jk}-\nabla_{k}R_{ij}]\right) -\end{array} -\end{equation} -} - - -It is obvious that there is a problem with the right closing parentheses. -Because of the two pairs ``\verb|\left( ... \right.|'' -and ``\verb|\left. ... \right)|'' -they have a different size because every pair does it in its own -way. Using the \Index{Bigg} command changes this into a better -typesetting: - -{\arraycolsep=2pt -\begin{equation} -\begin{array}{rcl} - \frac{1}{2}\Delta(f_{ij}f^{ij}) & = & 2\Bigg({\displaystyle - \sum_{i<j}}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}+f^{ij}% - \nabla_{j}\nabla_{i}(\Delta f)+\\ -& & +\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2 - \nabla_{i}R_{jk}-\nabla_{k}R_{ij}]\Bigg) -\end{array} -\end{equation} -} -\begin{lstlisting} -{\arraycolsep=2pt -\begin{equation} -\begin{array}{rcl} - \frac{1}{2}\Delta(f_{ij}f^{ij}) & = & 2\Bigg({\displaystyle - \sum_{i<j}}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}+f^{ij}% - \nabla_{j}\nabla_{i}(\Delta f)+\\ -& & +\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2 - \nabla_{i}R_{jk}-\nabla_{k}R_{ij}]\Bigg) -\end{array} -\end{equation} -} -\end{lstlisting} - -Section~\vref{sec:Specials-for-multline} shows another solution -for getting the right size for parentheses when breaking the equation -in smaller pieces. - -\begin{align*} - B(r,\phi,\lambda) = & \,\dfrac{\mu}{r} - \Bigg[\sum_{n=2}^{\infty} \Bigg( \left( \dfrac{R_e}{r} \right)^n J_nP_n(s\phi) \\ - & +\sum_{m=1}^n \left( \dfrac{R_e}{r} \right) ^n - (C_{nm}\cos m\lambda+S_{nm}\sin m\lambda)P_{nm}(s\phi) \Bigg)\Bigg] -\end{align*} - -\begin{lstlisting} -\begin{align*} - B(r,\phi,\lambda) = & \,\dfrac{\mu}{r} - \Bigg[\sum_{n=2}^{\infty} \Bigg( \left( \dfrac{R_e}{r} \right)^n J_nP_n(s\phi) \\ - & +\sum_{m=1}^n \left( \dfrac{R_e}{r} \right) ^n - (C_{nm}\cos m\lambda+S_{nm}\sin m\lambda)P_{nm}(s\phi) \Bigg)\Bigg] -\end{align*} -\end{lstlisting} - - -\subsubsection{Middle bar} -See section~\vref{sec:braket} for examples and the use of package \PIndex{braket}. - -\subsection{New delimiters}\label{subsec:delim} -The default delimiters\index{Delimiter} are defined in the file \verb|fontmath.ltx|\index{fontmath.ltx} -which is stored in general -in \path{[TEXMF]/tex/latex/base/fontmath.ltx}. If we need for example a thicker vertical symbol -than the existing \CIndex{vert} symbol we can define in the preamble: - -\begin{lstlisting} -\DeclareMathDelimiter{\Norm} - {\mathord}{largesymbols}{"3E}{largesymbols}{"3E} -\end{lstlisting} - -The character number $3E_{16}$ (decimal $62$) from the \FIndex{cmex10} font is the small -thick vertical rule. Now the new delimiter \verb|\Norm| can be used in the usual way: - -\begin{LTXexample}[width=0.3\linewidth,wide] -$\left\Norm *BLA* \right\Norm$ - -$\left\Norm \dfrac{*BLA*}{*BLUB*} \right\Norm$ -\end{LTXexample} - - - -\subsection{Problems with parentheses}\label{subsec:Problems-with-parenthesis} -\mPar{\CMD{delimitershortfall}\\\CMD{delimiterfactor}}% -It is obvious that the following -equation has not the right size of the parenthesis in the -second integral, the inner one should be a bit smaller than the outer one. -% -\begin{LTXexample}[width=0.425\linewidth,wide] -\[ -\int_\gamma F'(z) dz =\int_\alpha^\beta -F'\left(\gamma (t)\right)\cdot\gamma '(t)dt -\] -\end{LTXexample} - -The problem is that \TeX{} controlls the height of the parenthesis with -\LIndex{delimitershortfall} and \CIndex{delimiterfactor}, with the default values -\begin{verbatim} -\delimitershortfall=5pt -\delimiterfactor=901 -\end{verbatim} - -\verb|\delimiterfactor/1000| is the relative size of the parenthesis for a given formula -environment. They could be of \verb|\delimitershortfall| too short. These values are valid -at the end of the formula, the best way is to set them straight before the math environment -or globally for all in the preamble. - - -\begin{LTXexample}[width=0.425\linewidth,wide] -{\delimitershortfall=-1pt -\[ -\int_\gamma F'(z) dz =\int_\alpha^\beta -F'\left(\gamma (t)\right)\cdot\gamma '(t)dt -\]} -\end{LTXexample} - -\section{Text in math mode}\label{sec:Text} - -Standard \index{Text}text in math mode should be written in upright shape and not -in the italic\index{Italic} one. This shape is reserved for the variable -names: $\boxed{{I\ am\ \textrm{text}\ inside\ math.}}$ (see also -Zable~\vref{cap:Spaces-in-math mode}). There are different ways to write text inside math. - -\mPar{\CMD{textstyle}\\\CMD{mbox}} - -\begin{itemize} -\mPar{\CMD{mathrm}} -\item \CMD{mathrm}. It is like math mode (no spaces), but in upright mode -\item \CMD{textrm}. Upright mode with printed spaces (real textmode) -\item \CMD{mbox}. The font size is still the one from \CIndex{textstyle} - (see section~\vref{sec:Styles}), so that you have to place additional -commands when you use \CIndex{mbox} in a super- or subscript for limits. -\end{itemize} - -Inserting long text is possible with a \CIndex{parbox}, which can be aligned as usual to the top, -bottom or center, \eg \index{Text!\textbackslash parbox} -\begin{eqnarray} - a+b+c+d+ef & = & g+h+i+j+k % - \qquad\textrm{\parbox[t]{.25\linewidth}{% - this is a very long description of a formula}% - } -\end{eqnarray} - -\begin{lstlisting} -\begin{eqnarray} - a+b+c+d+ef & = & g+h+i+j+k % - \qquad\textrm{\parbox[t]{.25\linewidth}{% - this is a very long description of a formula}% - } -\end{eqnarray} -\end{lstlisting} - -Additional commands for text inside math are provided by \AmSmath (see -section \vref{sec:Text-in-math mode}). - -%$ -\section{Font commands} - -\subsection{Old-style font commands} - -Should never be used, but are still present and supported by \LaTeX{}. The -default syntax for the old commands is - -\begin{lstlisting} -{\XX test} -\end{lstlisting} -Table~\vref{cap:Old-Fontstyle-commands} shows what has to be replaced for the \verb+XX+. -The major difference to the new style is that these -\CMD{XX} are toggling the actual math mode into -the ``XX{}'' one, whereas the new commands start which, at its end, -switches back to the previous mode. - -\begin{table}[!htb] -\centering -\begin{tabular}{rc|rc|rc|cc|cc} -\CMD{bf}\index{bf@\textbackslash bf} & ${\bf {\bf test}}$ & -\CMD{cal}\index{cal@\textbackslash cal} & ${\cal TEST}$ & -\CMD{it}\index{it@\textbackslash it} & -${\it test}$ & -\CMD{rm}\index{rm@\textbackslash rm} & -${\rm test}$ & -\CMD{tt}\index{tt@\textbackslash tt} & -${\tt test}$\tabularnewline -\end{tabular} -\caption{Old font style commands}\label{cap:Old-Fontstyle-commands} -\end{table} - -\subsection{New-style font commands}\label{sub:New-Style-Fontcommands} - -% -\mPar{\CMD{mathrm}\\ -\CMD{mathfrak}\\ -\CMD{mathcal}\\ -\CMD{mathsf}\\ -\CMD{mathbb}\\ -\CMD{mathtt}\\ -\CMD{mathit}\\ -\CMD{mathbf}} - -The default syntax is - -\begin{lstlisting} -\mathXX{test} -\end{lstlisting} -Table~\ref{cap:Fonts-in-math-mode} shows what has to be -replaced for the XX. See section~\vref{sec:euscript.sty} for additional packages. - -\begin{table}[htb] -\caption{Fonts in math mode}\label{cap:Fonts-in-math-mode} -\centering -\includegraphics{styles} -\iffalse -\begin{table}[!htb] -\begin{minipage}{\linewidth} -\centering -\begin{tabularx}{.9\linewidth}{l|X} -\textbf{Command} & \textbf{Test}\tabularnewline\hline -default & $ABCDEFGHIJKLMNOPQRSTUVWXYZ$ - -$abcdefghijklmnopqrstuvwxyz$\tabularnewline -\CMD{mathfrak} & -$\mathfrak{{ABCDEFGHIJKLMNOPQRSTUVWXYZ}}$ -$\mathfrak{{abcdefghijklmnopqrstuvwxyz}}$\tabularnewline -\CMD{mathcal}% -\footnote{Not available for lower letters. For mathcal exists a - non free font for lower letters (http://www.pctex.com)}\addtocounter{mpfootnote}{-1} & -$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\tabularnewline -\CMD{mathsf}& -$\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ -$\mathsf{abcdefghijklmnopqrstuvwxyz}$\tabularnewline - -\CMD{mathbb}${}^a$ & $\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\tabularnewline -\CMD{mathtt} & $\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ - -$\mathtt{abcdefghijklmnopqrstuvwxyz}$\tabularnewline -\CMD{mathit} & $\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ - -$\mathit{abcdefghijklmnopqrstuvwxyz}$\tabularnewline -\CMD{mathrm} & $\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ - -$\mathrm{abcdefghijklmnopqrstuvwxyz}$\tabularnewline -\CMD{mathbf} & $\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ - -$\mathbf{abcdefghijklmnopqrstuvwxyz}$\tabularnewline - -\CMD{mathds}${}^b$ & $\mathds{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\tabularnewline -\end{tabularx} -\end{minipage} -\fi -\end{table} - -\index{mathfrak@\textbackslash mathfrak}\index{mathsf@\textbackslash mathsf} -\index{mathbb@\textbackslash mathbb}\index{mathcal@\textbackslash mathcal} -\index{mathbf@\textbackslash mathbf}\index{mathit@\textbackslash mathit} -\index{mathrm@\textbackslash mathrm}\index{mathtt@\textbackslash mathtt} -\index{mathds@\textbackslash mathds}\index{double stroke} -\index{dsfont@\texttt{dsfont}}\index{Set symbol} -%\end{comment} - -\section{Space} -\subsection{Math typesetting}\label{subsec:mathskip} - -\mPar{\CMD{thinmuskip}\\ -\CMD{medmuskip}\\ -\CMD{thickmuskip}} -\LaTeX\ defines the three math lengths\footnote{For more -information see: \url{http://www.tug.org/utilities/plain/cseq.html}} with the following -values\footnote{see \texttt{\small fontmath.ltx}}: - -\begin{lstlisting} -\thinmuskip=3mu -\medmuskip=4mu plus 2mu minus 4mu -\thickmuskip=5mu plus 5mu -\end{lstlisting} - -\noindent where \verb|mu| is the abbreviation for \Index{math unit}. -\[ -1 \mathrm{mu}= \dfrac{1}{18} \mathrm{em} -\] - -\begin{table}[htb] -\centering -\begin{tabular}{ll} -\fboxsep=0pt -\text{default} & $\boxed{f(x)=x^2+3x_0\cdot\sin x}$\\ -\CMD{thinmuskip=0mu} & {\thinmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\ -\CMD{medmuskip=0mu} & {\medmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\ -\CMD{thickmuskip=0mu} & {\thickmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\ -all set to zero & {\thickmuskip=0mu\thinmuskip=0mu\medmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\ -\end{tabular} -\caption{The meaning of the math spaces}\label{tab:mathSpaces} -\end{table} - -These lengths can have all glue and are -used for the horizontal spacing in math expressions where \TeX{} puts spaces between symbols -and operators. The meaning of these different -horizontal skips is shown in table~\ref{tab:mathSpaces}. For a better typesetting \LaTeX{} -inserts different spaces between the symbols. - -\begin{description} -\item[\CIndex{thinmuskip}] space between ordinary and operator atoms -\item[\CIndex{medmuskip}] space between ordinary and binary atoms in display and text styles -\item[\CIndex{thickmuskip}] space between ordinary and relation atoms in display and text styles -\end{description} - -\subsection{Additional horizontal spacing} -\mPar{\CMD{thinspace}\\ -\CMD{medspace}\\ -\CMD{thickspace}\\ -\CMD{negthinspace}\\ -\CMD{negmedspace}\\ -\CMD{negthickspace}} - -\begin{table}[!htb] -\def\arraystretch{1.2} -\centering -\begin{tabular}{ll|ll} -\multicolumn{2}{l|}{Positive Space}&\multicolumn{2}{l}{Negative Space}\\\hline -\verb|$ab$| & $\boxed{a}\boxed{b}$\\ -\verb|$a b$| & $\boxed{a} \boxed{b}$\\ -\verb|$a\ b$| & $\boxed{a}\ \boxed{b}$\\ -\verb|$a\mbox{\textvisiblespace}b$| & $\boxed{a}\mbox{\textvisiblespace}\boxed{b}$\\ -\verb|$a\,b$|\index{,@\textbackslash ,} (\verb|$a\thinspace b$|)\index{thinspace@\textbackslash thinspace} & $\boxed{a}\,\boxed{b}$& -\verb|$a\! b$|\index{negthinspace@\textbackslash negthinspace} & $\boxed{a}\!\boxed{b}$\\ -\verb|$a\: b$|\index{:@\textbackslash :} (\verb|$a\medspace b$|)\index{medspace@\textbackslash medspace}& -$\boxed{a}\:\boxed{b}$& -\verb|$a\negmedspace b$|\index{negmedspace@\textbackslash negmedspace} & $\boxed{a}\negmedspace\boxed{b}$\\ -\verb|$a\; b$|\index{;@\textbackslash ;} (\verb|$a\thickspace b$|\index{thickspace@\textbackslash thickspace}& -$\boxed{a}\;\boxed{b}$& -\verb|$a\negthickspace b$|\index{negthickspace@\textbackslash negthickspace}& -$\boxed{a}\negthickspace\boxed{b}$\\ -\verb|$a\quad b$|\index{quad@\textbackslash quad} & $\boxed{a}\quad\boxed{b}$\\ -\verb|$a\qquad b$|\index{qquad@\textbackslash qquad} & $\boxed{a}\qquad\boxed{b}$\\ -\verb|$a\hspace{0.5cm}b$|\index{hspace@\textbackslash hspace}& $\boxed{a}\hspace{0.5cm}\boxed{b}$& -\verb|$a\hspace{-0.5cm}b$| & $\boxed{a}\hspace{-0.5cm}\boxed{b}$\\ -\verb|$a\kern0.5cm b$|\index{kern@\textbackslash kern} & $\boxed{a}\kern0.5cm \boxed{b}$ & \verb|$a\kern-0.5cm b$| & $\boxed{a}\kern-0.5cm \boxed{b}$\\ -\verb|$a\hphantom{xx}b$|\index{hphantom@\textbackslash hphantom} & $\boxed{a}\hphantom{xx}\boxed{b}$\\ -\verb|$axxb$| & $\boxed{a}xx\boxed{b}$ -\end{tabular} -\caption{Spaces in math mode}\label{cap:Spaces-in-math mode} -\end{table} -%$ - -LaTeX defines the following short commands: - -\begin{verbatim} -\def\>{\mskip\medmuskip} -\def\;{\mskip\thickmuskip} -\def\!{\mskip-\thinmuskip} -\end{verbatim} -In math mode there is often a need for additional tiny spaces between variables, -\eg $L\dfrac{di}{dt}$ written with a tiny space between $L$ and -$\dfrac{di}{dt}$ looks nicer: $L\:\dfrac{di}{dt}$. Table~\ref{cap:Spaces-in-math mode} -shows a list of all commands for horizontal space which can be used -in math mode. The ``space{}'' is seen ``between{}'' the boxed a -and b. For all examples a is \verb+\boxed{a}+ and -b is \verb+\boxed{b}+. The short forms for some -\mPar{\CMD{hspace}\\ -\CMD{hphantom}\\ -\CMD{kern}} -spaces may cause problems with other packages. In this case use the -long form of the commands. - -\subsection{Problems}\label{space:problems} -Using \CIndex{hphantom} in mathmode depends to on object. \CIndex{hphantom} -reserves only the space of -the exact width without any additional space. In the following example the second line is -wrong: \verb+& \hphantom{\rightarrow} b\\+. It does not reserve any additional space. - -\begin{LTXexample}[width=0.15\linewidth,wide] -\begin{align*} -a & \rightarrow b\\ - & \hphantom{\rightarrow} b\\ - & \mkern\thickmuskip\hphantom{\rightarrow}\mkern\thickmuskip b\\ - & \mathrel{\hphantom{\rightarrow}} b -\end{align*} -\end{LTXexample} - -This only works when the math symbol is a mathrel one, otherwise you have to change the -horizontal space to \CIndex{medmuskip} or \CIndex{thinmuskip} or to use an empty group after -the \CIndex{hphantom} command. For more informations -about the math objects look into \verb+fontmath.ltx+ or \PIndex{amssymb} or use the \CIndex{show} -macro, which prints out the type of the mathsymbol, \eg \verb+\show\rightarrow+ with the -output: - -\begin{lstlisting} -> \rightarrow=\mathchar"3221. -l.20 \show\rightarrow -\end{lstlisting} - -The first digit represents the type: - -\begin{tabular}{l@{ : }l} -0 & ordinary\\ -1 & large operator\\ -2 & binary operation\\ -3 & relation\\ -4 & opening\\ -5 & closing\\ -6 & punctuation\\ -7 & variable family -\end{tabular} - - -%\iffalse -\begingroup -\thinmuskip=3mu -\medmuskip=4mu plus 2mu minus 4mu -\thickmuskip=5mu plus 5mu - -\medskip -Grouping a math symbol can change the behaviour in horizontal spacing. Compare -$50\mkern\thinmuskip\times\mkern\thinmuskip10^{12}$ and $50{\times}10^{12}$, the first one is typeset with -\verb+$50\times10^{12}$+ and the second one with \verb+$50{\times}10^{12}$+. -\endgroup -%\fi -Another possibilty is to use the \PIndex{numprint} package.\footnote{% -\href{ftp://ftp.dante.de/tex-archive/macros/latex/contrib/numprint/}% -{CTAN://macros/latex/contrib/numprint/}} - -\subsection{Dot versus comma}\label{subsec:dot-comma} -\mPar{\CMD{mathpunct}\\\CMD{mathord}}% -In difference to a \Index{decimal point} and a \Index{comma} as a marker of thousands a lot of -countries prefer it vice versa. To get the same behaviour the meaning of \Index{dot} and -comma has to be changed: - - -\begin{align} -1,234,567.89 & \text{ default}\\ -1.234.567,89 & \text{ vice versa, wrong spacing}\label{eq:comma}\\ -1\mathpunct{.}234\mathpunct{.}567{,}89 & \text{ correct spacing} -\end{align} - - -\begin{lstlisting} -%\usepackage{amsmath} -1,234,567.89 & \text{ default}\\ -1.234.567,89 & \text{ vice versa, wrong spacing}\\ -1\mathpunct{.}234\mathpunct{.}567{,}89 & \text{ correct spacing} -\end{lstlisting} - -The original definitions from \verb+fontmath.ltx+\footnote{% -Located in \url{texmf/tex/latex/base/}} are - -\begin{verbatim} -\DeclareMathSymbol{,}{\mathpunct}{letters}{"3B} -\DeclareMathSymbol{.}{\mathord}{letters}{"3A} -\end{verbatim} - -\noindent\CIndex{mathord} and \CIndex{mathpunct} -can be changed for a documentwide other behaviour. In the above equation~\ref{eq:comma} -the comma is only set in a pair of braces \verb+{,}+, which is the same as writing -\verb+\mathord{,}+ because \LaTeX{} handles everything -inside of parenthises as a formula, which gets the same spacing. - -It is also possible to use the package \PIndex{icomma}\footnote{% -\href{ftp://ftp.dante.de/tex-archive/macros/latex/contrib/was/}% -{CTAN:// macros/latex/contrib/was/}} for a documentwide -correct spacing. - -\subsection{Vertical whitespace}\label{subsec:vwhitespace} -\subsubsection{Before/after math expressions}\label{subsubsec:displayskip} - -There are four predefined lengths, which control the vertical whitespace -of displayed formulas: -\begin{verbatim} -\abovedisplayskip=12pt plus 3pt minus 9pt -\abovedisplayshortskip=0pt plus 3pt -\belowdisplayskip=12pt plus 3pt minus 9pt -\belowdisplayshortskip=7pt plus 3pt minus 4pt -\end{verbatim} -\index{abovedisplayskip@\textbackslash abovedisplayskip} -\index{abovedisplayshortskip@\textbackslash abovedisplayshortskip} -\index{belowdisplayskip@\textbackslash belowdisplayskip} -\index{belowdisplayshortskip@\textbackslash belowdisplayshortskip} -The short skips are used if the formula starts behind the end of the foregoing -last line. Only for demonstration the shortskips -are set to \verb|0pt| in the following examples and the normal skips to -\verb|20pt| without any glue: - -\medskip -\noindent\fbox{\begin{minipage}{\linewidth-2\fboxsep-2\fboxrule} -\abovedisplayshortskip=0pt -\belowdisplayshortskip=0pt -\abovedisplayskip=20pt -\belowdisplayskip=20pt -\noindent The line ends before. -\begin{equation} -f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x -\end{equation} -\noindent The line doesn't end before the formula. -\begin{equation} -f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x -\end{equation} -\noindent And the next line starts as usual with some text ... -\end{minipage}} - -\medskip -\begin{lstlisting} -\abovedisplayshortskip=0pt -\belowdisplayshortskip=0pt -\abovedisplayskip=20pt -\belowdisplayskip=20pt -\noindent The line ends before. -\begin{equation} - f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x -\end{equation} -\noindent The line doesn't end before the formula. -\begin{equation} - f(x) = \int\frac{\sin x}{x}\,\mathrm{d}x -\end{equation} -\noindent And the next line starts as usual with some text ... -\end{lstlisting} -%$ - - -\mPar{\texttt{fleqn} class option}% -When using the \verb+fleqn+\index{fleqn@\texttt{fleqn}} classoption for left -aligned equations the math environments \uIndex{equation} -and \CIndex{[}\ldots\CIndex{]} are typeset as a list. This is the reason why the -vertical space is defined by the length registers for a list, especially -\LIndex{topsep}, instead of \LIndex{abovedisplayskip} and \LIndex{belowdisplayskip}. -This doesn't effect the \UIndex{eqnarray}. - - -\subsubsection{Inside math expressions}\label{subsec:vspacing} - -\paragraph{\CMD{\textbackslash [<length>]}} -This works inside the math mode in the same way as in the text mode. - - -\paragraph{\CMD{jot}}\mPar{\CMD{jot}} -The vertical space between the lines for all math expressions which allow multiple -lines can be changed with the length \LIndex{jot}, which is predefined as - -\begin{verbatim} -\newdimen\jot \jot=3pt -\end{verbatim} - -The following three formulas show this for the default value, \verb|\setlength\jot{0pt}| -and \verb|\setlength\jot{10pt}|. - -\begin{minipage}{0.3\linewidth} -\begin{eqnarray*} - y & = & d\\ - y & = & c\frac{1}{x}+d\\ - y & = & b\frac{1}{x^{2}}+cx+d\\ -\end{eqnarray*} -\end{minipage}\hfill -\begin{minipage}{0.3\linewidth} -\setlength\jot{0pt} -\begin{eqnarray*} - y & = & d\\ - y & = & c\frac{1}{x}+d\\ - y & = & b\frac{1}{x^{2}}+cx+d\\ -\end{eqnarray*} -\end{minipage}\hfill -\begin{minipage}{0.3\linewidth} -\setlength\jot{10pt} -\begin{eqnarray*} - y & = & d\\ - y & = & c\frac{1}{x}+d\\ - y & = & b\frac{1}{x^{2}}+cx+d\\ -\end{eqnarray*} -\end{minipage} - -Defining a new environment with a parameter makes things easier, because changes to the -length are locally. -\begin{lstlisting} -\newenvironment{mathspace}[1]{% - \setlength{\jot}{#1}% - \ignorespaces% -}{% - \ignorespacesafterend% -} -\end{lstlisting} - -\paragraph{\CMD{arraystretch}}\cIndex{arraystretch} -\mPar{\CMD{arraystretch}}% -The vertical space between the lines for all math expressions which contain an -\UIndex{array} can be changed with the command -\CIndex{arraystretch}, which is predefined -as -\begin{verbatim} -\renewcommand\arraystretch{1} -\end{verbatim} - -Renewing this definition is global to all following math expressions, so it should be used -in the same way as \LIndex{jot}. - -\paragraph{\CMD{vskip}}\index{Vertical spacing}\index{Spacing!vertical} -Another spacing for single lines is possible with the \CIndex{vskip} macro: - -\begin{LTXexample}[width=0.4\linewidth] -\[ -\begin{pmatrix} -0 & 1 & 1 & 0 & 0 & 1 \\ -1 & 0 & 0 & 1 & 1 & 0 \\ -\noalign{\vskip2pt} -0 & 1 & 1 & 0 & \dfrac{1}{\sqrt{2}} & 1\\ -\noalign{\vskip2pt} -1 & 0 & 1 & 0 & 1 & 0 \\ -0 & 1 & 0 & 1 & 0 & 1 \\ -\end{pmatrix} -\] -\end{LTXexample} - - - -\paragraph{Package \texttt{setspace}} -To have all formulas with another vertical spacing, one can choose -the package \PIndex{setspace} and redefining some of the math macros, \eg - -\begingroup -\newcommand*\Array[2][1]{\setstretch{#1}\array{#2}} -\let\endArray\endarray - -\begin{lstlisting} -\newcommand*\Array[2][1]{\setstretch{#1}\array{#2}} -\let\endArray\endarray -\end{lstlisting} - -\begin{LTXexample}[width=0.25\linewidth] -\[ -\begin{Array}[2]{cc} -a =&b\\ -a =&b\\ -a =&b -\end{Array} -\] - -text $\begin{Array}{cc} -a =&b\\ -a =&b\\ -a =&b -\end{Array}$ text -\end{LTXexample} -\endgroup - -\section{Styles}\label{sec:Styles} - -\begin{table}[htb] -\newlength\formula -\settowidth{\formula}{$f(t)=\frac{T}{2\pi }\int \frac{1}{\sin \frac{\omega }{t}}dt$} -\begin{tabular}{l|ll} -Mode & Inline & Displayed\\\hline -default & $f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt$& -\begin{minipage}{\formula}\[ -f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt\] -\end{minipage}\\ -\CMD{displaystyle} & -${\displaystyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$& -\begin{minipage}{\formula}\[ -{\displaystyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\] -\end{minipage}\\ -\CMD{scriptstyle} & -${\scriptstyle {\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}}$& -\begin{minipage}{\formula}\[ -{\textstyle {\scriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}}\] -\end{minipage}\tabularnewline -\CMD{scriptscriptstyle} & -${\scriptscriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$& -\begin{minipage}{\formula}\[ -{\scriptscriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\] -\end{minipage}\tabularnewline -\CMD{textstyle} & -${\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$& -\begin{minipage}{\formula}\[ -{\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\] -\end{minipage} -\end{tabular} -\caption{Math styles}\label{cap:Mathstyles} -\end{table} -%$ -\makeatletter -\newenvironment{smallequation}[1]{% - \skip@=\baselineskip - #1% - \baselineskip=\skip@ - \equation -}{\endequation \ignorespacesafterend} -\makeatother - -This depends on the environment in which they are used. An inline -formula has a default math % -\mPar{\CMD{textstyle}\\ -\CMD{displaystyle}\\ -\CMD{scriptstyle}\\ -\CMD{scripscriptstyle}} fontsize called \CIndex{textstyle}, -which is smaller than the one for a display formula (see section~\ref{display}), which is called -\CIndex{displaystyle}. -Beside this predefinition there are two other special fontstyles for -math, \CIndex{scriptstyle} and \CIndex{scriptscriptstyle}. -They are called ``style{}'' in difference to ``size{}'', because -they have a dynamic character, their real fontsize belongs to the -environment in which they are used. A fraction for example is by default in scriptstyle when it is in an -inline formula like this $\frac{a}{b}$, which can be changed to -${\displaystyle \frac{a}{b}}$. -This may be in some cases useful but it looks in general ugly because -the line spacing is too big. -These four styles\index{Style} are predefined and together in a -logical relationship. It is no problem to use the other styles like -\Index{large}, \CIndex{Large}, \ldots\ \textbf{outside} the math environment. -For example a fraction written with \CIndex{Huge}: {\Huge$\frac{a}{b}$} -(\verb|\Huge$\frac{a}{b}$|). This may cause some problems when you want to write -a displayed formula in another fontsize\index{Fontsize}, because it also affects the interline spacing of -the preceding part of the paragraph. -If you end the paragraph, you get problems with spacing and page breaking -above the equations. So it is better to declare the font size and then -restore the baselines: -\begin{smallequation}{\tiny} -\int_1^2\,\frac{1}{x^2}\,\mathrm{d}x=0.5 -\end{smallequation} -\begin{lstlisting} -\makeatletter -\newenvironment{smallequation}[1]{% - \skip@=\baselineskip - #1% - \baselineskip=\skip@ - \equation -}{\endequation \ignorespacesafterend} -\makeatother - -\begin{smallequation}{\tiny} -\int_1^2\,\frac{1}{x^2}\,\mathrm{d}x=0.5 -\end{smallequation} -\end{lstlisting} -If you use this the other way round for huge fontsizes, don't forget to load package -\PIndex{exscale} (see section~\vref{sec:exscale}). Also see this section for diffent symbol sizes. - - - -\section{Dots\label{sec:Dots}} - -\mPar{\CMD{cdots}\\ -\CMD{dots}\\ -\CMD{dotsb}\\ -\CMD{dotsc}\\ -\CMD{dotsi}\\ -\CMD{dotsm}\\ -\CMD{dotso}\\ -\CMD{ldots}\\ -\CMD{vdots}}% -In addition to the above decorations there are some more different -dots which are single commands and not by default over/under a letter. -It is not easy to see the differences between some of them. Dots from -lower left to upper right are possible with -\verb|\reflectbox{$\ddots$}|\index{reflectbox@\textbackslash reflectbox} -\reflectbox{$\ddots$} - -\begin{table}[htb] -\centering -\begin{tabular}{*{5}{rc}} -\CMD{cdots}\index{cdots@\textbackslash cdots}&$\cdots$ & -\CMD{ddots}\index{ddots@\textbackslash ddots}&$\ddots$ & -\CMD{dotsb}\index{dotsb@\textbackslash dotsb}&$\dotsb$ & -\CMD{dotsc}\index{dotsc@\textbackslash dotsc}&$\dotsc$ & -\CMD{dotsi}\index{dotsi@\textbackslash dotsi}&$\dotsi$ \\\hline -\CMD{dotsm}\index{dotsm@\textbackslash dotsm}&$\dotsm$ & -\CMD{dotso}\index{dotso@\textbackslash dotso}&$\dotso$ & -\CMD{ldots}\index{ldots@\textbackslash ldots}&$\ldots$ & -\CMD{vdots}\index{vdots@\textbackslash vdots}&$\vdots$ -\end{tabular} -\caption{Dots in math mode} -\end{table} - - - -\section{Accents}\label{sec:Accents} - -The letter ``a{}'' is only for demonstration. The table \ref{cap:Accents-in-math mode} -shows all in standard \LaTeX{} available accents and also the ones placed under a character. -With package \PIndex{amssymb} it is easy to define new accents. For -more information see section~\vref{amssymb} or -other possibilities at section \vref{sec:package-accent}. - - -\begin{table}[htb] -\makebox[\textwidth]{% -\begin{tabular}{rc|rc|rc} -\CIndex{acute}\index{acute@\textbackslash acute} &$\acute{a}$& -\CIndex{bar}\index{bar@\textbackslash bar}&$\bar{a}$& -\CIndex{breve}\index{breve@\textbackslash breve} & $\breve{a}$\\ -\CIndex{bar}\index{bar@\textbackslash bar}&$\bar{a}$& -\CIndex{breve}\index{breve@\textbackslash breve} &$\breve{a}$\tabularnewline -\CIndex{check}\index{check@\textbackslash check} &$\check{a}$& -\CIndex{dddot} \index{dddot@\textbackslash dddot}&$\dddot{a}$& -\CIndex{ddot}\index{ddot@\textbackslash ddot}&$\ddot{a}$\tabularnewline -\CIndex{dot}\index{dot@\textbackslash dot}&$\dot{a}$& -\CIndex{grave}\index{grave@\textbackslash grave}&$\grave{a}$& -\CIndex{hat}\index{hat@\textbackslash hat}&$\hat{a}$\tabularnewline -\CIndex{mathring}\index{mathring@\textbackslash mathring}&$\mathring{a}$& -\CIndex{overbrace}\index{overbrace@\textbackslash overbrace}&$\overbrace{a}$& -\CIndex{overleftarrow}\index{overleftarrow@\textbackslash overleftarrow}&$\overleftarrow{a}$\tabularnewline -\CIndex{overleftrightarrow}\index{overleftrightarrow@\textbackslash overleftrightarrow}&$\overleftrightarrow{a}$& -\CIndex{overline}\index{overline@\textbackslash overline}&$\overline{a}$& -\CIndex{overrightarrow}\index{overrightarrow@\textbackslash overrightarrow}&$\overrightarrow{a}$\tabularnewline -\CIndex{tilde}\index{tilde@\textbackslash tilde}&$\tilde{a}$& -\CIndex{underbar}\index{underbar@\textbackslash underbar}&$\underbar{a}$& -\CIndex{underbrace}\index{underbrace@\textbackslash underbrace}&$\underbrace{a}$\tabularnewline -\CIndex{underleftarrow}\index{underleftarrow@\textbackslash underleftarrow}&$\underleftarrow{a}$& -\CIndex{underleftrightarrow}\index{underleftrightarrow@\textbackslash underleftrightarrow}& -$\underleftrightarrow{a}$& -\CIndex{underline}\index{underline@\textbackslash underline}&$\underline{a}$\tabularnewline -\CIndex{underrightarrow}\index{underrightarrow@\textbackslash underrightarrow}&$\underrightarrow{a}$& -\CIndex{vec}\index{vec@\textbackslash vec}&$\vec{a}$& -\CIndex{widehat}\index{widehat@\textbackslash widehat}&$\widehat{a}$\tabularnewline -\CIndex{widetilde}\index{widetilde@\textbackslash widetilde}&$\widetilde{a}$ & & & & -\end{tabular}% -} -\caption{Accents in math mode}\label{cap:Accents-in-math mode} -\end{table} - -The letters \verb+i+ and \verb+j+ can be substituted with the macros \CIndex{imath} -and \CIndex{jmath} when an accents is placed over these letters and the dot should -disappear: $\vec{\imath}\ \dddot{\jmath}$ (\verb+$\vec{\imath}\ \dddot{\jmath}$+). - -Accents can be used in different ways, \eg strike a single character with a horizontal line like -\verb+$\mathaccent`-A$+: $\mathaccent`-A$ or \verb+$\mathaccent\mathcode`-A$+: $\mathaccent\mathcode`-A$. -In section~\vref{cancel.sty} is a better solution for more than one character. - -\subsection{Over- and underbrackets} -There are no \CIndex{underbracket} and \CIndex{overbracket} -commands in the list of accents. They can be defined in the preamble -with the following code. - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1cm] -\makeatletter -\def\underbracket{% - \@ifnextchar[{\@underbracket}{\@underbracket [\@bracketheight]}% -} -\def\@underbracket[#1]{% - \@ifnextchar[{\@under@bracket[#1]}{\@under@bracket[#1][0.4em]}% -} -\def\@under@bracket[#1][#2]#3{%\message {Underbracket: #1,#2,#3} - \mathop{\vtop{\m@th \ialign {##\crcr $\hfil \displaystyle {#3}\hfil $% - \crcr \noalign {\kern 3\p@ \nointerlineskip }\upbracketfill {#1}{#2} - \crcr \noalign {\kern 3\p@ }}}}\limits} -\def\upbracketfill#1#2{$\m@th \setbox \z@ \hbox {$\braceld$} - \edef\@bracketheight{\the\ht\z@}\bracketend{#1}{#2} - \leaders \vrule \@height #1 \@depth \z@ \hfill - \leaders \vrule \@height #1 \@depth \z@ \hfill \bracketend{#1}{#2}$} -\def\bracketend#1#2{\vrule height #2 width #1\relax} -\makeatother -\end{lstlisting} -%$ -\begin{enumerate} -\item \verb/\underbrace{...}/ is an often used command: -\begin{eqnarray} -\underbrace{{x^{2}+2x+1}} & = & f(x)\\ -\left(x+1\right)^{2}\,\,\,\nonumber -\end{eqnarray} - -\item Sometimes an under\textbf{bracket} is needed, which can be used in - more ways than \verb/\underbrace{...}/. An example for \verb/\underbracket{...}/: - - -\begin{eqnarray*} -\textrm{Hate Science }& \underbracket[0.5pt]{1\rightarrow2\rightarrow3\rightarrow4} - \underbracket[0.75pt][0.75em]{\rightarrow5\rightarrow6\rightarrow7} - \underbracket[1pt][1em]{\rightarrow8\rightarrow9\rightarrow10} & \textrm{Love Science}\\ - & \textrm{low}\hspace{1.5cm}\textrm{medium}\hspace{1.5cm}\textrm{high} - \end{eqnarray*} - - -\end{enumerate} - -\subsubsection{Use of \CMD{underbracket\{...\}}} - -The \verb/\underbracket{...}/ command has two optional parameters: - -\begin{itemize} -\item the line thickness in any valid latex unit, \eg \verb/1pt/ -\item the height of the edge brackets, \eg \verb/1em/ -\end{itemize} -using without any parameters gives the same values for thickness and -height as predefined for the \CIndex{underbrace} command. - - -\vspace{0.3cm} -\begin{center} -\begin{tabular}{|c|c|c|} -\hline -1.& \verb/$\underbracket{foo~bar}$/ & $\underbracket{foo~bar}$ \tabularnewline\hline -2.& \verb/$\underbracket[2pt]{foo~bar}$/ & $\underbracket[2pt]{foo~bar}$ \tabularnewline\hline -3.& \verb/$\underbracket[2pt][1em] {foo~bar}$/& $\underbracket[2pt][1em] {foo~bar}$\tabularnewline\hline -\end{tabular} -\end{center} - - -\subsubsection{Overbracket} - -In addition to the underbracket an overbracket is also useful, which can be used in -more ways than \verb/\overbrace{...}/. For example: - - -\begin{eqnarray*} -\textrm{Hate Science }& \overbracket[0.5pt]{1\rightarrow2\rightarrow3\rightarrow4} - \overbracket[0.75pt][0.75em]{\rightarrow5\rightarrow6\rightarrow7} - \overbracket[1pt][1em]{\rightarrow8\rightarrow9\rightarrow10} & \textrm{Love Science}\\ - & \textrm{low}\hspace{1.5cm}\textrm{medium}\hspace{1.5cm}\textrm{high}\nonumber - \end{eqnarray*} - - -The \verb/\overbracket{...}/ command has two optional parameters: - -\begin{itemize} -\item the line thickness in any valid latex unit, \eg \verb/1pt/ -\item the height of the edge brackets, \eg \verb/1em/ -\end{itemize} -using without any parameters gives the same values for thickness and -height as predefined for the \CIndex{overbrace} command. - - -\vspace{0.3cm} -\begin{center}\begin{tabular}{|c|c|c|} -\hline -1.&\verb/$\overbracket {foo\ bar}$/ & $\overbracket {foo\ bar}$ \tabularnewline\hline -2.&\verb/$\overbracket[2pt] {foo\ bar}$/ &$\overbracket[2pt] {foo\ bar}$ \tabularnewline\hline -3.&\verb/$\overbracket[2pt] [1em] {foo\ bar}$/&$\overbracket[2pt] [1em] {foo\ bar}$\tabularnewline\hline -\end{tabular} -\end{center} - -%$ -\subsection{Vectors} - -Especially for vectors\index{Vector} there is the package \PIndex{esvect}% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/esvect/}% - {CTAN://macros/latex/contrib/esvect/}} package, which looks better than the -\CMD{overrightarrow}\index{overrightarrow@\textbackslash overrightarrow}, \eg - -\begin{table}[!htb] -\centering -\begin{tabular}{c|c} -\textbackslash{}vv\{...\}&\textbackslash{}overrightarrow\{...\}\tabularnewline\hline -$\vv{a}$ & $\overrightarrow{a}$\tabularnewline -$\vv{abc}$ & $\overrightarrow{abc}$\tabularnewline -$\vv{\imath}$ & $\overrightarrow{\imath}$\tabularnewline -$\vv*{A}{x}$ & $\overrightarrow{A}_{x}$\tabularnewline -\end{tabular} -\caption[Vectors with package \texttt{esvect}]% - {Vectors with package \texttt{esvect} (in the right column the default one from \LaTeX{})} -\end{table} - - -Look into the documentation for more details about the package \PIndex{esvect}. - -%$ -\section{Exponents and indices}\label{sec:exponents} -The two active characters \verb|_| and \verb|^| can only be used in math mode. The -\textbf{following} character will be printed as an index (\verb|$y=a_1x+a_0$|: $y=a_1x+a_0$) -or as an exponent (\verb|$x^2+y^2=r^2$|: $x^2+y^2=r^2$). For more than the next character -put it inside of \verb|{}|, like \verb|$a_{i-1}+a_{i+1}<a_i$|: $a_{i-1}+a_{i+1}<a_i$. - -Especially for multiple exponents \index{Multiple exponents} -there are several possibilities. For example: -\begin{equation} -((x^2)^3)^4 = {({(x^2)}^3)}^4 = {\left({\left(x^2\right)}^3\right)}^4 -\end{equation} - -\begin{lstlisting} -((x^2)^3)^4 = -{({(x^2)}^3)}^4 = -{\left({\left(x^2\right)}^3\right)}^4 -\end{lstlisting} - -\index{Upright letters} -For variables with both exponent\index{Exponent} and indice index\index{Indice} -the order is not important, \verb|$a_1^2$| is -exactly the same than \verb|$a^2_1$|: $a_1^2=a^2_1$. By default all exponents and indices -are set as italic characters. It is possible to change this behaviour -to get upright characters. The following example shows this for the indices. - -\bgroup -\begin{LTXexample}[width=4.5cm,preset=\raggedright] -$A_{abc_{xyz}123def}^{abc123def}aa$ - -\makeatletter -\catcode`\_\active -\def_#1{\sb{\operator@font#1}} -\makeatother - -$A_{abc_{xyz}123def}^{abc123def}aa$ -\end{LTXexample} -\egroup - -\section{Operators}\label{sec:ltxOperators} - -They are written in upright font shape and are placed with some additional -space before and after for a better typesetting. With the \AmSmath -package it is possible to define one's own operators\index{Operator} (see -section~\vref{OperatorNames}). Table~\vref{tab:operator} and \vref{tab:operator2} show a list of -the predefined ones for standard \LaTeX{}. - -\begin{table}[htb] -\centering -\begin{tabular}{llllll} -\verb+\coprod+ &$\coprod$ &\verb+\bigvee+ &$\bigvee$ &\verb+\bigwedge+&$\bigwedge$\\ -\verb+\biguplus+&$\biguplus$&\verb+\bigcap+ &$\bigcap$ &\verb+\bigcup+ &$\bigcup$ \\ -\verb+\intop+ &$\intop$ &\verb+\int+ &$\int$ &\verb+\prod+ &$\prod$ \\ -\verb+\sum+ &$\sum$ &\verb+\bigotimes+&$\bigotimes$&\verb+\bigoplus+&$\bigoplus$\\ -\verb+\bigodot+ &$\bigodot$ &\verb+\ointop+ &$\ointop$ &\verb+\oint+ &$\oint$\\ -\verb+\bigsqcup+&$\bigsqcup$&\verb+\smallint+ &$\smallint$ -\end{tabular} -\caption{The predefined operators of \texttt{fontmath.ltx}}\label{tab:operator} -\end{table} -The difference between \CIndex{intop} and \CIndex{int} is that the first one has by default -over/under limits and the second subscript/superscript limits. Both can be changed -with the \CIndex{limits} or \CIndex{nolimits} command. The same behaviour happens to the -\CIndex{ointop} and \CIndex{oint} Symbols. - -\begin{table}[htb] -\centering -\begin{tabular}{llllll} -\verb+\log+ & $\log$ &\verb+\lg+ & $\lg$ &\verb+\ln+ & $\ln$ \\ -\verb+\lim+ & $\lim$ &\verb+\limsup+ & $\limsup$ &\verb+\liminf+ & $\liminf$ \\ -\verb+\sin+ & $\sin$ &\verb+\arcsin+ & $\arcsin$ &\verb+\sinh+ & $\sinh$ \\ -\verb+\cos+ & $\cos$ &\verb+\arccos+ & $\arccos$ &\verb+\cosh+ & $\cosh$ \\ -\verb+\tan+ & $\tan$ &\verb+\arctan+ & $\arctan$ &\verb+\tanh+ & $\tanh$ \\ -\verb+\cot+ & $\cot$ &\verb+\coth+ & $\coth$ &\verb+\sec+ & $\sec$ \\ -\verb+\csc+ & $\csc$ &\verb+\max+ & $\max$ &\verb+\min+ & $\min$ \\ -\verb+\sup+ & $\sup$ &\verb+\inf+ & $\inf$ &\verb+\arg+ & $\arg$ \\ -\verb+\ker+ & $\ker$ &\verb+\dim+ & $\dim$ &\verb+\hom+ & $\hom$ \\ -\verb+\det+ & $\det$ &\verb+\exp+ & $\exp$ &\verb+\Pr+ & $\Pr$ \\ -\verb+\gcd+ & $\gcd$ &\verb+\deg+ & $\deg$ &\verb+\bmod+ & $\bmod$ \\ -\verb+\pmod{a}+& $\pmod{a}$ -\end{tabular} -\caption{The predefined operators of \texttt{latex.ltx}}\label{tab:operator2} -\end{table} - - -\makeatletter -\newcommand\foo{\mathop{\operator@font foo}\nolimits} -\makeatother -For more predefined operator names see table~\vref{tab:amsopn}. It is easy -to define a new operator with -% -\begin{lstlisting} -\makeatletter -\newcommand\foo{\mathop{\operator@font foo}\nolimits} -\makeatother -\end{lstlisting} - -Now you can use \verb|\foo| in the usual way: -% -\begin{LTXexample}[width=4cm] -\[ \foo_1^2 = x^2 \] -\end{LTXexample} -In this example \verb|\foo| is defined with \verb|\nolimits|, means -that limits\index{Limits} are placed in -superscript/subscript mode and not over under. This is still possible with \verb|\limits| in the -definition or the equation: -\begin{LTXexample}[width=4cm] -\[ \foo\limits_1^2 = x^2 \] -\end{LTXexample} - -\AmSmath has an own macro for a definition, have a look at section~\vref{OperatorNames}. - - -\section{Greek letters}\label{sec:greek} -The \AmSmath package simulates a bold font for the greek letters, it writes a -greek character twice with a small kerning. The \verb|\mathbf{<character>}| -doesn't work with lower greek character. See -section \vref{sec:greek-AMS} for the \CIndex{pmb} macro, which makes it possible -to print bold lower greek\index{Greek} letters. Not all upper case letters have -own macro names. If there is no difference to the roman font, then the default -letter is used, \eg A for the upper case of -$\alpha$. Table \ref{tab:greek-letters} shows only those upper case letters -which have own macro names. Some of the lower case letters have an additional -\verb|var| option for an alternative. - -\bgroup -\tabcolsep=3pt -\begin{longtable}{lclccc} -lower & default & upper & default & \verb|\mathbf| & \verb|\mathit|\\\hline -\endhead -\verb|\alpha| & $\alpha$ \\ -\verb|\beta| & $\beta$ \\ -\verb|\gamma| & $\gamma$ - & \verb|\Gamma| & $\Gamma$ & $\mathbf{\Gamma}$ & $\mathit{\Gamma}$\\ -\verb|\delta| & $\delta$ - & \verb|\Delta| & $\Delta$ & $\mathbf{\Delta}$ & $\mathit{\Delta}$\\ -\verb|\epsilon| & $\epsilon$\\ -\verb|\varepsilon| & $\varepsilon$\\ -\verb|\zeta| & $\zeta$\\ -\verb|\eta| & $\eta$ \\ -\verb|\theta| & $\theta$ - & \verb|\Theta| & $\Theta$ & $\mathbf{\Theta}$ & $\mathit{\Theta}$\\ -\verb|\vartheta| & $\vartheta$\\ -\verb|\iota| & $\iota$\\ -\verb|\kappa| & $\kappa$\\ -\verb|\lambda| & $\lambda$ - & \verb|\Lambda| & $\Lambda$ & $\mathbf{\Lambda}$ & $\mathit{\Lambda}$\\ -\verb|\mu| & $\mu$ \\ -\verb|\nu| & $\nu$\\ -\verb|\xi| & $\xi$ - & \verb|\Xi| & $\Xi$ & $\mathbf{\Xi}$ & $\mathit{\Xi}$\\ -\verb|\pi| & $\pi$ - & \verb|\Pi| & $\Pi$ & $\mathbf{\Pi}$ & $\mathit{\Pi}$\\ -\verb|\varpi| & $\varpi$ \\ -\verb|\rho| & $\rho$\\ -\verb|\varrho| & $\varrho$\\ -\verb|\sigma| & $\sigma$ - & \verb|\Sigma| & $\Sigma$ & $\mathbf{\Sigma}$ & $\mathit{\Sigma}$\\ -\verb|\varsigma| & $\varsigma$\\ -\verb|\tau| & $\tau$\\ -\verb|\upsilon| & $\upsilon$ - & \verb|\Upsilon| & $\Upsilon$ & $\mathbf{\Upsilon}$ & $\mathit{\Upsilon}$\\ -\verb|\phi| & $\phi$ - & \verb|\Phi| & $\Phi$ & $\mathbf{\Phi}$ & $\mathit{\Phi}$\\ -\verb|\varphi| & $\varphi$\\ -\verb|\chi| & $\chi$ \\ -\verb|\psi| & $\psi$ - & \verb|\Psi| & $\Psi$ & $\mathbf{\Psi}$ & $\mathit{\Psi}$\\ -\verb|\omega| & $\omega$ - & \verb|\Omega| & $\Omega$ & $\mathbf{\Omega}$ & $\mathit{\Omega}$\\[5pt] -\caption{The greek letters}\label{tab:greek-letters}\\ -\end{longtable} -\egroup - -Bold \Index{greek} letters are possible with the package \PIndex{bm} (see section~\vref{sec:bm}) -and if they should also be upright with the package \PIndex{upgreek}: -\index{greek!upright}\index{greek!bold} - -\medskip -\verb+$\bm{\upalpha}, \bm{\upbeta} ... $+ $ \bm{\upalpha}, \bm{\upbeta} ... $ - -A useful definition maybe: - -\begin{lstlisting} -\usepackage{upgreek} -\makeatletter -\newcommand{\bfgreek}[1]{\bm{\@nameuse{up#1}}} -\makeatother -\end{lstlisting} - -\makeatletter -\newcommand{\bfgreek}[1]{\bm{\@nameuse{up#1}}} -\makeatother -Then -\verb|$\bfgreek{mu}$| will allow you to type $\bfgreek{mu}$ to obtain an upright boldface $\mu$. - - - -\section{Pagebreaks} -\mPar{\CMD{allowdisplaybreaks}}By default a displayed formula cannot -have a pagebreak. This makes some sense, but sometimes it gives a better -typesetting when a pagebreak is possible. - -\begin{verbatim} -\allowdisplaybreaks -\end{verbatim} - -\CIndex{allowdisplaybreaks} enables \TeX{} to insert pagebreaks into -displayed formulas whenever a newline command appears.\index{Pagebreak} -With the command \CIndex{displaybreak} it is also possible to insert a -pagebreak at any place. - -\section{\CMD{stackrel}} - -\CIndex{stackrel} puts a character on top of another one which may be important if a -used symbol is not predefined. For example ``$\stackrel{\wedge}{=}$'' -(\verb|\stackrel{\wedge}{=}|). \mPar{\CMD{stackrel}} -The syntax is - -\begin{lstlisting} -\stackrel{top}{base} -\end{lstlisting} - -Such symbols may be often needed so that a macro definition in the preamble makes some sense: - -\begin{lstlisting} -\newcommand{\eqdef}{% - \ensuremath{\mathrel{\stackrel{\mathrm{def}}{=}}}} -\end{lstlisting} -% -With the \CIndex{ensuremath} command we can use the new \CIndex{eqdef} command in text -and in math mode, \LaTeX{} switches automatically in math mode, which -saves some keystrokes like the following command, which is written -without the delimiters (\texttt{\$...\$}) for the math mode \eqdef , -only \CMD{eqdef} with a space at the end. In math mode -together with another material it may look like -$\vec{x}\eqdef\left(x_{1},\ldots,x_{n}\right)$ and as command sequence - -\begin{lstlisting} -$\vec{x}\eqdef\left(x_{1},\ldots,x_{n}\right)$ -\end{lstlisting} - -The fontsize of the top is one size smaller than the one from the -base, but it is no problem to get both the same size, just increase the -top or decrease the base. - -\section{\CMD{choose}} - -\CIndex{choose}\index{Binom} is like \CIndex{atop} -with delimiters or like \CIndex{frac} -without the fraction line and also with delimiters. It is often used -for binomial coefficients and has the following syntax:\mPar{\CMD{choose}} - -\begin{lstlisting} -{above \choose below} -\end{lstlisting} -The two braces are not really important but it is safe to use them. - -\begin{equation} -{{m+1 \choose n}}={{m \choose n}}+{{m \choose k-1}}\label{eq:choose} -\end{equation} - -\begin{lstlisting} -{{m+1 \choose n}}={{m \choose n}}+{{m \choose k-1}}\label{eq:choose} -\end{lstlisting} - - -See section~\vref{sub:Binoms} for the \AmSmath equivalents and enhancements. - -\section{Color in math expressions}\label{sec:color} -\index{Color}There is no difference in using colored text and colored math expressions. With -\begin{verbatim} -\usepackage{color} -\end{verbatim} - -\noindent in the preamble the macro \verb|\textcolor{<color>}{<text or math>}| exists. -\begin{equation} -\textcolor{blue}{f(x)} = \int\limits_1^{\infty}\textcolor{red}{\frac{1}{x^2}}\,\mathrm{d}x=1 -\end{equation} -\mPar{\CMD{textcolor}} -\begin{lstlisting} -\begin{equation} -\textcolor{blue}{f(x)} = \int\limits_1^{\infty}\textcolor{red}{\frac{1}{x^2}}\,\mathrm{d}x=1 -\end{equation} -\end{lstlisting} - -If all math expressions should be printed in the same color, then it is better -to use the \verb+everydisplay+ macro (section~\vref{sec:other}). - - -\section{Boldmath}\label{sec:boldmath} - -\mPar{\CMD{mathversion}\\\CMD{boldmath}\\\CMD{unboldmath}}% -Writing a whole formula in bold\index{boldmath@\textbackslash boldmath} is possible with the command sequence -\CMD{boldmath} \ldots\ \CMD{unboldmath}, which itself must be written in textmode (outside the -formula) or with the command \verb+{\mathversion{bold} ... }+. -\index{mathversion@\textbackslash mathversion}\index{boldmath@\textbackslash -boldmath}\index{unboldmath@\textbackslash unboldmath} - -\noindent\begin{minipage}{0.49\linewidth} -\[ -\sum_{% - \makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}% - }a_{ij}b_{jk}c_{ki} -\] -\end{minipage}\hfill -\begin{minipage}{0.49\linewidth} -\boldmath -\[ -\sum_{% - \makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}% - }a_{ij}b_{jk}c_{ki} -\] -\unboldmath -\end{minipage} - -\medskip -\begin{lstlisting} -\boldmath -\[ -\sum_{% - \makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}% - }a_{ij}b_{jk}c_{ki} -\] -\unboldmath -\end{lstlisting} - -The \verb+\mathversion+ macro defines a math style which is valid for all following -math expressions. If you want to have all math in bold then use this macro instead of -\CIndex{boldmath}. But it is no problem to put \CIndex{mathversion} inside a group to hold -the changes locally. - -{\mathversion{bold}% -\begin{equation} -y(x) = ax^3+bx^2+cx+d -\end{equation}} - -\begin{lstlisting} -{\mathversion{bold}% -\begin{equation} -y(x) = ax^3+bx^2+cx+d -\end{equation}} -\end{lstlisting} - - -Single characters inside a formula can be written in bold with \CIndex{mathbf}, -but only in upright mode, which is in general not useful as shown in -equation~\ref{eq:bold}. It is better -to use package \PIndex{bm} (see section~\vref{sec:bm}). - -\begin{equation}\label{eq:bold} -\sum_{% - \makebox[0pt]{$% - {{\scriptscriptstyle 1\le j\le p\atop {% - {1\le j\le q\atop 1\le k\le r}}}}% - $}% - }a_{ij}\mathbf{b_{jk}}c_{ki} -\end{equation} - -\subsection[Bold math titles and items]{Bold math expressions as part of titles and items}\label{sec:titleItem} -By default the titles in sections, subsections, a.s.o. are printed in bold. Same for the -\verb|description| environment. The problem is that a math expression in one of these -environments is printed in default font shape, like the following example for a \verb|section| and -\UIndex{description}: - -\medskip -\fbox{% -\begin{minipage}{.75\linewidth} -\section*{\thesection\ Function $f(x)=x^2$} -\begin{description} -\item[This is $y=f(x)$] Only a demonstration. -\item[And $z=f(x,y)$] Another demonstration. -\end{description} -\end{minipage}% -} - -\medskip -With a redefinition of the \CIndex{section} and -\CIndex{item} macros it is possible to get everything in bold font. - -\medskip -\fbox{% -\begin{minipage}{.75\linewidth} -\let\itemOld\item -\makeatletter -\renewcommand\item[1][]{% - \def\@tempa{#1} - \ifx\@tempa\@empty\itemOld\else\boldmath\itemOld[#1]\unboldmath\fi% -} -\makeatother -\section*{\thesection\ \boldmath Function $f(x)=x^2$\unboldmath} -\begin{description} -\item[This is $y=f(x)$] Only a demonstration. -\item[And $z=f(x,y)$] Another demonstration. -\end{description} -\end{minipage}% -} - - -\medskip -\begin{lstlisting} -\let\itemOld\item -\makeatletter -\renewcommand\item[1][]{% - \def\@tempa{#1} - \ifx\@tempa\@empty\itemOld\else\boldmath\itemOld[#1]\unboldmath\fi% -} -\makeatother -\let\sectionOld\section -\renewcommand\section[2][\empty]{% - \boldmath\sectionOld[#1]{#2}\unboldmath% -} -\end{lstlisting} - -\section{Multiplying numbers} -When the dot is used as the decimal marker as in the United States, the preferred sign -for the multiplication of -numbers or values of quantities is a cross (\verb|\times| $\times$ ), not a half-high and -centered dot (\verb|\cdot| $\cdot$ ). - -When the comma is used as the decimal marker as in Europe, the preferred sign for the -multiplication of -numbers is the half-high dot. The multiplication of quantity symbols (or numbers in -parentheses or values of -quantities in parentheses) may be indicated in one of the following ways: $ab$, -$a\cdot b$, $a\times b$. - -For more information see ``Nist Guide to SI Units -More on Printing and Using Symbols and -Numbers in Scientific and -Technical Documents''\footnote{\url{http://physics.nist.gov/Pubs/SP811/sec10.html}} or -the German DIN 1304, Teil 1. - - -\section{Other macros}\label{sec:other} -\mPar{\CMD{everymath}\\\CMD{everydisplay}\\\CMD{underline}}% -There are some other macros which are not mentioned in the foregoing text. Here comes -a not really complete list of these macros. -\begin{description} -\item[\CMD{everymath}] \index{everymath@\textbackslash everymath} puts the argument before -any inlined math expression, \eg \verb+\everymath{\displaysize}+. Using this macro doesn't really -make sense, when one is using footnotes because the footnote number is printed as superscript in -inline mathmode and an \CMD{everymath} will be valid, too. -\item[\CMD{everydisplay}] \index{everydisplay@\textbackslash everydisplay} puts the -argument before any displayed math expression, \eg \verb+\everydisplay{\color{blue}}+. -\item[\CMD{underline}] \index{underline@\textbackslash underline} underlines a math -expression and has to be used inside the math mode. -\[ -\underline{F(x)=\int f(x)\,\mathrm{d}x} -\] -\end{description} - - - -\part{\texorpdfstring{\AmSmath}{amsmath} package}\label{par:AMSmath-package} - -In general the \AmS packages are at least a collection of three different ones: -\begin{enumerate} -\item \verb|amsmath.sty| -\item \verb|amssymb.sty| -\item \verb|amsfonts.sty| -\end{enumerate} -In the following only the first one is described in detail. - -The \AmSmath has the following options: - -\bigskip\noindent -\begin{tabularx}{\linewidth}{@{}lX@{}} -\verb+centertags+\index{centertags} & (default) For a split equation, place -equation numbers vertically centered on the total height of the equation.\\\hline -\verb+tbtags+\index{tbtags} & `Top-or-bottom tags' For a split equation, -place equation numbers level with the last (resp. first) line, if -numbers are on the right (resp. left).\\\hline -\verb+sumlimits+\index{sumlimits} & (default) Place the subscripts and superscripts -of summation symbols above and below, in displayed equations. This -option also affects other symbols of the same type -- $\prod$, $\coprod$, -$\bigotimes$, $\bigoplus$, and so forth -- but excluding integrals -(see below).\\\hline -\verb+nosumlimits+\index{nosumlimits} & Always place the subscripts and -superscripts of summation-type symbols to the side, even in displayed -equations.\\\hline -\verb+intlimits+\index{intlimits} & Like sumlimits, but for integral symbols.\\\hline -\verb+nointlimits+\index{nointlimits} & (default) Opposite of intlimits.\\\hline -\verb+namelimits+\index{namelimits} & (default) Like sumlimits, but for -certain `operator names' such as \verb+det+, \verb+inf+, \verb+lim+, \verb+max+, \verb+min+, that traditionally -have subscripts placed underneath when they occur in a displayed equation.\\\hline -\verb+nonamelimits+\index{nonamelimits} & Opposite of namelimits.\\\hline -\end{tabularx} -\bigskip - -To use one of these package options, put the option name in the optional -argument, \eg -\verb|\usepackage[intlimits]{amsmath}|. The %%% ----- Martin ----- -\AmSmath also recognises the following options which are normally -selected (implicitly or explicitly) through the \verb|documentclass| -command, and thus need not be repeated in the option list of the \verb|\usepackage{amsmath}| statement. %%% ----- Martin ----- - -\bigskip\noindent -\begin{tabularx}{\linewidth}{@{}lX@{}} -\verb+leqno+\index{leqno} & Place equation numbers on the left.\\\hline -\verb+reqno+\index{reqno} & (default) Place equation numbers on the right.\\\hline -\verb+fleqn+\index{fleqn} & Position equations at a fixed indent from the -left margin rather than centered in the text column. \AmSmath defines the -length \CMD{mathindent} and uses it when the equations have only one -tabbing character (\verb+&+).\index{mathindent@\textbackslash mathindent}\\\hline -\end{tabularx} - -\bigskip\noindent All math environments are displayed ones, so there is no special inline -math. - -\section{\texttt{align} environments} - -There are four different align environments, described in the following -subsections. Their behaviour is shown in table \ref{cap:align}. The symbolic -code for all align environments is: - -\begin{lstlisting} -\begin{<name>} - <name> &= x & x &= x\\ - <name> &= x & x &= x -\end{<name>} -\end{lstlisting} - -\begin{table}[htb] -\caption[Comparison between the different align environments]{Comparison between the different align environments -with the same code, where the first three can have an equation number}\label{cap:align} -\begin{align*} -\framebox[0.125\columnwidth]{align} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x}&= \framebox[0.125\columnwidth]{x}\\ -\framebox[0.125\columnwidth]{align}&= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} -\end{align*} - -\begin{alignat*}{2} -\framebox[0.125\columnwidth]{alignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ -\framebox[0.125\columnwidth]{alignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} -\end{alignat*} - -\begin{flalign*} -\framebox[0.125\columnwidth]{flalign} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ -\framebox[0.125\columnwidth]{flalign} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} -\end{flalign*} - -\begin{xalignat*}{2} -\framebox[0.125\columnwidth]{xalignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ -\framebox[0.125\columnwidth]{xalignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} -\end{xalignat*} - -\begin{xxalignat}{2} -\framebox[0.125\columnwidth]{xxalignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\ -\framebox[0.125\columnwidth]{xxalignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x} -\end{xxalignat} - -\end{table} - -In difference to the \UIndex{eqnarray} from standard \LaTeX{} -(section~\ref{display:eqnarray}), the ``three'' parts -of one equation \verb+expr.-symbol-expr.+ are divided by only one ampersand %%% ----- Martin ----- -in two parts. In general the ampersand should be before the symbol to get the right spacing, -\eg \verb+y &= x+. Compare the following three equations, the second one has a wrong spacing. %%% ----- Martin ----- - - -\noindent -~\hfill\includegraphics{amsalign} - -\iffalse -\begin{minipage}{0.4\linewidth} -\begin{align} -\rnode[lt]{a}{y} &= \rnode[rt]{A}{x} -\end{align} -\vspace*{-3\abovedisplayskip} -\begin{align} -y =& x -\end{align} -\vspace*{-3\abovedisplayskip} -\begin{align} -\rnode[lb]{b}{y} ={}& \rnode[rb]{B}{x} -\end{align} -\ncline[nodesep=-10pt,linewidth=0.1pt]{A}{B} -\ncline[nodesepA=-11pt,nodesepB=-10pt,linewidth=0.1pt]{a}{b} -\end{minipage} -\hfill\begin{minipage}{0.4\linewidth} -\begin{lstlisting} - y &= x - y =& x - y ={}& x -\end{lstlisting} -\end{minipage} -\fi - -\subsection{The default \texttt{align} environment} - -The \texttt{eqnarray} environment has a not so good spacing between -the cells. Writing the equations no. \ref{eq:2} to \ref{eq:5} with -the \texttt{align} environment gives: - -\begin{align} - y & =d\label{eq:IntoSection}\\ - y & =cx+d\\ - y_{12} & =bx^{2}+cx+d\\ - y(x) & =ax^{3}+bx^{2}+cx+d -\end{align} - -\noindent The code looks like: -\begin{lstlisting} -\begin{align} - y & =d\label{eq:IntoSection}\\ - y & =cx+d\\ - y_{12} & =bx^{2}+cx+d\\ - y(x) & =ax^{3}+bx^{2}+cx+d -\end{align} -\end{lstlisting} - -\begin{itemize} -\item The \texttt{align} environment has an implicit \textbf{\{rlrl...\}} -horizontal alignment with a vertical column-alignment, \eg -\begin{LTXexample}[width=0.5\linewidth] -\begin{align*} - 1 & 2 & 3 -\end{align*} -\end{LTXexample} - -\item A nonumber-version \texttt{\small \textbackslash{}begin\{align{*}\}...\textbackslash{}end\{align{*}\}} -exists. -\item Unnumbered single rows are possible with \CMD{nonumber}. %%% ----- Martin ----- -\item The \texttt{align} environment takes the whole horizontal space if -you have more than two columns: -\begin{align} -y & =d & z & =1\\ -y & =cx+d & z & =x+1\\ -y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\ -y(x) & =ax^{3}+bx^{2}+cx+d & z & =x^{3}+x^{2}+x+1 -\end{align} - -\end{itemize} -The code for this example looks like% -\begin{lstlisting} -\begin{align} - y & =d & z & =1\\ - y & =cx+d & z & =x+1\\ - y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\ - y(x) & =ax^{3}+bx^{2}+cx+d & z & =x^{3}+x^{2}+x+1 -\end{align} -\end{lstlisting} - -\subsection{\texttt{alignat} environment\label{sec:alignat environment}} -\mPar{\CMD{begin\{align\}\\...\\\CMD{end\{align\}}}} -\renewcommand{\theequation}{% - \thepart-\arabic{equation}% -} - -\begin{leftbar} ->From now the counting of the equation changes. It is introduced with a foregoing command, -which doesn't really make sense, it is only for demonstration:\\ -\verb|\renewcommand{\theequation}{\thepart-\arabic{equation}}|. -\end{leftbar} - - -This means ``align at several places{}'' and is something like -more than two \verb+align+ environment side by side. -Parameter is the number of the \verb+align+ environments, which -is not important for the user. The -above last \verb+align+ example looks like: - -\begin{alignat}{2} -y & =d & z & =1\label{eq:newCounting}\\ -y & =cx+d & z & =x+1\\ -y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\ -y(x) & =ax^{3}+bx^{2}+cx+d\quad & z & =x^{3}+x^{2}+x+1\end{alignat} - - -The parameter was 2 and it is 3 for the following example: %%% ----- Martin ----- - -\begin{alignat}{3} -i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\ -i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ -i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11}\end{alignat} - - -For this example the code is: -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{alignat}{3} - i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ - i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ - i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11} -\end{alignat} -\end{lstlisting} - -With the \verb+alignat+ environment one can easily align equations vertically -at more than one marker: - -\begin{alignat}{3} - abc &= xxx &&= xxxxxxxxxxxx &&= aaaaaaaaa \\ - ab &= yyyyyyyyyyyyyyy &&= yyyy &&= ab -\end{alignat} -\begin{lstlisting} -\begin{alignat}{3} - abc &= xxx &&= xxxxxxxxxxxx &&= aaaaaaaaa \\ - ab &= yyyyyyyyyyyyyyy &&= yyyy &&= ab -\end{alignat} -\end{lstlisting} - - - - -\begin{itemize} -\item The \texttt{alignat} environment has an implicit \{rlrl...rlrl\} -horizontal alignment with a vertical column alignment. -\item A nonumber-version \texttt{\small -\textbackslash{}begin\{alignat{*}\}...\textbackslash{}end\{alignat{*}\}} -exists. -\item Unnumbered single rows are possible with \CMD{nonumber}. %%% ----- Martin ----- -\end{itemize} - -\subsection{\texttt{flalign} environment}\label{ams:flalign} -\mPar{\CMD{begin\{flalign\}\\...\\\CMD{end\{flalign\}}}}This is the new replacement for the \texttt{xalignat} and \texttt{xxalignat} -environments. It is nearly the same as the \texttt{xalignat} environment, only -more ``out spaced'' and ``left aligned''. - -\begin{LTXexample}[width=0.5\linewidth] -\begin{flalign} -i_{11} & =0.25\nonumber \\ -i_{21} & =\frac{1}{3}i_{11}\\ -i_{31} & =0.33i_{22} -\end{flalign} -\end{LTXexample} - -\medskip -As seen, the equations are not really left aligned, when they have only one -ampersand. In this case \verb+flalign+ has the same behaviour as the \verb+align+ -environment.\index{Alignment!left}\index{Indentation} - - -When there are more than one tabbing characters (\verb+&+), then the equations are -really left aligned. This is also an easy way to get an equation with only one -ampersand left aligned, see equation \ref{eq:leftaligned} below. -\begin{flalign} -i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\ -i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ -i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} -\end{flalign} -The code looks like: - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{flalign} - i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ - i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ - i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11} -\end{flalign} -\end{lstlisting} - -\medskip -This environment can be used to mix centered and left aligned\index{Left aligned} -equations without -using the document wide valid option \verb|fleqn|. -\begin{align}\label{eq:centered} - f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x -\end{align} - -\begin{flalign}\label{eq:leftaligned} - f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x & -\end{flalign} -Equation \ref{eq:leftaligned} is left aligned in fact of the second tabbing -character \verb|&|. - -\begin{lstlisting} -\begin{align}\label{eq:centered} - f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x -\end{align} - -\begin{flalign}\label{eq:leftaligned} - f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x & -\end{flalign} -\end{lstlisting} - -Another case is placing text left aligned, whereas the formulas should be right aligned. - -\begin{flalign*} - && 12(x-1)+20(y-3)+14(z-2) &= 0\\ -\text{same as } && 6x+10y+7z &= 0 -\end{flalign*} - -\begin{lstlisting} -\begin{flalign*} - && 12(x-1)+20(y-3)+14(z-2) &= 0\\ -\text{same as } && 6x+10y+7z &= 0 -\end{flalign*} -\end{lstlisting} - - -\subsection{\texttt{xalignat} environment} -\mPar{\CMD{begin\{xalignat\}\\...\\\CMD{end\{xalignat\}}}}% -This is an obsolete macro but still supported by the \AmSmath package. -Same as \texttt{alignat} environment, only a little more ``out spaced{}''. -\begin{xalignat}{3} -i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\ -i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ -i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} -\end{xalignat} -The same code looks like: - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{xalignat}{3} - i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ - i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ - i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11} -\end{xalignat} -\end{lstlisting} - -\subsection{\texttt{xxalignat} environment} -\mPar{\CMD{begin\{xxalignat\}\\...\\\CMD{end\{xxalignat\}}}}% -Like \texttt{xalignat} an obsolete macro but still supported by the \AmSmath package. -Same as \texttt{align} environment, only extremely ``out spaced{}'', -therefore no equation number! -\begin{xxalignat}{3} -i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\\ -i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\ -i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} -\end{xxalignat} -The same code looks like: - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{xxalignat}{3} - i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\ - i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\ - i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11} -\end{xxalignat} -\end{lstlisting} - - -\subsection{\texttt{aligned} environment}\label{sec:aligned} - -\mPar{\CMD{begin\{aligned\}\\...\\\CMD{end\{aligned\}}}}In difference to the -\verb|split| environment (section \vref{split})\index{Split equation}, the -\verb|aligned| environment allows more than one horizontal alignment but has -also only one equation number: -% -\begin{equation} -\begin{aligned} - 2x+3 &= 7 & 2x+3-3 &=7-3 \\ - 2x &= 4 & \frac{2x}2 &=\frac42\\ - x &= 2 -\end{aligned} -\end{equation} - -\begin{lstlisting} -\begin{equation} -\begin{aligned} - 2x+3 &= 7 & 2x+3-3 &= 7-3 \\ - 2x &= 4 & \frac{2x}2 &= \frac42\\ - x &= 2 -\end{aligned} -\end{equation} -\end{lstlisting} - -The \verb|aligned| environment is similar to the \verb|array|\index{array} -environment, there exists no -starred version and it has only one equation number and has to be part of -another math environment, which should be \verb|equation| environment. -The advantage of \verb|aligned| is the much - better horizontal and vertical spacing. %%% ----- Martin ----- - - -\subsection{Problems} -When using one of the \verb+align+ environments, there should be no \verb+\\+ at the -end of the last line, otherwise you'll get another equation number for this -``empty{}'' line: %%% ----- Martin ----- - -\begin{LTXexample}[width=0.65\linewidth] -\begin{align} - 2x+3 &= 7\\ -\end{align} -\end{LTXexample} - -\begin{LTXexample}[width=0.65\linewidth] -\begin{align} - 2x+3 &= 7 -\end{align} -\end{LTXexample} -\section{Other environments} - - -\subsection{\texttt{gather} environment} - -\mPar{\CMD{begin\{gather\}\\...\\\CMD{end\{gather\}}}} -This is like a multi line environment with no special horizontal alignment. -All rows are centered and can have an own equation number: -% -\begin{gather} -i_{11}=0.25\\ -i_{21}=\frac{1}{3}i_{11}\nonumber \\ -i_{31}=0.33i_{22} -\end{gather} -% -For this example the code looks like: -\begin{lstlisting} -\begin{gather} - i_{11} = 0.25\\ - i_{21} = \frac{1}{3}i_{11}\nonumber\\ - i_{31} =0.33i_{22} -\end{gather} -\end{lstlisting} - -\begin{itemize} -\item The \texttt{gather}\index{gather} environment has an implicit \texttt{\{c\}} -horizontal alignment with no vertical column alignment. It is just -like an one column array/table. -\item A nonumber-version \texttt{\small \textbackslash{}begin\{gather{*}\}...\textbackslash{}end\{gather{*}\}} -exists. -Look at section \vref{split} for an example. -\end{itemize} - -\subsection{\texttt{gathered} environment} -\mPar{\CMD{begin\{gathered\}[c]\\...\\\CMD{end\{gathered\}}}} - -The \verb+gathered+ environment is like the \verb+aligned+ or \verb+alignat+ -\index{gathered}\index{aligned}\index{alignat} -environment. They use only so much horizontal space as the widest line needs. -In difference to the \verb+gather+ environment it must be itself inside the -math mode. -% -\begin{align} -\rule{2cm}{1pt} -\begin{gathered} -\quad i_{11}=0.25\\ -\quad i_{21}=\frac{1}{3}i_{11}\\ -\quad i_{31}=0.33i_{22} -\end{gathered} -\rule{2cm}{1pt} -\end{align} - -% -\begin{lstlisting} -\begin{align} -\rule{2cm}{1pt} -\begin{gathered} -\quad i_{11}=0.25\\ -\quad i_{21}=\frac{1}{3}i_{11}\\ -\quad i_{31}=0.33i_{22} -\end{gathered} -\rule{2cm}{1pt} -\end{align} -\end{lstlisting} -% - -The optional argument can be used for setting the vertical alignment which is -by default c (centered). It can also be t for top or b for bottom. - -\begin{align} -\rule{1cm}{1pt} -\begin{gathered}[t] -\quad A=a\\ -\quad B=b\\ -\quad C=c -\end{gathered} -% -\begin{gathered}[c] -\quad A=a\\ -\quad B=b\\ -\quad C=c -\end{gathered} -% -\begin{gathered}[b] -\quad A=a\\ -\quad B=b\\ -\quad C=c -\end{gathered} -\ \rule{1cm}{1pt} -\end{align} - -\begin{lstlisting} -\begin{align} -\rule{1cm}{1pt} -\begin{gathered}[t] -\quad A=a\\ -\quad B=b\\ -\quad C=c -\end{gathered} -% -\begin{gathered}[c] -\quad A=a\\ -\quad B=b\\ -\quad C=c -\end{gathered} -% -\begin{gathered}[b] -\quad A=a\\ -\quad B=b\\ -\quad C=c -\end{gathered} -\ \rule{1cm}{1pt} -\end{align} -\end{lstlisting} - - -When using a square bracket as first character inside the environment, then -everything is ignored by \AmS until a following closing bracket, because \AmS takes this -as an optional argument: -% -\begin{align} -\begin{gathered} -[A]\quad A=a\\ -[B]\quad B=b\\ -[C]\quad C=c -\end{gathered} -\end{align} -% -\begin{lstlisting} -\begin{align} -\begin{gathered} -[A]\quad A=a\\ -[B]\quad B=b\\ -[C]\quad C=c -\end{gathered} -\end{align} -\end{lstlisting} -% -The \verb+[A]+ is completely ignored, which can be avoided by using the -optional argument \verb+[c]+ or at least an empty one directly -after the \verb+\begin{gather}+. Another possibility is using the package \verb+empheq+, -which fixes this behaviour by default. -% -\begin{align} -\begin{gathered}[] -[A]\quad A=a\\ -[B]\quad B=b\\ -[C]\quad C=c -\end{gathered} -\end{align} -% -\begin{lstlisting} -\begin{align} -\begin{gathered}[] -[A]\quad A=a\\ -[B]\quad B=b\\ -[C]\quad C=c -\end{gathered} -\end{align} -\end{lstlisting} -% - - -\subsection{\texttt{multline} environment} -\mPar{\CMD{begin\{multline\}\\...\\\CMD{end\{multline\}}}} -This is also like a multi line% -\footnote{It is no typo, the name of the environment is \texttt{multline}, no -missing i here!} environment with a special vertical alignment. The \textbf{first} -row is \textbf{left aligned}, the second and all following ones except -the last one are \textbf{centered} and the \textbf{last} line is \textbf{right -aligned}. It is often used to write extremely long formulas: - - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{multline} - A = \lim _{n\rightarrow \infty }\Delta x\left( a^{2}+\left( a^{2}+2a\Delta x - +\left( \Delta x\right) ^{2}\right)\right.\\ - +\left( a^{2}+2\cdot 2a\Delta x+2^{2}\left( \Delta x\right) ^{2}\right)\\ - +\left( a^{2}+2\cdot 3a\Delta x+3^{2}\left( \Delta x\right) ^{2}\right)\\ - + \ldots\\ - \left.+\left( a^{2}+2\cdot (n-1)a\Delta x +(n-1)^{2}\left( \Delta x\right) ^{2}\right) \right)\\ - = \frac{1}{3}\left( b^{3}-a^{3}\right) -\end{multline} -\end{lstlisting} -\begin{multline} -A=\lim_{n\rightarrow\infty}\Delta x\left(a^{2}+\left(a^{2}+2a\Delta x+\left(\Delta x\right)^{2}\right)\right.\label{eq:reset}\\ -+\left(a^{2}+2\cdot2a\Delta x+2^{2}\left(\Delta x\right)^{2}\right)\\ -+\left(a^{2}+2\cdot3a\Delta x+3^{2}\left(\Delta x\right)^{2}\right)\\ -+\ldots\\ -\left.+\left(a^{2}+2\cdot(n-1)a\Delta x+(n-1)^{2}\left(\Delta x\right)^{2}\right)\right)\\ -=\frac{1}{3}\left(b^{3}-a^{3}\right) -\end{multline} - - -\begin{figure}[htb] -\begin{multline} -\framebox[0.5\columnwidth]{x}\\ -\framebox[0.5\columnwidth]{x}\\ -\framebox[0.5\columnwidth]{x}\\ -\shoveright{\framebox[0.5\columnwidth]{x}}\\ -\framebox[0.5\columnwidth]{x}\\ -\framebox[0.5\columnwidth]{x} -\end{multline} -\caption{\texttt{multline} Alignment demo -(the fourth row is shifted to the right with \CMD{shoveright})} -\label{cap:multline-Alignment-Demo} -\end{figure} - -\begin{figure}[htb] -\begin{minipage}[c]{0.45\textwidth}% -\fbox{\parbox{\columnwidth}{\begin{multline} -\framebox[0.5\columnwidth]{\textrm{\textbackslash multlinegap=}}\\ -\framebox[0.5\columnwidth]{\the\multlinegap}\end{multline} -}} -\end{minipage}% -\hfill{}\begin{minipage}[c]{0.45\textwidth}% -{\setlength{\multlinegap}{0pt}\fbox{\parbox{\columnwidth}{\begin{multline} -\framebox[0.5\columnwidth]{\textbackslash\textrm{multlinegap=}}\\ -\framebox[0.5\columnwidth]{\the\multlinegap}\end{multline} -}}} -\end{minipage}% -\caption{\label{cap:multlinegap}Demonstration of \CMD{multlinegap} (default is 0pt)} -\end{figure} - - - -\begin{itemize} -\item A nonumber-version \CMD{begin\{multline{*}\}...}\CMD{end\{multline{*}\}} -exists. -\item By default only the last line (for right equation numbers) or the -first line (for left equation numbers) gets a number, the others can't. -\item The alignment of a single line can be changed with the command -\CMD{shoveright}\index{shoveright@\textbackslash shoveright} (figure \vref{cap:multline-Alignment-Demo}) -\item The first line and the last line have a small gap to the text border.% -\footnote{When the first (numbers left) or last line (numbers right) has an -equation number then \CMD{multlinegap} is not used -for these ones, only for the line without a number.} See figure \ref{cap:multlinegap}, where the length of \CMD{multlinegap}\index{multlinegap@\textbackslash multlinegap} -is set to \texttt{0pt} for the right one. -\end{itemize} - -\subsubsection{Examples for \texttt{multline}}\label{sec:Specials-for-multline} - -With the multline environment the equation~\vref{eq:braces} looks like: - -\begin{multline} -\frac{1}{2}\Delta(f_{ij}f^{ij})=2\left(\sum_{i<j}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2} - +f^{ij}\nabla_{j}\nabla_{i}(\Delta f)+\right.\\ -+\left.\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}\left[2\nabla_{i}R_{jk}-\nabla_{k}R_{ij} - \right]\right) -\end{multline} -% -which is again a bad typesetting because of the two unequal parentheses. -Each one has a size which is correct for the line but not for the -whole formula. \LaTeX{} accepts only pairs of parentheses for one -line and has an ``empty{}'' parentheses, the dot ``\texttt{\textbackslash{}left.}'' -or ``\texttt{\textbackslash{}right.}''{} to get only one of the ``pair{}''. -There are different solutions to get the right size of the parentheses. -One of them is to use the \CMD{vphantom} command, -which reserves the vertical space without any horizontal one, like -a vertical rule without any thickness. The sum symbol from the first -line is the biggest one and responsible for the height, so this one is -the argument of \CMD{vphantom} which has to be -placed anywhere. - -\begin{multline} -\frac{1}{2}\Delta(f_{ij}f^{ij})= - 2\left(\sum_{i<j}\chi_{ij}(\sigma_{i}- - \sigma_{j})^{2}+f^{ij}\nabla_{j}\nabla_{i}(\Delta f)+\right.\\ - \left.+\nabla_{k}f_{ij}\nabla^{k}f^{ij}+ - f^{ij}f^{k}\left[2\nabla_{i}R_{jk}- - \nabla_{k}R_{ij}\right]\vphantom{\sum_{i<j}}\right) -\end{multline} -% -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{multline} -\frac{1}{2}\Delta(f_{ij}f^{ij})= - 2\left(\sum_{i<j}\chi_{ij}(\sigma_{i}- - \sigma_{j})^{2}+f^{ij}\nabla_{j}\nabla_{i}(\Delta f)+\right.\\ - \left.+\nabla_{k}f_{ij}\nabla^{k}f^{ij}+ - f^{ij}f^{k}\left[2\nabla_{i}R_{jk}- - \nabla_{k}R_{ij}\right]\vphantom{\sum_{i<j}}\right) -\end{multline} -\end{lstlisting} -% -Instead of using the \CMD{vphantom} command it is -also possible to use fixed-width parentheses, which is described in -section \vref{sec:Brackets,-Braces-and}. - - -A math expression with a very long fraction like the following one, which runs out -of the margin -could be written as a multiplication to avoid the fraction line. -% -%\begin{LTXexample}[pos=t,xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{equation} -\frac{\mathrm{d}G_\infty}{\mathrm{d}n}=\frac{\left[1-e^{-pn}\right] - \left[Q\left(n\right)-pR\left(n\right)+R'\left(n\right)\right]e^{-pn} - -\left[-\frac{Q \left(n\right)e^{-pn}}{p}+\frac{Q\left(0\right)}{p}+R - \left(n\right)e^{-pn} - A\right] pe^{-pn}}{\left({1-e^{-pn}}\right)^2} = 0 -\end{equation} -%\end{LTXexample} -% -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{equation} -\frac{\mathrm{d}G_\infty}{\mathrm{d}n}=\frac{\left[1-e^{-pn}\right] - \left[Q\left(n\right)-pR\left(n\right)+R'\left(n\right)\right]e^{-pn} - -\left[-\frac{Q \left(n\right)e^{-pn}}{p}+\frac{Q\left(0\right)}{p}+R - \left(n\right)e^{-pn} - A\right] pe^{-pn}}{\left({1-e^{-pn}}\right)^2} = 0 -\end{equation} -\end{lstlisting} -% -With the \verb+multline+ environment it can then be split into two or more parts: -% -\begin{LTXexample}[pos=t,xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{multline} -\frac{\mathrm{d}G_\infty}{\mathrm{d}n} = - \frac{1}{\left( {1-e^{-pn}} \right)^2 }\cdot - \left\{\vphantom{\frac{Q}{p}}% >>>> to get the correct height <<<<< - \left[ 1-e^{-pn} \right] \left[ Q \left( n \right) - pR - \left( n \right) + R'\left( n \right) \right]e^{-pn}\right.\\ - - \left.\left[-\frac{Q \left( n \right) e^{-pn}}{p} + - \frac{Q \left( 0 \right)}{p} + R \left( n \right) e^{-pn} - - A\right] pe^{-pn}\right\} = 0 -\end{multline} -\end{LTXexample} - - - -\subsection{\texttt{split} environment}\label{split} - -\mPar{\CMD{begin\{split\}\\...\\\CMD{end\{split\}}}}% -\makeatletter -\@removefromreset{equation}{section} -\makeatother -% -\begin{leftbar} -\noindent From now on the counting of the equations changes. It is introduced with a -foregoing command, which doesn't really make sense, it is only -for demonstration: -\begin{lstlisting} -\makeatletter -\@removefromreset{equation}{section} -\makeatother -\end{lstlisting} -\end{leftbar} - - -The \verb|split| environment is like the \verb|multline|\index{multline} -or \verb|array| environment for equations longer than the column -width. Just like the array environment and in contrast to \verb|multline|, -\verb|split| can only be used as \textbf{part of another environment}. -\verb|split| itself has no own numbering, this is given by the other -environment. Without an ampersand all lines in the split environment -are right-aligned and can be aligned at a special point by using an -ampersand. In difference to the \verb|aligned| environment (section \vref{sec:aligned}), the \verb|split| environment permits more than one horizontal alignment. - -It is important that the split environment has another behaviour when used inside one of the %%% ----- Martin ----- -``old'' \LaTeX{} environments \verb+\[...\]+ or \verb+\begin{equation}+ \verb+...+\verb+ \end{equation}+, in this -case more than one horizontal alignment tabs are possible. - -\hspace*{-\marginparwidth}% -\begin{minipage}{0.5\columnwidth} -\[ -\begin{split} - \framebox[0.35\columnwidth]{x}\\ - \framebox[0.75\columnwidth]{x}\\ - \framebox[0.65\columnwidth]{x}\\ - \framebox[0.95\columnwidth]{x} -\end{split} -\] -\end{minipage}\hfill% -\begin{minipage}{0.5\columnwidth} -\footnotesize\begin{verbatim} -\[ -\begin{split} - \framebox[0.35\columnwidth]{x}\\ - \framebox[0.75\columnwidth]{x}\\ - \framebox[0.65\columnwidth]{x}\\ - \framebox[0.95\columnwidth]{x} -\end{split} -\] -\end{verbatim} -\end{minipage} -\vspace{2ex} - -\hspace*{-\marginparwidth}% -\begin{minipage}{0.5\columnwidth} -\[ -\begin{split} - \vec{a} = {}&\framebox[0.35\columnwidth]{x}\\ - &\framebox[0.75\columnwidth]{x}\\ - &\framebox[0.65\columnwidth]{x}\\ - &\framebox[0.95\columnwidth]{x} -\end{split} -\] -\end{minipage}\hspace{1cm}% -\begin{minipage}{0.5\columnwidth} -\footnotesize% -\begin{verbatim} -\[ -\begin{split} - \vec{a} = {}&\framebox[0.35\columnwidth]{x}\\ - &\framebox[0.75\columnwidth]{x}\\ - &\framebox[0.65\columnwidth]{x}\\ - &\framebox[0.95\columnwidth]{x} -\end{split} -\] -\end{verbatim} -\end{minipage} -\vspace{1ex} - -The following example shows the \texttt{split} environment as part -of the \texttt{equation} environment: - -\begin{equation} -\begin{split}A_{1} & =\left|\int_{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right|+\left|\int_{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right|\\ - & =\left|\int_{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right|+\left|\int_{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right|\\ - & =\left|\frac{x^{3}}{3}-\frac{3}{2}x^{2}\right|_{0}^{1}+\left|\frac{x^{3}}{3}-\frac{5}{2}x^{2}+6x\right|_{1}^{2}\\ - & =\left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}-\frac{5}{2}+6\right)\right|\\ - & =\left|-\frac{7}{6}\right|+\left|\frac{14}{3}-\frac{23}{6}\right|=\frac{7}{6}+\frac{5}{6}=2\,\textrm{FE}\end{split} -\label{eq:Beispiel-Integral}\end{equation} - - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{equation} - \begin{split} - A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left| - \int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\ - & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left| - \int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\ - & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+ - \left| \frac{x^{3}}{3}- - \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\ - & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left| - \frac{8}{3}-\frac{20}{2}+12- - \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\ - & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6} - \right| =\frac{7}{6}+\frac{5}{6}=2\, \textrm{FE} - \end{split} -\end{equation} -\end{lstlisting} - -\bigskip{} -The same using the \verb|array| environment with \verb|{rl}|-alignment -instead of \verb|split| gives same horizontal alignment, but another %%% ----- Martin ----- -vertical spacing% -\footnote{Can be changed with \texttt{\textbackslash renewcommand\textbackslash arraystretch\{1.5\}}} and the -symbols are only in scriptsize and not textsize:\footnote{See section \vref{sec:Styles}} %%% ----- Martin ----- - -\begin{equation} -\begin{array}{rl} -A_{1} & =\left|\int_{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right|+\left|\int_{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right|\\ - & =\left|\int_{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right|+\left|\int_{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right|\\ - & =\left|\frac{x^{3}}{3}-\frac{3}{2}x^{2}\right|_{0}^{1}+\left|\frac{x^{3}}{3}-\frac{5}{2}x^{2}+6x\right|_{1}^{2}\\ - & =\left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}-\frac{5}{2}+6\right)\right|\\ - & =\left|-\frac{7}{6}\right|+\left|\frac{14}{3}-\frac{23}{6}\right|=\frac{7}{6}+\frac{5}{6}=2\,\textrm{FE} - \end{array} - \end{equation} - -Compare the following two examples for typesetting the minus sign. In the first case it -is typeset similiar to the plus character, and in the second example it is typeset -without the additional space for a binary math atom. - -\begin{minipage}{0.49\linewidth} -\begin{align} -\begin{split} -a = {} & -b + c \\ - & -d + e -\end{split} -\end{align} -% -\begin{align} -\begin{split} -a = {} & {-}b + c \\ - & {-}d + e -\end{split} -\end{align} -\end{minipage}\hfill -\begin{minipage}{0.49\linewidth} -\begin{lstlisting} -\begin{align} -\begin{split} -a = {} & -b + c \\ - & -d + e -\end{split} -\end{align} -% -\begin{align} -\begin{split} -a = {} & {-}b + c \\ - & {-}d + e -\end{split} -\end{align} -\end{lstlisting} -\end{minipage} - -\begin{itemize} -\item There exists no starred version (\texttt{\textbackslash{}begin\{split{*}\}}) %%% ----- Martin ----- -of the \texttt{split} environment. -\end{itemize} - - -\subsection{\texttt{cases} environment } - -This gives support for an often used mathematical construct.\index{cases@\textbackslash cases} -You can also choose the more than once described way to convert some -text into math, like -{\footnotesize\begin{verbatim} -$x=\begin{cases} - 0 & \text{if A=...}\\ - 1 & \text{if B=...}\\ - x & \textrm{this runs with as much text as you like, - but without an automatic linebreak, it runs out - of page....} -\end{cases}$ -\end{verbatim}} -\noindent which gives equation~\vref{eq:cases}. It is obvious what the problem -is. - -\begin{eqnarray} -x & = & \begin{cases} -0 & \text{if A=...}\\ -1 & \text{if B=...}\\ -x & \textrm{this runs with as much text as you like, but without a linebreak, it runs out of page....}\end{cases}\label{eq:cases}\end{eqnarray} - - -In this case it is better to use a parbox\index{parbox@\textbackslash parbox} -for the text part with a \texttt{flushleft} command for a better view. - -\begin{equation} -x=\begin{cases} -0 & \text{if A=...}\\ -1 & \text{if B=...}\\ -x & \parbox{5cm}{\flushleft this runs with as much text as you like, but without an automatic linebreak, it runs out of page....}\end{cases}\end{equation} - - - -\begin{lstlisting} -\begin{equation} -x=\begin{cases} - 0 & \text{if A=...}\\ - 1 & \text{if B=...}\\ - x & \parbox{5cm}{% - \flushleft% - this runs with as much text as you like, - but without an automatic linebreak, - it runs out of page....}% -\end{cases} -\end{equation} -\end{lstlisting} - -\begin{leftbar} -\noindent From now on the counting of the equations changes. It is introduced -with a foregoing command, which doesn't really make sense, it is only for -demonstration: -\begin{lstlisting} -\renewcommand\theequation{\arabic{equation}} -\end{lstlisting} -\end{leftbar} - -\renewcommand\theequation{\arabic{equation}} - - -\subsection{Matrix environments}\label{sec:ams-matrix} -% -\begin{table}[htb] -\centering\begin{tabular}{rcrcrc} -\textbackslash{}Vmatrix\index{Vmatrix@\textbackslash Vmatrix}& -$\begin{Vmatrix}a & b\\ -c & d\end{Vmatrix}$& -\textbackslash{}Bmatrix\index{Bmatrix@\textbackslash Bmatrix}& -$\begin{Bmatrix}a & b\\ -c & d\end{Bmatrix}$& -\textbackslash{}matrix\index{matrix@\textbackslash matrix}& -$\begin{matrix}a & b\\ -c & d\end{matrix}$\tabularnewline -\rule{0pt}{0.85cm}\textbackslash{}vmatrix\index{vmatrix@\textbackslash vmatrix}& -$\begin{vmatrix}a & b\\ -c & d\end{vmatrix}$& -\textbackslash{}bmatrix\index{bmatrix@\textbackslash bmatrix}& -$\begin{bmatrix}a & b\\ -c & d\end{bmatrix}$& -\textbackslash{}pmatrix\index{pmatrix@\textbackslash pmatrix}& -$\begin{pmatrix}a & b\\ -c & d\end{pmatrix}$\tabularnewline[10pt] -&&&&\textbackslash{}smallmatrix\index{smallmatrix@\textbackslash smallmatrix}& -$\begin{smallmatrix}a & b\\ -c & d\end{smallmatrix}$ -\end{tabular} -\caption{Matrix environments} -\end{table} - -All matrix environments can be nested and an element may also contain -any other math environment, so that very complex structures are possible. -By default all cells have a centered alignment, which is often not the best -when having different decimal numbers or plus/minus values. Changing the -alignment to right (not for the \verb+smallmatrix+) is possible with -\mPar{% -\texttt{matrix}\\ -\texttt{vmatrix}\\ -\texttt{Vmatrix}\\ -\texttt{bmatrix}\\ -\texttt{Bmatrix}\\ -\texttt{pmatrix}\\ -\texttt{smallmatrix}% -}% - -\begin{lstlisting} -\makeatletter -\def\env@matrix{\hskip -\arraycolsep - \let\@ifnextchar\new@ifnextchar - \array{*\c@MaxMatrixCols r}} -\makeatother -\end{lstlisting} - -The special matrix environment \verb+smallmatrix+, which decreases -horizontal and vertical space is typeset in scriptstyle. The \verb|smallmatrix| -\index{smallmatrix@\textbackslash smallmatrix} environment makes some sense -in the inline mode to decrease the line height. -For dots over several columns look for \CMD{hdotsfor} in the following section. - - - -\section{Vertical whitespace}\label{sec:ams-whitespace} -See section~\vref{subsec:vwhitespace} for the lengths which control the -vertical whitespace. There is no difference to \AmSmath. - -\section{Dots}\label{sec:ams-dots} - -In addition to section~\vref{sec:Dots} \AmSmath has two more commands -for dots: \CMD{dddot}\{...\}\footnote{already mentioned in section \ref{sec:Accents}} and \CMD{ddddot}\{...\} -\index{dddot@\textbackslash dddot}\index{ddddot@\textbackslash ddddot} - -\verb|$\dddot{y}$|: $\dddot{y}$ - -\verb|$\ddddot{y}$|: $\ddddot{y}$ - - -Another interesting dot command is \CMD{hdotsfor}\index{hdotsfor@\textbackslash hdotsfor} -with the syntax: - -\begin{lstlisting} -\hdotsfor[<spacing factor>]{<number of columns>} -\end{lstlisting} - -With the spacing factor the width of the dots can be stretched or -shrinked. The number of columns allows a continuing dotted line over -more columns. Equation \ref{eq:tridiagonal} shows the definition -of a tridiagonal matrix. - -\begin{equation} -\underline{A}=\left[\begin{array}{ccccccc} -a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0\\ -a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0\\ -0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0\\ -\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ -\hdotsfor{7}\cr\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ -0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0\\ -0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n}\\ -0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn} -\end{array}\right]\label{eq:tridiagonal} -\end{equation} - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{equation} -\underline{A}=\left[\begin{array}{ccccccc} -a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0\\ -a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0\\ -0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0\\ -\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ -\hdotsfor{7}\cr\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\ -0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0\\ -0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n}\\ -0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn} -\end{array}\right] -\end{equation} -\end{lstlisting} - - -\section{\texttt{fraction} commands}\label{sec:ams-fraction} - - -\subsection{Standard} - -Additional to the font size problem described in subsection~\vref{sub:fraction command} -\AmSmath supports some more commands for fractions\index{Fraction}. The \CMD{frac} command -described in \cite{MathGuide}, does no more exist in \AmSmath. %%% ----- Martin ----- - -\begin{itemize} -\item The global fraction definition has five parameters\index{genfrac@\textbackslash genfrac} -\index{fraction@\textbackslash frac} -\begin{lstlisting}[xleftmargin=-1em,xrightmargin=-1em] -\genfrac{<left delim>}{<right delim>}{<thickness>}{<mathstyle>}{<nominator>}{<denominator>} -\end{lstlisting} -where thickness can have any length with a valid unit like \\ -\verb|genfrac{}{}{1pt}{}{x^2+x+1}{3x-2}| -$\rightarrow\genfrac{}{}{1pt}{}{x^2+x+1}{3x-2}$ -\item \CMD{cfrac}\index{cfrac@\textbackslash cfrac} (continued fraction) which is -by default set in the display mathstyle and useful for fractions like -\begin{equation} -\cfrac{1}{\sqrt{2}+\cfrac{1}{\sqrt{3}+\cfrac{1}{\sqrt{4}+\cfrac{1}{\ldots}}}}\label{cfrac} -\end{equation} -which looks with the default \CMD{frac} command like -\begin{equation} - \frac{1}{\sqrt{2}+\frac{1}{\sqrt{3}+\frac{1}{\sqrt{4}+\frac{1}{\ldots}}}} -\end{equation} -where the mathstyle decreases for every new level in the fraction. -The \CMD{cfrac} command can be called with an optional -parameter which defines the placing of the nominator, which can be -\texttt{[l]}eft, \texttt{[r]}ight or \texttt{[c]}enter (the default - see -equation~\ref{cfrac}):\\ -\begin{minipage}[c]{0.40\textwidth}% -\[ -\cfrac[l]{1}{\sqrt{2}+\cfrac[l]{1}{\sqrt{3}+\cfrac[l]{1}{\sqrt{4}+\cfrac[l]{1}{\ldots}}}} -\] -\end{minipage}% -\hfill{}\begin{minipage}[c]{0.40\textwidth}% -\[\cfrac[r]{1}{\sqrt{2}+\cfrac[r]{1}{\sqrt{3}+\cfrac[r]{1}{\sqrt{4}+\cfrac[r]{1}{\ldots}}}}\] -\end{minipage}% - -\item \CMD{dfrac}\index{dfrac@\textbackslash dfrac} -which takes by default the displaystyle\index{displaystyle@\textbackslash displaystyle}, so that -fractions in inline mode $\dfrac{1}{2}$ have the same size than in -display mode. -\item \CMD{tfrac}\index{tfrac@\textbackslash tfrac} (vice versa to \CMD{dfrac}) which takes by default -the scriptstyle\index{scriptstyle@\textbackslash scriptstyle}, so that fractions in display -mode have the same size than in inline mode. -\end{itemize} - -\[\tfrac{2}{3} \text{\hspace{0.5cm}\CMD{tfrac\{2\}\{3\}}} \] -\[\frac{2}{3} \text{\hspace{0.5cm}\CMD{frac\{2\}\{3\}}} \] - - -\subsection{Binoms}\label{sub:Binoms} - -\mPar{\CMD{binom}\\\CMD{dbinom}\\\CMD{tbinom}}They are like fractions without a rule and its syntax is different -to the \CMD{choose} command from standard \LaTeX{} -(see section \vref{sub:fraction command}). \AmSmath{} provides three -different commands for binoms just like the ones for fractions. - -\begin{table}[htb] -\centering% -\begin{tabular}{lcl} -Command & Inlinemath & Displaymath\tabularnewline -\hline -\texttt{\textbackslash{}binom\{m\}\{n\}} & $\binom{m}{n}$& -${\displaystyle \binom{m}{n}}$\tabularnewline -\texttt{\rule{0pt}{0.75cm}\textbackslash{}dbinom\{m\}\{n\}}& -$\dbinom{m}{n}$& -${\displaystyle \dbinom{m}{n}}$\tabularnewline -\texttt{\rule{0pt}{0.5cm}\textbackslash{}tbinom\{m\}\{n\}}& -$\tbinom{m}{n}$& -${\displaystyle \tbinom{m}{n}}$\tabularnewline -\end{tabular} -\caption{binom commands} -\end{table} - - -\section{Roots}\label{sec:Roots-ams} - -The typesetting for roots\index{uproot@\textbackslash uproot} is sometimes not -the best. Some solutions for better typesetting are % -\mPar{\CMD{leftroot}\\\CMD{uproot}}% -described in section~\vref{sec:Roots} for standard \LaTeX{}. \AmSmath -has some more commands for the $n$-th root: - -\begin{lstlisting} -\sqrt[\leftroot{<number>}\uproot{<number>}<root>]{< ... >} -\end{lstlisting} - -\noindent \verb+<number>+ indicates a value for the points% -\footnote{In PostScript units (bp -- Big Points).} of which the root can be -adjusted to the left and/or to the top, \eg -$\sqrt[k_n]{a}$ (\verb+$\sqrt[k_n]{a}$+) has a too deep exponent, whereas $\sqrt[\uproot{2}k_n]{a}$ \verb+$\sqrt[\uproot{2}k_n]{a}$+ looks nicer. - - - -\subsection{Roots with \CMD{smash} command} - -\mPar{\CMD{smash}}The default for a root\index{Root} with $\lambda_{k_{i}}$ as root -argument looks like $\sqrt{\lambda_{k_{i}}}$, which may be not the %%% ----- Martin ----- -best typesetting. It is possible to reduce the lowest point of the root -to the baseline with the \CMD{smash} command: $\sqrt{\lambda_{k_{i}}}\xrightarrow{\text{with \textbackslash smash}}\sqrt{\smash[b]{\lambda_{k_{i}}}}$ - - -The syntax of the \CMD{smash} command% -\footnote{In \texttt{latex.ltx} \CMD{smash} is defined without an optional argument.} renewed by the \AmSmath package is %%% ----- Martin ----- - -\begin{lstlisting} -\smash[<position>]{<argument>} -\end{lstlisting} -The optional argument for the position can be: - -\begin{description} -\item [t]keeps the bottom and annihilates the top -\item [b]keeps the top and annihilates the bottom -\item [tb]annihilates top and bottom (the default) -\end{description} - -\section{Accents}\label{amssymb} - -With the macro \verb|\mathaccent| it is easy to define new accent types, for example - -\begin{lstlisting} -\def\dotcup{$\mathaccent\cdot\cup$} -\end{lstlisting} - -$\mathaccent\cdot\cup$ - -\def\curvearrowleftright{% - \ensuremath{% - \mathaccent\curvearrowright{\mkern-5mu\curvearrowleft}% - }% -} - -Overwriting of two symbols is also possible: - -{\huge -$\curvearrowleft\curvearrowright\curvearrowleftright$} - -In this case the second symbol has to be shifted to the left for a length %%% ----- Martin ----- -of $5mu$ (mu: math unit\index{Math unit}). - -\begin{lstlisting} -\def\curvearrowleftright{% - \ensuremath{% - \mathaccent\curvearrowright{\mkern-5mu\curvearrowleft}% - }% -} -\end{lstlisting} - -For other possibilities to define new accents see section \vref{sec:package-accent}. %%% ----- Martin ----- - -\section{\CMD{mod} command} - -In standard \LaTeX{} the modulo command is not an operator, though %%% ----- Martin ----- -it is often used in formulas. \AmSmath provides two (three) different -commands for modulo, which are listed in tabular~\vref{cap:The-modulo commands}. - -\begin{itemize} -\item They all insert some useful space before and behind the mod-operator. -\end{itemize} - -\begin{table}[htb] -\centering\begin{tabular}{rrl} -a\textbackslash{}mod\{n\^{}2\}=b& -$\rightarrow$& -$a\mod{n^{2}}=b$\tabularnewline -a\textbackslash{}pmod\{n\^{}2\}=b& -$\rightarrow$& -$a\pmod{n^{2}}=b$\tabularnewline -a\textbackslash{}pod\{n\^{}2\}=b& -$\rightarrow$& -$a\pod{n^{2}}=b$\tabularnewline -\end{tabular} -\caption{\label{cap:The-modulo commands}The modulo commands and their meaning} -\end{table} - - - -\section{Equation numbering\label{sec:Equation-numbering}} - -See section \vref{sub:Equationnumbering} for equation numbering\index{Equation!numbering}. -It is mostly the % -\mPar{\textbackslash{}numberwithin% -}same, only one command is new to \AmSmath. If you want -a numbering like ``\ref{eq:IntoSection}{}'' then write either in the preamble %%% ----- Martin ----- -or like this example anywhere in your doc: - -\begin{lstlisting} -\numberwithin{equation}{section} -\end{lstlisting} - -\begin{leftbar} -\numberwithin{equation}{section}From now on the numbering looks like %%% ----- Martin ----- -equation \vref{eq:IntoSection}. For the book-class you can get the -same for chapters. -\end{leftbar} - -If you want to get rid of the parentheses then write in the preamble: %%% ----- Martin ----- - -\begin{lstlisting} -\makeatletter -\def\tagform@#1{\maketag@@@{\ignorespaces#1\unskip\@@italiccorr}} -\makeatother -\end{lstlisting} - -Now the following four subequation numbers have no parentheses. - - - - -\makeatletter -\let\oldTagForm\tagform@ -\def\tagform@#1{\maketag@@@{\ignorespaces#1\unskip\@@italiccorr}} -\makeatother - -\subsection{Subequations}\label{ams:subeqn} - -Amsmath supports this with the environment \verb|subequation|\index{Subequations}. -For example: -\begin{subequations} -\begin{align} -y & = d\\ -y & = cx+d\\ -y & = bx^{2}+cx+d\\ -y & = ax^{3}+bx^{2}+cx+d -\end{align} -\end{subequations} - -\begin{lstlisting} -\begin{subequations} -\begin{align} -y & = d\\ -y & = cx+d\\ -y & = bx^{2}+cx+d\\ -y & = ax^{3}+bx^{2}+cx+d -\end{align} -\end{subequations} -\end{lstlisting} - -\makeatletter -\let\tagform@\oldTagForm -\makeatother - - -Inside of subequations only complete other environments (\texttt{\textbackslash{}begin\{...\} -... \textbackslash{}end\{...\}}) are possible. - -\begin{lstlisting} -\renewcommand{\theequation}{% - \theparentequation{}-\arabic{equation}% -} -\end{lstlisting} - -\begin{subequations} -\renewcommand{\theequation}{% - \theparentequation -\arabic{equation}% -}% -\begin{align} -y & = d\\ -y & = cx+d\label{eq:subequation-neu}\\ -y & = bx^{2}+cx+d\\ -y & = ax^{3}+bx^{2}+cx+d -\end{align} -\end{subequations} - -A ref to a subequation is possible like the one to equation \ref{eq:subequation-neu}. -The environment chooses the same counter ``\texttt{equation}'' -but saves the old value into ``\texttt{parentequation}''. - -\newcounter{mySubCounter} -\newcommand{\twocoleqn}[2]{ - \setcounter{mySubCounter}{0}% - \let\OldTheEquation\theequation% - \renewcommand{\theequation}{\OldTheEquation\alph{mySubCounter}}% - \noindent% - \begin{minipage}{.49\textwidth} - \begin{equation}\refstepcounter{mySubCounter} - #1 - \end{equation} - \end{minipage}\hfill% - \addtocounter{equation}{-1}% - \begin{minipage}{.49\textwidth} - \begin{equation}\refstepcounter{mySubCounter} - #2 - \end{equation} - \end{minipage} - \let\theequation\OldTheEquation -} - -It is also possible to place two equations side by side with counting as subfigures: - -\twocoleqn{y=f(x)}{y=f(z)} - -\vspace{1ex} -In this case, the \AmSmath internal subfigure counter cannot be used and an own -counter has to be defined: - -\begin{lstlisting} -\newcounter{mySubCounter} -\newcommand{\twocoleqn}[2]{ - \setcounter{mySubCounter}{0}% - \let\OldTheEquation\theequation% - \renewcommand{\theequation}{\OldTheEquation\alph{mySubCounter}}% - \noindent% - \begin{minipage}{.49\textwidth} - \begin{equation}\refstepcounter{mySubCounter} - #1 - \end{equation} - \end{minipage}\hfill% - \addtocounter{equation}{-1}% - \begin{minipage}{.49\textwidth} - \begin{equation}\refstepcounter{mySubCounter} - #2 - \end{equation} - \end{minipage}% - \let\theequation\OldTheEquation -} -[ ... ] -\twocoleqn{y=f(x)}{y=f(z)} -\end{lstlisting} - - -\section{Labels and tags}\label{sec:Labels-and-Tags} - -For the \CMD{label} command\index{label@\textbackslash label} \mPar{\textbackslash{}tag% -} -see section \vref{sec:Labels}, it is just the same behaviour. \AmSmath -allows to define own single ``equation numbers\index{Equation number}'' -with the \CMD{tag} command. -\begin{align} -f(x) & =a\tag{linear}\label{eq:linear}\\ -g(x) & =\,\mathrm{d}x^{2}+cx+b\tag{quadratic}\label{eq:quadratic}\\ -h(x) & =\sin x\tag*{trigonometric} -\end{align} - -\begin{lstlisting} -\begin{align} -f(x) & =a\tag{linear}\label{eq:linear}\\ -g(x) & =\,\mathrm{d}x^{2}+cx+b\tag{quadratic}\label{eq:quadratic}\\ -h(x) & =\sin x\tag*{trigonometric} -\end{align} -\end{lstlisting} - -\begin{itemize} -\item The \CMD{tag} command is also possible for unnumbered -equations, \LaTeX{} changes the behaviour when a tag is detected. -\item There exists a starred version \verb|\tag{*}{...}|, %%% ----- Martin ----- -which supresses any annotations like parentheses for equation numbers\index{Equation!number}. -\item There exist two package options for tags, \verb|ctagsplit|\index{ctagsplit} %%% ----- Martin ----- -and \verb|righttag|\index{righttag} (look at the beginning of this -part on page~\pageref{par:AMSmath-package}). -\end{itemize} - - -\section{Limits}\label{sec:limit-AMS} - -By default the sum/prod has the limits above/below and the integral -at the side. To get the same behaviour for all symbols which can have -limits load the package \AmSmath in the preamble as %%% ----- Martin ----- - -\begin{lstlisting} -\usepackage[sumlimits,intlimits]{amsmath} -\end{lstlisting} - -There exist also options for the vice versa (see page~\pageref{par:AMSmath-package}). %%% ----- Martin ----- -See also Section~\ref{sec:misc-AMS} for the additional commands \CMD{underset} and \CMD{overset}. - - - -\subsection{Multiple limits} - -For general information about limits\index{Limits} read section -\vref{sub:Limits-Inline}. Standard \LaTeX{} provides the \texttt{\textbackslash{}atop}\index{atop@\textbackslash atop} command -for multiple limits (section \vref{sub:Multiple-Limits}). \AmSmath \mPar{\textbackslash{}substack% -} -has an additional command for that, which -can have several lines with the following syntax: -\mPar{\CMD{begin\{Sb\}}\\...\\\CMD{end\{Sb\}}\\\CMD{begin\{Sp\}}\\...\\\CMD{end\{Sp\}}% -} - -\begin{lstlisting} -\substack{...\\...\\...} -\end{lstlisting} - -The environments described in \cite{MathGuide} - -\begin{lstlisting} -\begin{Sb} ... \end{Sb} -\begin{Sp} ... \end{Sp} -\end{lstlisting} -are obsolete and no more part of \AmSmath. - -The example equation \vref{eq:atop} with the \CMD{substack}\index{substack@\textbackslash substack} command -looks like: - -\begin{equation}\label{eq:multlimits} -\sum_{\substack{1\le i\le p\\ -1\le j\le q\\ -1\le k\le r} -}a_{ij}b_{jk}c_{ki} -\end{equation} - - -Insert these limits in the following way: -\begin{lstlisting} -\begin{equation} - \sum_{% - \substack{1\le i\le p\\ - 1\le j\le q\\ - 1\le k\le r} - }% - a_{ij}b_{jk}c_{ki} -\end{equation} -\end{lstlisting} - -\subsection{Problems}\label{subsec:ams-limits} - -There are still some problems with limits and the following math -expression. For example: - -\[ -X = \sum_{1\le i\le j\le n}X_{ij} -\] -\begin{lstlisting} -\[ -X = \sum_{1\le i\le j\le n}X_{ij} -\] -\end{lstlisting} - -\noindent does not look nice because of the long limit. Using a -\CMD{makebox} also does not really solve the problem, because -\CMD{makebox} is in \TeX{} horizontal mode and knows nothing about -the appropriate math font size, because limits have a smaller font size. -It is better to define a \CMD{mathclap}\index{mathclap@\textbackslash mathclap} macro, similiar to the two -macros \CMD{llap} and \CMD{rlap} and uses the also new defined \CMD{mathclap} macro\index{clap@\textbackslash clap}: - -\begin{lstlisting} -\def\mathllap{\mathpalette\mathllapinternal} -\def\mathllapinternal#1#2{% - \llap{$\mathsurround=0pt#1{#2}$}% $ -} -\def\clap#1{\hbox to 0pt{\hss#1\hss}} -\def\mathclap{\mathpalette\mathclapinternal} -\def\mathclapinternal#1#2{% - \clap{$\mathsurround=0pt#1{#2}$}% -} -\def\mathrlap{\mathpalette\mathrlapinternal} -\def\mathrlapinternal#1#2{% - \rlap{$\mathsurround=0pt#1{#2}$}% $ -} -\end{lstlisting} - - -Now we can write limits which have a boxwidth of 0pt and the right font -size and the following math expression appears just behind the symbol: - -\[ -X = \sum_{\mathclap{1\le i\le j\le n}}X_{ij} -\] -\begin{lstlisting} -\[ -X = \sum_{\mathclap{1\le i\le j\le n}}X_{ij} -\] -\end{lstlisting} - -Another problem occurs when having operators with stacked limits in braces:\index{substack@\textbackslash substack} -\index{Braces!Problems} -\index{Stacked limits} -\begin{align} -\left[\sum_{\substack{i,j\\i>j}} \dots \right] -\end{align} - -This case is not easy to handle when some other math expressions are around the braces -which should be on the same baseline. However, the following may help in some cases -to get better looking braces. - -\begin{LTXexample}[width=0.45\linewidth,wide] -\begin{align} -foo \left[\begin{array}{@{}c@{}} - \displaystyle\sum_{\substack{i,j\\i>j}} \dots - \end{array}\right] bar -\end{align} -\end{LTXexample} - - -\subsection{\CMD{sideset}} - -This is a command for a very special purpose, to combine over/under -limits with superscript/subscripts for \mPar{\CMD{sideset}}the -sum-symbol. For example: it is not possible to place the prime -for the equation \ref{eq:sideset} near to the sum\index{sum@\textbackslash sum} symbol, -because it becomes an upper limit when writing without an preceeding \verb|{}|. -\begin{equation} -\sum_{n<k\atop n\ \textrm{odd}}{}'nE_{n}\label{eq:sideset} -\end{equation} - -The command \CMD{sideset}\index{sideset@\textbackslash sideset} -has the syntax - -\begin{lstlisting} -\sideset{<before>}{<behind>} -\end{lstlisting} - -It can place characters on all four corners of the sum-symbol: -\[ -\sideset{_{LowerLeft}^{UpperLeft}}{_{LowerRight}^{UpperRight}}\sum_{B}^{T} -\] - -\begin{lstlisting} -\[ -\sideset{_{LowerLeft}^{UpperLeft}}{_{LowerRight}^{UpperRight}}\sum_{B}^{T} -\] -\end{lstlisting} - -Now it is possible to write the equation \ref{eq:sideset} in a proper -way with the command \verb|\sideset{}{'}| before -the sum symbol: -\begin{equation} -\sideset{}{'}\sum_{n<k\atop n\ \textrm{odd}}nE_{n} -\end{equation} - - -\section{Operator names}\label{OperatorNames} - -\mPar{\CMD{operatorname}}% -By default variables are written in italic\index{Italic} and operator -names\index{Operator!names} in upright mode, like $y=\sin(x)$.% -\footnote{See section \vref{sec:ltxOperators}, where all the standard \LaTeX{} %%% ----- Martin ----- -known operator names are listed. Package \AmSmath has -some more (see documentation).} This happens only for the known operator names, but creating a new -one is very easy with: - -\begin{lstlisting} -\newcommand{\mysin}{\operatorname{mysin}} -\end{lstlisting} - -Now \CMD{mysin} is also written in upright mode -$y=\mysin(x)$ and with some additional space before and behind. - -It is obvious, that only those names can be defined as new operator -names which are not commands in another way. Instead of using the -new definition as an operator, it is also possible to use the text -mode. But it is better to have all operators of the same type, so that -changing the style will have an effect for all operators. - -\mPar{\CMD{operatornamewithlimits}}% -The new defined operator names cannot have limits\index{Limits}, only -superscript/subscript is possible. \verb+amsopn.sty+ has an additional command -\CMD{operatornamewithlimits}\index{operatornamewithlimits@\textbackslash operatornamewithlimits}, -which supports over/under limits like the one from \CMD{int} -or \CMD{sum}. - -\mPar{\CMD{mathop}} -It is also possible to use the macro \verb+\mathop+ to declare anything -as operator, like -\[ \sideset{_1}{}{\mathop{\mathrm{B}}} \] -\begin{lstlisting} -\[ \sideset{_1}{}{\mathop{\mathrm{B}}} \] -\end{lstlisting} -With this definition it is possible to use \CMD{sideset} for a forgoing index, which -is only possible for an operator. - -For a real \LaTeX{} definition have a look at section \vref{sec:ltxOperators}. - - -\section{Text in math mode}\label{sec:Text-in-math mode} - -If you need complex structures between formulas, look also at section \ref{sec:verticalAlignment}. - -\subsection{\CMD{text} command} -\mPar{% -\CMD{text}\\ -\CMD{mbox}\\ -\CMD{textnormal}\\ -\CMD{mathrm}% -}% -This is the equivalent command to \CMD{mathrm}\index{mathrm@\textbackslash mathrm} -or \CMD{mbox}\index{mbox@\textbackslash mbox} -from the standard \LaTeX{} (section~\vref{sec:Text}) with the exception, that \CMD{mathrm} -always uses the roman font and \CMD{text} the actual one and that the font size is different -when used in super- and subscript. - -For example: $\boxed{f(x)=x\quad\text{this was math}}$. - -\bigskip -{\sffamily\huge -$A^{\mbox{text}}_{\mbox{text}}$\quad -$A^{\text{text}}_{\text{text}}$\quad -$A^{\textnormal{text}}_{\textnormal{text}}$\quad -$A^{\mathrm{text}}_{\mathrm{text}}$ -} -\medskip -\begin{lstlisting} -$\boxed{f(x)=x\quad\text{this was math}}$ - -{\sffamily\huge -$A^{\mbox{text}}_{\mbox{text}}$\quad -$A^{\text{text}}_{\text{text}}$\quad -$A^{\textnormal{text}}_{\textnormal{text}}$\quad -$A^{\mathrm{text}}_{\mathrm{text}}$ -} -\end{lstlisting} - -The \verb+\text+ macro can be used at any place and can be in some cases a better -solution as \verb+\intertext+ (see section~\ref{subsec:intertext}). - -\begin{flalign*} - && 12(x-1) + 20(y-3) + 14(z-2) & = 0 &&\\ - \text{and} && 6x + 10y + 7z & = 0 && -\end{flalign*} - -\begin{align} - && 12(x-1) + 20(y-3) + 14(z-2) & = 0\\ - \text{and} && 6x + 10y + 7z & = 0 -\end{align} - -\begin{lstlisting} -\begin{flalign*} - && 12(x-1) + 20(y-3) + 14(z-2) & = 0 &&\\ - \text{and} && 6x + 10y + 7z & = 0 && -\end{flalign*} - -\begin{align} - && 12(x-1) + 20(y-3) + 14(z-2) & = 0\\ - \text{and} && 6x + 10y + 7z & = 0 -\end{align} -\end{lstlisting} - - - -\subsection{\CMD{intertext} command}\label{subsec:intertext} - -This is useful when you want to place some text between two parts -of math stuff without leaving the math mode, like the name -``intertext\index{intertext@\textbackslash intertext}'' %%% ----- Martin ----- -says. For example we write the equation~\vref{eq:Beispiel-Integral} -with an additional command after the second line. - -\[ - \begin{split} - A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left| \int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\ - & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left| \int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\ - \intertext{Now the limits of the integrals are used} - & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+\left| \frac{x^{3}}{3}- - \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\ - & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left| \frac{8}{3}-\frac{20}{2}+12- - \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\ - & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6}\right| =\frac{7}{6}+ - \frac{5}{6}=2\, \textrm{FE} - \end{split} -\] - -The code looks like:\\ - - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\begin{equation} - \begin{split} - A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left| \int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\ - & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left| \int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\ - \intertext{Now the limits of the integrals are used} - & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+\left| \frac{x^{3}}{3}- - \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\ - & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left| \frac{8}{3}-\frac{20}{2}+12- - \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\ - & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6}\right| =\frac{7}{6}+ - \frac{5}{6}=2\, \textrm{FE} - \end{split} -\end{equation} -\end{lstlisting} - -Writing very long text is possible by using a \verb+parbox+, see section~\vref{sec:Text} for %%% ----- Martin ----- -an example with \verb+\textrm+, which behaves in the same way as \verb+\text+. - - - - -\section{Extensible arrows} -\mPar{% - \CMD{xrightarrow}\\ - \CMD{xleftarrow}\\ - \CMD{xmapsto}}To write something like $\xrightarrow[\text{below}]{\text{above the arrow}}$ you can use the following macro - -\begin{verbatim} -$\xrightarrow[\text{below}]{\text{above the arrow}}$ -\end{verbatim} -\index{Arrows}\index{Extensible arrows} - -\noindent and the same with \verb|\xleftarrow|. You can define your own extensible arrow macros -if you need other than these two predefined ones. To get a doublelined extensible -arrow like \verb|$\Longleftrightarrow$| ($\Longleftrightarrow$) but with the same -behaviour as an extensible one, write in the preamble %%% ----- Martin ----- - -\begin{lstlisting} -\newcommand\xLongLeftRightArrow[2][]{% - \ext@arrow 0055{\LongLeftRightArrowfill@}{#1}{#2}} -\def\LongLeftRightArrowfill@{% - \arrowfill@\Leftarrow\Relbar\Rightarrow} -\newcommand\xlongleftrightarrow[2][]{% - \ext@arrow 0055{\longleftrightarrowfill@}{#1}{#2}} -\def\longleftrightarrowfill@{% - \arrowfill@\leftarrow\relbar\rightarrow} -\end{lstlisting} - -The three parts \verb|\Leftarrow\Relbar\Rightarrow| define left|middle|right of the -arrow, where the middle part would be stretched in a way that the arrow is at least -as long as the text above and/or below it. This macro has one optional and one -standard parameter. The optional one is written below and the standard one above this %%% ----- Martin ----- -arrow. Now we can write - -\begin{verbatim} -$\xLongLeftRightArrow[\text{below}]{\text{above the arrow}}$ -$\xlongleftrightarrow[\text{below}]{\text{above the arrow}}$ -\end{verbatim} - -\noindent to get $\xLongLeftRightArrow[\text{below}]{\text{above the arrow}}$ or -$\xlongleftrightarrow[\text{below}]{\text{above the arrow}}$. -The ``number'' $0055$ after \verb+\ext@arrow+ defines the position relative to the extended arrow and is -not a number but four parameters for additional space in the math unit \verb+mu+. -\index{mapstofill@\CMD{mapstofill}} - -\makeatletter -\def\mapstofill@{% - \arrowfill@{\mapstochar\relbar}\relbar\rightarrow} -\renewcommand*\xmapsto[6][]{% - \ext@arrow #3#4#5#6\mapstofill@{#1}{#2}} -\makeatother -\begin{lstlisting} -\def\mapstofill@{% - \arrowfill@{\mapstochar\relbar}\relbar\rightarrow} -\newcommand*\xmapsto[2][]{% - \ext@arrow <four digits>\mapstofill@{#1}{#2}} -\end{lstlisting} - -{\fboxsep=0pt -\verb+$\ext@arrow 0000$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0000$} - -\verb+$\ext@arrow 9000$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}9000$} - -\verb+$\ext@arrow 0900$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0900$} - -\verb+$\ext@arrow 0009$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0009$} - -\verb+$\ext@arrow 0090$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0090$} - -\verb+$\ext@arrow 0099$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0099$} - -\verb+$\ext@arrow 9999$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}9999$} -} - -% $ -\begin{itemize} -\item 1st digit: space left -\item 2nd digit: space right -\item 3rd digit: space left and right -\item 4th digit: space relativ to the tip of the ``arrow'' -\end{itemize} - -The two macros \verb+\xrightarrow+ and \verb+\xleftarrow+ are defined as: -\begin{lstlisting} -\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}} -\newcommand{\xleftarrow}[2][]{\ext@arrow 3095\leftarrowfill@{#1}{#2}} -\end{lstlisting} - - - -\section{Frames}\label{sec:ams-frames} -\mPar{\CMD{boxed}}% -\AmSmath knows the macro \verb|\boxed|\index{boxed@\textbackslash boxed} which can -be used for inline $a\boxed{b+c}$ and displayed math expressions: - -\begin{align} -\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1} -\end{align} - -\begin{lstlisting} -\begin{align} -\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1} -\end{align} -\end{lstlisting} - -For coloured boxes use package \verb|empheq|. For an example see section \vref{sec:empheq}. - -\section{Greek letters}\label{sec:greek-AMS} -\mPar{\CMD{pmb}\\\CMD{boldsymbol}}% -The \AmSmath package simulates a bold font for the greek letters by writing a greek %%% ----- Martin ----- -character twice with a small kerning. This is done with the macro -\verb|\pmb{<letter>}|\index{pmb@\textbackslash pmb}\index{Bold greek letters}. The -\verb|\mathbf{<character>}| doesn't work with lower greek character. However, -using the \CMD{boldsymbol} macro from \AmSmath{} is the better way when the font -has a bold symbol. -\index{boldsymbol@\CMD{boldsymbol}} - -Uppercase greek letters are by default in upright mode. \AmSmath\ supports also -such letters in italic mode with a preceeding \verb+var+ e.g., \verb+\varGamma+ - -\medskip -\begin{tabular}{ccc|cc} -\emph{letter} & \CMD{pmb}\verb+{letter}+ & \CMD{boldsymbol}\verb+{letter}+ & \emph{letter} & \emph{italic}\\ -$\alpha$ & $\pmb{\alpha}$ & $\boldsymbol{\alpha}$ & $\Gamma$ & $\varGamma$\\ -$\beta$ & $\pmb{\beta}$ & $\boldsymbol{\beta}$ & $\Delta$ & $\varDelta$\\ -$\gamma$ & $\pmb{\gamma}$ & $\boldsymbol{\gamma}$ & $\Theta$ & $\varTheta$\\ -$\delta$ & $\pmb{\delta}$ & $\boldsymbol{\delta}$ & $\Lambda$ & $\varLambda$\\ -$\epsilon$ & $\pmb{\epsilon}$ & $\boldsymbol{\epsilon}$ & $\Xi$ & $\varXi$\\ -$\varepsilon$ & $\pmb{\varepsilon}$ & $\boldsymbol{\varepsilon}$ & $\Pi$ & $\varPi$\\ -$\zeta$ & $\pmb{\zeta}$ & $\boldsymbol{\zeta}$ & $\Sigma$ & $\varSigma$\\ -$\eta$ & $\pmb{\eta}$ & $\boldsymbol{\eta}$ & $\Upsilon$ & $\varUpsilon$\\ -$\theta$ & $\pmb{\theta}$ & $\boldsymbol{\theta}$ & $\Phi$ & $\varPhi$\\ -$\vartheta$ & $\pmb{\vartheta}$ & $\boldsymbol{\vartheta}$ & $\Psi$ & $\varPsi$\\ -$\iota$ & $\pmb{\iota}$ & $\boldsymbol{\iota}$ & $\Omega$ & $\varOmega$\\ -$\ldots$ & $\ldots$ & $\ldots$ -\end{tabular} - - -\section{Miscellaneous commands}\label{sec:misc-AMS} - -There are several commands which can be used in math mode:\mPar{\CMD{overset}\\\CMD{underset}} - -Some examples are shown in table~\vref{cap:Different-Mathcommands-supported-AMS}. - -\begin{table}[htb] -\centering -{\renewcommand{\arraystretch}{2} -\begin{tabular}{r|>{\raggedright}p{2cm}} -\verb|$\underset{under}{baseline}$| \index{underset@\textbackslash underset} & -$\underset{under}{baseline}$\tabularnewline -\verb|$\overset{over}{baseline}$| \index{overset@\textbackslash overset} & -$\overset{over}{baseline}$\tabularnewline -\verb+\boldsymbol{\Omega}+ & $\boldsymbol{\Omega}$ -\end{tabular}} -\caption{Different mathcommands}\label{cap:Different-Mathcommands-supported-AMS} -\end{table} - -\CMD{underset} is a useful macro for having limits under non-operators -(see page~\pageref{sec:amsopn}). %%% ----- Martin ----- -\CMD{boldsymbol} can be used for a math symbol that remains unaffected by -\CMD{mathbf} if the current math font set includes a bold version of that symbol. - - -\section{Problems with \texttt{amsmath}} -\AmSmath{} is an excellent package with some ``funny features''. -When using an \verb+align+ environment inside a \verb+gather+ environment, it should -be centered just like the other lines. This is only true, when there is a number/tag or -an additional ampersand: - - -%\begin{LTXexample}[pos=t] -\begin{gather*} - \begin{align*} - m_2 &= m_2' + m_2''\\ - &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} - \end{align*}\\ - \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ -\end{gather*} -\begin{gather*} - \begin{align*} - m_2 &= m_2' + m_2''\\ - &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} & %<<<==== - \end{align*}\\ - \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ -\end{gather*} -%\end{LTXexample} - -\begin{lstlisting} -\begin{gather*} - \begin{align*} - m_2 &= m_2' + m_2''\\ - &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} - \end{align*}\\ - \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ -\end{gather*} -\begin{gather*} - \begin{align*} - m_2 &= m_2' + m_2''\\ - &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} & %<<<==== - \end{align*}\\ - \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\ -\end{gather*} -\end{lstlisting} - - -This effect depends to the horizontal width, which is wrong in the first example, -in fact of a missing tag or number the right whitespace is cut, but the left one -is still there. The additional ampersand prevents \AmSmath{} to change the right -margin. - -Another kind of curiousity is the following example, which depends to the -same problem of cutting whitespace only on one side. - -\bigskip\noindent% -%\begin{LTXexample}[pos=t] -\fbox{% -\begin{minipage}{10cm} -\begin{align*} - a&=b \\ c&=d -\end{align*} -\end{minipage}} - -\noindent\fbox{% -\begin{minipage}{10cm} -\noindent\begin{align*} - a&=b \\ c&=d -\end{align*} -\end{minipage}} -%\end{LTXexample} - -\bigskip -\begin{lstlisting} -\bigskip\noindent\fbox{% -\begin{minipage}{10cm} -\begin{align*} - a&=b \\ c&=d -\end{align*} -\end{minipage}} - -\noindent\fbox{% -\begin{minipage}{10cm} -\noindent\begin{align*} - a&=b \\ c&=d -\end{align*} -\end{minipage}} -\end{lstlisting} - - - -\part{\TeX{} and math} - -There is in general no need to use the \TeX{} macros, because the ones defined with \LaTeX{} -or with \AmSmath{} are much more useful. Nevertheless there may be situations, where someone %%% ----- Martin ----- -has to use one of the \TeX{} macros or special \TeX{} math length. One can not expect, that all -macros work in the usual way, a lot of them are redefined by \LaTeX{} %%% ----- Martin ----- -or \AmSmath{}. On the other hand some of these basic macros or length definitions are used -in the \TeX{} way, so it might be interesting to have all declared in a short way for some -information. - -\section{Length registers} - -\subsection{\CMD{abovedisplayshortskip}} -\cIndex{abovedisplayshortskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. - -\subsection{\CMD{abovedisplayskip}} -\cIndex{abovedisplayskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. - -\subsection{\CMD{belowdisplayshortskip}} -\cIndex{belowdisplayshortskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. - -\subsection{\CMD{belowdisplayskip}} -\cIndex{belowdisplayskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example. - - -\subsection{\CMD{delimiterfactor}} -\cIndex{delimiterfactor}The height of a delimiter is often not optimally calculated by \TeX{}. In some cases it is %%% ----- Martin ----- -too short. With \verb+\delimiterfactor+ one can correct this height. The delimiterheight -is $<\textrm{calculated height}>\cdot <\textrm{\#1}>/1000$ where \verb+#1+ is the parameter of -\verb+\delimiterfactor+. The default value is $901$. - -\begin{LTXexample}[width=0.4\linewidth] -\[ -y = \left\{% - \begin{array}{ll} - x^2+2x &\textrm{if }x<0,\\ - x^3 &\textrm{if }0\le x<1,\\ - x^2+x &\textrm{if }1\le x<2,\\ - x^3-x^2 &\textrm{if }2\le x. - \end{array}% -\right. -\] -\end{LTXexample} - -\begin{LTXexample}[width=0.4\linewidth] -\[ -\delimiterfactor=1500 -y = \left\{% - \begin{array}{ll} - x^2+2x &\textrm{if }x<0,\\ - x^3 &\textrm{if }0\le x<1,\\ - x^2+x &\textrm{if }1\le x<2,\\ - x^3-x^2 &\textrm{if }2\le x. - \end{array}% -\right. -\] -\end{LTXexample} - -\subsection{\CMD{delimitershortfall}} -\cIndex{delimitershortfall}Additionally to the forgoing \verb+\delimiterfactor+ one can modify the height of the -delimiter with another value. \TeX{} makes the delimiter larger than the values of -$<\textrm{calculated height}>\cdot <\textrm{delimiterfactor}>/1000$ and $<\textrm{calculated height}>-<\textrm{delimitershortfall}>$. This makes it possible to always get different heights %%% ----- Martin ----- -of a sequence of delimiters. - -\begin{LTXexample}[width=0.3\linewidth] -$x\cdot\left(\left(x^2-y^2\right)-3\right)$\\[7pt] - -$ -\delimitershortfall-1pt -x\cdot\left(\left(x^2-y^2\right)-3\right)$ -\end{LTXexample} - -\begin{LTXexample}[width=0.2\linewidth] -$\left(\left(\left(A\right)\right)\right)$\\[7pt] - -$\delimitershortfall-1pt -\left(\left(\left(A\right)\right)\right)$ -\end{LTXexample} - - -\subsection{\CMD{displayindent}} -\cIndex{displayindent}This is the left shift amount of a line holding displayed equation. -By default it is $0pt$ but -gets the value of an indented paragraph when there is an environment like the quotation one.\index{Indentation} - -The following formula is typeset in the usual way without modifying anything. - -\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] - -Now we start a quotation environment which sets \CIndex{labelwidth} to new values for a -greater %%% ----- Martin ----- -left margin. - -\begin{itemize} -\item The following formula is typeset in the usual way without modifying anything. - -\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] - -\item Now we write the same equation, but now with modifying \Index{displayindent}, it is set to -the negative \verb+\leftskip+: - -\[ - \displayindent=-\labelwidth - f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x -\] -\end{itemize} - -\begin{lstlisting} -\[ - \displayindent=-\leftskip - f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x -\] -\end{lstlisting} - -\subsection{\CMD{displaywidth}} -\cIndex{displaywidth}The width of the line holding a displayed equation, which is by default -\verb+\linewidth+. In the -second example the formula is centered for a display width of \verb+0.5\linewidth+. - -\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] -\[ - \displaywidth=0.5\linewidth - f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x -\] -\begin{lstlisting} -\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] -\[ - \displaywidth=0.5\linewidth - f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x -\] -\end{lstlisting} - -\subsection{\CMD{mathsurround}} -\cIndex{mathsurround}Extra space added when switching in and out of the -inline math mode (see section~\ref{subsec:whitespace}). - -\subsection{\CMD{medmuskip}} -\cIndex{medmuskip}See section~\ref{subsec:mathskip} for an example. - -\subsection{\CMD{mkern}} -\cIndex{mkern}Similiar to \verb+\kern+, but adds a math kern item to the current math list. Length must be a math unit. - -\subsection{\CMD{mskip}} -\cIndex{mskip}Similiar to \verb+\skip+, but adds math glue to the current math list. Length must be a math unit. - -\subsection{\CMD{muskip}} -\cIndex{muskip}Assigns a length with a math unit to one of the 256 \verb+\muskip+ register. - -\subsection{\CMD{muskipdef}} -\cIndex{muskipdef}Defines a symbolic name for a \verb+\muskip+ register. - -\subsection{\CMD{nonscript}} -\cIndex{nonscript}Ignores immediately following glue or kern in script and -scriptscript styles, which makes a redefinition of \verb+\mathchoice+ superfluous. - -\subsection{\CMD{nulldelimiterspace}} -\cIndex{nulldelimiterspace}This is the width of a null or missing delimiter, -\eg \verb+\right.+ or for the left one. - -\subsection{\CMD{predisplaysize}} -\cIndex{predisplaystyle}Is the effective width of the line preceeding a displayed equation, whether -\verb+\abovedisplayskip+ or \verb+abovedisplayshortskip+ is used for the vertical skip. - -\subsection{\CMD{scriptspace}} -\cIndex{scriptspace}The space inserted after an exponent or index, predefined as \verb+\scriptspace=0.5pt+ %%% ----- Martin ----- - -\subsection{\CMD{thickmuskip}} -\cIndex{thickmuskip}See section~\ref{subsec:mathskip}. - -\subsection{\CMD{thinmuskip}} -\cIndex{thinmuskip}The short version for positive skip is defined as \verb+\def\,{\mskip\thinmuskip}+ and the one -for a negative skip as \verb+\def\!{\mskip-\thinmuskip}+ (see also Section~\ref{subsec:mathskip}). - - -\begin{LTXexample}[width=0.35\linewidth] -$\sqrt 2 x$ -- $\sqrt 2\,x$\\ -$\sqrt{\log x}$ -- $\sqrt{\,\log x}$\\ -$P\left({1/\sqrt n}\right)$ -- $P\left({1/ \sqrt n}\,\right)$\\[8pt] - $[0,1)$ -- $[\,0,1)$\\ -$x^2/2$ -- $x^2\!/2$\\ -\end{LTXexample} - -\begin{LTXexample}[width=0.35\linewidth] -\[\int\int_D \mathrm{d}x\mathrm{d}y \quad - \int\!\int_D \mathrm{d}x\,\mathrm{d}y\] -\[\int\!\!\int_D \mathrm{d}x\,\,\mathrm{d}y \quad - \int\!\!\!\int_D \mathrm{d}x\,\,\,\mathrm{d}y\] -\[\int\!\!\!\!\int_D \mathrm{d}x\,\,\,\,\mathrm{d}y \quad - \int\!\!\!\!\!\int_D \mathrm{d}x\,\,\,\,\,\mathrm{d}y\] -\[\int\!\!\!\int_D \mathrm{d}x\,\mathrm{d}y\] -\end{LTXexample} - -\subsection{\CMD{medmuskip}} -See section~\ref{subsec:mathskip}. - - -\section{Math font macros} -\subsection{\CMD{delcode}} -\cIndex{delcode}Each character has not only a \CIndex{catcode} and \CIndex{mathcode} but also -a \verb+\delcode+ -which defines for a single chracter how it should look when used as a math delimiter. - -\subsection{\CMD{delimiter}} -\cIndex{delimiter}Every character can be declared as a delimiter, but \TeX{} -must know which characters -should be used for the default and the big size. For \LaTeX{} -the macro \CIndex{DeclareMathDelimiter} should be used (see section~\vref{subsec:delim}). - -In the following example \verb+\tdela+ is the character $0x22$ ($\uparrow$) from -font number $2$ (\verb+csmy+) and character $0x78$ from font number $3$ (\verb+cmex+) -for the big version. \verb+\tdelb+ is the same vice versa ($\downarrow$). -\begin{LTXexample}[width=0.35\linewidth] -\def\tdela{\delimiter"4222378\relax} -\def\tdelb{\delimiter"5223379\relax} - -$\tdela x-y\tdelb(x+y)=x^2-y^2$ - -\[\tdela\sum_{n=0}^\infty {1\over2^n}\tdelb^2 = 4\] - -\[\left\tdela\sum_{n=0}^\infty {1\over2^n}\right\tdelb^2 = 4\] -\end{LTXexample} - -\subsection{\CMD{displaystyle}} -\cIndex{displaystyle}See section~\ref{sec:Styles} for an example. - -\subsection{\CMD{fam}} -\cIndex{fam}When \TeX{} switches into the math mode, it typesets everything using one of the 16 -possible families of fonts. \verb+\fam+ is an internal register where other macros can check which font is the actual one. At the beginning \TeX{} starts with \verb+\fam=-1+. - -\bigskip -\noindent -\includegraphics{family} -\iffalse - -\begin{center} -\begin{tabular}{ll} -\verb+\fam=-1+ & $\fam=-1 123abcABC\alpha\beta\gamma$\\ -\verb+\fam=0+ & $\fam=0 123abcABC\alpha\beta\gamma$\\ -\verb+\fam=1+ & $\fam=1 123abcABC\alpha\beta\gamma$\\ -\verb+\fam=2+ & $\fam=2 123abcABC\alpha\beta\gamma$\\ -\verb+\fam=3+ & $\fam=3 123abcABC\alpha\beta\gamma$\\ -\verb+\fam=4+ & $\fam=4 123abcABC\alpha\beta\gamma$\\ -\verb+\fam=5+ & $\fam=5 123abcABC\alpha\beta\gamma$ -\end{tabular} -\end{center} - - -\begin{LTXexample}[width=0.3\linewidth] -$\mathrm{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] -$\mathbf{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] -$\mathit{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] -$\mathtt{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] -$\mathsf{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt] -$\mathnormal{123abcABC\alpha\beta\gamma (\the\fam)}$ -\end{LTXexample} -\fi - -\subsection{\CMD{mathaccent}} -\cIndex{mathaccent}Requires three parameter as one number, the class, the font family and the character. - -\begin{LTXexample}[width=0.3\linewidth] -\def\dA{\mathaccent"7015\relax} -{\Large $\dA{A}$} -\end{LTXexample} - -\subsection{\CMD{mathbin}} -\cIndex{mathbin}Declares a following character as a binary symbol with another -spacing before and behind such a symbol. - -\begin{LTXexample}[width=0.3\linewidth] -{\Large -$a|b \quad a\mathbin| b$} -\end{LTXexample} - -\subsection{\CMD{mathchar}} -\cIndex{mathchar}Declares a math character by three integer numbers as Parameters, giving its class, %%% ----- Martin ----- -font family, and font position. In the following example \verb+\mathchar+ defines a -character of class 1 (big operators), font family 3 (math extension font) and number -58 (big sum character). - -\begin{LTXexample}[width=0.3\linewidth] -{\Large -$a\sum\limits_{i=1}^{\infty} b \quad - a\mathchar"1358\limits_{i=1}^{\infty} b$} -\end{LTXexample} - -\subsection{\CMD{mathchardef}} -\cIndex{mathchardef}This is in principle the same as \CIndex{mathchar}, -it only allows to make such definitions permanent. - -\begin{LTXexample}[width=0.25\linewidth] -\bgroup -\mathchardef\sum="1358 -$a\sum\limits_{i=1}^{\infty}\sqrt{i+1}$\\[5pt] -\egroup - -$a\sum\limits_{i=1}^{\infty}\sqrt{i+1}$ -\end{LTXexample} - - -\subsection{\CMD{mathchoice}} -\cIndex{mathchoice}Specifies specific subformula sizes for the 4 main styles: -\CIndex{displaystyle} -- \CIndex{textstyle} -- -\CIndex{scriptstyle} -- \CIndex{scriptscriptstyle}. - -\begin{LTXexample}[width=0.15\linewidth] -\Large -\def\myRule{{% - \color{red}% - \mathchoice{\rule{2pt}{20pt}}{\rule{1pt}{10pt}}% - {\rule{0.5pt}{5pt}}{\rule{0.25pt}{2.5pt}}% - \mkern2mu}} -$\myRule\sum\limits_{\myRule i=1}^{\myRule\infty}% - \myRule\frac{\myRule\sqrt{\myRule i+1}}{\myRule i^2}$ -\end{LTXexample} - -\subsection{\CMD{mathclose}}\label{subsec:mathclose} -\cIndex{mathclose}Assigns class 5 (closing character) to the following -parameter, which can hold a single character or a subformula. - -\begin{LTXexample}[width=0.2\linewidth] -{\large -$A:\frac{B}{C}:D$\\[5pt] -$A\mathopen:\frac{B}{C}\mathclose: D $} -\end{LTXexample} - - -\subsection{\CMD{mathcode}} -\cIndex{mathcode}A math font is far different from a text font. A lot of the characters has to be defined with -\verb+\mathcode+, which defines the character with its class, font family and character number, \eg -\verb+\mathcode`\<="313C+. It defines the character ``<''{} as a realtion symbol (class 3) from -the font family 1 and the character number 0x3C, which is 60 decimal. - -\subsection{\CMD{mathop}} -\cIndex{mathop}Assigns class 1 (large operator) to the parameter, which can be a single character or a subformula. - -\begin{LTXexample}[width=0.2\linewidth] -\[ A_{i=1}^{\infty} \] -\[ \mathop{A}_{i=1}^{\infty} \] -\end{LTXexample} - -\subsection{\CMD{mathopen}} -\cIndex{mathopen}Vice versa to \verb+\mathclose+ (see section~\ref{subsec:mathclose}). - - -\subsection{\CMD{mathord}} -\cIndex{mathord}Assigns class 0 (ordinary character) to the following parameter, which can be a single character -or a subformula. - -\begin{LTXexample}[width=0.2\linewidth] -{\large -$y = f(x)$\\[5pt] -$y \mathord= f(x)$} -\end{LTXexample} - -\subsection{\CMD{mathpunct}} -\cIndex{mathpunct}Assigns class 6 (punctuation) to the following parameter, which can be a single character -or a subformula (see section~\ref{subsec:dot-comma} for an example). - -\subsection{\CMD{mathrel}} -\cIndex{mathrel}Assigns class 3 (relation) to the following parameter, which can be a single character -or a subformula. - -\begin{LTXexample}[width=0.25\linewidth] -{\large -$x_1 o x_2 o x_3$\\[5pt] -$x_1\mathrel o x_2\mathrel o x_3$} -\end{LTXexample} - - -\subsection{\CMD{scriptfont}} -\cIndex{scriptfont}Specifies the scriptstyle font (used for super/subscript) for a family. - -\begin{LTXexample}[width=0.25\linewidth] -$A_1$ -\font\tenxii=cmr12 -\scriptfont0=\tenxii -$A_1$ -\end{LTXexample} - - -\subsection{\CMD{scriptscriptfont}} -\cIndex{scriptscriptfont}Specifies the scriptscriptstyle font for a family. - -\subsection{\CMD{scriptscriptstyle}} -\cIndex{scriptscriptstyle}Selects scriptscript style for the following characters. - -\subsection{\CMD{scriptstyle}} -\cIndex{scriptstyle}Selects script style for the following characters. - - -\subsection{\CMD{skew}} -\cIndex{skew}Especially for italic characters double accents are often misplaced. \verb+\skew+ has three arguments -\begin{description} -\item[horizontal shift:] A value in math units for the additional shift of the accent. -\item[the accent:] The symbol which is placed above the character. -\item[the character:] This is in general a single character, but can also include itself an accent. -\end{description} - -\AmSmath\ redefines the setting of double accents. This is the reason why there are only a few -cases where someone has to use \verb+\skew+ when the package \PIndex{amsmath} is loaded, like -in this document. - -\begin{LTXexample}[width=0.2\linewidth] -\large -$\tilde i$ \qquad $\tilde{A}$\\[5pt] -$\skew{3}{\tilde}{i}$ \qquad $\skew{7}{\tilde}{A}$ -\end{LTXexample} - -\subsection{\CMD{skewchar}} -\cIndex{skewchar}Is -1 or the character (reference symbol) used to fine-tune the positioning of math accents. - -\subsection{\CMD{textfont}} -\cIndex{textfont}Specifies the text font for a family. - -\subsection{\CMD{textstyle}} -\cIndex{textstyle}Selects the text style for the following characters. - - - -\section{Math macros} - - -\subsection{\CMD{above}} -\cIndex{above} -\begin{LTXexample}[width=0.2\linewidth] -$a\above0pt b$\\[8pt] - -${a\above1pt b}$\\[8pt] - -${a\above2.5pt b}$\\[8pt] - -$\displaystyle{a\above0pt b}$ -\end{LTXexample} - - - -\subsection{\CMD{abovewithdelims}} -\cIndex{abovewithdelims} -\begin{LTXexample}[width=0.2\linewidth] -$a\abovewithdelims()0pt b$\\[8pt] - -\def\fdelimA{\abovewithdelims\{)1.0pt} -${a\fdelimA b}$\\[8pt] - -\def\fdelimB{\abovewithdelims[]2.0pt} -${a\fdelimB b}$\\[8pt] - -\def\fdelimC{\abovewithdelims\{.0pt} -$\displaystyle{a\fdelimC b}$ -\end{LTXexample} - -\subsection{\CMD{atop}} -\cIndex{atop} - -\begin{LTXexample}[width=0.2\linewidth] -$a\atop b$\\[8pt] - -$({n \atop k}) = {n!\above1pt k!(n-k)!}$\\[8pt] - -$\displaystyle{a\atop b}$ -\end{LTXexample} - - -\subsection{\CMD{atopwithdelims}} -\cIndex{atopwithdelims} -\begin{LTXexample}[width=0.2\linewidth] -$a\atopwithdelims() b$\\[8pt] - -${n \atopwithdelims() k} = {n!\above1pt k!(n-k)!}$\\[8pt] - -$\displaystyle{a\atopwithdelims\{. b}$ -\end{LTXexample} - -\subsection{\CMD{displaylimits}} -\cIndex{displaylimits}Resets the conventions for using limits with operators to the standard for the used environment. - -\subsection{\CMD{eqno}}\label{subsec:eqno} -\cIndex{eqno}Puts an equation number at the right margin, the parameter can hold anything. \verb+\eqno+ places -only the parameter, but doesn't increase any equation counter. - -\begin{LTXexample}[width=0.5\linewidth] -\[ y=f(x) \eqno{(A12)} \] -\end{LTXexample} - -\subsection{\CMD{everydisplay}} -\cIndex{everydisplay}Inserts the parameter at the start of every switch to display math mode. - -\begin{LTXexample}[width=0.4\linewidth] -\everydisplay{\color{red} -} -\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] -\[ g(x) = \int \frac{\sin^2 x}{x^2}\,\mathrm{d}x \] -\end{LTXexample} - -\subsection{\CMD{everymath}} -\cIndex{everymath}Same as \CIndex{everydisplay}, but now for the inline mode. -In the following example -the displaystyle is used (besides using color red) for every inline math expression. - -\bgroup -\begin{LTXexample}[width=0.45\linewidth] -\everymath{\color{red}% - \displaystyle} -\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \] -Instead of $\frac{\sin x}{x}$ - now with $\frac{\cos x}{x}$: -\[ g(x) = \int \frac{\cos x}{x}\,\mathrm{d}x \] -\end{LTXexample} -\egroup - -Pay attention for side effects on footnotes and other macros which use the math mode for superscript -and other math related modes. In this case you'll get the footnotes also in red. - -\subsection{\CMD{left}} -\cIndex{left}\TeX{} calculates the size of the following delimiter needed at the left side of a formula. -Requires an additional \verb+right+. - -\subsection{\CMD{leqno}} -\cIndex{leqno}Vice versa to \verb+\eqno+ (see section~\vref{subsec:eqno}). - -\subsection{\CMD{limits}} -\cIndex{limits}Typesets limits above and/or below operators (see section~\vref{sec:limits}). - -\subsection{\CMD{mathinner}} -\cIndex{mathinner}Defines the following parameter as subformula. - -\subsection{\CMD{nolimits}} -\cIndex{nolimits}The opposite of \CIndex{limits}, instead of above/below limits are placed to the right of large -operators (class 1). - - -\subsection{\CMD{over}} -\cIndex{over}Is equivalent to the fraction macro of \LaTeX{} and equivalent to the -\verb+\overwithdelims+, see section~\vref{subsec:overwithdelims}. - -\begin{LTXexample}[width=0.2\linewidth] -$ {a\over b} \qquad {{m\over n}\over{a+b}} $ -\[ {m\over n}\over{a+b} \] -\end{LTXexample} - - -\subsection{\CMD{overline}} -\cIndex{overline}Puts a line over the following character or subformula and has the same problems with different -heights as underlines (see section~\ref{subsec:underline}). - -\begin{LTXexample}[width=0.2\linewidth] -$\overline{x}+\overline{y}=\overline{z}$\\ -\let\ol\overline -$ \ol{x} + \ol{A} = \ol{z} $\\[5pt] -\def\yPh{\vphantom{A}} -$ \ol{x\yPh} + \ol{A} = \ol{z\yPh} $ -\end{LTXexample} - -\subsection{\CMD{overwithdelims}}\label{subsec:overwithdelims} -\cIndex{overwithdelims}Is a generalized fraction command with preset fraction bar thickness. %%% ----- Martin ----- - -\begin{LTXexample}[width=0.25\linewidth] -$ {a\overwithdelims() b} \qquad {{m\over n}\overwithdelims[]{a+b}} $ -\[ {m\over n}\overwithdelims\{.{a+b} \] -\end{LTXexample} - - -\subsection{\CMD{radical}} -\cIndex{radical}Makes a radical atom from the delimiter (27-bit number) and the math field. - -\begin{LTXexample}[width=0.2\linewidth] -\def\mySqrt{\radical"0270371\relax} -$ \mySqrt{\frac{1}{7}} $\\[5pt] - -\def\mySqrt{\radical"0270372\relax} -$ \mySqrt{\frac{1}{7}} $\\[5pt] - -\def\mySqrt{\radical"0270373\relax} -$ \mySqrt{\frac{1}{7}} $\\[5pt] - -\def\mySqrt{\radical"0270374\relax} -$ \mySqrt{\frac{1}{7}} $\\[5pt] -\end{LTXexample} - -\subsection{\CMD{right}} -\cIndex{right}Opposite to \verb+\left+, makes \TeX{} calculate the size of the -delimiter needed at the right of a formula. - -\subsection{\CMD{underline}}\label{subsec:underline} -\cIndex{underline}When there is a combination of variables with and without an index, the underlines are typeset %%% ----- Martin ----- -with a different depth. Using \verb+\vphantom+ in this case is a good choice. - -\begin{LTXexample}[width=0.2\linewidth] -$\underline{x}+\underline{y}=\underline{z}$\\ - -\let\ul\underline -\def\yPh{\vphantom{y}} -$ \ul{x\yPh} + \ul{y} = \ul{z\yPh} $\\ - -$ \ul{x_1} + \ul{y_2} = \ul{z_3} $ -\end{LTXexample} - -\subsection{\CMD{vcenter}} -\cIndex{vcenter}Centers vertical material with respect to the axis. - - -\section{Math penalties} - -\subsection{\CMD{binoppenalty}} -\cIndex{binoppenalty}A penalty for breaking math expressions between lines in a paragraph. TeX breaks lines only -when the binary symbol is not the last one and when the penalty is below 10,000. - -\subsection{\CMD{displaywidowpenalty}} -\cIndex{displaywidowpenalty}The penalty which is added after the penultimate line immediately preceeding a display math formula. - -\subsection{\CMD{postdisplaypenalty}} -\cIndex{postdisplaypenalty}Is added immediately after a math display ends. - -\subsection{\CMD{predisplaypenalty}} -\cIndex{predisplaypenalty}Is added immediately before a math display starts. - -\subsection{\CMD{relpenalty}} -\cIndex{relpenalty}The penalty for a line break after a relation symbol (if a break is possible). - - -\part{Other packages} -The following sections are not a replacement for the package documentation! -\section{List of available math packages} -\markboth{Math packages}{Math packages} - -\begin{center} -\noindent -\begin{tabular}{llll} -\href{http://www.dante.de/CTAN/help/Catalogue/entries/accents.html}{accents}& -\href{http://www.dante.de/CTAN/help/Catalogue/entries/alphalph.html}{alphalph}& -\href{http://www.dante.de/CTAN/help/Catalogue/entries/amsart.html}{amsart}& -\href{http://www.dante.de/CTAN/help/Catalogue/entries/amsbook.html}{amsbook}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsbsy.html}{amsbsy}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amscd.html}{amscd}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amscls.html}{amscls}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsfonts.html}{amsfonts}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amslatex.html}{amslatex}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsltx11.html}{amsltx11}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsmath.html}{amsmath}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsppt.html}{amsppt}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsppt1.html}{amsppt1}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsproc.html}{amsproc}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amssym.html}{amssym (plain TeX)}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amssymb.html}{amssymb (LaTeX)}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amstex.html}{amstex (Plain TeX)}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amstext.html}{amstext}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsthm.html}{amsthm}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/bez123.html}{bez123}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/bitfield.html}{bitfield}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/brclc.html}{brclc}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/breqn.html}{breqn}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/cancel.html}{cancel}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/cases.html}{cases}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/comma.html}{comma}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/datenumber.html}{datenumber}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/diagxy.html}{diagxy}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/doublestroke.html}{doublestroke}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/easyeqn.html}{easyeqn}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/easybmat.html}{easybmat}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/easymat.html}{easymat}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/eqnarray.html}{eqnarray}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/esvect.html}{esvect}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/fixmath.html}{fixmath}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/fltpoint.html}{ftlpoint}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/icomma.html}{icomma}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/leftidx.html}{leftidx}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathdots.html}{mathdots}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathtools.html}{mathtools}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathematica.html}{mathematica}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/mil3.html}{mil3}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/mtbe.html}{mtbe}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/nath.html}{Nath}\\ -\href{http://www.dante.de/CTAN//help/Catalogue/entries/numprint.html}{numprint}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/random.html}{random}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/romannum.html}{romannum}& -\href{http://www.dante.de/CTAN//help/Catalogue/entries/texaide.html}{TeXaide} -\end{tabular} -\end{center} - -The following examples depend on the listed versions of the packages: %%% ----- Martin ----- - -{\small -\begin{verbatim} - amsopn.sty 1999/12/14 v2.01 operator names - bm.sty 1999/07/05 v1.0g Bold Symbol Support (DPC/FMi) - empheq.sty 2007/12/03 v2.12 Emphasizing equations (MH) - amscd.sty 1999/11/29 v2.0 - accents.sty 2000/08/06 v1.2 Math Accent Tools - framed.sty 2007/10/04 v 0.95: framed or shaded text with page breaks -pstricks.sty 2004/05/06 v0.2k LaTeX wrapper for `PSTricks' (RN,HV) -pstricks.tex 2003/03/07 v97 patch 15 `PSTricks' (tvz) -pst-node.tex 2008/11/26 v1.01 PSTricks package for nodes (tvz,hv) -delarray.sty 1994/03/14 v1.01 array delimiter package (DPC) - xypic.sty 1999/02/16 Xy-pic version 3.7 - exscale.eps Graphic file (type veps) -\end{verbatim} -} - - -\subsection{\texttt{accents}}\label{sec:package-accent} -If you want to write for example an underlined M, then you can do it by %%% ----- Martin ----- - -\medskip -\begin{tabular}{ll} -\verb|\underline{$M$}| & \underline{$M$}\\ -\verb|\underbar{$M$}| & \underbar{$M$}\\ -\verb|\underaccent{\bar}{M}| & $\underaccent{\bar}{M}$ -\end{tabular} -\medskip - -As seen, there is no difference between \CMD{underline} and \CMD{underbar}. For %%% ----- Martin ----- -some reasons it may be better to use the \PIndex{accent} package with the -\CMD{underaccents} macro. - -\subsection{\texttt{amscd} -- commutative diagrams} - -The \PIndex{amscd} package is part of the \AmSmath bundle -or available at CTAN% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amscd.dtx}% -{CTAN://macros/latex/required/amslatex/math/amscd.dtx}} and has no options for the -\verb|\usepackage| command. -\texttt{amscd} does not support diagonal arrows but is much %%% ----- Martin ----- -easier to handle than the complex \PIndex{pstricks} package or -the \PIndex{xypic} package. On the other hand simple diagrams -can be written with the \UIndex{array} or look at \cite{taylor00}. - -\[ -\begin{CD} - R\times S\times T @>\text{restriction}>> S\times T \\ - @VprojVV @VVprojV \\ - R\times S @<<\text{inclusion}< S -\end{CD} -\] - -\begin{lstlisting} -\[ -\begin{CD} - R\times S\times T @>\text{restriction}>> S\times T \\ - @VprojVV @VVprojV \\ - R\times S @<<\text{inclusion}< S -\end{CD} -\] -\end{lstlisting} - - -\subsection{\texttt{amsopn}}\label{sec:amsopn} -With the \PIndex{amsopn} package it is very easy to declare new math operators, which are written in -upright mode: - -$\underset{s=p}{Res}\quad\text{versus}\quad\underset{s=p}{\Res}$ - -\medskip -\begin{lstlisting} -\documentclass[10pt]{article} -\usepackage{amsmath} -\usepackage{amsopn} -\DeclareMathOperator{\Res}{Res} -\begin{document} -$\underset{s=p}{Res}\quad\underset{s=p}{\Res}$ -\end{document} -\end{lstlisting} - -Table~\ref{tab:amsopn} shows the predefined operatornames of \verb+amsopn+. - -\begin{table}[htb] -\centering -\begin{tabular}{llllll} -\verb+\arccos+ & $\arccos$ & \verb+\arcsin+ & $\arcsin$ & \verb+\arctan+ & $\arctan$\\ -\verb+\arg+ & $\arg$ & \verb+\cos+ & $\cos$ & \verb+\cosh+ & $\cosh$\\ -\verb+\cot+ & $\cot$ & \verb+\coth+ & $\coth$ & \verb+\csc+ & $\csc$\\ -\verb+\deg+ & $\deg$ & \verb+\det+ & $\det$ & \verb+\dim+ & $\dim$\\ -\verb+\exp+ & $\exp$ & \verb+\gcd+ & $\gcd$ & \verb+\hom+ & $\hom$\\ -\verb+\inf+ & $\inf$ & \verb+\injlim+ & $\injlim$ & \verb+\ker+ & $\ker$\\ -\verb+\lg+ & $\lg$ & \verb+\lim+ & $\lim$ & \verb+\liminf+ & $\liminf$\\ -\verb+\limsup+ & $\limsup$ & \verb+\ln+ & $\ln$ & \verb+\log+ & $\log$\\ -\verb+\max+ & $\max$ & \verb+\min+ & $\min$ & \verb+\Pr+ & $\Pr$\\ -\verb+\projlim+& $\projlim$& \verb+\sec+ & $\sec$ & \verb+\sin+ & $\sin$\\ -\verb+\sinh+ & $\sinh$ & \verb+\sup+ & $\sup$ & \verb+\tan+ & $\tan$\\ -\verb+\tanh+ & $\tanh$ -\end{tabular} -\caption{The predefined operators of \texttt{amsopn.sty}}\label{tab:amsopn} -\end{table} - - -\subsection{\texttt{bigdel}}\label{sec:bigdelim} -This is a very useful package together with the \PIndex{multirow} package. -In the following example we need additional parentheses for a different -number of rows. This is also possible with the \UIndex{array}, -but not as easy as with the \PIndex{bigdelim} package. The trick is that you need one -separate column for a big delimiter, but with empty cells in all rows, which -the delimiter spans. - -\[ - \begin{pmatrix} - & x_{11} & x_{12} & \dots & x_{1p} & \rdelim\}{4}{3cm}[some text]\\ - \ldelim[{5}{1cm}[text] & x_{21} & x_{22} & \dots & x_{2p} \\ - & \vdots\\ - & x_{n_1 1}& x_{n_1 2} & \dots & x_{n_1 p}\\ - & x_{n_1+1,1}&x_{n_1+1,2} & \dots & x_{n_1+1, p} & - \rdelim\}{3}{3cm}[some more text]\\ - & \vdots\\ - & x_{n_1+n_2, 1} & x_{n_1+n_2,2} & \dots & x_{n_1+n_2,p}\\ - & \vdots \\ - \end{pmatrix} -\] - -\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm] -\[ - \begin{pmatrix} - & x_{11} & x_{12} & \dots & x_{1p} & \rdelim\}{4}{3cm}[some text]\\ - \ldelim[{5}{1cm}[text] & x_{21} & x_{22} & \dots & x_{2p} \\ - & \vdots\\ - & x_{n_1 1}& x_{n_1 2} & \dots & x_{n_1 p}\\ - & x_{n_1+1,1}&x_{n_1+1,2} & \dots & x_{n_1+1, p} & - \rdelim\}{3}{3cm}[some more text]\\ - & \vdots\\ - & x_{n_1+n_2, 1} & x_{n_1+n_2,2} & \dots & x_{n_1+n_2,p}\\ - & \vdots \\ - \end{pmatrix} -\] -\end{lstlisting} - -As seen in the above listing the left big delimiter is placed in the first -column, all other rows start with second column. It is possible to use all -columns above and below the delimiter. For the \UIndex{array} -there must be two more columns defined, in case of a big delimiter left and -right. The syntax of \CIndex{ldelim} and \CIndex{rdelim} is: -% -\begin{verbatim} -\ldelim<delimiter>{<n rows>}{<added horizontal space>}[<text>] -\rdelim<delimiter>{<n rows>}{<added horizontal space>}[<text>] -\end{verbatim} - -Any delimiter which is possible for the \CIndex{left} or \CIndex{right} command -is allowed, \eg ``\verb/()[]{}|/''. The text is an optional argument and -always typeset in text mode. - -\subsection{\texttt{bm}}\label{sec:bm} -By default the math macro \CIndex{mathbf} writes everything in bold and in upright mode -$\mathbf{y=f(x)}$ (\verb|$\mathbf{y=f(x)}$|), but it should be in italic mode especially -for variables $\bm{y=f(x)}$ (\verb|$\bm{y=f(x)}$|), which is possible with the package \PIndex{bm}. -For writing a whole formula in bold have a look at section~\vref{sec:boldmath}. - - -\subsection{\texttt{braket}}\label{sec:braket} -It is available at - \href{http://www.ctan.org/tex-archive/macros/latex/contrib/other/misc/braket.sty}% -{CTAN://macros/latex/contrib/other/misc/braket.sty} -and provides several styles for writing math expressions inside brakets. For example: - -\[ \left\{ x\in\mathbf{R} | 0<{|x|}<\frac{5}{3}\right\} \] - -\begin{lstlisting} -\[ \left\{ x\in\mathbf{R} | 0<{|x|}<\frac{5}{3}\right\} \] -\end{lstlisting} - -\noindent looks not quite right and it is not really easy to get the first vertical line in the same -size as the outer braces. Some solution may be using \CIndex{vphantom}: - -\[ -\left\{\vphantom{\frac{5}{3}}x\in\mathbf{R} \right|\left. 0<{|x|}<\frac{5}{3}\right\} -\] - -\begin{lstlisting} -\[ -\left\{\vphantom{\frac{5}{3}}x\in\mathbf{R} \right|\left. 0<{|x|}<\frac{5}{3}\right\} -\] -\end{lstlisting} - -The package \PIndex{braket} has the macros - -\begin{lstlisting} -\Bra{<math expression>} -\Ket{<math expression>} -\Braket{<math expression>} -\Set{<math expression>} -\end{lstlisting} - -\noindent and the same with a leading lower letter, which are not really interesting. - -\[ \Bra{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\[ \Ket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\[ \Braket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\[ \Braket{x\in\mathbf{R} | 0<\vert x\vert <\frac{5}{3}} \] -\[ \Set{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] - -\begin{lstlisting} -\[ \Bra{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\[ \Ket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\[ \Braket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\[ \Braket{x\in\mathbf{R} | 0<\vert x\vert <\frac{5}{3}} \] -\[ \Set{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \] -\end{lstlisting} - -The difference between the \CIndex{Set} and the \CIndex{Braket} macro is the handling of the -vertical lines. In \CIndex{Set} only the first one gets the same size as the -braces\index{Braces} and in \CIndex{Braket} all. - -\[ \Braket{ \phi | \frac{\partial^2}{\partial t^2} | \psi }\] -\[ \Set{ \phi | \frac{\partial^2}{\partial t^2} | \psi }\] -\begin{lstlisting} -\[\Braket{\phi | \frac{\partial^2}{\partial t^2} | \psi}\] -\[\Set{\phi | \frac{\partial^2}{\partial t^2} | \psi}\] -\end{lstlisting} - - -\CMD{Bra} and \CMD{Ket} do nothing with the inner vertical lines. - - -\subsection{\texttt{cancel}}\label{cancel.sty} -This is a nice package for canceling anything in mathmode with a slash, -backslash or a \verb+X+. To get -a horizontal line we can define an additional macro called \CIndex{hcancel} -with an optional argument -for the line color (requires package \PIndex{color}): -% -\begin{lstlisting} -\newcommand\hcancel[2][black]{\setbox0=\hbox{#2}% - \rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} -\end{lstlisting} - -It is no problem to redefine the \CIndex{cancel} macros to get also colored lines. -A horizontal line for -single characters is also decribed in section~\vref{sec:Accents}. - -\medskip -\noindent -\verb+\cancel+: $f(x)=\dfrac{\left(x^2+1\right)\cancel{(x-1)}}{\cancel{(x-1)}(x+1)}$\\[0.5cm] -\verb+\bcancel+: $\bcancel{3}\qquad\bcancel{1234567}$\\[0.5cm] -\verb+\xcancel+: $\xcancel{3}\qquad\xcancel{1234567}$\\[0.5cm] -\verb+\hcancel+: $\hcancel{3}\qquad\hcancel[red]{1234567}$ - -\bigskip -\begin{lstlisting} -$f(x)=\dfrac{\left(x^2+1\right)\cancel{(x-1)}}{\cancel{(x-1)}(x+1)}$\\[0.5cm] -$\bcancel{3}\qquad\bcancel{1234567}$\\[0.5cm] -$\xcancel{3}\qquad\xcancel{1234567}$\\[0.5cm] -$\hcancel{3}\qquad\hcancel[red]{1234567}$ -\end{lstlisting} - - -\subsection{\texttt{cool}}\label{cool} -The \PIndex{cool} package defines a lot of special mathematical expressions -to use them by the macro name. The following list shows only some of -them, for more informations look at the example file, which comes with -the package. - -\bgroup -\parindent=0pt -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{Sin}\verb|{x}| & $\displaystyle \Sin{x}$\\ -\CIndex{Cos}\verb|{x}| & $\displaystyle \Cos{x}$\\ -\CIndex{Tan}\verb|{x}| & $\displaystyle \Tan{x}$\\ -\CIndex{Csc}\verb|{x}| & $\displaystyle \Csc{x}$\\ -\CIndex{Sec}\verb|{x}| & $\displaystyle \Sec{x}$\\ -\CIndex{Cot}\verb|{x}| & $\displaystyle \Cot{x}$ -\end{tabular} - -\bigskip -\Style{ArcTrig=inverse}% -\CMD{Style\{ArcTrig=inverse\}} (default) - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{ArcSin}\verb|{x}|& $\displaystyle \ArcSin{x}$\\ -\CIndex{ArcCos}\verb|{x}|& $\displaystyle \ArcCos{x}$\\ -\CIndex{ArcTan}\verb|{x}|& $\displaystyle \ArcTan{x}$ -\end{tabular} - -\bigskip -\Style{ArcTrig=arc} -\CMD{Style\{ArcTrig=arc\}} - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{ArcSin}\verb|{x}| & $\displaystyle \ArcSin{x}$\\ -\CIndex{ArcCos}\verb|{x}| & $\displaystyle \ArcCos{x}$\\ -\CIndex{ArcTan}\verb|{x}| & $\displaystyle \ArcTan{x}$\\ -\CIndex{ArcCsc}\verb|{x}| & $\displaystyle \ArcCsc{x}$\\ -\CIndex{ArcSec}\verb|{x}| & $\displaystyle \ArcSec{x}$\\ -\CIndex{ArcCot}\verb|{x}| & $\displaystyle \ArcCot{x}$ -\end{tabular} - - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{Factorial}\verb|{n}| & $\displaystyle \Factorial{n}$\\ -\CIndex{DblFactorial}\verb|{n}| & $\displaystyle \DblFactorial{n}$\\ -\CIndex{Binomial}\verb|{n}{k}| & $\displaystyle \Binomial{n}{k}$\\ -\CIndex{Multinomial}\verb|{1,2,3,4}|& $\displaystyle \Multinomial{i_1,\ldots,i_n}$ -\end{tabular} - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{GammaFunc}\verb|{x}| & $\displaystyle \GammaFunc{x}$\\ -\CIndex{IncGamma}\verb|{a}{x}| & $\displaystyle \IncGamma{a}{x}$\\ -\CIndex{GenIncGamma}\verb|{a}{x}{y}|& $\displaystyle \GenIncGamma{a}{x}{y}$ \\ -\CIndex{RegIncGamma}\verb|{a}{x}|& $\displaystyle \RegIncGamma{a}{x}$ \\ -\CIndex{RegIncGammaInv}\verb|{a}{x}|& $\displaystyle \RegIncGammaInv{a}{x}$ \\ -\CIndex{GenRegIncGamma}\verb|{a}{x}{y}| & $\displaystyle \GenRegIncGamma{a}{x}{y}$\\ -\CIndex{GenRegIncGammaInv}\verb|{a}{x}{y}|& $\displaystyle \GenRegIncGammaInv{a}{x}{y}$\\ -\CIndex{Pochhammer}\verb|{a}{n}| & $\displaystyle \Pochhammer{a}{n}$ \\ -\CIndex{LogGamma}\verb|{x}| & $\displaystyle \LogGamma{x}$ -\end{tabular} - - -\bigskip - -\begin{tabular}{@{}ll@{}} -\CIndex{Hypergeometric}\verb|{0}{0}{}{}{x}| & $\displaystyle \Hypergeometric{0}{0}{}{}{x}$\\ -\CIndex{Hypergeometric}\verb|{0}{1}{}{b}{x}|& $\displaystyle \Hypergeometric{0}{1}{}{b}{x}$ -\end{tabular} - - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{RegHypergeometric}\verb|{0}{0}{}{}{x}| & $\displaystyle \RegHypergeometric{0}{0}{}{}{x}$\\ -\CIndex{RegHypergeometric}\verb|{0}{1}{}{b}{x}|& $\displaystyle \RegHypergeometric{0}{1}{}{b}{x}$ -\end{tabular} - - - -\bigskip -\begin{tabular}{@{}l@{}} -\CIndex{MeijerG}\verb|[a,b]{n}{p}{m}{q}{x}| \\ - \hspace*{2cm} $\displaystyle \MeijerG[a,b]{n}{p}{m}{q}{x}$ \\ -\CIndex{MeijerG}\verb|{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}| \\ - \hspace*{2cm} $\displaystyle \MeijerG{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}$ -\end{tabular} - -\index{Zeta!Functions} -\index{Polylogarithm} -\index{Zeta!Riemann} -\index{Zeta!Hurwitz} -\index{Zeta} - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{RiemannZeta}\verb|{s}| & $\displaystyle \RiemannZeta{s}$\\ -\CIndex{Zeta}\verb|{s}| & $\displaystyle \Zeta{s}$\\ -\CIndex{HurwitzZeta}\verb|{s}{a}|& $\displaystyle \HurwitzZeta{s}{a}$\\ -\CIndex{Zeta}\verb|{s,a}| & $\displaystyle \Zeta{s,a}$ \\ -\CIndex{RiemannSiegelTheta}\verb|{x}|& $\displaystyle \RiemannSiegelTheta{x}$ \\ -\CIndex{RiemannSiegelZ}\verb|{x}| & $\displaystyle \RiemannSiegelZ{x}$ \\ -\CIndex{StieltjesGamma}\verb|{n}| & $\displaystyle \StieltjesGamma{n}$ -\end{tabular} - - -\index{Mathieu!Functions} -\index{Mathieu!Characteristics} - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{MathieuC}\verb|{a}{q}{z}| & $\displaystyle \MathieuC{a}{q}{z}$ \\ -\CIndex{MathieuS}\verb|{a}{q}{z}| & $\displaystyle \MathieuS{a}{q}{z}$ -\end{tabular} - - -\bigskip -\begin{tabular}{@{}ll@{}} -\CIndex{MathieuCharacteristicA}\verb|{r}{q}|& $\displaystyle \MathieuCharacteristicA{r}{q}$ \\ -\CIndex{MathieuCharisticA}\verb|{r}{q}| & $\displaystyle \MathieuCharisticA{r}{q}$ \\ - -%%%%%%% Characteristic Value of Even Mathieu Fucntion b_r(q) -\CIndex{MathieuCharacteristicB}\verb|{r}{q}|& $\displaystyle \MathieuCharacteristicB{r}{q}$ \\ -\CIndex{MathieuCharisticB}\verb|{r}{q}|& $\displaystyle \MathieuCharisticB{r}{q}$ \\ - -%%%%%%%% Characteristic Exponent of a Mathieu Fucntion r(a,q) -\CIndex{MathieuCharacteristicExponent}\verb|{a}{q}|& $\displaystyle \MathieuCharacteristicExponent{a}{q}$\\ -\CIndex{MathieuCharisticExp}\verb|{a}{q}|& $\displaystyle \MathieuCharisticExp{a}{q}$ -\end{tabular} -\egroup - -\subsection{\texttt{delarray}}\label{delarray} - -Package \PIndex{delarray}% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/required/tools/delarray.dtx}{CTAN://macros/latex/required/tools/delarray.dtx}% -} supports different delimiters which are defined together with the -beginning of an array: - -\begin{lstlisting} -\begin{array}<delLeft>{cc}<delRight> -... -\end{lstlisting} - -\noindent defines an array with two centered columns and the delimiters\\ -``\texttt{<delLeft><delRight>}{}'', \eg ``\texttt{()}{}''. - -\medskip{} -\begin{minipage}[c]{0.45\textwidth}% -\begin{lstlisting} -\[ -A=\begin{array}({cc}) - a & b\\ - c & d -\end{array} -\] -\end{lstlisting} - -\end{minipage}% -\hfill{}\begin{minipage}[c]{0.45\textwidth}% -\[ -A=\begin{array}({cc}) -a & b \\ -c & d -\end{array} -\] -\end{minipage}% - -\medskip{} - -The \PIndex{delarray} package expects a pair of delimiters. If you need only -one (like the cases structure) then use the dot for an ``empty'' -delimiter, \eg - -\medskip{} -\begin{minipage}[c]{0.45\textwidth}% -\begin{lstlisting} -\[ -A=\begin{array}\{{cc}. - a & b\\ - c & d -\end{array} -\] -\end{lstlisting} - -\end{minipage}% -\hfill{}\begin{minipage}[c]{0.45\textwidth}% -\[A=\begin{array}\{{cc}. -a & b \\ -c & d -\end{array}\] -\end{minipage}% - -\medskip{} - -\noindent which is a useful command for a cases structure without the \AmSmath -package, which is described in the \AmSmath part. - - -\subsection{\texttt{dotseqn}}\label{dotseqn} -This package% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/dotseqn/}% -{CTAN://macros/latex/contrib/dotseqn}} fills the space between the math -expression and the equation -number with dots. Expect problems when using this package together with \AmSmath. - -\begingroup -\makeatletter -% package couldn't be loaded, it redefines the math -% environments -\newcommand\EqnDots{\leaders\hbox{\kern4\p@ .\kern4\p@}\hfill} -\@ifundefined{mathindent}{\newdimen\mathindent \mathindent\leftmargini}{} -\renewcommand{\[}{\relax \ifmmode\@badmath \else - \begin{trivlist}% - \@beginparpenalty\predisplaypenalty \@endparpenalty\postdisplaypenalty - \item[]\leavevmode \hbox to\linewidth\bgroup $\m@th\displaystyle %$ - \hskip\mathindent\bgroup - \fi} -\renewcommand{\]}{\relax\ifmmode \egroup $\hfil% $ - \egroup \end{trivlist}% - \else \@badmath \fi} -\renewenvironment{equation}% - {\@beginparpenalty\predisplaypenalty \@endparpenalty\postdisplaypenalty - \refstepcounter{equation}\trivlist \item[]\leavevmode - \hbox to\linewidth\bgroup $\m@th% $ - \displaystyle \hskip\mathindent}% - {$\EqnDots % $ Replace `\hfil' with dotted leaders `\EqnDots'. - \displaywidth\linewidth\hbox{\@eqnnum}\egroup \endtrivlist} -\renewenvironment{eqnarray}{% - \stepcounter{equation}% - \def\@currentlabel{\p@equation\theequation}% - \global\@eqnswtrue \m@th \global\@eqcnt\z@ \tabskip\mathindent - \let\\\@eqncr \setlength\abovedisplayskip\topsep - \ifvmode \addtolength\abovedisplayskip\partopsep \fi - \addtolength\abovedisplayskip\parskip - \setlength\belowdisplayskip\abovedisplayskip - \setlength\belowdisplayshortskip\abovedisplayskip - \setlength\abovedisplayshortskip\abovedisplayskip - $$\everycr{}\halign to\linewidth% $$ - \bgroup - \hskip\@centering - $\displaystyle\tabskip\z@skip{##}$\@eqnsel&% - \global\@eqcnt\@ne \hfil${\DEQ@acs##\DEQ@acs}$\hfil&% - \global\@eqcnt\tw@ $\displaystyle{##}$\hskip\@centering\cr% - }% end of "\begin" part - {\@@eqncr - \noalign{% vertical skip up to overlay phantom line - \penalty\@M \vskip-\prevdepth - \edef\@tempa{\omit\span\omit\span\omit % span three columns - \vrule\@depth\the\prevdepth \@width\z@ % strut of proper depth - \kern-\mathindent \kern\linewidth}% % full line width - \nointerlineskip \expandafter % use saved |\@tempa| outside group - }\@tempa\cr - \egroup - \global\advance\c@equation\m@ne$$% $$ - \global\@ignoretrue - } -\def\@@eqncr{\let\reserved@a\@empty - \ifcase\@eqcnt \def\reserved@a{& &}\or \def\reserved@a{&}\fi - \reserved@a - \if@eqnsw \egroup $\EqnDots \@eqnnum $\bgroup \stepcounter{equation}% - \fi \global\@eqnswtrue\global\@eqcnt\z@\cr} -\def\DEQ@acs{\hskip\tw@\arraycolsep} -\makeatother -\begin{eqnarray} - F(x) &=& \int f(x)\,\mathrm{d}x + C -\end{eqnarray} -% -\begin{equation} - F(x)=\int f(x)\,\mathrm{d}x + C -\end{equation} -\endgroup - -\begin{lstlisting} -\begin{eqnarray} - F(x) &=& \int f(x)\,\mathrm{d}x + C -\end{eqnarray} -% -\begin{equation} - F(x)=\int f(x)\,\mathrm{d}x + C -\end{equation} -\end{lstlisting} - - -\subsection{\texttt{empheq}}\label{sec:empheq} - -This package\footnote{The package is part of the \texttt{mh}-bundle -of Morten H\o gholm (\href{http://www.ctan.org/tex-archive/macros/latex/contrib/mh/}{CTAN://macros/latex/contrib/mh/}).} -supports different frames for math environments of the \AmSmath -package. It doesn't support all the environments from standard \LaTeX{} which -are not modified by \AmSmath, \eg \UIndex{eqnarray}. - -With the optional argument of the \UIndex{empheq} -the preferred box type -can be specified. A simple one is \CIndex{fbox} - -\begin{empheq}[box=\fbox]{align} - f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 -\end{empheq} - -\begin{lstlisting} -\begin{empheq}[box=\fbox]{align} - f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 -\end{empheq} -\end{lstlisting} - -The same is possible with the macro \verb|\colorbox|: -\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align} - f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 -\end{empheq} - -\begin{lstlisting} -\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align} - f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 -\end{empheq} -\end{lstlisting} - -The key \verb|box| can hold any possible \LaTeX{} command sequence. Boxing -subequations is also no problem, the \UIndex{empheq} works in the same way: - -\begin{subequations} -\begin{empheq}[box={\fboxsep=10pt\colorbox{cyan}}]{align} - f(x) & =\int_1^{\infty}\frac{1}{x^1}\,\mathrm{d}x=1\\ - f(x) & =\int_2^{\infty}\frac{1}{x^2}\,\mathrm{d}x=0.25 -\end{empheq} -\end{subequations} - -\begin{lstlisting} -\begin{subequations} -\begin{empheq}[box={\fboxsep=10pt\colorbox{cyan}}]{align} - f(x) & =\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1\\ - f(x) & =\int_2^{\infty}\frac{1}{x^2}\,\mathrm{d}x=0.25 -\end{empheq} -\end{subequations} -\end{lstlisting} - -For more information on \PIndex{empheq} package have a look at the documentation of the package -which is available at any CTAN server. - -\subsection{\texttt{esint}}\label{sec:esint} -This is a very useful package when you want nice double or triple integral or curve -integral symbols. The ones from the \PIndex{wasysym} package% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/wasysym/}% -{CTAN://macros/latex/contrib/wasysym/}} are not the best. -\verb|esint|\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/esint/}% -{CTAN://macros/latex/contrib/esint/} -\href{http://www.ctan.org/tex-archive/fonts/ps-type1/esint/}{CTAN://fonts/ps-type1/esint/}} supports the following symbols: - -\allowdisplaybreaks -\begin{align} -\text{\CMD{int}} &: \int\\ -\text{\CMD{iint}} &: \iint\\ -\text{\CMD{iiintop}} &: \iiintop\\ -\text{\CMD{iiiintop}} &: \iiiintop\\ -\text{\CMD{dotsintop}}&: \dotsintop\\ -\text{\CMD{ointop}} &: \ointop\\ -\text{\CMD{oiint}} &: \oiint\\ -\text{\CMD{sqint}} &: \sqint\\ -\text{\CMD{sqiint}} &: \sqiint\\ -\text{\CMD{ointctrclockwise}} &: \ointctrclockwise\\ -\text{\CMD{ointclockwise}} &: \ointclockwise\\ -\text{\CMD{varointclockwise}} &: \varointclockwise\\ -\text{\CMD{varointctrclockwise}} &: \varointctrclockwise\\ -\text{\CMD{fint}} &: \fint\\ -\text{\CMD{varoiint}} &: \varoiint\\ -\text{\CMD{landupint}} &: \landupint\\ -\text{\CMD{landdownint}} &: \landdownint -\end{align} - - -\subsection{\texttt{eucal} and \texttt{euscript}}\label{sec:euscript.sty} - -These packages should be part of your local \TeX{} installation, because -they come with the \AmSmath packages. Otherwise get them from CTAN% -\footnote{\href{http://www.ctan.org/tex-archive/fonts/amsfonts/latex/euscript.sty}% -{CTAN://fonts/amsfonts/latex/euscript.sty}}. They support a scriptwriting of only uppercase -letters: - -\begin{center} -\includegraphics{EuScript} -%\texttt{\textbackslash{}mathscr\{...\}}\index{EuScript@\textbackslash EuScript} -%{$\EuScript{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$} -\end{center} - -Read the documentation for the interdependence to the %%% ----- Martin ----- -\verb|\mathcal| command. For the above example the -package \PIndex{eucal} was loaded with the option \verb|mathscr|. - - -\subsection{\texttt{exscale}}\label{sec:exscale} - -The following formula is written with the default fontsize where everything -looks more or less well: - -\[ -\int_{-1}^{+1}\frac{f(x)}{\sqrt{1-x^{2}}}\,% -\,\mathrm{d}x\approx\frac{\pi}{n}\sum_{i=1}^{n}f\left(\cos\left(\frac{2i-1}{2n}\right)\right)\] - - -Writing the same with the fontsize \CIndex{huge} gives -a surprising result, which belongs to the historical development of -\LaTeX{}, the \CIndex{int} and \CIndex{sum} symbols -are not stretched. This extreme fontsize is often needed for slides -and not only written ``just for fun{}''. - -\begin{center} -\includegraphics{exscale} -\end{center} - -Using the \PIndex{exscale} package% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/base/}% -{CTAN://macros/latex/base/}} package, which should be part of any local \TeX{} -installation, all symbols get the right size. - -\begin{minipage}[c]{1.0\textwidth}% -\centering\huge\[ -\int_{-1}^{+1}\frac{f(x)}{\sqrt{1-x^{2}}}\,\mathrm{d}x\approx\frac{\pi}{n}% -\sum_{i=1}^{n}f\left(\cos\left(\frac{2i-1}{2n}\right)\right)\] -\end{minipage}% - -\subsection{\texttt{mathtools}}\label{sec:mathtools} -This package comes with a lot of additional features for typesetting math code. -Sometimes it is useful when only such equations are numbered which are -referenced in the text. This is possible with the switch \verb+\showonlyrefs+. - -Matrices are set by default with a centered horizontal alignment, which is -often not the best way. The \PIndex{mathtools} package provides a starred version of -the matrix environments which allow an optional argument for the horizontal -alignment: - -\[ -\begin{pmatrix*}[r] - 1 & -1 & 0 \\ - -1 & 1 & -1 \\ - 1 & -1 & 0 \\ --11 & 11 &-11 \\ -\end{pmatrix*} -\] - -\begin{lstlisting} -\[ -\begin{pmatrix*}[r] - 1 & -1 & 0 \\ - -1 & 1 & -1 \\ - 1 & -1 & 0 \\ --11 & 11 &-11 \\ -\end{pmatrix*} -\] -\end{lstlisting} - -\PIndex{mathtools} also provides some more environments for setting equations. -Very interesting is the \UIndex{lgathered}, which allows to typeset a formula in -the following way: - -\begin{LTXexample}[width=0.6\linewidth] -\begin{align} - x &= - \begin{lgathered}[t] - a + b + c \\ - d + e + - \!\begin{gathered}[t] - f + g + h \\ - i + j + k - \end{gathered} - \end{lgathered} -\end{align} -\end{LTXexample} - -The \CMD{!}\index{*@\textbackslash\char033} revokes the internal horizontal space -in front of the \UIndex{gathered}. - - - -\subsection{\texttt{nicefrac}}\label{sec:nicefrac} -Typesetting fractions\index{Fraction} in the inline mode is often a bad choice, the vertical spacing -increases in fact of the fraction. The \PIndex{nicefrac} package defines the macro -\CIndex{nicefrac}, which is used in the same way as the \CIndex{frac} command, but it -typesets the fraction with a less height: \nicefrac{2}{3} \lstinline|\nicefrac{2}{3}|. -The package is part of the \PIndex{units} package bundle and can be found in the -directory of \PIndex{units}. - - - -\subsection{\texttt{relsize}}\label{sec:relsize} -Often consecutives math operators are used, like two sum symbols, \eg -% -\[ \sum\sum_{i=1}^n i^2 \] - - -As seen the sums are of the same size. To increase the first operator size, someone -can use the \CIndex{scalebox} macro from package \UIndex{graphicx} and write an own macro %%% ----- Martin ----- -\verb+\Sum+, \eg \index{Operator!size}\index{Size!Operator} - -\begin{lstlisting} -\def\Sum{\ensuremath\mathop{\scalebox{1.2}{$\displaystyle\sum$}}} -\[ \Sum_{j=1}\sum_{i=1}^\infty i \] -\end{lstlisting} - -\def\Sum{\ensuremath\mathop{\scalebox{1.2}{$\displaystyle\sum$}}} -\[ \Sum_{j=1}\sum_{i=1}^\infty i \] - -Another solution is to use the \PIndex{relsize} package% -\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/ltxmisc/}{CTAN://macros/latex/ltxmisc/}} -together with the \PIndex{exscale} one. \PIndex{relsize} defines a useful macro \CIndex{mathlarger}: - -\begin{LTXexample} -\[ \mathlarger{\sum}\sum_{i=1}^n i^2 \] -\end{LTXexample} - - -\subsection{\texttt{xypic}}\label{xypic.sty} - -The \CIndex{xymatrix} macro is part of the \PIndex{xypic} package% -\footnote{\href{http://www.ctan.org/tex-archive/support/latex2html/}% -{CTAN://macros/generic/diagrams/xypic/xy-3.7/}} which can be loaded with several options -which are not so important here.% -\footnote{For more information look at the package documentation or the -package \PIndex{xy} itself, which is often saved in \texttt{/usr/share/texmf/tex/generic}}. - -\begin{equation} -\xymatrix{A\POS[];[d]**\dir{~},[];[dr]**\dir{-} & B & C\\ -D & E\POS[];[l]**\dir{.},[];[r]**\dir{~} & F\POS[];[dl]**\dir{~}\\ -G & H & I} -\label{eq:xymatrix} -\end{equation} - - -This matrix was created with - -\begin{lstlisting} -\[ -\xymatrix{ A\POS [];[d]**\dir {~},[];[dr]**\dir {-} & B & C\\ - D & E\POS [];[l]**\dir {.},[];[r]**\dir {~} & F\POS [];[dl]**\dir {~}\\ - G & H & I} -\] -\end{lstlisting} - - - - -\part{Math fonts} -Typesetting text and math is far different. There exist a lot of free text fonts without -additional math characters. This is the reason why we have to buy a commercial math font, e.\,g. -\Index{Palatino} (\PIndex{pamath}) or \Index{Helvetica} (\PIndex{hvmath}), or to -combine the free text font with another free math font. - -\section{Computer modern} -This is the default font, designed by Knuth.\index{cmr}\index{Computer modern} For the PDF output -the Type 1 fonts cm-super and BlueSky were used. - -\Mbox{cm-crop} - -\section{Latin modern} -This is the new designed font which comes with an own Type 1 version.\FIndex{lm}\index{Latin modern} - -\Mbox{lm-crop} - -\section{Palatino} -There is a free package mathpazo.\PIndex{mathpazo}\index{Palatino} - -\Mbox{pazo-crop} - -\section{Palatino -- microimp} -There is the package \PIndex{pamath} for the nonfree palatino font.\PIndex{mathpazo}\index{Palatino} - -\Mbox{pamath-crop} - -\section{cmbright} - -\Mbox{cmbright-crop} - -\section{minion} - -\Mbox{minionpro-crop} - - - -\part{Special symbols} - -In this section only those symbols are defined, which are not part of the %%% ----- Martin ----- -list of all available symbols: -\href{http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}% -{CTAN://info/symbols/comprehensive/symbols-a4.pdf}. With -\verb+fontmath.ltx+ \LaTeX{} itself defines the following special symbols for using inside math: %%% ----- Martin ----- - -\begin{table}[htb] -\centering -\begin{tabular}{l|c} -Name & Meaning\\\hline -\verb+\mathparagraph+ & $\mathparagraph$\\ -\verb+\mathsection+ & $\mathsection$\\ -\verb+\mathdollar+ & $\mathdollar$\\ -\verb+\mathsterling+ & $\mathsterling$\\ -\verb+\mathunderscore+ & $\mathunderscore$\\ -\verb+\mathellipsis+ & $\mathellipsis$\\ -\end{tabular} -\caption{Predefined math symbols from \texttt{fontmath.ltx}}\label{fontmath.ltx} -\end{table} - -\section{Integral symbols} -\index{Integral symbols} - -\def\Xint#1{\mathchoice - {\XXint\displaystyle\textstyle{#1}}% - {\XXint\textstyle\scriptstyle{#1}}% - {\XXint\scriptstyle\scriptscriptstyle{#1}}% - {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}% - \!\int} -\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$} - \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}} -\def\ddashint{\Xint=} -\def\dashint{\Xint-} -\def\clockint{\Xint\circlearrowright} % GOOD! -\def\counterint{\Xint\rotcirclearrowleft} % Good for Computer Modern! -\def\rotcirclearrowleft{\mathpalette{\RotLSymbol{-30}}\circlearrowleft} -\def\RotLSymbol#1#2#3{\rotatebox[origin=c]{#1}{$#2#3$}} - -\begin{center} -\begin{tabular}{lc} -Name & Symbol\\\hline -\verb|\dashint| & $\dashint$\\ -\verb|\ddashint| & $\ddashint$\\ -\verb|\clockint| & $\clockint$\\ -\verb|\counterint| & $\counterint$ -\end{tabular} -\end{center} - -%$ -For all new integral symbols limits can be used in the usual way: - -\begin{equation} -\ddashint_01=\dashint_10<\oint\limits_{-\infty}^\infty = \clockint\counterint_A -\end{equation} - -\begin{lstlisting} -\ddashint_01=\dashint_10<\oint\limits_{-\infty}^\infty = \clockint\counterint_A -\end{lstlisting} - -Put the following definitions into the preamble to use one or all of these new -integral symbols. - -\begin{lstlisting} -\def\Xint#1{\mathchoice - {\XXint\displaystyle\textstyle{#1}}% - {\XXint\textstyle\scriptstyle{#1}}% - {\XXint\scriptstyle\scriptscriptstyle{#1}}% - {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}% - \!\int} -\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$} - \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}} -\def\ddashint{\Xint=} -\def\dashint{\Xint-} -\def\clockint{\Xint\circlearrowright} % GOOD! -\def\counterint{\Xint\rotcirclearrowleft} % Good for Computer Modern! -\def\rotcirclearrowleft{\mathpalette{\RotLSymbol{-30}}\circlearrowleft} -\def\RotLSymbol#1#2#3{\rotatebox[origin=c]{#1}{$#2#3$}} -\end{lstlisting} - -%\clearpage -\section{Harpoons} -\LaTeX{} knows no stretchable harpoon\index{Harpoon} symbols, like \verb|\xrightarrow|. -The following code defines several harpoon symbols.% -\index{xrightharpoondown@\textbackslash xrightharpoondown} -\index{xrightharpoonup@\textbackslash xrightharpoonup} -\index{xleftharpoondown@\textbackslash xleftharpoondown} -\index{xleftharpoonup@\textbackslash xleftharpoonup} -\index{xleftrightharpoons@\textbackslash xleftrightharpoons} -\index{xrightleftharpoons@\textbackslash xrightleftharpoons}% -% -\mPar{\CMD{xrightharpoondown}\\% -\CMD{xrightharpoonup}\\% -\CMD{xleftharpoondown}\\% -\CMD{xleftharpoonup}\\% -\CMD{xleftrightharpoons}\\% -\CMD{xrightleftharpoons}% -} - -\begin{lstlisting} -\def\rightharpoondownfill@{% - \arrowfill@\relbar\relbar\rightharpoondown} -\def\rightharpoonupfill@{% - \arrowfill@\relbar\relbar\rightharpoonup} -\def\leftharpoondownfill@{% - \arrowfill@\leftharpoondown\relbar\relbar} -\def\leftharpoonupfill@{% - \arrowfill@\leftharpoonup\relbar\relbar} -\newcommand{\xrightharpoondown}[2][]{% - \ext@arrow 0359\rightharpoondownfill@{#1}{#2}} -\newcommand{\xrightharpoonup}[2][]{% - \ext@arrow 0359\rightharpoonupfill@{#1}{#2}} -\newcommand{\xleftharpoondown}[2][]{% - \ext@arrow 3095\leftharpoondownfill@{#1}{#2}} -\newcommand{\xleftharpoonup}[2][]{% - \ext@arrow 3095\leftharpoonupfill@{#1}{#2}} -\newcommand{\xleftrightharpoons}[2][]{\mathrel{% - \raise.22ex\hbox{% - $\ext@arrow 3095\leftharpoonupfill@{\phantom{#1}}{#2}$}% - \setbox0=\hbox{% - $\ext@arrow 0359\rightharpoondownfill@{#1}{\phantom{#2}}$}% - \kern-\wd0 \lower.22ex\box0}% -} -\newcommand{\xrightleftharpoons}[2][]{\mathrel{% - \raise.22ex\hbox{% - $\ext@arrow 3095\rightharpoonupfill@{\phantom{#1}}{#2}$}% - \setbox0=\hbox{% - $\ext@arrow 0359\leftharpoondownfill@{#1}{\phantom{#2}}$}% - \kern-\wd0 \lower.22ex\box0}% -} -\end{lstlisting} - -\begin{tabular}{ll} -\verb|\xrightharpoondown[under]{over}| & $\xrightharpoondown[under]{over}$\\[10pt] -\verb|\xrightharpoonup[under]{over}| & $\xrightharpoonup[under]{over}$ \\[10pt] -\verb|\xleftharpoondown[under]{over}| & $\xleftharpoondown[under]{over}$\\[10pt] -\verb|\xleftharpoonup[under]{over}| & $\xleftharpoonup[under]{over}$ \\[10pt] -\verb|\xleftrightharpoons[under]{over}|& $\xleftrightharpoons[under]{over}$\\[10pt] -\verb|\xrightleftharpoons[under]{over}|& $\xrightleftharpoons[under]{over}$ -\end{tabular} - -%$ - -\section{Bijective mapping arrow} - -To get something like \bijmap~we can define: -\begin{lstlisting} -\def\bijmap{% - \ensuremath{% - \mathrlap{\rightarrowtail}\rightarrow% - }% -} -\end{lstlisting} - -This uses the \CIndex{mathrlap} definition from section~\vref{subsec:ams-limits}. With this -definition a huge symbol is also possible: \verb+{\Huge\bijmap}+ {\Huge\bijmap}. - -\section{Stacked equal sign} -There are several symbols stacked with an equal sign, \eg \CIndex{doteq}, \CIndex{equiv} or -\CIndex{cong} ($\doteq$, $\equiv{}$, $\cong$ ). But there are still some missing, which are -shown in table~\ref{tab:equal} and the following definitions. - -\begin{table}[htb] -\centering -\begin{tabular}{ll} -\verb+\eqdef+ & \eqdef\\ -\verb+\eqexcl+ & \eqexcl\\ -\verb+\eqhat+ & \eqhat -\end{tabular} -\caption{New symbols in combination with the equal sign}\label{tab:equal} -\end{table} - -\begin{lstlisting} -\newcommand{\eqdef}{\ensuremath{\mathrel{\stackrel{\mathrm{def}}{=}}}} -\newcommand{\eqexcl}{\ensuremath{\mathrel{\stackrel{\mathrm{!}}{=}}}} -\newcommand{\eqhat}{\ensuremath{\mathrel{\widehat{=}}}} -\end{lstlisting} - -\section{Other symbols} - -\begin{minipage}{0.7\linewidth} -\begin{lstlisting} -\newcommand*{\threesim}{% - \mathrel{\vcenter{\offinterlineskip - \hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}} -$\threesim ABC$ -\end{lstlisting}% -\end{minipage}\hfill -\begin{minipage}{0.15\linewidth} -$\threesim ABC$ -\end{minipage} - - -\noindent -\begin{minipage}{0.7\linewidth} -\begin{lstlisting} -\newcommand\Let{\mathrel{\mathop:\!\!=}}% Upper case L! -\newcommand\teL{\mathrel{=\!\!\mathop:}} -$x\Let y$ $y\teL x$ -\end{lstlisting}% -\end{minipage}\hfill -\newcommand\Let{\mathrel{\mathop:\!\!=}}% Upper case L! -\newcommand\teL{\mathrel{=\!\!\mathop:}} -$x\Let y$ $y\teL x$ -\begin{minipage}{0.15\linewidth} -\end{minipage} - - -%\lstset{xrightmargin=-\marginparwidth} - -\part{Examples} -\section{Tuning math typesetting} -Chapter 18 of the \TeX book is named ,,Fine Points of Mathematics Typing``~\cite{knuth86} -and it -shows on 20 pages some more or less important facts when typesetting mathematical -expressions. Often inline formulas contain a \Index{punctuation} character like a -\Index{dot}, \Index{comma}, \Index{colon}, \etc. It is a general rule to write -those characters outside the math mode. Compare - -\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] -$a, b, c, d, e, \textrm{and }f$ \\[5pt] -$a$, $b$, $c$, $d$, $e$, and $f$ -\end{LTXexample} - -Having such math as single expressions enables \TeX\ to insert a linebreak at several -places (see Section~\vref{subsec:linebreak}). - -Writing an \Index{ellipses} as three single dots, doesn't look very nice, one should -always use the \CIndex{ldots} command: - -\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] -$1,...,10$\\[5pt] -$1,\ldots,10$ -\end{LTXexample} - -This is correct as long as on the left and right are a comma as a separator. -For sums the \CIndex{cdot} command should be used instead: - -\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] -$1+2+\cdots+10$\\[5pt] -$x_n=x_{n-1}=\cdots=n_0=1$ -\end{LTXexample} - -For a multiplication it is important which character is used, in european countries -often a centered dot. In such a case it is appropriate not to use the \CIndex{cdots} -command for a ellipsis. - -For typesetting integrals\index{Integral} or differential equations\index{differential equation} -it makes sense to define the following short macros: - -\begin{lstlisting} -\newcommand*{\diff}{\mathop{}\!\mathrm{d}} -\newcommand*\dst{\,\frac{\diff s}{\diff t} -\end{lstlisting} - -\newcommand*{\diff}{\mathop{}\!\mathrm{d}} - - -\iffalse -\newcommand*\dy{\,\mathrm{d}y} -\newcommand*\dx{\,\mathrm{d}x} -\newcommand*\dyx{\,\frac{\mathrm{d}y}{\mathrm{d}x}} -\newcommand*\ds{\,\mathrm{d}s} -\newcommand*\dt{\,\mathrm{d}t} -\newcommand*\dst{\,\frac{\mathrm{d}s}{\mathrm{d}t}} -\fi - -\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] -\begin{align*} -F(x) &= \int\!f(x)\diff x\\ -v(t) &= \dst\\ -a(t) &= \frac{\diff{}^2s}{\diff t^2} -\end{align*} -\end{LTXexample} - -\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth] -\begin{align*} -G(t) &= \underbrace{\,\int\cdots\!\int\!\!}_D\;\diff x\diff y\ldots\\ -u_C(t) &= \int\!\,i_C(t)\diff t -\end{align*} -\end{LTXexample} - -\bigskip -\section{Matrix} -\subsection{Identity matrix} - -There are several possibilities to write this matrix. Here is a solution -with the default array environment. - -\begin{LTXexample}[width=0.4\linewidth] -\[ -\left( - \begin{array}{ccccc} - 1\\ - & 1 & & \text{{\huge{0}}}\\ - & & 1\\ - & \text{{\huge{0}}} & & 1\\ - & & & & 1 - \end{array} -\right) -\] -\end{LTXexample} - -\subsection{System of linear equations} - -\begin{LTXexample}[pos=t] -\[ -\begin{array}{l@{\:=\:}*{5}{l@{\:+\:}}l} -y_1 & a_{11}x_1 & a_{12}x_2 & a_{13}x_3 & \dots & a_{1(n-1)}x_{n-1} & a_{1n}x_n \\ -y_2 & a_{21}x_1 & a_{22}x_2 & a_{23}x_3 & \dots & a_{2(n-1)}x_{n-1} & a_{2n}x_n \\ -\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots\\ -y_{n-1} & a_{(n-1)1}x_1 & a_{(n-1)2}x_2 & a_{(n-1)3}x_3 & \dots & a_{(n-1)(n-1)}x_{n-1} & a_{(n-1)n}x_n\\ -y_n & a_{n1}x_1 & a_{n2}x_2 & a_{n3}x_3 & \dots & a_{(n)(n-1)}x_{n-1} & a_{nn}x_n -\end{array} -\] -\end{LTXexample} - -\subsection{Matrix with comments on top} - - -\begin{LTXexample}[width=0.35\linewidth] -\def\rb#1{\rotatebox{90}{$\xleftarrow{#1}$}} -\begin{tabular}{c} -$\begin{matrix} -\rb{text1}&\rb{text1}&\rb{text1}&\rb{text1}\\ -\end{matrix}$\\ -$\begin{bmatrix} -X_x & Y_x & Z_x & T_x \\ -X_y & Y_y & Z_y & T_y \\ -X_z & Y_z & Z_z & T_z \\ -0 & 0 & 0 & 1 -\end{bmatrix}$ -\end{tabular} -\end{LTXexample} - -%$ - - - - -\section{Cases structure} - -\index{Cases!numbered lines}Sometimes it is better to use the array environment instead of amsmath's %%% ----- Martin ----- -cases environment. To get optimal horizontal spacing for the conditions, -there are two matrixes in series, one $3\times 1$ followed by $3\times 3$ matrix. -To minimize the horizontal space around the variable $z$ a - -\begin{lstlisting} -\addtolength{\arraycolsep}{-3pt} -\end{lstlisting} -is a useful command. - -\begin{equation} -\addtolength{\arraycolsep}{-3pt} -I(z)=\delta_{0}\left\{% - \begin{array}{lcrcl} - D+z & \quad & -D & \le z\le & -p\\ - D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right)% - & \quad & -p & \le z\le & \phantom{-}p\\ - D-z & \quad & p & \le z\le & \phantom{-}D - \end{array}\right. -\end{equation} - -\begin{lstlisting} -\begin{equation} -\addtolength{\arraycolsep}{-3pt} -I(z)=\delta_{0}\left\{% - \begin{array}{lcrcl} - D+z & \quad & -D & \le z\le & -p\\ - D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right)% - & \quad & -p & \le z\le & \phantom{-}p\\ - D-z & \quad & p & \le z\le & \phantom{-}D - \end{array}\right. -\end{equation} -\end{lstlisting} - - -The \CMD{phantom}\index{phantom@\textbackslash phantom} command -replaces exactly that place with whitespace which the argument needs. - -\subsection{Cases with numbered lines} -This is not possible in an easy way, because \verb+cases+ uses the array -environment for typesetting which has by default no numbering. However, there -are some tricky ways to get numbered lines. The following three examples -use the \verb+tabular+, the \verb+tabularx+ and the \verb+array+ environment. - -\bigskip\noindent -\begin{tabular}{rc} -\ldelim\{{2}{2.75cm}[some text here] & %%% ----- Martin ----- - \parbox{{\linewidth-3cm-4\tabcolsep}}{ - \vspace*{1ex} - \begin{flalign} - x & = 2\quad\text{if }y >2 &\\ - x & = 3\quad\text{if }y \le 2& - \end{flalign}} -\end{tabular} - -\bigskip -\begin{lstlisting} -\begin{tabular}{rc} -\ldelim\{{2}{2.75cm}[some text here] & - \parbox{{\linewidth-3cm-4\tabcolsep}}{ - \vspace*{1ex} - \begin{flalign} - x & = 2\quad\text{if }y >2 &\\ - x & = 3\quad\text{if }y \le 2& - \end{flalign}} -\end{tabular} -\end{lstlisting} - - -\bigskip\noindent -\begin{tabularx}{\linewidth}{rXc} -\ldelim\{{2}{2.75cm}[some text here] %%% ----- Martin ----- - & $ x = 2\quad\text{if }y > 2 $ & \refstepcounter{equation}(\theequation)\\ - & $ x = 3\quad\text{if }y \le 2$ &\refstepcounter{equation}(\theequation) -\end{tabularx} - -\bigskip -\begin{lstlisting} -\begin{tabularx}{\linewidth}{rXc} -\ldelim\{{2}{2.75cm}[some text here] - & $x=2\quad\text{if }y>2$ &\refstepcounter{equation}(\theequation)\\ - & $x=3\quad\text{if }y\le2$&\refstepcounter{equation}(\theequation) -\end{tabularx} -\end{lstlisting} - - -\bigskip -\[ -\begin{array}{rc@{\qquad}c} -\ldelim\{{2}{2.75cm}[some text here] %%% ----- Martin ----- - & x = 2\quad\text{if }y > 2 & \refstepcounter{equation}(\theequation)\\ - & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation) -\end{array} -\] - - -\bigskip -\begin{lstlisting} -\[ -\begin{array}{rc@{\qquad}c} -\ldelim\{{2}{2.75cm}[some text here] - & x = 2\quad\text{if }y > 2 & \refstepcounter{equation}(\theequation)\\ - & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation) -\end{array} -\] -\end{lstlisting} - -%$ - -\section{Arrays} - -There is a general rule that a lot of mathematical stuff should be -divided in smaller pieces. But sometimes it is difficult to get a nice -horizontal alignment when splitting a formula. The following ones -uses the \texttt{array} environment to get a proper alignment. - - -\subsection{Quadratic equation} - -\begin{equation} -\begin{array}{rcll} -y & = & x^{2}+bx+c\\ - & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\ - & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle% - \left(\frac{b}{2}\right)^{2}+c}\\ - & & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\ - & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle% - \frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle% - \frac{b}{2}}\right)^{2}-c\right.\\ -y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle% - \frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\ -y-y_{S} & = & (x-x_{S})^{2}\\ -S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle% - \frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right) -\end{array} -\end{equation} - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\begin{equation} -\begin{array}{rcll} -y & = & x^{2}+bx+c\\ - & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\ - & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle% - \left(\frac{b}{2}\right)^{2}+c}\\ - & & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\ - & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle% -\frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle% -\frac{b}{2}}\right)^{2}-c\right.\\ -y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle% -\frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\ -y-y_{S} & = & (x-x_{S})^{2}\\ -S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle% -\frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right) -\end{array} -\end{equation} -\end{lstlisting} - - - -\subsection{Vectors and matrices} -\index{Vector} -\begin{equation} -\begin{array}{rcl} -\underline{RS} & = & \left(\begin{array}{cccccccc} -01 & a4 & 55 & 87 & 5a & 58 & db & 9e\\ -a4 & 56 & 82 & f3 & 1e & c6 & 68 & e5\\ -02 & a1 & fc & c1 & 47 & ae & 3d & 19\\ -a4 & 55 & 87 & 5a & 58 & db & 9e & 03\end{array}\right)\\ -\\ -\left(\begin{array}{c} - s_{i,0}\\ - s_{i,1}\\ - s_{i,2}\\ - s_{i,3} -\end{array}\right) & = & \underline{RS}\cdot% -\left(\begin{array}{c} - m_{8i+0}\\ - m_{8i+1}\\ - \cdots\\ - m_{8i+6}\\ - m_{8i+7} -\end{array}\right)\\ -\\ -S_{i} & = & \sum_{j=0}^{3}s_{i,j}\cdot2^{8j}\qquad i=0,1,...,k-1\\ -\\ -S & = & \left(S_{k-1},S_{k-2},...,S_{1},S_{0}\right) -\end{array} -\end{equation} - -\begin{lstlisting} -\begin{equation} -\begin{array}{rcl} -\underline{RS} & = & \left(\begin{array}{cccccccc} -01 & a4 & 55 & 87 & 5a & 58 & db & 9e\\ -a4 & 56 & 82 & f3 & 1e & c6 & 68 & e5\\ -02 & a1 & fc & c1 & 47 & ae & 3d & 19\\ -a4 & 55 & 87 & 5a & 58 & db & 9e & 03\end{array}\right)\\ -\\ -\left(\begin{array}{c} - s_{i,0}\\ - s_{i,1}\\ - s_{i,2}\\ - s_{i,3} -\end{array}\right) & = & \underline{RS}\cdot% -\left(\begin{array}{c} - m_{8i+0}\\ - m_{8i+1}\\ - \cdots\\ - m_{8i+6}\\ - m_{8i+7} -\end{array}\right)\\ -\\ -S_{i} & = & \sum_{j=0}^{3}s_{i,j}\cdot2^{8j}\qquad i=0,1,...,k-1\\ -\\ -S & = & \left(S_{k-1},S_{k-2},...,S_{1},S_{0}\right) -\end{array} -\end{equation} -\end{lstlisting} - - -\subsection{Cases with (eqn)array environment} - -This solution is important when \AmSmath can't be used. %%% ----- Martin ----- - -$\lim\limits_{n->\infty}q^{n}=\left\{% - \begin{array}{lc@{\kern2pt}c@{\kern2pt}r} - \textrm{divergent}\ & q & \le & -1\\ - 0 & |q| & < & 1\\ - 1 & q & = & 1\\ - \infty & q & > & 1 - \end{array}\right.$ - -\medskip -\begin{lstlisting} -$\lim\limits_{n->\infty}q^{n}=\left\{% - \begin{array}{lc@{\kern2pt}c@{\kern2pt}r} - \textrm{divergent}\ & q & \le & -1\\ - 0 & |q| & < & 1\\ - 1 & q & = & 1\\ - \infty & q & > & 1 - \end{array}\right.$ -\end{lstlisting} -%$ - -\subsection{Arrays inside arrays} -The array environment is a powerful one because it can be nested in several ways: - -\[ -\left( -\begin{array}{c@{}c@{}c} -\begin{array}{|cc|} -\hline -a_{11} & a_{12} \\ -a_{21} & a_{22} \\ -\hline -\end{array} & 0 & 0 \\ -0 & \begin{array}{|ccc|} - \hline - b_{11} & b_{12} & b_{13}\\ - b_{21} & b_{22} & b_{23}\\ - b_{31} & b_{32} & b_{33}\\ - \hline - \end{array} & 0 \\ -0 & 0 & \begin{array}{|cc|} - \hline - c_{11} & c_{12} \\ - c_{21} & c_{22} \\ - \hline - \end{array} \\ -\end{array} -\right) -\] - -\begin{lstlisting} -\[ -\left( -\begin{array}{c@{}c@{}c} - \begin{array}{|cc|}\hline - a_{11} & a_{12} \\ - a_{21} & a_{22} \\\hline - \end{array} & \mathbf{0} & \mathbf{0} \\ - \mathbf{0} & - \begin{array}{|ccc|}\hline - b_{11} & b_{12} & b_{13}\\ - b_{21} & b_{22} & b_{23}\\ - b_{31} & b_{32} & b_{33}\\\hline - \end{array} & \mathbf{0} \\ - \mathbf{0} & \mathbf{0} & - \begin{array}{|cc|}\hline - c_{11} & c_{12} \\ - c_{21} & c_{22} \\\hline - \end{array} \\ -\end{array} -\right) -\] -\end{lstlisting} - -\[ -Y^1= -\begin{array}{c} - \null\\[1ex]% kann weg - \left[\begin{array}{rrrr} - 0 & 0 & 1 & 0\\ - 1 & 0 & 1 & 0\\ - 1 & 1 & 1 & 1 - \end{array}\right]\\[3ex]\hline - \begin{array}{rrrr} -% \hdotsfor{4}\\% statt \\[3ex]\hline - 2 & 1 &3 & 1 - \end{array} -\end{array} -\] - -\begin{lstlisting} -\[ -Y^1= -\begin{array}{c} - \null\\[1ex]% only vor vertical alignment - \left[\begin{array}{rrrr} - 0 & 0 & 1 & 0\\ - 1 & 0 & 1 & 0\\ - 1 & 1 & 1 & 1 - \end{array}\right]\\[3ex]\hline - \begin{array}{rrrr} -% \hdotsfor{4}\\%( needs \AmSmath) instead of \\[3ex]\hline - 2 & 1 &3 & 1 - \end{array} -\end{array} -\] -\end{lstlisting} - -\subsection{Colored cells}\label{sub:color} -In general there is no difference in coloring tabular or array cells. The following example -shows how one can put \index{color}colors in rows, columns and cells. -\index{rowcolor@\textbackslash rowcolor}\index{columncolor@\textbackslash columncolor} - -\medskip\noindent -\includegraphics[width=\columnwidth]{colArray} - -%\[ -%\left[\, -%\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}} -% {h_{k,1,0}(n)} & {h_{k,1,1}(n)} & {h_{k,1,2}(n)} & \zero & \zero \\ -% {h_{k,2,0}(n)} & {h_{k,2,1}(n)} & {h_{k,2,2}(n)} & \zero & \zero \\ -% {h_{k,3,0}(n)} & {h_{k,3,1}(n)} & {h_{k,3,2}(n)} & \zero & \zero \\ -% {h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & {h_{k,4,2}(n)} & \zero & \zero \\ -% \zero & {h_{k,1,0}(n-1)} & {h_{k,1,1}(n-1)} & {h_{k,1,2}(n-1)} & \zero \\ -% \zero & {h_{k,2,0}(n-1)} & {h_{k,2,1}(n-1)} & {h_{k,2,2}(n-1)} & \zero \\ -% \zero & {h_{k,3,0}(n-1)} & {h_{k,3,1}(n-1)} & {h_{k,3,2}(n-1)} & \zero \\ -% \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & {h_{k,4,1}(n-1)} & {h_{k,4,2}(n-1)} & \zero \\ -% \zero & \zero & {h_{k,1,0}(n-2)} & {h_{k,1,1}(n-2)} & {h_{k,1,2}(n-2)}\\ -% \rowcolor[gray]{0.75}% -% \zero & \zero & {h_{k,2,0}(n-2)} & {h_{k,2,1}(n-2)} & {h_{k,2,2}(n-2)}\\ -% \zero & \zero & {h_{k,3,0}(n-2)} & {h_{k,3,1}(n-2)} & {h_{k,3,2}(n-2)}\\ -% \zero & \zero & {h_{k,4,0}(n-2)} & {h_{k,4,1}(n-2)} & {h_{k,4,2}(n-2)} -%\end{array} \,\right] -%\end] - - -\medskip -\begin{lstlisting}[xrightmargin=-\marginparwidth] -... -\usepackage{array} -\usepackage{colortbl} -\definecolor{umbra}{rgb}{0.8,0.8,0.5} -\def\zero{\multicolumn{1}{>{\columncolor{white}}c}{0}} -\def\colCell#1#2{\multicolumn{1}{>{\columncolor{#1}}c}{#2}} -\begin{document} -\[\left[\, -\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}} - h_{k,1,0}(n) & h_{k,1,1}(n) & h_{k,1,2}(n) & \zero & \zero\\ - h_{k,2,0}(n) & h_{k,2,1}(n) & h_{k,2,2}(n) & \zero & \zero\\ - h_{k,3,0}(n) & h_{k,3,1}(n) & h_{k,3,2}(n) & \zero & \zero\\ - h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & h_{k,4,2}(n) & \zero & \zero\\ - \zero & h_{k,1,0}(n-1) & h_{k,1,1}(n-1) & h_{k,1,2}(n-1) & \zero\\ - \zero & h_{k,2,0}(n-1) & h_{k,2,1}(n-1) & h_{k,2,2}(n-1) & \zero\\ - \zero & h_{k,3,0}(n-1) & h_{k,3,1}(n-1) & h_{k,3,2}(n-1) & \zero\\ - \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & h_{k,4,1}(n-1) & h_{k,4,2}(n-1) & \zero\\ - \zero & \zero & h_{k,1,0}(n-2) & h_{k,1,1}(n-2) & h_{k,1,2}(n-2)\\ - \zero & \zero & h_{k,2,0}(n-2) & h_{k,2,1}(n-2) & h_{k,2,2}(n-2)\\ - \zero & \zero & h_{k,3,0}(n-2) & h_{k,3,1}(n-2) & h_{k,3,2}(n-2)\\ - \zero & \zero & h_{k,4,0}(n-2) & h_{k,4,1}(n-2) & h_{k,4,2}(n-2) -\end{array} \,\right]_{12\times 5}\] -... -\end{lstlisting} - - -\subsection{Boxed rows and columns} - -\begin{LTXexample}[width=0.35\linewidth] -\[ -\overrightarrow{A}=\left[ - \begin{array}{cccc} - 1 & 2 & 3 & 4\\ - 1 & 2 & 3 & 4\\\hline - \multicolumn{1}{|c}{1} & 2 & 3 & - \multicolumn{1}{c|}{4}\\\hline - 1 & 2 & 3 & 4 - \end{array}\right] -\] -\end{LTXexample} - - -\begin{LTXexample}[width=0.35\linewidth] -\[ -\overrightarrow{A}=\left[ - \begin{array}{cc|c|c}\cline{3-3} - 1 & 2 & 3 & 4\\ - 1 & 2 & 3 & 4\\ - 1 & 2 & 3 & 4\\ - 1 & 2 & 3 & 4\\\cline{3-3} - \end{array}\right] -\] -\end{LTXexample} - -\begin{LTXexample}[width=0.35\linewidth] -\[ -\overrightarrow{A}=\left[ - \begin{array}{cc|c|c}\cline{3-3} - 1 & 2 & 3 & 4\\ - 1 & 2 & 3 & 4\\\hline - \multicolumn{1}{|c}{1} & 2 & 3 & - \multicolumn{1}{c|}{4}\\\hline - 1 & 2 & 3 & 4\\\cline{3-3} - \end{array}\right] -\] -\end{LTXexample} - - - -\section{Over- and underbraces} -\subsection{Braces and roots} -To put an underbrace in a root without enlarging the root symbol is possible with -the \verb+\makebox+ macro: - -\[ z =\;\;\underbrace{\makebox[\widthof{~$x^2+y^2$}][r]{$\sqrt{x^2+y^2}$}}_{=z^2} \] - -\begin{lstlisting} -\[ -z =\;\;\underbrace{% - \makebox[\widthof{~$x^2+y^2$}][r]{% - $\sqrt{x^2+y^2}$}}_{=z^2} -\] -\end{lstlisting} - - - -\subsection{Overlapping braces} -Overlapping under- and overbraces like% -\parbox{10em}{\begin{align*} -\qquad\overbrace{\qquad\qquad}^o\qquad\\[-16pt] -\underbrace{\qquad\qquad}_{u1}\underbrace{\qquad\qquad}_{u2} -\end{align*}} needs some tricky code, because we cannot have parts of the argument inside -\verb+overbrace+\index{overbrace@\textbackslash overbrace} and also \verb+underbrace+. -\index{underbrace@\textbackslash underbrace} The following equation~\vref{eq:pqFormel} -is an example for such a construction: - -\begin{align}\label{eq:pqFormel} -y &= 2x^2 -3x +5\nonumber\\ - & \hphantom{= \ 2\left(x^2-\frac{3}{2}\,x\right. }% - \textcolor{blue}{% - \overbrace{\hphantom{+\left(\frac{3}{4}\right)^2- % - \left(\frac{3}{4}\right)^2}}^{=0}}\nonumber\\[-11pt] - &= 2\left(\textcolor{red}{% - \underbrace{% - x^2-\frac{3}{2}\,x + \left(\frac{3}{4}\right)^2}% - }% - \underbrace{% - - \left(\frac{3}{4}\right)^2 + \frac{5}{2}}% - \right)\\ - &= 2\left(\qquad\textcolor{red}{\left(x-\frac{3}{4}\right)^2} - \qquad + \ \frac{31}{16}\qquad\right)\nonumber\\ -y\textcolor{blue}{-\frac{31}{8}} - &= 2\left(x\textcolor{cyan}{-\frac{3}{4}}\right)^2\nonumber -\end{align} - -\medskip -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\begin{align}\label{eq:pqFormel} -y &= 2x^2 -3x +5\nonumber\\ - & \hphantom{= \ 2\left(x^2-\frac{3}{2}\,x\right. }% - \textcolor{blue}{% - \overbrace{\hphantom{+\left(\frac{3}{4}\right)^2- % - \left(\frac{3}{4}\right)^2}}^{=0}}\nonumber\\[-11pt] - &= 2\left(\textcolor{red}{% - \underbrace{% - x^2-\frac{3}{2}\,x + \left(\frac{3}{4}\right)^2}% - }% - \underbrace{% - - \left(\frac{3}{4}\right)^2 + \frac{5}{2}}% - \right)\\ - &= 2\left(\qquad\textcolor{red}{\left(x-\frac{3}{4}\right)^2} - \qquad + \ \frac{31}{16}\qquad\right)\nonumber\\ -y\textcolor{blue}{-\frac{31}{8}} - &= 2\left(x\textcolor{cyan}{-\frac{3}{4}}\right)^2\nonumber -\end{align} -\end{lstlisting} - -\subsection[Vertical alignment]{Vertical alignment of different braces} -When having several braces in one formula line, then it looks better when all -braces are also on the same line, \eg - -\begin{equation} - \binom{x_R}{y_R} = \underbrace{r\vphantom{\binom{A}{B}}}_{\text{Scaling}}\cdot% - \underbrace{% - \begin{pmatrix} - \sin \gamma & -\cos \gamma \\ - \cos \gamma & \sin \gamma \\ - \end{pmatrix}% - }_{\text{Rotation}} - \binom{x_K}{y_K} + - \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} -\end{equation} - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\begin{equation} -\binom{x_R}{y_R} = \underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\cdot% - \underbrace{% - \begin{pmatrix} - \sin \gamma & -\cos \gamma \\ - \cos \gamma & \sin \gamma \\ - \end{pmatrix}% - }_{\text{Rotation}} -\binom{x_K}{y_K} + \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} -\end{equation} -\end{lstlisting} - -It is again the \verb+\vphantom+ macro which reserves the needed vertical space. -Nevertheless the horizontal space around the \verb+r+ of the first underbrace and the last \verb|+| should -be decreased to get a better typesetting. This is possible with \verb+\hspace+ or -simply \verb+\kern+: - -\[ \binom{x_R}{y_R} = % - \kern-10pt\underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\kern-10pt% - \cdot\underbrace{% - \begin{pmatrix} - \sin \gamma & -\cos \gamma \\ - \cos \gamma & \sin \gamma \\ - \end{pmatrix}% - }_{\text{Rotation}} - \binom{x_K}{y_K} +\kern-5pt% - \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} \] - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\[ \binom{x_R}{y_R} = % - \kern-10pt\underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\kern-10pt% - \cdot\underbrace{% - \begin{pmatrix} - \sin \gamma & -\cos \gamma \\ - \cos \gamma & \sin \gamma \\ - \end{pmatrix}% - }_{\text{Rotation}} - \binom{x_K}{y_K} +\kern-5pt% - \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} \] -\end{lstlisting} - - -\subsection[Alignment]{Vertical and horizontal alignment} -The forgoing example simply uses \verb+\hspace+ to decrease the horizontal width between two -\index{underbrace@\textbackslash underbrace} underbraces. This may be okay for a single solution, but in general it is better to have some %%% ----- Martin ----- -code which works in any case. - -The following example looks simple but it needs some tricky code to get vertical and horizontal -alignment.\index{substack@\textbackslash substack} - -\def\num#1{\hphantom{#1}} -\def\vsp{\vphantom{\rangle_1}} - -\begin{equation*} - \frac{300}{5069}% - \underbrace{\longmapsto\vphantom{\frac{1}{1}}}_{% - \mathclap{\substack{% - \Delta a=271\num9\vsp \\[2pt] - \Delta b=4579\vsp\\[2pt] - \text{$1$ iteration}% - }}} \frac{29}{490}% - \underbrace{\longmapsto \frac{19}{321}\longmapsto}_{% - \mathclap{\substack{% - \Delta a=10\num{9}=\langle271\rangle_{29}\num{20}\\[2pt] - \Delta b=169=\langle4579\rangle_{490}\\[2pt] - \text{$2$ iterations} - }}} \frac{9}{152} - \underbrace{\longmapsto \frac{8}{135}\longmapsto\dots\longmapsto}_{% - \substack{% - \Delta a=1\num{7}=\langle10\rangle_{9}\num{119}\\[2pt] - \Delta b=17=\langle169\rangle_{152}\\[2pt] - \text{$8$ iterations} - }} \frac{1}{16} - \underbrace{\longmapsto\dots\longmapsto\vphantom{\frac{8}{135}}}_{% - \substack{% - \Delta a=0=\langle1\rangle_{1}\num{76} \\[2pt] - \Delta b=1=\langle17\rangle_{16} \\[2pt] - \text{$8$ iterations} - }} \frac{1}{1} -\end{equation*} - -It uses the macro \verb+\mathclap+ defined in section\vref{subsec:ams-limits} -\index{mathclap@\textbackslash mathclap}\index{vphantom@\textbackslash vphantom}\index{hphantom@\textbackslash hphantom} -, which gives a better result. %%% ----- Martin ----- -It is also possible to use \verb+\makebox[0pt]{...}+ but it works only in text mode -and this needs some more \verb+$...$+.\index{substack@\textbackslash substack} - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\def\num#1{\hphantom{#1}} -\def\vsp{\vphantom{\rangle_1}} - -\begin{equation*} - \frac{300}{5069}% - \underbrace{\longmapsto\vphantom{\frac{1}{1}}}_{% - \mathclap{\substack{% - \Delta a=271\num9\vsp \\[2pt] - \Delta b=4579\vsp\\[2pt] - \text{$1$ iteration}% - }}} \frac{29}{490}% - \underbrace{\longmapsto \frac{19}{321}\longmapsto}_{% - \mathclap{\substack{% - \Delta a=10\num{9}=\langle271\rangle_{29}\num{20}\\[2pt] - \Delta b=169=\langle4579\rangle_{490}\\[2pt] - \text{$2$ iterations} - }}} \frac{9}{152} - \underbrace{\longmapsto \frac{8}{135}\longmapsto\dots\longmapsto}_{% - \substack{% - \Delta a=1\num{7}=\langle10\rangle_{9}\num{119}\\[2pt] - \Delta b=17=\langle169\rangle_{152}\\[2pt] - \text{$8$ iterations} - }} \frac{1}{16} - \underbrace{\longmapsto\dots\longmapsto\vphantom{\frac{8}{135}}}_{% - \substack{% - \Delta a=0=\langle1\rangle_{1}\num{76} \\[2pt] - \Delta b=1=\langle17\rangle_{16} \\[2pt] - \text{$8$ iterations} - }} \frac{1}{1} -\end{equation*} -\end{lstlisting} - - -\section{Integrals}\label{sec:Integrals} -\index{underset@\textbackslash underset} -\def\Q#1#2{\frac{\partial #1}{\partial #2}} -% -The \emph{first theorem of Green} is: -\[ -\underset{\mathcal{G}\quad}\iiint\!% - \left[u\nabla^{2}v+\left(\nabla u,\nabla v\right)\right]\mathrm{d}^{3}V% - =\underset{\mathcal{S}\quad}\oiint u\,\Q{v}{n}\,\,\mathrm{d}^{2}A -\] - -The \emph{second theorem of Green} is: - -\[ -\underset{{\mathcal{G}\quad}}\iiint\!% - \left[u\nabla^{2}v-v\nabla^{2}u\right]\mathrm{d}^{3}V% - =\underset{\mathcal{S}\quad}\oiint% - \left(u\,\Q{v}{n}-v\,\Q{u}{n}\right)\mathrm{d}^{2}A -\] - - -They are both written with the \PIndex{esint} package% -\footnote{See section~\vref{sec:Integrals}.}, which gives nice integral symbols. -The \LaTeX{} code for the first equation is: - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\[ -\underset{\mathcal{G}\quad}\iiint\!% - \left[u\nabla^{2}v+\left(\nabla u,\nabla v\right)\right]\mathrm{d}^{3}V% - =\underset{\mathcal{S}\quad}\oiint u\,\Q{v}{n}\,\,\mathrm{d}^{2}A -\] -\end{lstlisting} - -\noindent with the following definition in the preamble for the partial derivation: - -\begin{lstlisting} -\def\Q#1#2{\frac{\partial#1}{\partial #2}} -\end{lstlisting} - -\noindent which makes things easier to write. - -%-------------------------------------------------------------------------- -\section{Horizontal alignment}\label{sec:verticalAlignment} -%-------------------------------------------------------------------------- -\subsection{Over more than one page} -%-------------------------------------------------------------------------- -Sometimes it may be useful to have a vertical alignment over the whole page with a mix of %%% ----- Martin ----- -formulas and text. Section \ref{sec:Text-in-math mode} shows the use of \CMD{intertext}. -There is another trick to get all formulas vertical aligned. Let's have the following -formulas distributed over the whole page: -% -\begin{align*} - f(x) &= a\\ - g(x) &= x^2-4x\\ -f(x)-g(x) &= x^2+x^3+x\\ - g(x) &= x^2+x^3+x^4+x^5+b -\end{align*} -% -They all have a different length of the left and right side. Now we want to write some -text and other objects between them, but let the alignment untouched. We choose the -longest left and the longest right side and take them for scaling with the \CMD{hphantom} -command: - -\begin{verbatim} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}} -\end{verbatim} - -This is the first (empty) line in every equation where now all other lines are aligned to -this one. For example: - -\bgroup -\medskip\noindent -\rule{\columnwidth}{1pt} -\newcommand{\x}{blah blah blah blah blah blah blah blah } -\addtolength\abovedisplayshortskip{-.5cm}% decrease the skip -\addtolength\abovedisplayskip{-.5cm} -\x\x\x -\begin{align} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ -f(x) &= a\\ -g(x) &= x^2-4x -\end{align} -% -\x\x\x -\begin{align} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ -f(x)-g(x) &= x^2+x^3+x -\end{align} -\x\x\x -% -\begin{align} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ -g(x) &= x^2+x^3+x^4+x^5+b -\end{align} -\x\x\x - -\noindent -\rule{\columnwidth}{1pt} -\egroup -\medskip - -The phantom line is empty but leaves the vertical space for a line. This could be -corrected with decreasing the \CMD{abovedisplayshortskip} length and done all -inside a group. - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\newcommand{\x}{blah blah blah blah blah blah blah blah } -\bgroup -\addtolength\abovedisplayshortskip{-0.5cm}% decrease the skip -\addtolength\abovedisplayskip{-0.5cm} -\x\x\x -\begin{align} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ -f(x) &= a\\ -g(x) &= x^2-4x -\end{align} -% -\x\x\x -\begin{align} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ -f(x)-g(x) &= x^2+x^3+x -\end{align} -\x\x\x -% -\begin{align} -\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\ -g(x) &= x^2+x^3+x^4+x^5+b -\end{align} -\x\x\x -\egroup -\end{lstlisting} - - - - -Another case of aligning equations inside an itemize environment is the following one. -With the \CIndex{makebox} macro one can have the same size on the left side of the -equal sign to get a vertical alignment. - -\newsavebox\lW -\sbox\lW{$P_{3}+P_{2}-P_{1}$}% $ - -\begin{itemize} -\item first function \\ - $\displaystyle\makebox[\wd\lW][r]{$P_1$}=\sum_a \in A$ -\item but another one \\ - $\makebox[\wd\lW][r]{$\sin\left(P_1\right)$}=blabla$ -\item or perhaps \\ - $P_{3}+P_{2}-P_{1}=blablub$ -\end{itemize} - - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\newsavebox\lW -\sbox\lW{$P_{3}+P_{2}-P_{1}$} - -\begin{itemize} -\item first function \\ - $\displaystyle\makebox[\wd\lW][r]{$P_1$}=\sum_a \in A$ -\item but another one \\ - $\makebox[\wd\lW][r]{$\sin\left(P_1\right)$}=blabla$ -\item or perhaps \\ - $P_{3}+P_{2}-P_{1}=blablub$ -\end{itemize} -\end{lstlisting} -%$ - -%-------------------------------------------------------------------------- -\subsection{Special text columns} -%-------------------------------------------------------------------------- -This one comes from Hartmut Henkel and offers a special form of placing -additional text between the equation and the \Index{equation number}. This makes only -sense when you load the documentclass with the option \verb+fleqn+. The example -places the additional text at \verb+0.5\textwidth+, changing this value is no -problem. - -\clearpage -\medskip -\noindent\rule{\linewidth}{1pt} -\begingroup -\small -text text text text text text text text text text text text text text -text text text text text text text text text text text text text text -text text text text text text text text text text text text text text -text text text text text text text text text text text text text text - -\makeatletter -\@fleqntrue -\let\old@mathmargin=\@mathmargin -\@mathmargin=-1sp -\let\oldmathindent=\mathindent -\let\mathindent=\@mathmargin -\newsavebox{\myendhook} % for the tabulars -\def\tagform@#1{{(\maketag@@@{\ignorespaces#1\unskip\@@italiccorr)} - \makebox[0pt][r]{% after the equation number - \makebox[0.5\textwidth][l]{\usebox{\myendhook}}}% - \global\sbox{\myendhook}{}% empty box -}} -\makeatother -\sbox{\myendhook}{% -\begin{footnotesize}% -\begin{tabular}{@{}ll} -$a_0$ & Bohrscher Radius ($\mathrm{= 0{,}53\,\mbox{\AA}}$)\\ -$e$ & Elementarladung\\ -$N_{si}$ & Anzahl der Siliziumatome\\ -& pro Einheitsvolumen\\ -$m$ & Atomgewicht\\ -$Z$ & Kernladungszahl -\end{tabular} -\end{footnotesize}} -% -\begin{equation} -\varepsilon = \frac{E \cdot 4 \cdot \pi \cdot \varepsilon_{0} -\cdot a_0 \cdot \left( Z_i^{\frac{2}{3}} + Z_{Si}^{\frac{2}{3}} -\right)^{-\frac{1}{2}}} {Z_i \cdot Z_{Si} \cdot e2 \cdot \left( 1 -+ \frac{m_i}{m_{Si}} \right)}\,; -\end{equation} - -\sbox{\myendhook}{abc} - -\begin{equation} -a2+b2=c2 -\end{equation} - -\begin{equation} -z = 9 -\end{equation} -text text text text text text text text text text text text text text -text text text text text text text text text text text text text text -text text text text text text text text text text text text text text -text text text text text text text text text text text text text text - -\endgroup -\noindent\rule{\linewidth}{1pt} - -\medskip -This solution works only with \AmSmath{}, without you have to redefine the -\LaTeX{} macro, which creates the equation number. - -\begin{lstlisting}[xrightmargin=-\marginparwidth] -\newsavebox{\myendhook} % for the tabulars -\def\tagform@#1{{(\maketag@@@{\ignorespaces#1\unskip\@@italiccorr)} - \makebox[0pt][r]{% after the equation number - \makebox[0.4\textwidth][l]{\usebox{\myendhook}}% - }% - \global\sbox{\myendhook}{}% clear box content -}} -[ ... ] -\sbox{\myendhook}{% -\begin{footnotesize}% -\begin{tabular}{@{}ll} -$a_0$ & Bohrscher Radius ($\mathrm{= 0{,}53\,\mbox{\AA}}$)\\ -$e$ & Elementarladung\\ -$N_{si}$ & Anzahl der Siliziumatome\\ -& pro Einheitsvolumen\\ -$m$ & Atomgewicht\\ -$Z$ & Kernladungszahl -\end{tabular} -\end{footnotesize}} -% -\begin{equation} -\varepsilon = \frac{E \cdot 4 \cdot \pi \cdot \varepsilon_{0} -\cdot a_0 \cdot \left( Z_i^{\frac{2}{3}} + Z_{Si}^{\frac{2}{3}} -\right)^{-\frac{1}{2}}} {Z_i \cdot Z_{Si} \cdot e2 \cdot \left( 1 -+ \frac{m_i}{m_{Si}} \right)}\,; -\end{equation} -% -\sbox{\myendhook}{abc} -% -\begin{equation} a2+b2=c2 \end{equation} -% -\begin{equation} z = 9 \end{equation} -\end{lstlisting} - - -%-------------------------------------------------------------------------- -\subsection{Centered vertical dots} -%-------------------------------------------------------------------------- - -By default the vertical dots of \CMD{vdots} are aligned to the left of -the $=$ symbol and not centered.\index{vdots@\textbackslash vdots} -% -\bgroup -\newsavebox{\eqbox}% Heiko Bauke -\sbox{\eqbox}{$\null=\null$} -\newcommand{\Vdots}{\makebox[\wd\eqbox]{\vdots}} -% -\begin{align} - a_1 & = b_1 & c_1 & = d_1 \\ - a_2 & = b_2 & c_2 & = d_2 \\ - a & \Vdots b & & \Vdots \nonumber \\ - a_n & = b_n & c_n & = d_n -\end{align} -\egroup -% -\begin{lstlisting} -\usepackage{amsmath} -... - -\newsavebox{\eqbox} -\sbox{\eqbox}{$\null=\null$} -\newcommand{\Vdots}{\makebox[\wd\eqbox]{\vdots}} - -\begin{align} - a_1 & = b_1 & c_1 & = d_1 \\ - a_2 & = b_2 & c_2 & = d_2 \\ - a & \Vdots b & & \Vdots \nonumber \\ - a_n & = b_n & c_n & = d_n -\end{align} -\end{lstlisting} - - -%------------------------------------------------------------------------------ -\section{Node connections} -%------------------------------------------------------------------------------ -This is a typical application for PSTricks and it needs the package \verb+pst-node+ -and doesn't work with \verb+pdflatex+. Use \verb+vlatex+, \verb+ps4pdf+ or \verb+ps2pdf+. - -\medskip -\noindent\fbox{\includegraphics[width=\linewidth]{node}} - -\iffalse -\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{% -\psset{nodesep=3pt} -\definecolor{lila}{rgb}{0.6,0.2,0.5} -\definecolor{darkyellow}{rgb}{1,0.9,0} -Die Bindungsenergie im Tr\"opfchenmodell setzt sich aus -folgenden Teilen zusammen: -\begin{itemize} -\item dem \rnode{b}{Oberfl\"achenanteil} -\item dem \rnode{a}{Volumenanteil},\\[0.75cm] -\def\xstrut{\vphantom{\frac{(A)^1}{(B)^1}}} -\begin{equation} -E = -\rnode[t]{ae}{\psframebox*[fillcolor=darkyellow, - linestyle=none]{\xstrut a_vA}} + -\rnode[t]{be}{\psframebox*[fillcolor=lightgray, - linestyle=none]{\xstrut -a_fA^{2/3}}} + -\rnode[t]{ce}{\psframebox*[fillcolor=green, - linestyle=none]{\xstrut -a_c\dfrac{Z(Z-1)}{A^{1/3}}}} + -\rnode[t]{de}{\psframebox*[fillcolor=cyan, - linestyle=none]{\xstrut -a_s\frac{(A-2Z)^2}{A}}} + -\rnode[t]{ee}{\psframebox*[fillcolor=yellow, - linestyle=none]{\xstrut E_p}} -\end{equation}\\ -\item dem \rnode{c}{Coulomb-Anteil} -\item der \rnode{d}{Symmetrieenergie} -\item sowie einem \rnode{e}{Paarbildungsbeitrag}. -\end{itemize} -\nccurve[angleA=-90,angleB=90]{->}{a}{ae} -\nccurve[angleB=45]{->}{b}{be} -\nccurve[angleB=-90]{->}{c}{ce} -\nccurve[angleB=-90]{->}{d}{de} -\nccurve[angleB=-90]{->}{e}{ee} -}} -\fi - -\medskip -\begin{lstlisting}[tabsize=4,xrightmargin=-\marginparwidth] -\psset{nodesep=3pt} -\definecolor{lila}{rgb}{0.6,0.2,0.5} -\definecolor{darkyellow}{rgb}{1,0.9,0} -Die Bindungsenergie im Tr\"opfchenmodell setzt sich aus -folgenden Teilen zusammen: -\begin{itemize} -\item dem \rnode{b}{Oberfl\"achenanteil} -\item dem \rnode{a}{Volumenanteil},\\[1cm] -\def\xstrut{\vphantom{\frac{(A)^1}{(B)^1}}} -\begin{equation} -E = -\rnode[t]{ae}{\psframebox*[fillcolor=darkyellow, - linestyle=none]{\xstrut a_vA}} + -\rnode[t]{be}{\psframebox*[fillcolor=lightgray, - linestyle=none]{\xstrut -a_fA^{2/3}}} + -\rnode[t]{ce}{\psframebox*[fillcolor=green, - linestyle=none]{\xstrut -a_c\frac{Z(Z-1)}{A^{1/3}}}} + -\rnode[t]{de}{\psframebox*[fillcolor=cyan, - linestyle=none]{\xstrut -a_s\frac{(A-2Z)^2}{A}}} + -\rnode[t]{ee}{\psframebox*[fillcolor=yellow, - linestyle=none]{\xstrut E_p}} -\end{equation}\\[0.25cm] -\item dem \rnode{c}{Coulomb-Anteil} -\item der \rnode{d}{Symmetrieenergie} -\item sowie einem \rnode{e}{Paarbildungsbeitrag}. -\end{itemize} -\nccurve[angleA=-90,angleB=90]{->}{a}{ae} -\nccurve[angleB=45]{->}{b}{be} \nccurve[angleB=-90]{->}{c}{ce} -\nccurve[angleB=-90]{->}{d}{de} \nccurve[angleB=-90]{->}{e}{ee} -\end{lstlisting} - - - - -%----------------------------------------------------------------------------- -\section[Special Placement]{Special placement of displayed equations} -%----------------------------------------------------------------------------- - -%----------------------------------------------------------------------------- -\subsection{Formulas side by side}\label{sec:sidebyside} -%----------------------------------------------------------------------------- - -Sometimes it may be useful to have numbered formulas side by side like the following ones: - -%\begin{framed} -\begin{mtabular}{*{2}{m{0.35\linewidth}m{0.15\linewidth}}} -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah}]\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub}] - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt -\end{mtabular} -%\end{framed} - - -And again a default display equation: -\begin{align} -F(x) &= \int_0^\infty\dfrac{1}{x}\,\mathrm{d}x -\end{align} - -\begin{lstlisting}[tabsize=4,xrightmargin=-\marginparwidth] -\begin{mtabular}{*{2}{m{0.35\linewidth}m{0.15\linewidth}}} -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah}]\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub}] - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt -\end{mtabular} -\end{lstlisting} - -The new environment \verb|mtabular| has two arguments, one optional and one which is the same -as the one from the \verb|tabular| environment. With the option \verb|long| it is possible to have %%% ----- Martin ----- -all the formulas in a \verb|longtable| environment, which allows a pagebreak. The new macro -\verb|\eqnCnt| controls the counting of these equations as subequations for one tabular -line. This macro can have an optional argument for a label. At least it counts -the equations. If the -equation number is not centered to the foregoing equation, then it needs some more horizontal -space in the tabular column. - -\begin{verbatim} -\eqnCnt[<optional label>] -\end{verbatim} - -The vertical space is controlled by the length \verb|mtabskip|, which -is by default \verb|-1.25cm| and can be modified in the usual way. -To define all these macros write into the preamble: -\begin{lstlisting}[tabsize=4,xrightmargin=-\marginparwidth] -\usepackage{amsmath} -\newcounter{subequation} -\newlength\mtabskip\mtabskip=-1.25cm -\newcommand\eqnCnt[1][]{% - \refstepcounter{subequation}% - \begin{align}#1\end{align}% - \addtocounter{equation}{-1}} -\def\mtabLong{long} -\makeatletter -\newenvironment{mtabular}[2][\empty]{% - \def\@xarraycr{% - \stepcounter{equation}% - \setcounter{subequation}{0}% - \@ifnextchar[\@argarraycr{\@argarraycr[\mtabskip]}} - \let\theoldequation\theequation% - \renewcommand\theequation{\theoldequation.\alph{subequation}} - \edef\mtabOption{#1} - \setcounter{subequation}{0}% - \tabcolsep=0pt - \ifx\mtabOption\mtabLong\longtable{#2}\else\tabular{#2}\fi% -}{% - \ifx\mtabOption\mtabLong\endlongtable\else\endtabular\fi% - \let\theequation\theoldequation% - \stepcounter{equation}} -\makeatother -\end{lstlisting} - - -As seen in equation~\ref{blub} and equation~\ref{blah}, everything of the table contents is -nonsense~\ldots And the following tabular is defined as a \Index{longtable} to enable pagebreaks. -%which is the reason for the following big skip, to show that it works. - - -%\vspace*{3cm} -%\begin{framed} -\begin{mtabular}[long]{*{2}{m{0.35\linewidth}m{0.15\linewidth}}} -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah2}]\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub2}] - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt -\end{mtabular} -%\end{framed} - -As seen in equation~\ref{blub2} and equation~\ref{blah2}, everything is nonsense ... - - -And again a default display equation: -\begin{align} -F(x) &= \int_0^\infty\dfrac{1}{x}\,\mathrm{d}x -\end{align} - -\begin{lstlisting}[tabsize=4] -\begin{mtabular}[long]{*{2}{m{0.375\linewidth}m{0.125\linewidth}}} -\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt % - & \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\ -\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt % - & \begin{align*} b = 1 \end{align*} & \eqnCnt\\ -\begin{align*} c =1 \end{align*} & \eqnCnt - & \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\ - -[ ... ] -\end{lstlisting} - -%----------------------------------------------------------------------------- -\subsection[Itemize environment]{Formulas inside an itemize enviroment}\label{sec:itemize} -%----------------------------------------------------------------------------- -Without any modification it is not possible to get a numbered equation -at the same height as the symbol of the itemize environment\index{itemize@\texttt{itemize}}. This depends on %%% ----- Martin ----- -the \LIndex{abovedisplayskip}. The formula has to be raised up for exactly this length. - -\begin{lstlisting} -\def\itemMath#1{% - \raisebox{-\abovedisplayshortskip}{% - \parbox{0.75\linewidth}{% - \begin{equation}#1\end{equation}}}} -% -\begin{itemize} -\item \itemMath{ f = l } -\item \itemMath{ g(x) = \int f(x)\,\mathrm{d}x } -\end{itemize} -\end{lstlisting} - -\def\itemMath#1{% - \raisebox{-\abovedisplayshortskip}{% - \parbox{0.75\linewidth}{% - \begin{equation}#1\end{equation}}}} -% -\begin{itemize} -\item \itemMath{ f = l } -\item \itemMath{ g(x) = \int f(x)\,\mathrm{d}x } -\end{itemize} - - -\section{Roots} -There exists no special symbol for roots\index{Root} which are longer than one line. In such -cases the root should be split into two or more one, like $\sqrt{a\cdot b\cdot c}=\sqrt{a}\cdot\sqrt{a}\cdot\sqrt{b}\cdot\sqrt{c}$ -if possible. If nothing helps one can use \CMD{overline}\cIndex{overline} for -following lines of the root. The following example uses the \verb+multline+ environment -to get only one equation number: - -\begin{multline} -d(P,Q)|_{Stat.,Dependent}=\\ - \sqrt{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ - \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+} \\ - \overline{\rule{0pt}{2.5ex} - \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} - (x_{1}-y_{1})(x_{3}-y_{3}) + \right.}\\ - \overline{\rule{0pt}{2.5ex} - \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]} -\end{multline} - - -\begin{lstlisting} -\begin{multline} -d(P,Q)|_{Stat.,Dependent}=\\ - \sqrt{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ - \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+} \\ - \overline{\rule{0pt}{2.5ex} - \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} - (x_{1}-y_{1})(x_{3}-y_{3}) + \right.}\\ - \overline{\rule{0pt}{2.5ex} - \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]} -\end{multline} -\end{lstlisting} - - -Alternative: - -\begin{multline} -d(P,Q)|_{Stat.,Dependent}=\\ - \Big(\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ - \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+ \\ - \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} - (x_{1}-y_{1})(x_{3}-y_{3}) + \right.\\ - \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]\Big)^{1/2} -\end{multline} - - -\begin{lstlisting} -\begin{multline} -d(P,Q)|_{Stat.,Dependent}=\\ - \left\{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+ - \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+\right. \\ - \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13} - (x_{1}-y_{1})(x_{3}-y_{3}) + \right.\\ - \left.\left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]\right\}^{1/2} -\end{multline} -\end{lstlisting} - - - -\part{Lists, bibliography and index} -\bgroup -\lhead{}\rhead{} -\clearpage\phantomsection\addcontentsline{toc}{section}{List of Figures} -\listoffigures -\clearpage\phantomsection\addcontentsline{toc}{section}{List of Tables} -\listoftables -\clearpage\phantomsection\addcontentsline{toc}{section}{Bibliography} - -{\nocite{*} -\raggedright -\bibliography{Mathmode} -\bibliographystyle{plain} -} -\clearpage\addcontentsline{toc}{section}{Index} -{\let\BSL\textbackslash -\renewcommand\textbackslash{{\ttfamily\BSL}} -\printindex{} -} -\egroup - - -\appendix -\section*{Appendix} -\section{Filelist} -This document was build with - -\begin{lstlisting}[breaklines,xrightmargin=-\marginparwidth] -This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) (format=pdflatex 2008.10.24) 30 OCT 2008 10:19 -\end{lstlisting} - -and with the following file and package versions: - - -\begin{lstlisting}[breaklines,xrightmargin=-\marginparwidth] - *File List* - article.cls 2005/09/16 v1.4f Standard LaTeX document class - size11.clo 2005/09/16 v1.4f Standard LaTeX file (size option) -fixltx2e.sty 2006/03/24 v1.1n fixes to LaTeX - fontenc.sty - t1enc.def 2005/09/27 v1.99g Standard LaTeX file -inputenc.sty 2006/05/05 v1.1b Input encoding file - latin1.def 2006/05/05 v1.1b Input encoding file - bera.sty 2004/01/31 (WaS) - fontenc.sty - t1enc.def 2005/09/27 v1.99g Standard LaTeX file -textcomp.sty 2005/09/27 v1.99g Standard LaTeX package - ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file -beraserif.sty 2004/01/30 (WaS) - keyval.sty 1999/03/16 v1.13 key=value parser (DPC) - t1fve.fd 2004/09/07 scalable font definitions for T1/fve. -berasans.sty 2004/01/30 (WaS) -beramono.sty 2004/01/31 (WaS) - ifpdf.sty 2007/12/12 v1.6 Provides the ifpdf switch (HO) - ifvtex.sty 2007/09/09 v1.3 Switches for detecting VTeX and its modes (HO) - comment.sty -graphicx.sty 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) -graphics.sty 2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR) - trig.sty 1999/03/16 v1.09 sin cos tan (DPC) -graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive - pdftex.def 2008/09/08 v0.04l Graphics/color for pdfTeX -varwidth.sty 2003/03/10 ver 0.9a; Variable-width minipages - array.sty 2005/08/23 v2.4b Tabular extension package (FMi) -delarray.sty 1994/03/14 v1.01 array delimiter package (DPC) -tabularx.sty 1999/01/07 v2.07 `tabularx' package (DPC) - amsmath.sty 2000/07/18 v2.13 AMS math features - amstext.sty 2000/06/29 v2.01 - amsgen.sty 1999/11/30 v2.0 - amsbsy.sty 1999/11/29 v1.2d - amsopn.sty 1999/12/14 v2.01 operator names - amssymb.sty 2002/01/22 v2.2d -amsfonts.sty 2001/10/25 v2.2f - bm.sty 2004/02/26 v1.1c Bold Symbol Support (DPC/FMi) - upgreek.sty 2003/02/12 v2.0 (WaS) - cancel.sty 2000/03/12 v2.1 Cancel math terms - amscd.sty 1999/11/29 v1.2d - accents.sty 2006/05/12 v1.3 Math Accent Tools - dsfont.sty 1995/08/01 v0.1 Double stroke roman fonts -multirow.sty -bigdelim.sty - framed.sty 2007/10/04 v 0.95: framed or shaded text with page breaks -longtable.sty 2004/02/01 v4.11 Multi-page Table package (DPC) -varioref.sty 2006/05/13 v1.4p package for extended references (FMi) - xcolor.sty 2007/01/21 v2.11 LaTeX color extensions (UK) - color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive - makeidx.sty 2000/03/29 v1.0m Standard LaTeX package - url.sty 2006/04/12 ver 3.3 Verb mode for urls, etc. -setspace.sty 2000/12/01 6.7 Contributed and Supported LaTeX2e package - empheq.sty 2007/12/03 v2.12 Emphasizing equations (MH) - mhsetup.sty 2007/12/03 v1.2 programming setup (MH) -mathtools.sty 2008/08/01 v1.06 mathematical typesetting tools (MH) - calc.sty 2005/08/06 v4.2 Infix arithmetic (KKT,FJ) -nicefrac.sty 1998/08/04 v0.9b Nice fractions - ifthen.sty 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) - exscale.sty 1997/06/16 v2.1g Standard LaTeX package exscale - relsize.sty 2003/07/04 ver 3.1 - xspace.sty 2006/05/08 v1.12 Space after command names (DPC,MH) - eucal.sty 2001/10/01 v2.2d Euler Script fonts -footmisc.sty 2007/06/12 v5.4a a miscellany of footnote facilities - esint.sty - esvect.sty -remreset.sty - cool.sty 2006/12/29 v1.35 COntent Oriented LaTeX -coollist.sty 2007/10/06 v1.2 COntent Oriented LaTeX Lists - coolstr.sty 2007/01/08 v2.1 COntent Oriented LaTeX Strings - forloop.sty 2006/09/18 v3.0 For Loops for LaTeX - bbm.sty 1999/03/15 V 1.2 provides fonts for set symbols - TH - xypic.sty 1999/02/16 Xy-pic version 3.7 - xy.sty -fancyhdr.sty -showexpl.sty 2007/02/03 v0.3h Typesetting example code (RN) -listings.sty 2007/02/22 1.4 (Carsten Heinz) - lstmisc.sty 2007/02/22 1.4 (Carsten Heinz) -listings.cfg 2007/02/22 1.4 listings configuration - lstmisc.sty 2007/02/22 1.4 (Carsten Heinz) -showexpl.cfg 2005/06/30 v0.02 Definitions for the showexpl package (hv) -lstlang1.sty 2004/09/05 1.3 listings language file -lstlang2.sty 2004/09/05 1.3 listings language file -lstlang3.sty 2004/09/05 1.3 listings language file -lstlang1.sty 2004/09/05 1.3 listings language file -lstlang2.sty 2004/09/05 1.3 listings language file -lstlang3.sty 2004/09/05 1.3 listings language file -lstlang1.sty 2004/09/05 1.3 listings language file -lstlang2.sty 2004/09/05 1.3 listings language file -lstlang3.sty 2004/09/05 1.3 listings language file -lstlang1.sty 2004/09/05 1.3 listings language file -lstlang2.sty 2004/09/05 1.3 listings language file -lstlang3.sty 2004/09/05 1.3 listings language file - lstmisc.sty 2007/02/22 1.4 (Carsten Heinz) -microtype.sty 2008/06/04 v2.3b Micro-typography with pdfTeX (RS) -microtype.cfg 2008/06/04 v2.3b microtype main configuration file (RS) -hyperref.sty 2008/09/29 v6.78l Hypertext links for LaTeX - ifxetex.sty 2008/09/18 v0.4 Provides ifxetex conditional - hycolor.sty 2008/09/08 v1.4 Code for color options of hyperref/bookmark (HO -) -xcolor-patch.sty 2008/09/08 xcolor patch - pd1enc.def 2008/09/29 v6.78l Hyperref: PDFDocEncoding definition (HO) -etexcmds.sty 2007/12/12 v1.2 Prefix for e-TeX command names (HO) -infwarerr.sty 2007/09/09 v1.2 Providing info/warning/message (HO) -hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive -kvoptions.sty 2007/10/18 v3.0 Keyval support for LaTeX options (HO) - bitset.sty 2007/09/28 v1.0 Data type bit set (HO) - intcalc.sty 2007/09/27 v1.1 Expandable integer calculations (HO) -bigintcalc.sty 2007/11/11 v1.1 Expandable big integer calculations (HO) -pdftexcmds.sty 2007/12/12 v0.3 LuaTeX support for pdfTeX utility functions ( -HO) -kvsetkeys.sty 2007/09/29 v1.3 Key value parser with default handler support -(HO) -atbegshi.sty 2008/07/31 v1.9 At begin shipout hook (HO) - hpdftex.def 2008/09/29 v6.78l Hyperref driver for pdfTeX - hypcap.sty 2008/09/08 v1.10 Adjusting anchors of captions (HO) - babel.sty 2008/07/06 v3.8l The Babel package - english.ldf 2005/03/30 v3.3o English support from the babel system - braket.sty - ts1cmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions -supp-pdf.tex - nameref.sty 2007/05/29 v2.31 Cross-referencing by name of section -refcount.sty 2008/08/11 v3.1 Data extraction from references (HO) -Mathmode.out -Mathmode.out -Mathmode.tex - mt-cmr.cfg 2008/02/29 v1.9a microtype config. file: Computer Modern Roman -(RS) - umsa.fd 2002/01/19 v2.2g AMS font definitions - mt-msa.cfg 2006/02/04 v1.1 microtype config. file: AMS symbols (a) (RS) - umsb.fd 2002/01/19 v2.2g AMS font definitions - mt-msb.cfg 2005/06/01 v1.0 microtype config. file: AMS symbols (b) (RS) - mt-eur.cfg 2006/07/31 v1.1 microtype config. file: AMS Euler Roman (RS) - uesint.fd - uesvect.fd - ts1fve.fd 2004/09/07 scalable font definitions for TS1/fve. - t1fvm.fd 2004/09/07 scalable font definitions for T1/fvm. -images/styles.pdf -images/amsalign.pdf - t1fvs.fd 2004/09/07 scalable font definitions for T1/fvs. -images/family.pdf -images/EuScript.pdf -images/exscale.pdf -images/cm-crop.pdf -images/lm-crop.pdf -images/pazo-crop.pdf -images/pamath-crop.pdf -images/cmbright-crop.pdf -images/minionpro-crop.pdf -images/colArray.pdf -images/node.pdf -Mathmode.bbl -Mathmode.ind -\end{lstlisting} - -%\clearpage -%\layout
\ No newline at end of file |