From 6c76d108053732941431a176e9a29a74d96a8587 Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Thu, 13 Feb 2014 00:41:23 +0000
Subject: voss-mathmode (13feb14)

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+%%
+%% This is file `Mathmode.tex',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Herbert Voss <hvoss at tug dot org>
+%% 2007-04-21
+%%
+%% 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
+%%
+\def\MathmodeVersion{2.32}
+%\ifvtex\title{\logo Math mode - v.\MathmodeVersion}\else
+  \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;
+  Heiko Bauke; Neal Becker; Andrea Blomenhofer; Alexander Boronka; Walter Brown; 
+  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; 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 Schöpf; Jens Schwaiger; Uwe Siart; Martin Sievers; Heiko Stamer; 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,
+%we have to consider, that 
+writing publications with such %a lot of mathematical
+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
+%I tried to collect all important
+facts in this paper. An advanced german version of this paper is available as a book \cite{voss06}.
+
+\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
+\tableofcontents{}
+
+\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{)}     \marginpar{\CMD{(}...\CMD{)}}, the problem is that \verb+\(+ is 
+not a robust macro (see section~\vref{subsec:mathInTitles}).
+\item \verb+$ ... $+   \marginpar{\$...\$}
+\item \CMD{begin\{math\}} ... \CMD{end\{math\}}, also not robust%
+\marginpar{\CMD{begin\{math\}}\\...\\\CMD{end\{math\}}}
+\end{enumerate}
+
+\index{*@\texttt{\textbackslash\char040}}\index{*@\texttt{\textbackslash\char041}}
+In general \verb+$...$+ 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 %
+\marginpar{\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 %
+\marginpar{\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 %
+\marginpar{\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{$@\texttt{\$}}
+
+The whole math expression appears in the default font shape and not
+in bold like the other text. Section~\vref{sec:titleItem}  describes how the math
+expressions can be printed also in bold.
+
+\marginpar{\CMD{texorpdfstring}}%
+There are problems with the \PIndex{hyperref} package  when there is no
+text part in a title. It is possible with the command \CIndex{texorpdfstring}
+to tell \verb+hyperref+ to use different
+commands, one for the title and another one for the bookmarks:
+
+\begin{verbatim}
+\texorpdfstring{<TeX part>}{<hyperref part>}
+\end{verbatim}
+
+
+\begin{minipage}{\fullwidth}
+\begin{lstlisting}
+\texorpdfstring{$\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}
+\marginpar{\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%
+\marginpar{\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\}}%
+\marginpar{\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 \marginpar{\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. \marginpar{\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 %
+\marginpar{\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}
+
+\marginpar{\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 %
+\marginpar{\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}
+%
+\marginpar{\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}
+\marginpar{\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}
+\marginpar{\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}
+\marginpar{\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}
+
+\marginpar{\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
+\marginpar{\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\}}.
+\marginpar{\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 %
+\marginpar{\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 %
+\marginpar{\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
+\marginpar{\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.
+
+\marginpar{\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%
+\marginpar{\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]
+\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}
+\caption{Difference between the default
+\CMD{bigg} and the \CMD{biggm} command}\label{cap:Difference-between-the-bigg}
+\end{table}
+
+
+\newcommand{\xstrut}{\rule{0pt}{0.55cm}}
+{\setlength{\hangindent}{-\marginparwidth}
+\begin{longtable}{l>{\raggedright}p{2.4cm}l>{\raggedright}p{5.7cm}}
+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
+& & &\\
+\caption{Use of the different parentheses for the ``big{}'' commands} \label{tab:big}\tabularnewline
+\end{longtable}}
+
+
+\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}
+
+
+\noindent 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}
+\marginpar{\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.
+
+\marginpar{\CMD{textstyle}\\\CMD{mbox}}
+
+\begin{itemize}
+\marginpar{\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}
+
+%
+\marginpar{\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}
+
+\marginpar{\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}
+\marginpar{\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
+\marginpar{\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}
+\marginpar{\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}
+%$
+
+
+\marginpar{\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}}\marginpar{\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}
+\marginpar{\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 %
+\marginpar{\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}}
+
+\marginpar{\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{esvec}]%
+    {Vectors with package \texttt{esvec} (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}
+\marginpar{\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}{=}|). \marginpar{\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{%
+		\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:\marginpar{\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}
+\marginpar{\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}
+
+\marginpar{\CMD{mathversion}\\\CMD{boldmath}\\\CMD{unboldmath}}%
+Writing a whole formula in bold\index{boldmath@\textbackslash boldmath} is possible with the command sequence
+\verb|\boldmath ... \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}
+\marginpar{\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}}
+\marginpar{\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}
+\marginpar{\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}
+\marginpar{\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}
+\marginpar{\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}
+
+\marginpar{\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}
+
+\marginpar{\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}
+\marginpar{\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}
+\marginpar{\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}
+
+\marginpar{\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
+\marginpar{%
+\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}
+
+\marginpar{\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 %
+\marginpar{\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}
+
+\marginpar{\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 %
+\marginpar{\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} \marginpar{\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 \marginpar{\textbackslash{}substack%
+}
+has an additional command for that, which
+can have several lines with the following syntax:
+\marginpar{\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 \marginpar{\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}
+
+\marginpar{\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.
+
+\marginpar{\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}.
+
+\marginpar{\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}
+\marginpar{%
+\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}
+\marginpar{%
+  \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}
+\marginpar{\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}\,dt=1}
+\end{align}
+
+\begin{lstlisting}
+\begin{align}
+\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=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}
+\marginpar{\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:\marginpar{\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    2004/08/03 v2.11 Emphasizing equations (MH)
+   amscd.sty    1999/11/29 v2.0
+ accents.sty    2000/08/06 v1.2 Math Accent Tools
+  framed.sty    2002/12/29 v 0.5: framed or shaded text with page breaks
+  pstcol.sty    2001/06/20 v1.1 PSTricks color colompatibility (DPC)
+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.sty    1997/03/25 package wrapper for PSTricks pst-node.tex
+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}|& $\displaystyle \Multinomial{1,2,3,4}$
+\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 supports different frames for math environments of the \AmSmath
+package. It doesn't support  all the environments from standard \LaTeX{} which    %%% ----- Martin -----
+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}\,dt=1
+\end{empheq}
+
+\begin{lstlisting}
+\begin{empheq}[box=\fbox]{align}
+	f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=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}\,dt=1
+\end{empheq}
+
+\begin{lstlisting}
+\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align}
+	f(x)=\int_1^{\infty}\frac{1}{x^2}\,dt=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}\,dt=1\\
+	f(x) & =\int_2^{\infty}\frac{1}{x^2}\,dt=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}\,dt=1\\
+	f(x) & =\int_2^{\infty}\frac{1}{x^2}\,dt=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}%
+%
+\marginpar{\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{\stackrel{\mathrm{def}}{=}}}
+\newcommand{\eqexcl}{\ensuremath{\stackrel{\mathrm{!}}{=}}}
+\newcommand{\eqhat}{\ensuremath{\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*\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}}
+\end{lstlisting}
+
+\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
+\begin{align*}
+F(x) &= \int\!f(x)\dx\\
+v(t) &= \dst\\
+a(t) &= \frac{\mathrm{d}^2s}{\mathrm{d}t^2}
+\end{align*}
+\end{LTXexample}
+
+\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
+\begin{align*}
+G(t)   &= \underbrace{\,\int\cdots\!\int\!\!}_D\;\dx\dy\ldots\\
+u_C(t) &= \int\!\,i_C(t)\dt  
+\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]
+\[
+\begin{array}{l@{\:=\:}*{5}{l@{\:+\:}}l}
+y_1 & x_{11} & x_{12} & x_{13} & \dots & x_{1(n-1)} & x_{1n} \\
+y_2 & x_{21} & x_{22} & x_{23} & \dots & x_{2(n-1)} & x_{2n} \\
+\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots\\
+y_{n-1} & x_{(n-1)1} & x_{(n-1)2} & x_{(n-1)3} & \dots & x_{(n-1)3} & x_{(n-1)n}\\
+y_n & x_{n1} & x_{n2} & x_{n3} & \dots & x_{(n-1)(n-1)} & x_{nn}
+\end{array} 
+\]
+\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}[xrightmargin=-\marginparwidth]
+\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}[xrightmargin=-\marginparwidth]
+\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}[xrightmargin=-\marginparwidth]
+\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}[xrightmargin=-\marginparwidth]
+\[
+\begin{array}{rc@{\qquad}c}
+\ldelim\{{2}{2.75cm}[some text here] 
+  & x = 2\quad\text{if }y > 2  & \refstepcounter{equation}(\theequation)\\
+  & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation)
+\end{array}
+\]
+\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}[xrightmargin=-\marginparwidth]
+\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}[xrightmargin=-\marginparwidth]
+$\lim\limits_{n->\infty}q^{n}=\left\{%
+  \begin{array}{lc@{\kern2pt}c@{\kern2pt}r}
+	\textrm{divergent}\  & q & \le & -1\\
+	0 & |q| & < & 1\\
+	1 &  q  & = & 1\\
+	\infty  & q & > & 1
+  \end{array}\right.$
+\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}[xrightmargin=-\marginparwidth]
+\[
+\left(
+\begin{array}{c@{}c@{}c}
+	\begin{array}{|cc|}\hline
+		a_{11} & a_{12} \\
+		a_{21} & a_{22} \\\hline
+	\end{array} & \mathbf{0} & \mathbf{0} \\
+	\mathbf{0} &
+	\begin{array}{|ccc|}\hline
+		b_{11} & b_{12} & b_{13}\\
+		b_{21} & b_{22} & b_{23}\\
+		b_{31} & b_{32} & b_{33}\\\hline
+	\end{array} & \mathbf{0} \\
+	\mathbf{0} & \mathbf{0} &
+	\begin{array}{|cc|}\hline
+		c_{11} & c_{12} \\
+		c_{21} & c_{22} \\\hline
+	\end{array} \\
+\end{array}
+\right)
+\]
+\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}[xrightmargin=-\marginparwidth]
+\[
+Y^1=
+\begin{array}{c}
+  \null\\[1ex]% only vor vertical alignment
+  \left[\begin{array}{rrrr}
+	0 & 0 & 1 & 0\\
+	1 & 0 & 1 & 0\\
+	1 & 1 & 1 & 1
+  \end{array}\right]\\[3ex]\hline
+  \begin{array}{rrrr}
+%	\hdotsfor{4}\\%( needs \AmSmath) instead of \\[3ex]\hline
+	2 & 1 &3 & 1
+  \end{array}
+\end{array}
+\]
+\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}
+\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) &= x2-4x\\
+f(x)-g(x) &= x2+x3+x\\
+        g &= x2+x3+x4+x5+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 3.141592-1.40.3 (Web2C 7.5.6) (format=pdflatex 2007.3.18)  21 APR 2007 09:54
+\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
+   ifpdf.sty    2006/02/20 v1.4 Provides the ifpdf switch (HO)
+  ifvtex.sty    2007/01/10 v1.2 Switches for detecting VTeX and its modes (HO)
+ comment.sty    
+graphicx.sty    1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
+  keyval.sty    1999/03/16 v1.13 key=value parser (DPC)
+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    2007/01/08 v0.04d 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    2003/07/21 v 0.8a: 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    2005/06/27  ver 3.2  Verb mode for urls, etc.
+setspace.sty    2000/12/01 6.7 Contributed and Supported LaTeX2e package
+  empheq.sty    2004/10/10 v2.11a Emphasizing equations (MH) 
+ mhsetup.sty    2004/10/10 v1.0b programming setup (MH)
+mathtools.sty   2004/10/10 v1.01a 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    2005/03/17 v5.3d a miscellany of footnote facilities
+   esint.sty    
+  esvect.sty    
+remreset.sty    
+    cool.sty    2006/12/29 v1.35 COntent Oriented LaTeX
+coollist.sty    2006/08/14 v1 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    2004/10/17 1.3b (Carsten Heinz)
+lstpatch.sty    2004/10/17 1.3b (Carsten Heinz)
+ lstmisc.sty    2004/09/07 1.3 (Carsten Heinz)
+listings.cfg    2004/09/05 1.3 listings configuration
+ lstmisc.sty    2004/09/07 1.3 (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
+ lstmisc.sty    2004/09/07 1.3 (Carsten Heinz)
+microtype.sty   2007/01/21 v2.0 Micro-typography with pdfTeX (RS)
+microtype.cfg   2007/01/14 v2.0 microtype main configuration file (RS)
+hyperref.sty    2007/02/07 v6.75r Hypertext links for LaTeX
+  pd1enc.def    2007/02/07 v6.75r Hyperref: PDFDocEncoding definition (HO)
+hyperref.cfg    2002/06/06 v1.2 hyperref configuration of TeXLive
+kvoptions.sty   2006/08/22 v2.4 Connects package keyval with LaTeX options (HO)
+ hpdftex.def    2007/02/07 v6.75r Hyperref driver for pdfTeX
+  hypcap.sty    2006/02/20 v1.5 Adjusting anchors of captions (HO)
+   babel.sty    2005/11/23 v3.8h The Babel package
+ english.ldf    2005/03/30 v3.3o English support from the babel system
+  braket.sty    
+supp-pdf.tex
+  mt-cmr.cfg    2005/11/07 v1.9 microtype config. file: Computer Modern Roman (RS)
+ nameref.sty    2006/12/27 v2.28 Cross-referencing by name of section
+refcount.sty    2006/02/20 v3.0 Data extraction from references (HO)
+Mathmode.out
+Mathmode.tex
+     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    
+   t1cmtt.fd    1999/05/25 v2.5h Standard LaTeX font definitions
+   omscmr.fd    1999/05/25 v2.5h Standard LaTeX font definitions
+   t1cmss.fd    1999/05/25 v2.5h Standard LaTeX font definitions
+Mathmode.bbl
+Mathmode.ind
+ ***********
+\end{lstlisting}
-- 
cgit v1.2.3

