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+%%
+%% This is file `Mathmode.ltx',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Herbert Voss <hvoss@tug.org>
+%% (C) 2008/2009
+%%
+%% 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{2.41}
+%
+\listfiles
+\documentclass[11pt,a4paper,english,twoside]{article}
+\usepackage{fixltx2e}%% the official fixes for LaTeX2e
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+%\usepackage{pamathx}%    use this if you have the commercial palatino math font
+%\usepackage{arev}%  use this if you do not have the palatino math font
+\usepackage{bera}
+%\usepackage{lmodern}
+%\usepackage[scaled=0.85]{luximono}%  use this if you do not have the palatino math font
+%
+\usepackage[marginparwidth=80pt,bmargin=3cm,tmargin=2cm]{geometry}
+\usepackage{ifpdf}
+\usepackage{ifvtex}
+\ifvtex\pdffalse\fi
+\usepackage{comment}
+\usepackage{graphicx}
+\usepackage{varwidth}
+\usepackage{array}
+\usepackage{delarray}
+\usepackage{tabularx}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsopn}
+\usepackage{bm}
+\usepackage{upgreek}
+\usepackage{ragged2e}
+\usepackage{cancel}
+\newcommand\hcancel[2][black]{\setbox0=\hbox{#2}%
+	\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2}
+\DeclareMathOperator{\Res}{Res}
+\usepackage{amscd}
+\usepackage{accents}
+\usepackage{dsfont}
+\usepackage{multirow}
+\usepackage{bigdelim}
+\usepackage{framed}
+\usepackage{longtable}
+\usepackage{varioref}
+%
+\ifvtex
+  \usepackage{pstricks}
+  \usepackage{pst-node}
+\else\ifpdf\usepackage{xcolor}\else
+  \usepackage{pstricks}
+  \usepackage{pst-node}
+\fi\fi
+\usepackage{makeidx}
+\makeindex
+\usepackage{url}
+\usepackage{setspace}
+\usepackage{framed}
+%
+%
+\DeclareMathDelimiter{\Norm}
+   {\mathord}{largesymbols}{"3E}{largesymbols}{"3E}
+%
+\makeatletter
+\def\mathllap{\mathstrut\mathpalette\mathllapinternal}
+%\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{$\mathsurround=0pt#1{#2}$}%
+}
+\def\bijmap{\ensuremath{%
+	\mathrlap{\rightarrowtail}\rightarrow}}
+% extensible Arrow
+\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}
+%
+%
+\def\@bracketheight{2pt}
+\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}
+\def\overbracket{\@ifnextchar[{\@overbracket}{\@overbracket[\@bracketheight]}}
+%
+\def\@overbracket[#1]{\@ifnextchar[{\@over@bracket[#1]}{\@over@bracket[#1][0.3em]}}
+\def\@over@bracket[#1][#2]#3{%\message {Overbracket: #1,#2,#3}
+   \mathop {\vbox {\m@th \ialign {##\crcr \noalign {\kern 3\p@
+   \nointerlineskip }\downbracketfill {#1}{#2}
+        \crcr \noalign {\kern 3\p@ }
+        \crcr  $\hfil \displaystyle {#3}\hfil $%
+        \crcr} }}\limits}
+\def\downbracketfill#1#2{$\m@th \setbox \z@ \hbox {$\braceld$}
+    \edef\@bracketheight{\the\ht\z@}\downbracketend{#1}{#2}
+    \leaders \vrule \@height #1 \@depth \z@ \hfill
+    \leaders \vrule \@height #1 \@depth \z@ \hfill
+\downbracketend{#1}{#2}$}
+\def\downbracketend#1#2{\vrule depth #2 width #1\relax}
+%
+\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}%
+}
+
+\usepackage[allowspaces]{empheq}% defines also harpoon macros
+\usepackage{mathtools}
+\usepackage{nicefrac}
+
+\newcommand*{\threesim}{%
+  \mathrel{\vcenter{\offinterlineskip
+  \hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}}
+%
+\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]{%
+  \parindent=0pt%
+  \def\@xarraycr{%
+    \global\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
+\def\zero{\multicolumn{1}{>{\columncolor{white}}c}{0}}
+\def\colCell#1#2{\multicolumn{1}{>{\columncolor{#1}}c}{#2}}
+%% For printing a cirumflex inside a formula
+\newcommand{\mathcircumflex}[0]{\mbox{\^{}}}
+\providecommand{\tabularnewline}{\\}
+\usepackage{exscale}
+\usepackage{relsize}
+\usepackage{xspace}
+\usepackage[mathscr]{eucal}
+\usepackage{dsfont}
+\usepackage[bottom]{footmisc}
+\usepackage{esint}
+\usepackage{esvect}
+\usepackage{remreset}
+\usepackage{calc}
+\usepackage{cool}
+\usepackage{xypic}
+\usepackage{fancyhdr}
+%
+\pagestyle{fancy}
+\fancyhead[LE,RO]{\leftmark}
+\fancyhead[LO,RE]{\rightmark}
+\fancyhead[C]{}
+\fancyfoot[LO,RE]{\footnotesize\ttfamily\jobname.tex\quad v.\MathmodeVersion}
+%\cfoot{}
+\fancyfoot[LE,RO]{\thepage}
+\fancyfoot[C]{}
+\renewcommand{\headrulewidth}{0pt}
+\renewcommand{\footrulewidth}{0pt}
+%
+\definecolor{umbra}{rgb}{0.8,0.8,0.5}
+\definecolor{gray90}{gray}{0.9}
+%
+\addtocontents{toc}{\hfill Page\endgraf\vspace{-4ex}}
+\addtocontents{lof}{\ Figure\hfill Page}
+\addtocontents{lot}{\ Table\hfill Page}
+\makeatletter
+\renewcommand\@pnumwidth{3.5em}
+\renewcommand*\l@subsection{\@dottedtocline{2}{1.75em}{3.25em}}
+\renewcommand*\l@subsubsection{\@dottedtocline{3}{4em}{4em}}
+\makeatother
+\let\myPart\part
+\renewcommand\part[1]{\clearpage\myPart{#1}}
+%
+%%%%%%%%%%%%% Math symbols %%%%%%%%%%%%%%%%%
+\newcommand{\mysin}{\operatorname{mysin}}
+\newcommand{\eqdef}{\ensuremath{\mathrel{\stackrel{\mathrm{def}}{=}}}}
+\newcommand{\eqexcl}{\ensuremath{\mathrel{\stackrel{\mathrm{!}}{=}}}}
+\newcommand{\eqhat}{\ensuremath{\mathrel{\widehat{=}}}}
+%
+\newlength{\fullwidth}
+\setlength\fullwidth{\textwidth}
+%\addtolength\fullwidth{\marginparsep}
+%\addtolength\fullwidth{\marginparwidth}
+\addtolength\fullwidth{\evensidemargin}
+%
+\newlength{\LBoxWidth}
+\newcommand{\LyXBox}[1]{%
+  \settowidth{\LBoxWidth}{#1}
+  \fbox{\parbox[c]{\LBoxWidth}{#1}}\xspace%
+}
+\newcommand{\logo}{%
+  \bgroup
+  \psset{unit=1in,linewidth=2pt}
+  \psline(-2.5,2.5)(-2.5,-\paperheight)
+  \psline(-2,2.5)(-2,-\paperheight)
+  \rput[lb]{90}(-2.05,-0.7\paperheight){\red\Huge\textbf{\AllTeX}}
+  \rput[lb]{90}(-2.15,-0.1\paperheight){\red\Huge\textbf{Documentation}}
+  \egroup
+}
+\newcommand*{\CMD}[1]{{\tt\textbackslash#1}}
+%
+\makeatletter
+\def\La{%
+  L\kern-.36em{%
+    \setbox0\hbox{T}%
+    \vbox to\ht0{%
+      \hbox{$\m@th$%
+        \csname S@\f@size\endcsname
+        \fontsize\sf@size\z@
+        \math@fontsfalse\selectfont A}%
+      \vss%
+    }%
+  }%
+}
+\def\AllTeX{(\La\kern-.075em)\kern-.075em\TeX\xspace}
+\def\AMS{American Mathematical Society\xspace}
+\def\AmS{$\mathcal{A}$\kern-.1667em\lower.5ex\hbox
+    {$\mathcal{M}$}\kern-.125em$\mathcal{S}$\xspace}
+\def\AmSmath{\AmS{}math\xspace}
+\def\AmSLaTeX{\AmS-\LaTeX\xspace}
+\def\AmSTeX{\AmS-\TeX\xspace}
+\makeatother
+%
+\def\cIndex#1{\index{#1@\CMD{#1}}}
+%
+\usepackage{showexpl}
+\lstset{language=[AlLaTeX]TeX}
+%
+\usepackage{microtype}
+\usepackage[%
+	pdftitle={TeX Mathmode},%
+	pdfauthor={Herbert Voss},%
+	urlcolor=blue,%
+	linktocpage,%
+	a4paper,%
+	colorlinks=true]{hyperref}
+\usepackage{hypcap}
+\usepackage{babel}
+
+\def\tIndex#1{\index{#1@{\UrlFont\texttt{#1}}}}
+\def\cIndex#1{\index{#1@\CMD{#1}}}
+\def\pIndex#1{\index{Parameter@\textbf{Parameter}!{\UrlFont\texttt{#1}}}}
+\def\PIndex#1{\texttt{#1}\index{Package@\textbf{Package}!\texttt{#1}}}
+\def\Index#1{#1\index{#1}}
+\def\CIndex#1{\CMD{#1}\index{#1@\CMD{#1}}\index{Macro@\textbf{Macro}!\CMD{#1}}}
+\def\DIndex#1{\texttt{#1}\index{#1@\texttt{#1}}\index{File@\textbf{File}!\texttt{#1}}}
+\def\LIndex#1{\CMD{#1}\index{#1@\CMD{#1}}\index{Length@\textbf{Length}!\CMD{#1}}}
+\def\ZIndex#1{\texttt{#1}\index{#1@\texttt{#1}}\index{Counter@\textbf{Counter}!\texttt{#1}}}
+\def\zIndex#1{\index{#1@\texttt{#1}}\index{Counter@\textbf{Counter}!\texttt{#1}}}
+\def\FIndex#1{\texttt{#1}\index{#1@\texttt{#1}}\index{Font@\textbf{Font}!\texttt{#1}}}
+\def\UIndex#1{\texttt{#1} environment\index{Environment@\textbf{Environment}!\texttt{#1}}\index{#1@\texttt{#1}}}
+\def\uIndex#1{\texttt{#1}\index{Environment@\textbf{Environment}!\texttt{#1}}\index{#1@\texttt{#1}}}
+%
+\newcommand*\eg{e.g.,\xspace}
+\newcommand*\Eg{E.g.,\xspace}
+\newcommand*\etc{etc.\@\xspace}
+\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}}
+%
+%
+\def\Mbox#1{\par
+\vspace{2ex}
+\noindent
+\resizebox{\linewidth}{!}{\fbox{\includegraphics{#1}}}\par\medskip}
+
+\usepackage{braket}% there were problems when loading before other packages ...
+
+%------------------------------------------ Index macros -------------------------------------
+\def\Lcs#1{{\ttfamily\textbackslash#1}%
+    \index{Macro!#1@\texttt{\textbackslash#1}}\index{#1@\texttt{\textbackslash#1}}}
+\def\LMcs#1{{\ttfamily\bfseries\textbackslash#1}%
+    \index{Macro!#1@\textbf{\texttt{\textbackslash#1}}}\index{#1@\textbf{\texttt{\textbackslash#1}}}}
+\def\Ldim#1{{\ttfamily\textbackslash#1}%
+    \index{Dimension!#1@\texttt{\textbackslash#1}}\index{#1@\texttt{\textbackslash#1}}}
+\def\LMdim#1{{\ttfamily\bfseries\textbackslash#1}%
+    \index{Dimension!#1@\textbf{\texttt{\textbackslash#1}}}\index{#1@\textbf{\texttt{\textbackslash#1}}}}
+\def\Lskip#1{{\ttfamily\textbackslash#1}%
+    \index{Skip!#1@\texttt{\textbackslash#1}}\index{#1@\texttt{\textbackslash#1}}}
+\def\LMskip#1{{\ttfamily\bfseries\textbackslash#1}%
+    \index{Skip!#1@\textbf{\texttt{\textbackslash#1}}}\index{#1@\textbf{\texttt{\textbackslash#1}}}}
+
+\def\LMcsStar#1{\LMcs{#1*}}
+\def\LMcsOptStar#1{{\ttfamily\bfseries\textbackslash#1\OptArg{*}}}
+\def\LMctr#1{{\ttfamily\bfseries#1}}
+\def\Loption#1{{\ttfamily#1}}
+\def\LClass#1{{\ttfamily#1}}
+\def\nxLcs#1{{\ttfamily\textbackslash#1}}
+\def\Lenv#1{{\ttfamily#1}}
+\def\nxLenv#1{{\ttfamily#1}}
+\def\Larg#1{{\itshape\ttfamily#1}}
+\def\Largb#1{{\itshape\ttfamily\{#1\}}}
+\def\Larga#1{{\itshape\ttfamily<#1>}}
+\def\Largr#1{{\itshape\ttfamily(#1)}}
+\def\Largs#1{{\itshape\ttfamily[#1]}}
+\def\LMBEG#1{{\ttfamily\textbackslash begin\{\textbf{#1}\}}}
+\def\LMBEGStar#1{{\ttfamily\textbackslash begin\{\textbf{#1*}\}}}
+\def\LMBEGOptStar#1{{\ttfamily\textbackslash begin\{\textbf{#1\OptArg{*}}\}}}
+\def\LEND#1{{\ttfamily\textbackslash end\{#1\}}}
+\def\LENDStar#1{{\ttfamily\textbackslash end\{#1*\}}}
+\def\LENDOptStar#1{{\ttfamily\textbackslash end\{#1\OptArg{*}\}}}
+\def\OptArg#1{{\colorbox{black!20}{\ttfamily#1}}}
+\def\Coordx#1{$x_{#1}$}
+\def\Coordy#1{$y_{#1}$}
+\def\Coordz#1{$z_{#1}$}
+\def\Coord#1{\Coordx{#1},\kern 1pt\Coordy{#1}}
+\def\CAny{\Coordx{},\kern 1pt\Coordy{}}
+\def\CIIIAny{\Coordx{},\kern 1pt\Coordy{},\kern 1pt\Coordz{}}%  hv
+% with brackets
+\def\coord#1{(\Coordx{#1},\kern 1pt\Coordy{#1})}
+\def\coordiii#1{(\Coordx{#1},\kern 1pt\Coordy{#1},\kern 1pt\Coordy{#1})}% hv
+\def\coordx#1{($x_{#1}$)}
+\def\coordy#1{($y_{#1}$)}
+\def\coordz#1{($z_{#1}$)}
+\def\cAny{(\Coordx{},\kern 1pt\Coordy{})}
+\def\ciiiAny{(\Coordx{},\kern 1pt\Coordy{},\kern 1pt\Coordy{})}% hv
+
+\def\mPar#1{\marginpar[\RaggedLeft\small#1]{\RaggedRight\small#1}}
+\usepackage{layout}
+
+\graphicspath{{images/}}
+\begin{document}
+
+\input{Mathmode.tex}
+
+\end{document}