rm voss-mathmode, obsolete

git-svn-id: svn://tug.org/texlive/trunk@42239 c570f23f-e606-0410-a88d-b1316a301751
author: Karl Berry <karl@freefriends.org> 2016-10-08 23:42:01 +0000
committer: Karl Berry <karl@freefriends.org> 2016-10-08 23:42:01 +0000
commit: dbc5c99e61c0ecccf7a954d6317c35a00228e97f (patch)
tree: 1777af887a7f3006e8fd3ede503c0d8613f55807 /Master/texmf-dist/doc/latex
parent: 8cfd90f7861d3ed698bafaa2dcdf6e17897aef37 (diff)
24 files changed, 0 insertions, 9120 deletions
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Changes b/Master/texmf-dist/doc/latex/voss-mathmode/Changes
deleted file mode 100644
index 4e4ddb5b663..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/Changes
+++ /dev/null
@@ -1,90 +0,0 @@
-..... Mathmode.ltx|tex|bib|ist
-2.47  2010-12-14  - added a note for missing equation*
-2.46  2010-12-10  - edited the bibliography
-2.45  2010-10-18  - fix bug with missing $ symbols
-2.44  2010-08-22  - typos
-2.43  2010-07-22  - typos
-2.42  2009-12-04  - typos
-2.41  2009-04-08  - typos
-2.40  2009-03-26  - update package versions
-2.39  2009-02-14  - typos
-2.38  2009-01-22  - use \mathrel for stacked definitions
-2.37  2009-01-14  - updated bibliography
-                  - switch to utf8
-2.36  2008-12-11  - fix missing line in code listing
-2.35  2008-11-21  - new command for typesetting differentials,
-                    like dx, dt aso.
-2.34  2008-10-30  - typo, small tweaks, and using bera fonts
-2.33  2008-04-23  - formatting of toc and some pages
-2.32  2008-02-29  - again typos
-2.31  2008-02-21  - typo
-2.30  2007-12-31  - added penalty values for no breaks in inline mode
-2.29  2007-11-30  - added two special symbols \Let and \teL
-2.28  2007-09-25  - typo with BlueSky
-		  - package fixltx2e with command \MakeRobust
-2.27  2007-09-06  - small example for \limits
-2.26  2007-05-01  - www.yandy.com -> www.pctex.com
-2.25  2007-04-21  - added an example for aligned vertical dots
-		  - typos
-		  - added an appendix for the package file list of
-		    the pdflatex run
-2.24  2007-04-08  - added an example for a root over several lines
-                  - fixed using \textrm inside array for cases
-2.23  2007-03-30  - added \boldsymbol and \varGREEK letters
-2.22  2007-02-01  - typos
-2.21  2006-10-26  - added examples for package dotseqn
-                  - one more example for split
-                  - some typos and small changes to the structure
-2.20  2006-10-08  - added examples for package cool
-	          - new section "Tuning math typesetting"
-		  - new subdirectory for the images
-2.19  2006-10-06  - some more infos for the fleqn class option
-                  - small fixes to the array environment
-		  - added an example for gathered and
-		    for boxed rows and columns of arrays
-		  - indice in upright font shape
-		  - a lot of modifications to the source code
-		  - extended index
-2.18  2006-09-27  - fix a problem & in align demo
-                  - add a short section of mathtools
-2.17  2006-09-25  fix problem with package showexpl
-2.16  2006-08-05  typo and one more bib entry
-2.15  2006-08-03  some typos, adding the missing 
-                  index and bibliography
-2.14  2006-04-23  http://www.yandy.com is obsolete
-2.13  2006-05-29  typos and adding a font demo section
-2.12  2006-05-17  typos and changes to the bib file
-2.11  2006-03-12  fix bug with \biggm
-2.10  2005-12-22  new section "Problems with amsmath"
-2.09  2005-10-24  fix problem with braket package
-2.08  2005-10-21  example for linear equation matrix
-                  typos
-2.07  2005-10-08  update everymath subsection
-2.06  2005-08-28  add an example for braces around operators with
-                  with stacked limits
-2.05  2005-08-15  add an example for vertical line spacing
-2.04  2005-07-07  small changes to the text
-2.03  2005-07-07  wrong references
-2.02  2005-07-07  typos
-2.01  2005-07-02  do not use PSTricks with pdflatex
-2.00  2005-06-30  typos
-1.99  2005-06-03  typos and bugfix with sqrt
-1.98  2005-05-13  small tweaks
-1.97  2005-05-08  small tweaks
-1.96  2005-05-03  small tweaks
-1.95  2005-04-23  added xlongleftrightarrow
-1.94  2005-04-10  small tweaks
-1.93  2005-02-22  one more example for different vertical spacing
-		  in arrays, amsmath without usind \def\arraystretch
-1.92  2005-02-02  minor changes
-1.91  2005-01-30  different sizes of operators
-1.90  2004-12-22  preventing linebreaks for inline mode
-1.89  2004-12-08  fixed typos
-1.87  2004-11-14  fixed typos
-1.86  2004-11-08  fixed a small bug with inline math
-1.85  2004-11-08  forgot a LateX run for the TOC
-1.84  2004-11-03  fixing typos
-1.83  2004-10-18  added an example for alignat
-                  Some more bib entries
-1.82  2004-10-01  TeX math macros
-
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.bib b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.bib
deleted file mode 100644
index e711dc72d95..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.bib
+++ /dev/null
@@ -1,253 +0,0 @@
-@STRING{bretter = {Bretter, die die Welt bedeuten} }
-@STRING{dtk             = {{D}ie {\TeX}nische {K}om{\"o}die} }
-@STRING{PS              = {{P}ost{S}cript} }
-
-@Manual{MathGuide,
-  Title          = {Short Math Guide for \LaTeX},
-  Author         = {Downes, Michael},
-  Organization   = {American Mathematical Society},
-  Address        = {\url{ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf}},
-  Note           = {},
-  year           = 2002,
-}
-
-@Manual{Notes,
-  Title          = {Technical notes on the \texttt{amsmath} package},
-  Author         = {Downes, Michael},
-  Organization   = {American Mathematical Society},
-  Address        = {\url{ftp://ftp.ams.org/pub/tex/doc/amsmath/technote.pdf}},
-  Note           = {},
-  year           = 1999,
-}
-
-@article{rahtz92,
-  Author	= {Sebastian Rahtz and Leonor Barroca},
-  Title		= {A style option for rotated objects in {\LaTeX}},
-  journal 	= {TUGboat},
-  year 		= 1992,
-  volume 	= 13,
-  number 	= 2,
-  pages 	= "156--180",
-  month 	= jul,
-}
-
-@Manual{mathwriting87,
-  Title=	{Mathematical Writing},
-  Author=	{Donald {E}. {K}nuth and {T}racy {L}arrabee and {P}aul {M}. Roberts},
-  Organization = {Stanford University, Computer Science Department},
-  Address        = {\url{http://sunburn.stanford.edu/~knuth/papers/mathwriting.tex.gz}},
-  Note           = {},
-  year           = 1987,
-}
-
-@Manual{harvard,
-  Title=	{An Introduction to Using {\TeX} in the {H}arvard {M}athematics {D}epartment},
-  Author=	{R. Kuhn and R. Scott and L. Andreev},
-  Organization = {Harvard University, Department of Mathematics},
-  Address        = {\url{http://abel.math.harvard.edu/computing/latex/manual/texman.html}},
-  Note           = {},
-  year           = {},
-}
-
-@book{graetzer00,
-  Title	= {Math into {\LaTeX}},
-  Author = {George Gr\"atzer},
-  Publisher = {Birkh\"auser Boston},
-  Edition=	{third},
-  Year= {2000},
-}
-
-@book{graetzer07,
-  Title	= {More Math into {\LaTeX}},
-  Author = {George Gr\"atzer},
-  Publisher = {Springer},
-  Edition=	{4th},
-  Year= {2007},
-  ISBN={978-0-387-32289-6},
-}
-
-
-@Manual{impatient,
-  Title= {{\TeX} for the {I}mpatient},
-  Author = {Paul W. Abrahams and Karl Berry and Kathryn Hargreaves},
-  Address        = {\url{http://tug.org/ftp/tex/impatient/book.pdf}},
-  Note           = {},
-  year           = {2003},
-}
-
-@book{knuth86,
-  Title	= {The {\TeX}book},
-  Author = {Donald E. Knuth},
-  Publisher = {Addison Wesley Professional},
-  Note =	{21st printing},
-  Year= {1986},
-}
-@book{companion94,
-  Title	= {The {\LaTeX} {C}ompanion},
-  Author = {Michel Goossens and Frank Mittelbach},
-  Publisher = {Addison Wesley},
-  Edition=	{2nd},
-  Year= {2004},
-}
-
-@Manual{eijkhout,
-  Title= {{\TeX} by {T}opic},
-  Author = {Victor Eijkhout},
-  Address        = {\url{http://www.eijkhout.net/tbt/}},
-  Note           = {},
-  year           = {1992},
-}
-@Manual{taylor00,
-  Title          = {Commutative Diagrams in \TeX},
-  Author         = {Paul Taylor},
-  Organization   = {Department of Computer Science, Queen Mary and Westfield College},
-  Address        = {\url{http://www.paultaylor.eu/diagrams/}},
-  Note           = {},
-  year           = 2000,
-}
-@Manual{selden00,
-  Title          = {Math cheat sheet},
-  Author         = {Steve Seiden},
-  Organization   = {TUG},
-  Address        = {\url{http://www.tug.org/texshowcase/#math}},
-  Note           = {},
-  year           = 2000,
-}
-
-@Manual{nist,
-  Title= {Typefaces for Symbols in Scientific
-Manuscripts},
-  Author         = {NIST},
-  Address        = {\url{http://physics.nist.gov/Document/typefaces.pdf}},
-  Note           = {},
-  year           = {2004},
-}
-
-@Manual{expressionsI,
-  Title= {Ecrire des math\'ematiques avec \LaTeX},
-  Author         = {David Cobac},
-  Address        = {\url{http://dcobac.free.fr/spip/IMG/pdf/prepdocmaths.pdf}},
-  Note           = {},
-  year           = {2004},
-}
-
-@Manual{expressionsII,
-  Title= {Atelier documents math\'ematiques},
-  Author         = {David Cobac},
-  Address        = {\url{http://dcobac.free.fr/spip/IMG/pdf/presentation4.pdf}},
-  Note           = {},
-  year           = {2004},
-}
-
-@Manual{kuester:2004,
-  Title= {Fonts for Mathematics},
-  Author= {Johannes K\"uster},
-  Address={\url{http://www.typoma.com/publ/20041002-atypi.pdf}},
-  Note           = {Vortrag auf der {AT}yp{I}-{K}onferenz in {P}rag},
-  month={oct},
-  year           = {2004},
-}
-
-@Manual{kuester:2004-2,
-  Title= {Designing Math Fonts},
-  Author= {Johannes K\"uster},
-  Address={\url{http://www.typoma.com/publ/20040430-bachotex.pdf}},
-  Note           = {Vortrag auf der polnischen {\TeX}-{K}onferenz {`Bacho\TeX'}},
-  month={apr},
-  year           = {2004},
-}
-
-@article{bouchie98,
-  Author	= {Thierry Bouche},
-  Title		= {Diversity in math fonts},
-  journal 	= {TUGboat},
-  year 		= 1998,
-  volume 	= 19,
-  number 	= 2,
-  pages 	= "121--135",
-  Address={\url{http://www.tug.org/TUGboat/Articles/tb19-2/tb59bouc.pdf}},
-}
- 
- @article{beccardi97,
-  Author	= {Claudio Beccari},
-  Title		= {Typesetting mathematics for science
-        and technology according to {ISO} 31/{XI}},
-  journal 	= {TUGboat},
-  year 		= 1997,
-  volume 	= 18,
-  number 	= 1,
-  pages 	= "39--47",
-  Address={\url{http://www.tug.org/TUGboat/Articles/tb18-1/tb54becc.pdf}},
-}
-
-@article{padovani03,
-  Author	= {Luca Padovani},
-  Title		= {Math{ML} formatting with {\TeX} rules and {\TeX} fonts},
-  journal 	= {TUGboat},
-  year 		= 2003,
-  volume 	= 24,
-  number 	= 1,
-  pages 	= "53--61",
-  Address={\url{http://www.tug.org/TUGboat/Articles/tb24-1/padovani.pdf}},
-}
-
-@article{lawrence04,
-  Author	= {Richard Lawrence},
-  Title		= {Math={T}ypography?},
-  journal 	= {TUGboat},
-  year 		= 2003,
-  volume 	= 24,
-  number 	= 2,
-  pages 	= "165--168",
-  Address={\url{http://www.tug.org/TUGboat/Articles/tb24-2/tb77lawrence.pdf}},
-}
-@Article{dtk04.2:voss,
-  author        = {Herbert Vo{\ss}},
-  title         = {Farbige {M}athematik},
-  journal       = dtk,
-  year          = 2004,
-  volume        = {2/04},
-  month         = mar,
-  pages         = {81--87},
-  annote        = bretter,
-  keywords      = {},
-}
-
-@Article{dtk04.3:voss,
-  author        = {Carole Siegfried and Herbert Vo{\ss}},
-  title         = {{M}athematik im {I}nline-{M}odus},
-  journal       = dtk,
-  year          = 2004,
-  volume        = {3/04},
-  month         = nov,
-  pages         = {25--32},
-  annote        = bretter,
-  keywords      = {},
-}
-
-@book{voss09,
-  Title	= {Mathematiksatz in {\LaTeX}},
-  Author = {Herbert Vo\ss},
-  Publisher = "LOB-media.de",
-  Edition=	{},
-  Address= {Berlin/Heidelberg},
-  Year= {2009},
-}
-
-@book{voss:mathe-E,
-  Title	= {Typesetting {M}athematics with {\LaTeX}},
-  Author = {Herbert Vo\ss},
-  Publisher = "UIT",
-  Edition=	{},
-  Address= {Cambridge},
-  Year= {2010},
-}
-
-@book{LaTeXRef,
- title      = "{\LaTeX} {R}eferenz",
- author     = "Herbert Vo\ss",
- publisher  = "LOB-media.de",
- address    = "Berlin, Heidelberg",
- edition    = {2.},
- year       = "2010",
-}
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ist b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ist
deleted file mode 100644
index ed2d4b94ac7..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ist
+++ /dev/null
@@ -1,35 +0,0 @@
-%%
-%% This is file `Letter.ist',
-%%
-%% The idea is from Ingo Kloeckl, Latex2e:
-%% Herbert Voss 000726
-%% 
-%% This is a MAKEINDEX style file which should be used to
-%% generate the formatted change history for use with the doc
-%% package. The TeX commands used below are defined in
-%% doc.sty.  The commands for MAKEINDEX like `level'
-%% `item_x1' are described in `` Makeindex, A General
-%% Purpose, Formatter-Independent Index Processor'' by
-%% Pehong Chen.
-%%
-headings_flag       1		% headings yes
-heading_prefix   "\\textbf{" 	% boldfont
-heading_suffix   "}\n"		% newline
-quote ">"
-preamble
-  "\\begin{theindex}\n"
-item_1
-  "\\par\\leavevmode\\hangindent10pt\\makebox[10pt][l]{--}"
-item_01
-  "\\par\\leavevmode\\hangindent10pt\\makebox[10pt][l]{--}"
-item_x1
-  "\\par\\leavevmode\\hangindent10pt\\makebox[10pt][l]{--}"
-item_2
-  "\\par\\leavevmode\\hangindent20pt\\makebox[20pt][l]{-- -- }"
-item_12
-  "\\par\\leavevmode\\hangindent20pt\\makebox[20pt][l]{-- -- }"
-item_x2
-  "\\par\\leavevmode\\hangindent20pt\\makebox[20pt][l]{-- -- }"
-%% 
-%%
-%% End of file `Letter.ist'.
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ltx b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ltx
deleted file mode 100644
index 067759d943c..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.ltx
+++ /dev/null
@@ -1,403 +0,0 @@
-%%
-%% This is file `Mathmode.ltx',
-%%
-%% IMPORTANT NOTICE:
-%%
-%% Herbert Voss <hvoss@tug.org>
-%% (C) 2008/2009/2010
-%%
-%% 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{2.47}
-%
-\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{paralist}
-\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{MathmodeOrig.tex}
-
-\end{document}
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.pdf
deleted file mode 100644
index 835562771e6..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.tex b/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.tex
deleted file mode 100644
index c8d4bdf844e..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/Mathmode.tex
+++ /dev/null
@@ -1,8282 +0,0 @@
-%%
-%% This is file `Mathmode.tex',
-%%
-%% IMPORTANT NOTICE:
-%%
-%% Herbert Voss <hvoss at tug dot org>
-%% 2010-10-18
-%%
-%% This program can be redistributed and/or modified under the terms
-%% of the LaTeX Project Public License Distributed from CTAN archives
-%% in directory macros/latex/base/lppl.txt.
-%%
-%% DESCRIPTION:
-%%   `Mathmode' is a document how the math mode works inside LaTeX
-%%
-  \ifpdf\title{Math mode~--~v.\,\MathmodeVersion}\else
-    \title{\logo Math mode~---~v.\,\MathmodeVersion}\fi%\fi
-%
-\author{Herbert Vo\ss\footnote{\sloppy Thanks for the feedback to:
-  Hendri Adriaens; Juan Mari Alberdi;
-  Luciano Battaia;
-  Heiko Bauke; Neal Becker; Andrea Blomenhofer; Alexander Boronka; Walter Brown; 
-  Alexander Buchner; Wilhelm Burger;
-  Marco Daniel;
-  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; Mico Loretan; Tim Love; Ladislav Lukas; Dan Luecking;
-  Hendrik Maryns; Heinz Mezera;
-  David Neuway;
-  Luis Trucco Passadore; Joachim Punter;
-  Carl Riehm; Will Robertson; Christoph Rumsm\"uller;
-  Jos\'e{} Carlos Santos;  Arnaud Schmittbuhl;
-    Rainer Sch\"opf; Jens Schwaiger; Uwe Siart; Martin Sievers; Heiko Stamer; 
-    G. Stengert; Uwe St\"ohr;
-  Guangjun Tan;
-  Carsten Thiel; 
-  Juan Luis Varona;
-  David Weenink;
-  Philipp Wook;
-  Michael Zedler;
-  Zou Yuan-Chuan;
-  and last but not least a special thanks to Monika Hattenbach for her 
-  excellent job of proofreading.
-}}
-\date{\today}
-
-\maketitle
-
-\begin{abstract}
-It is often said that \TeX{} was designed for mathematical or technical purposes.
-This may be true when we remember the reasons why Donald Knuth created \TeX{}. But nowadays 
-there are many examples in which \TeX\ is
- used for publications with no mathematical or technical background content.  However,
-writing publications with such 
-material is one of the important advantages of \TeX{}.  Because it 
-seems impossible to
-know all existing macros and options of \AllTeX{} and the several additional packages,
-especially of \AmSmath. This is the reason why I have attempted to gather
-all the relevant
-facts in this paper. An advanced version of this paper is available as a german book~\cite{voss09}
-and also as an english translation~\cite{voss:mathe-E}. 
-Members of DANTE e.\,V., the german \TeX\ users group, may ask for a special price of the german edition (\url{http://www.dante.de})!
-
-\vspace{3cm}
-\noindent Please report typos or any other comments to this documentation to
-\href{mailto:hvoss@tug.org}{hvoss@tug.org}.
-%\noindent This document was written with the \LaTeX{} editor \verb+Kile 1.8+ 
-%\verb+(Qt 3.3+ \verb+KDE 3.4)+  
-%\href{http://sourceforge.net/projects/kile/}{http://sourceforge.net/projects/kile/} 
-%and the PDF output was built with the Linux version of \texttt{V\TeX/Free}, Version 8.46 
-%(\href{http://www.micropress-inc.com/linux/}{http://www.micropress-inc.com/linux/})
-
-This file can be redistributed and/or modified under the terms
-of the \LaTeX\ Project Public License Distributed from \verb+CTAN+ archives
-in directory \url{CTAN://macros/latex/base/lppl.txt}.
-
-\end{abstract}
-
-
-
-\clearpage
-%\fancypagestyle{plain}
-\tableofcontents{}
-
-\clearpage
-\pagestyle{fancy}
-\part{Standard \protect\LaTeX{} math mode}
-
-\section{Introduction}
-The following sections describe all the math commands which are available
-without any additional package. Most of them also work with special
-packages and some of them are redefined. 
-At first some important facts for typesetting math expressions.
-
-\section{The Inlinemode}\label{sec:The-Inlinemode}
-As the name says there are always math expressions which are in a standard
-textline, like this one: $f(x)=\int_{a}^{b}\frac{\sin x}{x}\,\mathrm{d}x$. There
-are no limitations for the height of the math expressions, so that
-the layout may be very lousy if you insert a big matrix in an inline mode
-like this:
-$\underline{A}=\left[\begin{array}{ccc}
-a & b & c\\
-d & e & f\\
-g & h & i\end{array}\right]$. In this case it is better to use the \verb|\smallmatrix| environment
-$\underline{A}=\left[\begin{smallmatrix}%
-a & b & c\cr
-d & e & f\cr
-g & h & i\end{smallmatrix}\right]$ from the \AmSmath{} package (see section \vref{sec:ams-matrix}) or the
-displaymath mode\index{Display math mode} (section~\vref{display}).
-
-This inline mode is possible with three different commands:
-
-\bigskip
-\begin{minipage}{0.35\fullwidth}
-\(\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)\)\\[10pt]
-$\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)$\\[10pt]
-\begin{math}
-  \sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)
-\end{math}
-\end{minipage}\hfill
-\begin{minipage}{0.62\fullwidth}
-\begin{lstlisting}
-\(\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)\)\\[10pt]
-$\sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)$\\[10pt]
-\begin{math}
-  \sum_{i=1}^{n}i=\frac{1}{2}n\cdot(n+1)
-\end{math}
-\end{lstlisting}
-\end{minipage}
-
-\begin{enumerate}
-\item \CMD{( ... }\CMD{)}     \mPar{\CMD{(}...\CMD{)}}, the problem is that \verb+\(+ is 
-not a robust macro (see section~\vref{subsec:mathInTitles}).
-\item \verb+$ ... $+   \mPar{\$...\$}
-\item \CMD{begin\{math\}} ... \CMD{end\{math\}}, also not robust%
-\mPar{\CMD{begin\{math\}}\\...\\\CMD{end\{math\}}}
-\end{enumerate}
-
-\index{*@\texttt{\textbackslash\char040}}\index{*@\texttt{\textbackslash\char041}}
-In general \verb+$...$+ is the best choice, but this does not work in environments like \verb+verbatim+
-or \verb+alltt+. In this case \verb+\(...\)+ works.\index{$@\texttt{\$}}
-
-
-\subsection{Limits}\label{sub:Limits-Inline}
-
-In the inline mode the \Index{limits} are by default only in
-super\index{Superscript} or subscript mode\index{Subscript} and
-the fractions\index{Fraction} are always in the \Index{scriptstyle}%
-\footnote{See section \vref{sec:Styles}.}\index{scriptstyle} 
-font size. For
-example: $\int_{1}^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1$, which is not too
-big for the textline. You %
-\mPar{\CMD{limits}}can change this with the command \CIndex{limits},
-which must follow a math operator\footnote{To define a new operator see
-page~\pageref{OperatorNames}}\index{Math operator} like %
-\mPar{\CMD{int}\\\CMD{lim}\\\CMD{prod}\\\CMD{sum}}
- an integral (\CIndex{int}), a sum (\CIndex{sum}),
-a product (\CIndex{prod}) or a limes
-(\CIndex{lim}). But this $\int\limits_{1}^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1$ 
-(\lstinline|$\int\limits_{1}^...|) %$
-does not look very nice in a text line when it appears between two lines,
-especially when there are multiline limits.\footnote{For more
-information about limits see section~\vref{sub:Multiple-Limits} or section~\vref{sec:limit-AMS}.}
-
-
-\subsection{Fraction command}\label{sub:fraction command}
-
-For inlined formulas the fractions\index{Fraction} are by default
-in the scriptstyle\index{scriptstyle@\textbackslash scriptstyle} (see tabular~\vref{cap:Mathstyles}),
-which is good for typesetting $y=\frac{a}{b+1}$, because the
-linespacing %
-\mPar{\CMD{frac}}is nearly the same, but not optimal, when the formula shows some important
-facts. There are two solutions to get a better reading:
-
-\begin{enumerate}
-\item choose the display mode instead of the inline mode, which is the better
-one;
-\item set the fontstyle to \CIndex{displaystyle}, which makes
-the fraction $y={\displaystyle\frac{a}{b+1}}$ more readable but
-the linespacing increases which is always a bad solution and should
-only be used when the first solution makes no sense.\footnote{For an abbreviation see
-section~\vref{sec:ams-fraction}, there is a special \CIndex{dfrac} macro.}
-
-\bigskip
-\begin{minipage}{0.25\fullwidth}
-$y=\frac{a}{b+1}={\displaystyle\frac{a}{b+1}}$
-\end{minipage}\hfill
-\begin{minipage}{0.72\fullwidth}
-\begin{lstlisting}
-$y=\frac{a}{b+1}={\displaystyle\frac{a}{b+1}}$
-\end{lstlisting}
-\end{minipage}
-\end{enumerate}
-
-
-\subsection[Math in Chapter/Section Titles]{\label{inline-chapter}Math in \CIndex{part},
-\CIndex{chapter}, \CIndex{section},
-... titles like $f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}\label{subsec:mathInTitles}
-
-All commands which appear in positions like contents, index, header,
-... must be robust\footnote{%
-\texttt{robust} means that the macro is not expanded before it is moved
-into for example the tableofcontents file (\texttt{*.toc}).  No robustness is 
-often a problem, when a macro is part of another macro.}
-which is the case for \verb+$...$+ but not for \verb+\(...\)+. 
-The latest package \PIndex{fixltx2e} defines an macro for declaring
-existing commands to be robust. The package itself does this already for: 
-
-\begin{lstlisting}
-\MakeRobust\(
-\MakeRobust\)
-\MakeRobust\[
-\MakeRobust\]
-\MakeRobust\makebox
-\MakeRobust\savebox
-\MakeRobust\framebox
-\MakeRobust\parbox
-\MakeRobust\rule
-\MakeRobust\raisebox
-\end{lstlisting}
-
-
-If you do not have any contents, index, a.s.o.
-you can write the mathstuff in \CIndex{chapter}, \CIndex{section},
-a.s.o without any restriction. Otherwise use \verb+\protect\(+ and \verb+\protect\)+ or the
-\verb+$...$+ version.\index{$@\texttt{\$}}
-
-The whole math expression appears in the default font shape and not
-in bold like the other text. Section~\vref{sec:titleItem}  describes how the math
-expressions can be printed also in bold.
-
-\mPar{\CMD{texorpdfstring}}%
-There are problems with the \PIndex{hyperref} package  when there is no
-text part in a title. It is possible with the command \CIndex{texorpdfstring}
-to tell \verb+hyperref+ to use different
-commands, one for the title and another one for the bookmarks:
-
-\begin{verbatim}
-\texorpdfstring{<TeX part>}{<hyperref part>}
-\end{verbatim}
-
-
-\begin{minipage}{\fullwidth}
-\begin{lstlisting}
-\texorpdfstring{$\int f(x)\,\mathrm{d}x$}{Integral function}
-\end{lstlisting}
-\end{minipage}
-
-
-
-\subsection{Equation numbering}
-
-It is obvious that the numbering of inline mathstuff makes no sense!
-
-\subsection{Framed math}
-With the \CIndex{fbox} macro everything of inline math can be framed\index{Framed inline
-math}\index{boxed inline math}, like the following one: 
-
-\bigskip
-\begin{minipage}{0.325\fullwidth}
-\fbox{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}
-\end{minipage}\hfill
-\begin{minipage}{0.67\fullwidth}
-\begin{lstlisting}
-\fbox{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}
-\end{lstlisting}
-\end{minipage}
-
-%$
-
-Parameters are the width of \LIndex{fboxsep} and \LIndex{fboxrule}, the predefined values
-from the file \verb|latex.ltx| are:
-
-\bigskip
-\begin{minipage}{\fullwidth}
-\begin{lstlisting}
-\fboxsep = 3pt
-\fboxrule = .4pt
-\end{lstlisting}
-\end{minipage}
-
-The same is possible with the \CIndex{colorbox}
-\colorbox{yellow}{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}
-from the color package.
-
-\bigskip
-\begin{minipage}{\fullwidth}
-\begin{lstlisting}
-\colorbox{yellow}{$f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)$}
-\end{lstlisting}
-\end{minipage}
-
-%$
-
-\subsection{Linebreak}\label{subsec:linebreak}
-
-\LaTeX{} can break an inline formula only when a relation symbol ($=, <, >, \ldots$) or a
-binary operation symbol ($+,-, \ldots$) exists and at least one of these symbols appears at
-the outer level of a formula.
-Thus \verb|$a+b+c$| can be broken across lines, but \verb|${a+b+c}$| not.\index{$@\texttt{\$}}
-
-\begin{itemize}
-\item The default: \hspace{1cm}
-$f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\ldots
-	+a_ix^i	+a_2x^2	+a_1x^1	+a_0$
-\item The same inside a group \{...\}:
-${f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\ldots
-	+a_ix^i	+a_2x^2	+a_1x^1	+a_0}$
-
-\item Without any symbol: \hspace{4cm}
-$f(x)=a_n\left(a_{n-1}\left(a_{n-2}\left(\ldots\right)\ldots\right)\ldots\right)$
-\end{itemize}
-
-If it is not possible to have any mathsymbol, then split the inline formula in two
-or more pieces (\verb|$...$ $...$|). If you do not want a linebreak for the whole
-document, you can set in the preamble:
-\begin{verbatim}
-\relpenalty=9999
-\binoppenalty=9999
-\end{verbatim}
-
-\noindent
-which is the extreme case of grudgingly allowing breaks in extreme cases, or
-%
-\begin{verbatim}
-\relpenalty=10000
-\binoppenalty=10000
-\end{verbatim}
-%
-for absolutely no breaks.
-
-\subsection{Whitespace}\label{subsec:whitespace}
-\LaTeX{} defines the length \LIndex{mathsurround} with the default value of
-\verb|0pt|. This length is added before and after an inlined math expression 
-(see table~\vref{tab:whitespace}).
-
-\begin{table}[htb]
-\hspace*{-0.1\linewidth}%
-\begin{tabular}{@{}cc@{}}
-foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar & 
-\begin{minipage}{0.7\linewidth}
-\begin{lstlisting}
-foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar
-\end{lstlisting}
-\end{minipage}\tabularnewline
-%
-foo \rule{20pt}{\ht\strutbox}\fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $}\rule{20pt}{\ht\strutbox} bar & 
-\begin{minipage}{0.7\linewidth}
-\begin{lstlisting}
-foo \rule{20pt}{\ht\strutbox}\fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $}\rule{20pt}{\ht\strutbox} bar
-\end{lstlisting}
-\end{minipage}\tabularnewline
-\setlength{\mathsurround}{20pt}foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar & 
-\begin{minipage}{0.7\linewidth}
-\begin{lstlisting}
-\setlength{\mathsurround}{20pt}
-foo \fbox{$ f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1 $} bar
-\end{lstlisting}
-\end{minipage}
-\end{tabular}
-%
-\caption{Meaning of \CMD{mathsurround}}\label{tab:whitespace}
-\end{table}
-
-%$
-
-\subsection{\AmSmath for the inline mode}
-
-None of the \AmSmath-functions are available in inline mode.
-
-\section{Displaymath mode}\label{display}
-This means, that every formula gets its own paragraph (line). There are
-some differences in the layout to the one from the title
-of \ref{inline-chapter}.
-
-
-\subsection{\texttt{equation} environment}
-
-For example:
-
-\bigskip\noindent
-\begin{tabular}{cc}
-\begin{minipage}{0.35\linewidth}
-\begin{equation}
-  f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)
-\end{equation}
-\end{minipage} & 
-\begin{minipage}{0.63\linewidth}
-\begin{lstlisting}
-\begin{equation}
-  f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)
-\end{equation}
-\end{lstlisting}
-\end{minipage}
-\end{tabular}
-
-\bigskip
-The delimiters\index{Delimiter}
-\CMD{begin\{equation\} ... }\CMD{end\{equation\}} are the only difference to the inline version. 
-There are some equivalent commands for the display-math mode:
-
-\begin{compactenum}
-\mPar{\CMD{begin\{displaymath\}}\\
-\ldots\\
-\CMD{end\{displaymath\}}}%
-\item \CMD{begin\{displaymath\}}\ldots\CMD{end\{displaymath\}}, same as
-\CMD{[} \ldots \CMD{]}
-%
-\item \CMD{[\ldots}\CMD{]}. (see above) the short form of a displayed formula, no number%
-\mPar{\texttt{\textbackslash[\ldots\textbackslash{}]}}
-\[
-f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)
-\]
-%
-displayed, no number. Same as 1.
-%
-\item \CMD{begin\{equation\}\ldots}\CMD{end\{equation\}}%
-\mPar{\CMD{begin\{equation\}}\\
-\ldots\\
-\CMD{end\{equation\}}}%
-%
-\begin{equation}
-f(x)=\prod_{i=1}^{n}\left(i-\frac{1}{2i}\right)
-\end{equation}
-%
-displayed, a sequential equation number, which may be reset when
-starting a new chapter or section.
-
-
-\begin{compactenum}
-\item There is only \textbf{one} equation number for the whole environment.
-\item \mPar{\CMD{nonumber}}In standard  \LaTeX\ there exists no star-version of the equation environment 
-because \CIndex{[}\ldots\CIndex{]} is the equivalent. However, with package \AmSmath\ it will be defined. 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{compactenum}
-\end{compactenum}
-
-
-\subsection{\texttt{eqnarray} environment}\label{display:eqnarray}
-
-This is by default an array with three columns and as many rows as
-you like. \mPar{\CMD{begin\{eqnarray\}}\\
-...\\
-\CMD{end\{eqnarray\}}} It is nearly the same as an array with a \verb|rcl|  column definition.
-
-It is \textbf{not possible} to change the internal behaviour of the \verb|eqnarray| environment without
-rewriting the environment.
-It is always an impli\-cit array with \textbf{three} columns and the horizontal
-alignment \verb|right-center-left (rcl)| and small \textbf{symbol} sizes for the
-middle column. All this can not be changed by the user without rewriting
-the whole environment in \verb|latex.ltx|.
-
-\bigskip\noindent
-\begin{tabular}{cc}
-\begin{minipage}{0.35\linewidth}
-\begin{eqnarray*}
-\mathrm{left} & \mathrm{middle} & \mathrm{right}\\
-\frac{1}{\sqrt{n}}= & \frac{\sqrt{n}}{n}= & \frac{n}{n\sqrt{n}}
-\end{eqnarray*} 
-\end{minipage} &
-\begin{minipage}{0.63\linewidth}
-\begin{lstlisting}
-\begin{eqnarray*}
-\mathrm{left} & \mathrm{middle} & \mathrm{right}\\
-\frac{1}{\sqrt{n}}= & \frac{\sqrt{n}}{n}= & \frac{n}{n\sqrt{n}}
-\end{eqnarray*}
-\end{lstlisting}
-\end{minipage}
-\end{tabular}
-
-\bigskip
-The \UIndex{eqnarray} should not be used as an array. As seen in the above
-example the typesetting is wrong for the middle column. The numbering of eqnarray
-environments is always for every row, means,
-that four lines get four different equation numbers (for the labels see 
-section~\vref{sec:Labels}):
-
-\bigskip
-\begin{minipage}{0.5\columnwidth}
-\begin{eqnarray}
-y & = & d\label{eq:2}\\
-y & = & cx+d\\
-y & = & bx^{2}+cx+d\\
-y & = & ax^{3}+bx^{2}+cx+d\label{eq:5}
-\end{eqnarray}
-\end{minipage}\hfill
-\begin{minipage}{0.43\columnwidth}
-\begin{lstlisting}
-\begin{eqnarray}
-y & = & d\label{eq:2}\\
-y & = & cx+d\\
-y & = & bx^{2}+cx+d\\
-y & = & ax^{3}+bx^{2}+cx+d\label{eq:5}
-\end{eqnarray}
-\end{lstlisting}
-\end{minipage}
-
-
-\medskip
-Suppressing the  numbering for \textbf{all} rows is possible with the starred version of eqnarray.
-
-\medskip
-\begin{minipage}{0.45\columnwidth}
-\begin{eqnarray*}
-y & = & d\label{eq:3}\\
-y & = & cx+d\\
-y & = & bx^{2}+cx+d\\
-y & = & ax^{3}+bx^{2}+cx+d\label{eq:4}
-\end{eqnarray*}
-\end{minipage}
-\begin{minipage}{0.53\columnwidth}
-\begin{lstlisting}
-\begin{eqnarray*}
-y & = & d\label{eq:3}\\
-y & = & cx+d\\
-y & = & bx^{2}+cx+d\\
-y & = & ax^{3}+bx^{2}+cx+d\label{eq:4}
-\end{eqnarray*}
-\end{lstlisting}
-\end{minipage}
-
-\medskip
-Toggling off/on for \textbf{single} rows is possible with the above
-mentioned \CIndex{nonumber} tag at the end of a row
-(before the newline command). For example:
-
-\medskip
-\begin{minipage}{0.45\columnwidth}
-\begin{eqnarray}
-	y & = & d\nonumber \\
-	y & = & cx+d\nonumber \\
-	y & = & bx^{2}+cx+d\nonumber \\
-	y & = & ax^{3}+bx^{2}+cx+d
-\end{eqnarray}
-\end{minipage}
-\begin{minipage}{0.53\columnwidth}
-\begin{lstlisting}
-\begin{eqnarray}
-	y & = & d\nonumber \\
-	y & = & cx+d\nonumber \\
-	y & = & bx^{2}+cx+d\nonumber \\
-	y & = & ax^{3}+bx^{2}+cx+d
-\end{eqnarray}
-\end{lstlisting}
-\end{minipage}
-
-
-\subsubsection{Short commands}\label{subsec:shortcommand}
-It is possible to define short commands for the \UIndex{eqnarray}
-%
-\begin{lstlisting}
-\makeatletter
-\newcommand{\be}{%
-  \begingroup
-% \setlength{\arraycolsep}{2pt}
-  \eqnarray%
-  \@ifstar{\nonumber}{}%
-}
-\newcommand{\ee}{\endeqnarray\endgroup}
-\makeatother
-\end{lstlisting}
-
-\makeatletter
-\newcommand{\be}{%
-    \begingroup
-%    \setlength{\arraycolsep}{2pt}
-    \eqnarray%
-	\@ifstar{\nonumber}{}%
-}
-\newcommand{\ee}{\endeqnarray\endgroup}
-\makeatother
-
-Now you can write the whole equation as
-
-
-\begin{LTXexample}[width=0.5\columnwidth,wide]
-\be
-  f(x) &=& \int\frac{\sin x}{x}\,\mathrm{d}x
-\ee
-\end{LTXexample}
-
-\medskip
-\noindent or, if you do not want to have a numbered equation as
-
-\begin{LTXexample}[width=0.5\columnwidth,wide]
-\be*
-  f(x) &=& \int\frac{\sin x}{x}\,\mathrm{d}x
-\ee
-\end{LTXexample}
-
-
-\subsection{Equation numbering}\label{sub:Equationnumbering}
-
-For all equations which can have one or %
-\mPar{\CMD{nonumber}}more equation numbers (for every line/row) the numbering
-for the whole equation can be disabled with switching from the unstarred to the star
-version. This is still for the whole formula and doesn't work for single rows.
-In this case use the \CIndex{nonumber} tag.
-
-\begin{itemize}
-\item This doc is written with the article-class, which counts the equations
-continuously over all parts/sections. You can change this behaviour
-in different ways (see the following subsections).
-\item In standard \LaTeX{} it is a problem with too long equations and the
-equation number, which may be printed with the equation one upon the other. In this case
-use the \AmSmath package, where the number is set above or below
-of a too long equation (see equation~\vref{eq:braces}).
-\item For counting subequations see section~\vref{ams:subeqn}.
-\end{itemize}
-
-\subsubsection{Changing the style}
-
-\mPar{\CMD{theequation}}%
-With the beginning of Section \vref{sec:alignat environment} the
-counting changes from ``\ref{eq:IntoSection}{}'' into the new style
-``\ref{eq:newCounting}''. The command sequence is
-
-\begin{lstlisting}
-\renewcommand\theequation{\thepart-\arabic{equation}}
-\end{lstlisting}
-
-See section~\vref{sec:Equation-numbering} for the \AmSmath command.
-
-
-\subsubsection{Resetting a counter style}
-
-Removing a given reset is possible with the \PIndex{remreset}.%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/supported/carlisle/remreset.sty}{CTAN://macros/latex/contrib/supported/carlisle/remreset.sty}} Write into the %
-\mPar{\CMD{@removefromreset}} preamble
-
-\begin{lstlisting}
-\makeatletter
-\@removefromreset{equation}{section}
-\makeatother
-\end{lstlisting}
-or anywhere in the text.
-
-Now the equation counter is no longer reset when a new section starts.
-You can see this after section~\vref{split}.
-
-
-\subsubsection{Equation numbers on the left side}
-
-Choose package \PIndex{leqno}%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/unpacked/leqno.sty}{CTAN://macros/latex/unpacked/leqno.sty}}
-or have a look at your document class, if such an option exists.
-
-\subsubsection{Changing the equation number style}
-The number style can be changed with a redefinition of
-
-\begin{verbatim}
-\def\@eqnnum{{\normalfont \normalcolor (\theequation)}}
-\end{verbatim}
-
-For example: if you want the numbers not in parentheses write
-
-\begin{lstlisting}
-\makeatletter
-\def\@eqnnum{{\normalfont \normalcolor \theequation}}
-\makeatother
-\end{lstlisting}
-
-For \AmSmath there is another macro, see section~\ref{sec:Equation-numbering} on
-page~\pageref{sec:Equation-numbering}.
-
-\subsubsection{More than one equation counter}
-You can have more than the default equation counter. With the following code you
-can easily toggle between roman and arabic equation counting.
-\makeatletter
-%Roman counter
-\newcounter{roem}
-\renewcommand{\theroem}{\roman{roem}}
-
-% save the original counter
-\newcommand{\c@org@eq}{}
-\let\c@org@eq\c@equation
-\newcommand{\org@theeq}{}
-\let\org@theeq\theequation
-
-%\setroem sets roman counting
-\newcommand{\setroem}{
-  \let\c@equation\c@roem
-  \let\theequation\theroem}
-
-%\setarab the arabic counting
-\newcommand{\setarab}{
-  \let\c@equation\c@org@eq
-  \let\theequation\org@theeq}
-\makeatother
-
-\begin{lstlisting}
-%code by Heiko Oberdiek
-\makeatletter
-%Roman counter
-\newcounter{roem}
-\renewcommand{\theroem}{\roman{roem}}
-
-% save the original counter
-\newcommand{\c@org@eq}{}
-\let\c@org@eq\c@equation
-\newcommand{\org@theeq}{}
-\let\org@theeq\theequation
-
-%\setroem sets roman counting
-\newcommand{\setroem}{
-  \let\c@equation\c@roem
-  \let\theequation\theroem}
-
-%\setarab the arabic counting
-\newcommand{\setarab}{
-  \let\c@equation\c@org@eq
-  \let\theequation\org@theeq}
-\makeatother
-\end{lstlisting}
-
-The following examples show how it works:
-
-\noindent
-\begin{minipage}{1.2\linewidth}
-\begin{minipage}{0.38\linewidth}
-\begin{align}
-f(x) &= \int\sin x\,\mathrm{d}x\label{eq:arab1}\\
-g(x) &= \int\frac{1}{x}\,\mathrm{d}x
-\end{align}
-%
-\setroem
-%
-\begin{align}
-F(x) &=-\cos x\\
-G(x) &=\ln x\label{eq:rom1}
-\end{align}
-%
-\setarab
-%
-\begin{align}
-f^{\prime} (x) &= \sin x\\
-g^{\prime} (x) &= \frac{1}{x}\label{eq:arab2}
-\end{align}
-\end{minipage}\hfill
-\begin{minipage}{0.58\linewidth}
-\begin{lstlisting}
-\begin{align}
-f(x) &= \int\sin x\,\mathrm{d}x\label{eq:arab1}\\
-g(x) &= \int\frac{1}{x}\,\mathrm{d}x
-\end{align}
-%
-\setroem
-%
-\begin{align}
-F(x) &=-\cos x\\
-G(x) &=\ln x\label{eq:rom1}
-\end{align}
-%
-\setarab
-%
-\begin{align}
-f^{\prime} (x) &= \sin x\\
-g^{\prime} (x) &= \frac{1}{x}\label{eq:arab2}
-\end{align}
-\end{lstlisting}
-\end{minipage}
-\end{minipage}
-
-\medskip
-There can be references to these equations in the usual way, like eq.\ref{eq:arab1},
-\ref{eq:arab2} and for the roman one eq.\ref{eq:rom1}.
-
-
-\subsection{Labels}\label{sec:Labels}
-
-Every numbered equation can have a label\index{Label} to which a
-reference\index{Reference} is possible.
-
-\begin{itemize}
-\item There is one restriction for the label names, they cannot include
-one of \LaTeX{}'s command characters.\footnote{\$ \_ \^{} \textbackslash{} \& \% \{ \}}
-\item The label names are replaced by the equation number.
-\end{itemize}
-%
-\mPar{\CMD{tag}}If you do not want a reference to the equation number but to a self
-defined name then use the \AmS{}math command \CMD{tag{...}},
-which is described in section \vref{sec:Labels-and-Tags}\index{tag@\textbackslash tag}.
-
-\subsection{Frames}\label{sec:Frames}
-Similiar to the inline mode, displayed equations can also be framed with
-the \CIndex{fbox} command, like equation \ref{eq:frame0}.
-The only difference is
-the fact, that the equation must be packed into a parbox or minipage. It is
-nearly the same for a colored box, where the \verb|\fbox{...}| has to be
-replaced with \verb|\colorbox{yellow}{...}|. The package \verb|color.sty| must
-be loaded and --important -- the \PIndex{calc} package to get a correct boxwidth.
-
-\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{%
-\begin{equation}\label{eq:frame0}
-f(x)=\int_1^{\infty}\dfrac{1}{x^2}\,\mathrm{d}x=1
-\end{equation}%
-}}
-
-\medskip
-\begin{lstlisting}
-\noindent\fbox{\parbox{\linewidth-2\fboxsep-2\fboxrule}{%
-\begin{equation}\label{eq:frame0}
-	f(x)=\int_1^{\infty}\dfrac{1}{x^2}\,\mathrm{d}x=1
-\end{equation}%
-}}
-\end{lstlisting}
-
-
-If the equation number should not be part of the frame, then it is a bit
-complicated. There is one tricky solution, which puts an unnumbered equation
-just beside an empty numbered equation. The \verb|\hfill| is only useful for
-placing the equation number right aligned, which is not the default. The
-following four equations \ref{eq:frame2}-\ref{eq:frame5} are the same,
-only the second one written with the \verb|\myMathBox| macro which has the
-border and background color as optional arguments with the defaults
-\verb|white| for background and \verb|black| for the frame. If there is only
-one optional argument, then it is still the one for the frame color (\ref{eq:frame3}).
-
-\makeatletter
-\def\myMathBox{\@ifnextchar[{\my@MBoxi}{\my@MBoxi[black]}}
-\def\my@MBoxi[#1]{\@ifnextchar[{\my@MBoxii[#1]}{\my@MBoxii[#1][white]}}
-\def\my@MBoxii[#1][#2]#3#4{%
-  \par\noindent%
-  \fcolorbox{#1}{#2}{%
-     \parbox{\linewidth-\labelwidth-2\fboxrule-2\fboxsep}{#3}%
-  }%
-  \parbox{\labelwidth}{%
-    \begin{eqnarray}\label{#4}\end{eqnarray}%
-  }%
-  \par%
-}
-\makeatother
-
-\begin{lstlisting}
-\makeatletter
-\def\myMathBox{\@ifnextchar[{\my@MBoxi}{\my@MBoxi[black]}}
-\def\my@MBoxi[#1]{\@ifnextchar[{\my@MBoxii[#1]}{\my@MBoxii[#1][white]}}
-\def\my@MBoxii[#1][#2]#3#4{%
-  \par\noindent%
-  \fcolorbox{#1}{#2}{%
-     \parbox{\linewidth-\labelwidth-2\fboxrule-2\fboxsep}{#3}%
-  }%
-  \parbox{\labelwidth}{%
-    \begin{eqnarray}\label{#4}\end{eqnarray}%
-  }%
-  \par%
-}
-\makeatother
-\end{lstlisting}
-
-\begin{equation}\label{eq:frame2}
-	f(x)=x^2 +x
-\end{equation}
-\myMathBox[red]{\[f(x)=x^2 +x\]}{eq:frame3}
-\myMathBox[red][yellow]{\[f(x)=x^2 +x\]}{eq:frame4}
-\myMathBox{\[f(x)=x^2 +x\]}{eq:frame5}
-
-\medskip
-\begin{lstlisting}
-\begin{equation}\label{eq:frame2}
-	f(x)=x^2 +x
-\end{equation}
-\myMathBox[red]{\[f(x)=x^2 +x\]}{eq:frame3}
-\myMathBox[red][yellow]{\[f(x)=x^2 +x\]}{eq:frame4}
-\myMathBox{\[f(x)=x^2 +x\]}{eq:frame5}
-\end{lstlisting}
-
-If you are using the \AmSmath package, then try the solutions from section
-\vref{sec:ams-frames}.
-
-\section{\texttt{array} environment}
-\mPar{\CMD{begin\{array\}}\\...\\\CMD{end\{array\}}}
-This is simply the same as the \UIndex{eqnarray} only with the
-possibility of variable rows \textbf{and} columns and the fact, that
-the whole formula has only \textbf{one} equation number and that the
-\verb|array| environment can only be part of another math environment,
-like the \UIndex{equation} or the \UIndex{displaymath}. With \verb+@{}+ before the
-first and after the last column the additional space \LIndex{arraycolsep}
-is not used, which maybe important when using left aligned equations.
-
-\begin{equation}
-\left.%
-\begin{array}{@{}r@{\quad}ccrr@{}}
-	\textrm{a}) & y & = & c & (constant)\\
-	\textrm{b}) & y & = & cx+d & (linear)\\
-	\textrm{c}) & y & = & bx^{2}+cx+d & (square)\\
-	\textrm{d}) & y & = & ax^{3}+bx^{2}+cx+d & (cubic)
-\end{array}%
-\right\} 	\textrm{Polynomes}
-\end{equation}
-
-
-\begin{lstlisting}
-\begin{equation}
-\left.%
-\begin{array}{@{}r@{\quad}ccrr@{}}
-	\textrm{a}) & y & = & c & (constant)\\
-	\textrm{b}) & y & = & cx+d & (linear)\\
-	\textrm{c}) & y & = & bx^{2}+cx+d & (square)\\
-	\textrm{d}) & y & = & ax^{3}+bx^{2}+cx+d & (cubic)
-\end{array}%
-\right\} 	\textrm{Polynomes}
-\end{equation}
-\end{lstlisting}
-
-
-The horizontal alignment of the columns is the same as the one from the
-\UIndex{tabular}.
-
-For arrays with delimiters see section~\vref{delarray}.
-
-\subsection{Cases structure}
-
-If you do not want to use the \AmSmath package then write your own
-cases structure\index{cases@\textbackslash cases} with the \verb|array| environment:
-
-\begin{LTXexample}[pos=b]
-\begin{equation}
-x=\left\{ \begin{array}{cl}
-0 & \textrm{if }A=\ldots\\
-1 & \textrm{if }B=\ldots\\
-x & \textrm{this runs with as much text as you like, but without an raggeright text.}\end{array}\right.
-\end{equation}
-\end{LTXexample}
-
-
-It is obvious, that we need a \CMD{parbox} if the text is longer than the possible linewidth.
-
-\begin{LTXexample}[pos=b]
-\begin{equation}
-x = \left\{%
-   \begin{array}{l>{\raggedright}p{.5\textwidth}}%
-      0 & if $A=\ldots$\tabularnewline
-      1 & if $B=\ldots$\tabularnewline
-      x & \parbox{0.5\columnwidth}{this runs with as much text as you like, %
-          because an automatic linebreak is given with %
-          a raggedright text. Without this %
-          \raggedright command, you'll get a formatted %
-          text like the following one ... but with a parbox ... it works}
-    \end{array}%
-  \right. %
-\end{equation}
-\end{LTXexample}
-
-
-
-\subsection{\texttt{arraycolsep}}\label{sec:arraycolsep}
-\mPar{\CMD{arraycolsep}}%
-All the foregoing math environments use the array to typeset the math
-expression. The predefined separation between two columns is the length
-\LIndex{arraycolsep}|, which is set by nearly all document classes to \verb|5pt|,
-which seems to be too big. The following equation is typeset with the
-default value and the second one with \verb|\arraycolsep=1.4pt|
-
-
-\bgroup
-\fboxsep=0pt
-\def\xstrut{\vphantom{\int\frac{\sin x}{x}}}
-\begin{eqnarray*}
-\boxed{f(x)\xstrut} & \boxed{=\xstrut} & \boxed{\int\frac{\sin x}{x}\,\mathrm{d}x}
-\end{eqnarray*}
-
-\vspace{-2ex}
-\arraycolsep=1.4pt
-\begin{eqnarray*}
-\boxed{f(x)\xstrut} & \boxed{=\xstrut} & \boxed{\int\frac{\sin x}{x}\,\mathrm{d}x}
-\end{eqnarray*}
-\egroup
-
-If this modification should be valid for all arrays/equations, then write it into the
-preamble, otherwise put it into a group or define your own environment as done
-in section~\vref{subsec:shortcommand}.
-
-\begin{lstlisting}
-\bgroup
-\arraycolsep=1.4pt
-\begin{eqnarray}
-f(x) & = & \int\frac{\sin x}{x}\,\mathrm{d}x
-\end{eqnarray}
-\egroup
-\end{lstlisting}
-
-\begin{lstlisting}
-\makeatletter
-\newcommand{\be}{%
-    \begingroup
-    \setlength{\arraycolsep}{1.4pt}
-[ ... ]
-\end{lstlisting}
-
-\section{Matrix}\label{sec:matrix}
-\mPar{\CMD{begin\{matrix\}}\\\ldots\\\CMD{end\{matrix\}}\\\CMD{bordermatrix}}%
-\TeX{} knows two macros and \LaTeX{} one more for typesetting a 
-matrix\index{bordermatrix@\textbackslash bordermatrix}:
-
-\begin{LTXexample}
-$\begin{matrix}
-  A & B & C \\
-  d & e & f \\
-  1 & 2 & 3 \\
-\end{matrix}$
-\end{LTXexample}
-\vspace{-10pt}
-\begin{LTXexample}
-$\bordermatrix{%
-   & 0 & 1 & 2 \cr
- 0 & A & B & C \cr
- 1 & d & e & f \cr
- 2 & 1 & 2 & 3 \cr
-}$
-\end{LTXexample}
-
-\iffalse   % smallmatrix belongs to amsmath
-\begin{minipage}{0.4\textwidth}
-\begin{center}
-$
-\begin{smallmatrix}%
- A & B & C \\
- d & e & f \\
- 1 & 2 & 3
-\end{smallmatrix}
-$
-\end{center}
-\end{minipage}\hfill
-\begin{minipage}{0.4\textwidth}
-\begin{lstlisting}
-\begin{smallmatrix}%
- A & B & C \\
- d & e & f \\
- 1 & 2 & 3
-\end{smallmatrix}
-\end{lstlisting}
-\end{minipage}
-\fi
-
-The first two macros are listed here for some historical reason, because the 
-\UIndex{array} or especially the
-\AmSmath package offers the same or better macros/environments. Nevertheless it is
-possible to redefine the \CIndex{bordermatrix} macro to get other parentheses and a star
-version which takes the left top part as matrix:
-
-\makeatletter
-\newif\if@borderstar
-\def\bordermatrix{\@ifnextchar*{%
-	\@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}%
-}
-\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}}
-\def\@bordermatrix@ii[#1]#2{%
-\begingroup
-	\m@th\@tempdima8.75\p@\setbox\z@\vbox{%
-		\def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}%
-		\ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace %
-			\hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut %
-			\hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit %
-			\strut\cr}}%
-	\setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}%
-	\setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}%
-	\setbox\tw@\hbox{%
-		$\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1%
-			\if@borderstar\kern2pt\else\kern -\wd\@ne\fi%
-		\global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}%
-		\vcenter{\if@borderstar\else\kern -\ht\@ne\fi%
-			\unvbox\z@\kern-\if@borderstar2\fi\baselineskip}%
-		\if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $%
-	}\null \;\vbox{\kern\ht\@ne\box\tw@}%
-\endgroup
-}
-\makeatother
-
-\begin{LTXexample}
-$\bordermatrix{%
-  &  1 &  2 \cr
-1 & x1 & x2 \cr
-2 & x3 & x4 \cr
-3 & x5 & x6
-}$
-\end{LTXexample}
-\vspace{-10pt}
-\begin{LTXexample}
-$\bordermatrix[{[]}]{%
-  &  1 &  2 \cr
-1 & x1 & x2 \cr
-2 & x3 & x4 \cr
-3 & x5 & x6
-}$
-\end{LTXexample}
-\vspace{-10pt}
-\begin{LTXexample}
-$\bordermatrix[\{\}]{%
-  &  1 &  2 \cr
-1 & x1 & x2 \cr
-2 & x3 & x4 \cr
-3 & x5 & x6
-}$
-\end{LTXexample}
-\vspace{-10pt}
-\begin{LTXexample}
-$\bordermatrix*{%
- x1 & x2 & 1 \cr
- x3 & x4 & 2 \cr
- x5 & x6 & 3 \cr
-  1 &  2
-}$
-\end{LTXexample}
-\vspace{-10pt}
-\begin{LTXexample}
-$\bordermatrix*[{[]}]{%
- x1 & x2 & 1 \cr
- x3 & x4 & 2 \cr
- x5 & x6 & 3 \cr
-  1 &  2
-}$
-\end{LTXexample}
-\vspace{-10pt}
-\begin{LTXexample}
-$\bordermatrix*[\{\}]{%
- x1 & x2 & 1 \cr
- x3 & x4 & 2 \cr
- x5 & x6 & 3 \cr
-  1 &  2
-}$
-\end{LTXexample}
-
-
-There is now an optional argument for the parenthesis with \verb|()| as the 
-default one. To get such a behaviour, write into the preamble:
-
-\begin{lstlisting}[xleftmargin=-0.75cm,xrightmargin=-0.75cm]
-\makeatletter
-\newif\if@borderstar
-\def\bordermatrix{\@ifnextchar*{%
-	\@borderstartrue\@bordermatrix@i}{\@borderstarfalse\@bordermatrix@i*}%
-}
-\def\@bordermatrix@i*{\@ifnextchar[{\@bordermatrix@ii}{\@bordermatrix@ii[()]}}
-\def\@bordermatrix@ii[#1]#2{%
-\begingroup
-  \m@th\@tempdima8.75\p@\setbox\z@\vbox{%
-    \def\cr{\crcr\noalign{\kern 2\p@\global\let\cr\endline }}%
-    \ialign {$##$\hfil\kern 2\p@\kern\@tempdima & \thinspace %
-    \hfil $##$\hfil && \quad\hfil $##$\hfil\crcr\omit\strut %
-    \hfil\crcr\noalign{\kern -\baselineskip}#2\crcr\omit %
-    \strut\cr}}%
-  \setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}%
-  \setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}%
-  \setbox\tw@\hbox{%
-    $\kern\wd\@ne\kern -\@tempdima\left\@firstoftwo#1%
-      \if@borderstar\kern2pt\else\kern -\wd\@ne\fi%
-    \global\setbox\@ne\vbox{\box\@ne\if@borderstar\else\kern 2\p@\fi}%
-    \vcenter{\if@borderstar\else\kern -\ht\@ne\fi%
-      \unvbox\z@\kern-\if@borderstar2\fi\baselineskip}%
-      \if@borderstar\kern-2\@tempdima\kern2\p@\else\,\fi\right\@secondoftwo#1 $%
-  }\null \;\vbox{\kern\ht\@ne\box\tw@}%
-\endgroup
-}
-\makeatother
-\end{lstlisting}
-
-The \UIndex{matrix} macro cannot be used together with the \AmSmath package, it redefines
-this environment (see section~\vref{sec:ams-matrix}). 
-
-\section{Super/Subscript and limits}\label{sec:limits}
-Writing $a_{min}$ and $a_{max}$ gives the same depth for the \Index{subscript}, but
-writing them in \Index{upright mode} with \verb+\mbox+ gives a different 
-depth: $a_{\mbox{min}}$ and $a_{\mbox{max}}$.
-The problem is the different height, which can be modified in several ways
-\begin{itemize}
-\item  \verb+$a_{\mbox{\vphantom{i}max}}$+: $a_{\mbox{min}}$ and $a_{\mbox{\vphantom{i}max}}$;
-\item \verb+$a_{\mathrm{max}}$+: $a_{\mathrm{min}}$ and $a_{\mathrm{max}}$;
-\item \verb+$a_{\max}$+: $a_{\min}$ and $a_{\max}$. Both are predefined 
-    operators (see section~\vref{sec:ltxOperators}).
-\end{itemize}
-%$
-
-\subsection{Multiple limits}\label{sub:Multiple-Limits}
-
-\mPar{\CMD{atop}}%
-For general information about limits\index{Limits} read section
-\vref{sub:Limits-Inline}. With the \TeX\ command \CIndex{atop} 
-multiple limits for a \CIndex{sum} or \CIndex{prod} are possible. The syntax is:
-
-\begin{LTXexample}[width=0.4\linewidth]
-\[ {above \atop below} \]
-\end{LTXexample}
-
-\noindent which is nearly the same as a fraction without a rule. This can
-be enhanced to \verb|a\atop b\atop c| and so on. For equation \ref{eq:atop} do the following steps:
-
-\begin{LTXexample}[width=0.4\linewidth]
-\begin{equation}\label{eq:atop}
-\sum_{{1\le j\le p\atop {%
-  {1\le j\le q\atop 1\le k\le r}}}%
-}a_{ij}b_{jk}c_{ki}
-\end{equation}
-\end{LTXexample}
-
-
-\bigskip
-\mPar{\CMD{shortstack}}%
-which is not the best solution because the space between the lines
-is too big. 
-The \AmSmath package provides several commands for 
-limits (section~\vref{sec:limit-AMS}) and the \CIndex{underset} and \CIndex{overset} 
-commands (see section~\vref{sec:misc-AMS}).
-
-\subsection{Problems}
-
-\begin{equation}\label{eq:disp-limits}
-\fboxsep=0pt\fboxrule=0.1pt
-\boxed{\sum_{
-	{{1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}%
-	}}%
-}\boxed{a_{ij}b_{jk}c_{ki}}
-\end{equation}
-
-The equation \ref{eq:disp-limits} shows that the horizontal alignment
-is not optimal, because the math expression on the right follows at the
-end of the limits which are a unit together with the sum symbol. There
-is an elegant solution with \AmSmath, described in subsection
-\vref{subsec:ams-limits}. If you do not want to use \AmSmath,
-then use \CIndex{makebox}. But there is a problem when the general fontsize
-is increased, \CMD{makebox} knows nothing about the actual math font
-size. Equation \ref{eq:disp-limits2} shows the effect and equation
-\ref{eq:disp-limits3} the view without the boxes.
-
-\vspace{\abovedisplayskip}
-\begin{subequations}
-\begin{minipage}{0.45\textwidth}
-\begin{equation}\label{eq:disp-limits2}
-\fboxsep=0pt\fboxrule=0.1pt
-\boxed{\sum_{%
-	\makebox[0pt]{$%
-		{{\scriptscriptstyle 1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}}%
-	$}%
-	}%
-}\boxed{a_{ij}b_{jk}c_{ki}}
-\end{equation}
-\end{minipage}\hfill
-\begin{minipage}{0.45\textwidth}
-\begin{equation}\label{eq:disp-limits3}
-\sum_{%
-	\makebox[0pt]{$%
-		{{\scriptscriptstyle 1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}}%
-	$}}a_{ij}b_{jk}c_{ki}
-\end{equation}
-\end{minipage}
-\end{subequations}
-
-\medskip
-\begin{lstlisting}
-\begin{equation}
-\sum_{\makebox[0pt]{$%
-	{{\scriptscriptstyle 1\le j\le p\atop {%
-	{1\le j\le q\atop 1\le k\le r}}}}%
-  $}}a_{ij}b_{jk}c_{ki}
-\end{equation}
-\end{lstlisting}
-
-
-
-\section{Roots}\label{sec:Roots}
-
-The square root\index{Root} \CIndex{sqrt} is the default 
-for \LaTeX{} and the $n$-th root can be inserted with the optional 
-parameter \CMD{sqrt[n]\{\ldots\}}.
-\mPar{\CMD{sqrt}}.
-
-\begin{center}
-\begin{tabular}{cc}
-  \verb|\sqrt{x}|    & $\sqrt{x}$\\
-  \verb|\sqrt[3]{x}| & $\sqrt[3]{x}$
-\end{tabular}
-\end{center}
-
-There is a different typesetting in roots. Equation~\vref{eq:root1}
-has different heights for the roots, whereas equation~\vref{eq:root2}
-has the same one. This is possible with the %
-\mPar{\CMD{vphantom}}%
-\CIndex{vphantom} command,
-which reserves the vertical space (without a horizontal one) of the
-parameter height.
-
-\begin{LTXexample}[width=0.35\linewidth,wide]
-\begin{equation}
-  \sqrt{a}\,%
-  \sqrt{T}\,%
-  \sqrt{2\alpha k_{B_1}T^i}\label{eq:root1}
-\end{equation}
-\end{LTXexample}
-
-
-\vspace{-10pt}
-\begin{LTXexample}[width=0.35\linewidth,wide]
-\begin{equation}\label{eq:root2}
-  \sqrt{a\vphantom{k_{B_1}T^i}}\,%
-  \sqrt{T\vphantom{k_{B_1}T^i}}\,%
-  \sqrt{2\alpha k_{B_1}T^i}
-\end{equation}
-\end{LTXexample}
-
-
-The typesetting looks much  better, especially when the formula
-has different roots in a row, like equation~\vref{eq:root1}. Using
-\AmSmath with the \CIndex{smash} command%
-\footnote{The \CMD{smash} command exists also in \LaTeX{}
-but without an optional argument, which makes the use for roots possible.} 
-gives some more possibilities for the typesetting of roots (see section~\vref{sec:Roots-ams}).
-
-
-\section[Brackets, braces \ldots]{Brackets, braces and parentheses}\label{sec:Brackets,-Braces-and}
-
-This is one of the major problems inside the math mode, because there is often a need for different 
-brackets, braces and parentheses in different size. At first we had to admit, that
-there is a difference between the characters ``\verb|()[]/\|
-$\lbrace\rbrace$
-|
-$\Vert$
-$\lfloor\rfloor$
-$\lceil\rceil$
-$\langle\rangle$
-$\uparrow\Uparrow$
-$\downarrow\Downarrow$
-$\updownarrow\Updownarrow${}''
-and their use as an argument %
-\mPar{\CMD{leftX}\\\CMD{rightX}} of the \CIndex{left} and \CIndex{right}
-command, where \LaTeX{} stretches the size in a way that everything between
-the pair of left and right parentheses is smaller than the parentheses themselves. In some cases%
-\footnote{See section \vref{cap:Use-of-the-vphantom} for example.} 
-it may be useful to choose a fixed height, which is possible with
-the \CMD{big}-series. Instead of writing \CMD{leftX}
-or \CMD{rightX} one of the following commands can
-be chosen:
-
-\medskip
-\mPar{\CMD{bigX}\\\CMD{BigX}\\\CMD{biggX}\\\CMD{BiggX}}
-\index{big@\textbackslash big}\index{Big@\textbackslash Big}%
-\index{bigg@\textbackslash bigg}\index{Bigg@\textbackslash Bigg}
-\begin{tabular}{rl}
-default & ()[]/\textbackslash$\lbrace\rbrace$|$\Vert$ $\lfloor\rfloor$
-$\lceil\rceil$ $\langle\rangle$ $\uparrow\Uparrow$ $\downarrow\Downarrow$%
-$\updownarrow\Updownarrow$\\[2pt]
-\CMD{bigX} & $\big(\big)$ $\big[\big]$
-$\bigl/\big\backslash\big\{\big\}$
-$\big|$ $\big\Vert$ $\big\lfloor\big\rfloor$ $\big\lceil\big\rceil$
-$\big\langle\big\rangle$ $\big\uparrow\big\Uparrow$ $\big\downarrow\big\Downarrow$
-$\big\updownarrow\big\Updownarrow$\\[2pt]
-\CMD{BigX} & $\Big(\Big)$
-$\Big[\Big]$ $\Bigl/\Big\backslash\Big\{\Big\}$
-$\Big|$ $\Big\Vert$ $\Big\lfloor\Big\rfloor$
-$\Big\lceil\Big\rceil$ $\Big\langle\Big\rangle$
-$\Big\uparrow\Big\Uparrow$ $\Big\downarrow\Big\Downarrow$
-$\Big\updownarrow\Big\Updownarrow$\\[4pt]
-\CMD{biggX} & $\bigg(\bigg)$
-$\bigg[\bigg]$ $\biggl/\bigg\backslash\bigg\{\bigg\}$%
-$\bigg|$ $\bigg\Vert$ $\bigg\lfloor\bigg\rfloor$ $\bigg\lceil\bigg\rceil$
-$\bigg\langle\bigg\rangle$ $\bigg\uparrow\bigg\Uparrow$
-$\bigg\downarrow\bigg\Downarrow$ $\bigg\updownarrow\bigg\Updownarrow$\\[8pt]
-\CMD{BiggX} & $\Bigg(\Bigg)$
-$\Bigg[\Bigg]$ $\Biggl/\Bigg\backslash\Bigg\{\Bigg\}$
-$\Bigg|$ $\Bigg\Vert$ $\Bigg\lfloor\Bigg\rfloor$
-$\Bigg\lceil\Bigg\rceil$ $\Bigg\langle\Bigg\rangle$
-$\Bigg\uparrow\Bigg\Uparrow$ $\Bigg\downarrow\Bigg\Downarrow$%
-$\Bigg\updownarrow\Bigg\Updownarrow$
-\end{tabular}
-
-\medskip{}
-Only a few commands can be written in a short form like \CMD{big(}.
-The ``X{}'' has to be replaced with one of the following characters
-or commands from table~\vref{tab:big}, which shows the parentheses
-character, its code for the use with one of the ``big{}'' commands
-and an example with the code for that.
-
-\mPar{\CMD{biglX}\\\CMD{bigrX}}%
-For all commands there exists a left/right version  \CIndex{bigl}, 
-\CIndex{bigr}, \CIndex{Bigl} and so on, which only makes sense when writing things like:
-
-\begin{LTXexample}[width=0.3\linewidth,wide]
-\begin{align} 
-  \biggl)\times \frac{a}{b} \times\biggr( 
-\end{align}
-\begin{align} 
-  \bigg)\times \frac{a}{b} \times\bigg( 
-\end{align}
-\end{LTXexample}
-
-\LaTeX{} takes the \verb|\biggl)| as a \Index{mathopen symbol}, which has by default
-another horizontal spacing.
-
-In addition to the above  commands there exist some more:
-\CIndex{bigm}, \CIndex{Bigm}, \CIndex{biggm} and \CIndex{Biggm},
-which work as the standard ones (without the addtional ``m{}'')
-but add some more horizontal space%
-\mPar{\CMD{bigmX}\\\CMD{bigmX}} %
-between the delimiter and the formula before and after (see 
-table~\vref{cap:Difference-between-the-bigg}).
-
-
-
-%$3\bigg|a^2-b^2-c^2\bigg|+2$
-%$3\biggm|a^2-b^2-c^2\biggm|+2$
-
-\begin{table}[!htb]
-\caption{Difference between the default
-\CMD{bigg} and the \CMD{biggm} command}\label{cap:Difference-between-the-bigg}
-\begin{LTXexample}
-$\bigg(\displaystyle\frac{1}{3}\bigg|\frac{3}{4}\bigg)$
-\end{LTXexample}
-\vspace{-15pt}
-\begin{LTXexample}
-$\bigg(\displaystyle\frac{1}{3}\biggm|\frac{3}{4}\bigg)$
-\end{LTXexample}
-\end{table}
-
-
-\newcommand{\xstrut}{\rule{0pt}{0.55cm}}
-{\setlength{\hangindent}{-\marginparwidth}
-\def\arraystretch{1.5}
-\begin{longtable}{@{}l>{\raggedright}p{2.4cm}l>{\raggedright}p{5.7cm}@{}}
-\caption{Use of the different parentheses for the ``big{}'' commands} \label{tab:big}\tabularnewline
-Char & Code & Example & Code\tabularnewline\hline
-\endfirsthead
-Char & Code & Example & Code\tabularnewline
-\hline
-\endhead
-\xstrut$(\ )$ & ( ) & %
-	$3\Big(a^{2}+b^{c^{2}}\Big)$ & %
-	\texttt{3\CMD{Big}( a\^{}2+b\^{}\{c\^{}2\}\CMD{Big})}\tabularnewline
-%
-\xstrut$[\ ]$ & {[} {]}&
-$3\Big[a^{2}+b^{c^{2}}\Big]$&
-\texttt{3\CMD{Big}{[} a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}{]}}\tabularnewline
-%
-\xstrut$/\ \backslash$ & \texttt{/}\CMD{backslash} & $3\Big/a^{2}+b^{c^{2}}\Big\backslash$ &
-\texttt{3\CMD{Big}/ a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{backslash}}\tabularnewline
-%
-\xstrut$\{\ \}$ & \CMD{\{}\CMD{\}}\\
- & $3\Big\{ a^{2}+b^{c^{2}}\Big\}$ &
-\texttt{3\CMD{Big}\CMD{\{} a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{\}}}\tabularnewline
-%
-\xstrut$\vert\ \Vert$ & | \CMD{Vert} & $3\Big|a^{2}+b^{c^{2}}\Big\Vert$ & \texttt{3\CMD{Big}|a\^{}2+b\^{}\{c\^{}2\}\CMD{Big}\CMD{Vert}}\tabularnewline
-%
-\xstrut$\lfloor\ \rfloor$ & \CMD{lfloor} \CMD{rfloor} & %
-	$3\Big\lfloor a^{2}+b^{c^{2}}\Big\rfloor$ & %
-	\texttt{3\CMD{Big}\CMD{lfloor} a\^{}2+b\^{}\{c\^{}2\}
-		\CMD{Big}\CMD{rfloor}}\tabularnewline
-%
-\xstrut$\lceil\ \rceil$ & \CMD{lceil}\CMD{rceil} &
-	$3\Big\lceil a^{2}+b^{c^{2}}\Big\rceil$ &
-	 \texttt{3\CMD{Big}\CMD{lceil} a\^{}2+b\^{}\{c\^{}2\} \CMD{Big}%
-	 	\CMD{rceil}}\tabularnewline
-%
-\xstrut$\langle\ \rangle$ & \CMD{langle}\CMD{rangle} &
-	$3\Big\langle a^{2}+b^{c^{2}}\Big\rangle$ &
-	\texttt{3\CMD{Big}\CMD{langle} a\^{}2+b\^{}\{c\^{}2\}%
-		\CMD{Big}\CMD{rangle}}\tabularnewline
-%
-\xstrut$\uparrow\ \Uparrow$ &
-	\CMD{uparrow} \CMD{Uparrow} &
-	$3\Big\uparrow a^{2}+b^{c^{2}}\Big\Uparrow$ &
-	\texttt{3\CMD{Big}\CMD{uparrow} a\^{}2+b\^{}\{c\^{}2\}%
-		\CMD{Big}\CMD{Uparrow}}\tabularnewline
-%
-\xstrut$\downarrow\ \Downarrow$ & \CMD{downarrow} \CMD{Downarrow} &
-	$3\Big\downarrow a^{2}+b^{c^{2}}\Big\Downarrow$ &
-	\texttt{3\CMD{Big}\CMD{downarrow} a\^{}2+b\^{}\{c\^{}2\}
-		\CMD{Big}\CMD{Downarrow}}\tabularnewline
-%
-\xstrut$\updownarrow\ \Updownarrow$ & \CMD{updownarrow} \CMD{Updownarrow} &
-	$3\Big\updownarrow a^{2}+b^{c^{2}}\Big\Updownarrow$ &
-	\texttt{3\CMD{Big}\CMD{updownarrow} a\^{}2+b\^{}\{c\^{}2\}
-		\CMD{Big}\CMD{Updownarrow}}\tabularnewline
-\end{longtable}}
-
-
-
-\clearpage
-
-
-\subsection{Examples}
-\subsubsection{Braces over several lines}\label{cap:Use-of-the-vphantom}
-The following equation in the single line mode looks like
-%
-\begin{equation}
-\frac{1}{2}\Delta(f_{ij}f^{ij})=2\left(\sum_{i<j}\chi_{ij}
-    (\sigma_{i}-\sigma_{j})^{2}+f^{ij}\nabla_{j}\nabla_{i}(\Delta f)
-    +\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2\nabla_{i}R_{jk}
-    -\nabla_{k}R_{ij}]\right)\label{eq:braces}
-\end{equation}
-%
-and is too long for the text width and the equation number has to be placed
-under the equation.\footnote{In standard \LaTeX{} the equation and the number are
-printed one over the other for too long
-formulas. Only \AmSmath puts it one line over (left numbers) or under (right
-numbers) the formula.} With the array environment the formula can be split in two smaller
-pieces:
-
-{\arraycolsep=2pt
-\begin{equation}
-\begin{array}{rcl}
-	\frac{1}{2}\Delta(f_{ij}f^{ij}) & = & 2\left({\displaystyle
-	\sum_{i<j}}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}+f^{ij}%
-	\nabla_{j}\nabla_{i}(\Delta f)+\right.\\
-&	& \left.+\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2
-	\nabla_{i}R_{jk}-\nabla_{k}R_{ij}]\right)
-\end{array}
-\end{equation}
-}
-
-
-It is obvious that there is a problem with the right closing parentheses.
-Because of the two pairs ``\verb|\left( ... \right.|''
-and ``\verb|\left. ... \right)|''
-they have a different size because every pair does it in its own
-way. Using the \Index{Bigg} command changes this into a better
-typesetting:
-
-{\arraycolsep=2pt
-\begin{equation}
-\begin{array}{rcl}
-	\frac{1}{2}\Delta(f_{ij}f^{ij}) & = & 2\Bigg({\displaystyle
-	\sum_{i<j}}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}+f^{ij}%
-	\nabla_{j}\nabla_{i}(\Delta f)+\\
-&	& +\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2
-	\nabla_{i}R_{jk}-\nabla_{k}R_{ij}]\Bigg)
-\end{array}
-\end{equation}
-}
-\begin{lstlisting}
-{\arraycolsep=2pt
-\begin{equation}
-\begin{array}{rcl}
-	\frac{1}{2}\Delta(f_{ij}f^{ij}) & = & 2\Bigg({\displaystyle
-	\sum_{i<j}}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}+f^{ij}%
-	\nabla_{j}\nabla_{i}(\Delta f)+\\
-&	& +\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}[2
-	\nabla_{i}R_{jk}-\nabla_{k}R_{ij}]\Bigg)
-\end{array}
-\end{equation}
-}
-\end{lstlisting}
-
-Section~\vref{sec:Specials-for-multline} shows another solution
-for getting the right size for parentheses when breaking the equation
-in smaller pieces.
-
-\begin{align*}
-  B(r,\phi,\lambda) = & \,\dfrac{\mu}{r} 
-    \Bigg[\sum_{n=2}^{\infty} \Bigg( \left( \dfrac{R_e}{r} \right)^n J_nP_n(s\phi) \\
-  & +\sum_{m=1}^n \left( \dfrac{R_e}{r} \right) ^n
-   (C_{nm}\cos m\lambda+S_{nm}\sin m\lambda)P_{nm}(s\phi) \Bigg)\Bigg]
-\end{align*}
-
-\begin{lstlisting}
-\begin{align*}
-  B(r,\phi,\lambda) = & \,\dfrac{\mu}{r} 
-    \Bigg[\sum_{n=2}^{\infty} \Bigg( \left( \dfrac{R_e}{r} \right)^n J_nP_n(s\phi) \\
-  & +\sum_{m=1}^n \left( \dfrac{R_e}{r} \right) ^n
-   (C_{nm}\cos m\lambda+S_{nm}\sin m\lambda)P_{nm}(s\phi) \Bigg)\Bigg]
-\end{align*}
-\end{lstlisting}
-
-
-\subsubsection{Middle bar}
-See section~\vref{sec:braket} for examples and the use of package \PIndex{braket}.
-
-\subsection{New delimiters}\label{subsec:delim}
-The default delimiters\index{Delimiter} are defined in the file \verb|fontmath.ltx|\index{fontmath.ltx}
-which is stored in general
-in \path{[TEXMF]/tex/latex/base/fontmath.ltx}. If we need for example a thicker vertical symbol
-than the existing \CIndex{vert} symbol we can define in the preamble:
-
-\begin{lstlisting}
-\DeclareMathDelimiter{\Norm}
-   {\mathord}{largesymbols}{"3E}{largesymbols}{"3E}
-\end{lstlisting}
-
-The character number $3E_{16}$ (decimal $62$) from the \FIndex{cmex10} font is the small
-thick vertical rule. Now the new delimiter \verb|\Norm| can be used in the usual way:
-
-\begin{LTXexample}[width=0.3\linewidth,wide]
-$\left\Norm *BLA* \right\Norm$
-
-$\left\Norm \dfrac{*BLA*}{*BLUB*} \right\Norm$
-\end{LTXexample}
-
-
-
-\subsection{Problems with parentheses}\label{subsec:Problems-with-parenthesis}
-\mPar{\CMD{delimitershortfall}\\\CMD{delimiterfactor}}%
-It is obvious that the following
-equation has not the right size of the parenthesis in the
-second integral, the inner one should be a bit smaller than the outer one.
-%
-\begin{LTXexample}[width=0.425\linewidth,wide]
-\[
-\int_\gamma F'(z) dz =\int_\alpha^\beta
-F'\left(\gamma (t)\right)\cdot\gamma '(t)dt
-\]
-\end{LTXexample}
-
-The problem is that \TeX{} controlls the height of the parenthesis with
-\LIndex{delimitershortfall} and \CIndex{delimiterfactor}, with the default values
-\begin{verbatim}
-\delimitershortfall=5pt
-\delimiterfactor=901
-\end{verbatim}
-
-\verb|\delimiterfactor/1000| is the relative size of the parenthesis for a given formula
-environment. They could be of \verb|\delimitershortfall| too short. These values are valid
-at the end of the formula, the best way is to set them straight before the math environment
-or globally for all in the preamble.
-
-
-\begin{LTXexample}[width=0.425\linewidth,wide]
-{\delimitershortfall=-1pt
-\[
-\int_\gamma F'(z) dz =\int_\alpha^\beta
-F'\left(\gamma (t)\right)\cdot\gamma '(t)dt
-\]}
-\end{LTXexample}
-
-\section{Text in math mode}\label{sec:Text}
-
-Standard \index{Text}text in math mode should be written in upright shape and not
-in the italic\index{Italic} one. This shape is reserved for the variable
-names: $\boxed{{I\  am\ \textrm{text}\  inside\  math.}}$ (see also 
-Table~\vref{cap:Spaces-in-math mode}). There are different ways to write text inside math.
-
-\mPar{\CMD{textstyle}\\\CMD{mbox}}
-
-\begin{itemize}
-\mPar{\CMD{mathrm}}
-\item \CMD{mathrm}. It is like math mode (no spaces), but in upright mode
-\item \CMD{textrm}. Upright mode with printed spaces (real textmode)
-\item \CMD{mbox}. The font size is still the one from \CIndex{textstyle} 
-    (see section~\vref{sec:Styles}), so that you have to place additional
-commands when you use \CIndex{mbox} in a super- or subscript for limits.
-\end{itemize}
-
-Inserting long text is possible with a \CIndex{parbox}, which can be aligned as usual to the top,
-bottom or center, \eg \index{Text!\textbackslash parbox}
-\begin{eqnarray}
-  a+b+c+d+ef & = & g+h+i+j+k %
-  \qquad\textrm{\parbox[t]{.25\linewidth}{%
-     this is a very long description of a formula}%
-  }
-\end{eqnarray}
-
-\begin{lstlisting}
-\begin{eqnarray}
-  a+b+c+d+ef & = & g+h+i+j+k %
-  \qquad\textrm{\parbox[t]{.25\linewidth}{%
-     this is a very long description of a formula}%
-  }
-\end{eqnarray}
-\end{lstlisting}
-
-Additional commands for text inside math are provided by \AmSmath (see
-section \vref{sec:Text-in-math mode}).
-
-%$
-\section{Font commands}
-
-\subsection{Old-style font commands}
-
-Should never be used, but are still present and supported by \LaTeX{}. The
-default syntax for the old commands is
-
-\begin{lstlisting}
-{\XX test}
-\end{lstlisting}
-Table~\vref{cap:Old-Fontstyle-commands} shows what has to be replaced for the \verb+XX+.
-The major difference to the new style is that these
-\CMD{XX} are toggling the actual math mode into
-the ``XX{}'' one, whereas the new commands start which, at its end,
-switches back to the previous mode.
-
-\begin{table}[!htb]
-\centering
-\begin{tabular}{rc|rc|rc|cc|cc}
-\CMD{bf}\index{bf@\textbackslash bf} & ${\bf {\bf test}}$ &
-\CMD{cal}\index{cal@\textbackslash cal} & ${\cal TEST}$ &
-\CMD{it}\index{it@\textbackslash it} &
-${\it test}$ &
-\CMD{rm}\index{rm@\textbackslash rm} &
-${\rm test}$ &
-\CMD{tt}\index{tt@\textbackslash tt} &
-${\tt test}$\tabularnewline
-\end{tabular}
-\caption{Old font style commands}\label{cap:Old-Fontstyle-commands}
-\end{table}
-
-\subsection{New-style font commands}\label{sub:New-Style-Fontcommands}
-
-%
-\mPar{\CMD{mathrm}\\
-\CMD{mathfrak}\\
-\CMD{mathcal}\\
-\CMD{mathsf}\\
-\CMD{mathbb}\\
-\CMD{mathtt}\\
-\CMD{mathit}\\
-\CMD{mathbf}}
-
-The default syntax is
-
-\begin{lstlisting}
-\mathXX{test}
-\end{lstlisting}
-Table~\ref{cap:Fonts-in-math-mode} shows what has to be
-replaced for the XX. See section~\vref{sec:euscript.sty} for additional packages.
-
-\begin{table}[htb]
-\caption{Fonts in math mode}\label{cap:Fonts-in-math-mode}
-\centering
-\includegraphics{styles}
-\iffalse
-\begin{table}[!htb]
-\begin{minipage}{\linewidth}
-\centering
-\begin{tabularx}{.9\linewidth}{l|X}
-\textbf{Command} & \textbf{Test}\tabularnewline\hline
-default & $ABCDEFGHIJKLMNOPQRSTUVWXYZ$
-
-$abcdefghijklmnopqrstuvwxyz$\tabularnewline
-\CMD{mathfrak} &
-$\mathfrak{{ABCDEFGHIJKLMNOPQRSTUVWXYZ}}$
-$\mathfrak{{abcdefghijklmnopqrstuvwxyz}}$\tabularnewline
-\CMD{mathcal}%
-\footnote{Not available for lower letters. For mathcal exists a
-  non free font for lower letters (http://www.pctex.com)}\addtocounter{mpfootnote}{-1} &
-$\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\tabularnewline
-\CMD{mathsf}&
-$\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
-$\mathsf{abcdefghijklmnopqrstuvwxyz}$\tabularnewline
-
-\CMD{mathbb}${}^a$ & $\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\tabularnewline
-\CMD{mathtt} & $\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
-
-$\mathtt{abcdefghijklmnopqrstuvwxyz}$\tabularnewline
-\CMD{mathit} & $\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
-
-$\mathit{abcdefghijklmnopqrstuvwxyz}$\tabularnewline
-\CMD{mathrm} & $\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
-
-$\mathrm{abcdefghijklmnopqrstuvwxyz}$\tabularnewline
-\CMD{mathbf} & $\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
-
-$\mathbf{abcdefghijklmnopqrstuvwxyz}$\tabularnewline
-
-\CMD{mathds}${}^b$ & $\mathds{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\tabularnewline
-\end{tabularx}
-\end{minipage}
-\fi
-\end{table}
-
-\index{mathfrak@\textbackslash mathfrak}\index{mathsf@\textbackslash mathsf}
-\index{mathbb@\textbackslash mathbb}\index{mathcal@\textbackslash mathcal}
-\index{mathbf@\textbackslash mathbf}\index{mathit@\textbackslash mathit}
-\index{mathrm@\textbackslash mathrm}\index{mathtt@\textbackslash mathtt}
-\index{mathds@\textbackslash mathds}\index{double stroke}
-\index{dsfont@\texttt{dsfont}}\index{Set symbol}
-%\end{comment}
-
-\section{Space}
-\subsection{Math typesetting}\label{subsec:mathskip}
-
-\mPar{\CMD{thinmuskip}\\
-\CMD{medmuskip}\\
-\CMD{thickmuskip}}
-\LaTeX\ defines the three math lengths\footnote{For more
-information see: \url{http://www.tug.org/utilities/plain/cseq.html}} with the following
-values\footnote{see \texttt{\small fontmath.ltx}}:
-
-\begin{lstlisting}
-\thinmuskip=3mu
-\medmuskip=4mu plus 2mu minus 4mu
-\thickmuskip=5mu plus 5mu
-\end{lstlisting}
-
-\noindent where \verb|mu| is the abbreviation for \Index{math unit}.
-\[
-1 \mathrm{mu}= \dfrac{1}{18} \mathrm{em}
-\]
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{ll}
-\fboxsep=0pt
-\text{default} & $\boxed{f(x)=x^2+3x_0\cdot\sin x}$\\
-\CMD{thinmuskip=0mu} & {\thinmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\
-\CMD{medmuskip=0mu} & {\medmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\
-\CMD{thickmuskip=0mu} & {\thickmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\
-all set to zero & {\thickmuskip=0mu\thinmuskip=0mu\medmuskip=0mu $\boxed{f(x)=x^2+3x_0\cdot\sin x}$}\\
-\end{tabular}
-\caption{The meaning of the math spaces}\label{tab:mathSpaces}
-\end{table}
-
-These lengths can have all glue and are
-used for the horizontal spacing in math expressions where \TeX{} puts spaces between symbols
-and operators. The meaning of these different
-horizontal skips is shown in table~\ref{tab:mathSpaces}. For a better typesetting \LaTeX{}
-inserts different spaces between the symbols.
-
-\begin{description}
-\item[\CIndex{thinmuskip}] space between ordinary and operator atoms
-\item[\CIndex{medmuskip}] space between ordinary and binary atoms in display and text styles
-\item[\CIndex{thickmuskip}] space between ordinary and relation atoms in display and text styles
-\end{description}
-
-\subsection{Additional horizontal spacing}
-\mPar{\CMD{thinspace}\\
-\CMD{medspace}\\
-\CMD{thickspace}\\
-\CMD{negthinspace}\\
-\CMD{negmedspace}\\
-\CMD{negthickspace}}
-
-\begin{table}[!htb]
-\def\arraystretch{1.2}
-\centering
-\begin{tabular}{ll|ll}
-\multicolumn{2}{l|}{Positive Space}&\multicolumn{2}{l}{Negative Space}\\\hline
-\verb|$ab$|   & $\boxed{a}\boxed{b}$\\
-\verb|$a b$|  & $\boxed{a} \boxed{b}$\\
-\verb|$a\ b$| & $\boxed{a}\ \boxed{b}$\\
-\verb|$a\mbox{\textvisiblespace}b$| & $\boxed{a}\mbox{\textvisiblespace}\boxed{b}$\\
-\verb|$a\,b$|\index{,@\textbackslash ,} (\verb|$a\thinspace b$|)\index{thinspace@\textbackslash thinspace} & $\boxed{a}\,\boxed{b}$&
-\verb|$a\! b$|\index{negthinspace@\textbackslash negthinspace} & $\boxed{a}\!\boxed{b}$\\
-\verb|$a\: b$|\index{:@\textbackslash :} (\verb|$a\medspace b$|)\index{medspace@\textbackslash medspace}&
-$\boxed{a}\:\boxed{b}$&
-\verb|$a\negmedspace b$|\index{negmedspace@\textbackslash negmedspace} & $\boxed{a}\negmedspace\boxed{b}$\\
-\verb|$a\; b$|\index{;@\textbackslash ;} (\verb|$a\thickspace b$|\index{thickspace@\textbackslash thickspace}&
-$\boxed{a}\;\boxed{b}$&
-\verb|$a\negthickspace b$|\index{negthickspace@\textbackslash negthickspace}&
-$\boxed{a}\negthickspace\boxed{b}$\\
-\verb|$a\quad b$|\index{quad@\textbackslash quad} & $\boxed{a}\quad\boxed{b}$\\
-\verb|$a\qquad b$|\index{qquad@\textbackslash qquad} & $\boxed{a}\qquad\boxed{b}$\\
-\verb|$a\hspace{0.5cm}b$|\index{hspace@\textbackslash hspace}& $\boxed{a}\hspace{0.5cm}\boxed{b}$&
-\verb|$a\hspace{-0.5cm}b$| & $\boxed{a}\hspace{-0.5cm}\boxed{b}$\\
-\verb|$a\kern0.5cm b$|\index{kern@\textbackslash kern} & $\boxed{a}\kern0.5cm \boxed{b}$ & \verb|$a\kern-0.5cm b$| & $\boxed{a}\kern-0.5cm \boxed{b}$\\
-\verb|$a\hphantom{xx}b$|\index{hphantom@\textbackslash hphantom} & $\boxed{a}\hphantom{xx}\boxed{b}$\\
-\verb|$axxb$| & $\boxed{a}xx\boxed{b}$
-\end{tabular}
-\caption{Spaces in math mode}\label{cap:Spaces-in-math mode}
-\end{table}
-%$
-
-LaTeX defines the following short commands:
-
-\begin{verbatim}
-\def\>{\mskip\medmuskip}
-\def\;{\mskip\thickmuskip}
-\def\!{\mskip-\thinmuskip}
-\end{verbatim}
-In math mode there is often a need for additional tiny spaces between variables,
-\eg $L\dfrac{di}{dt}$ written with a tiny space between $L$ and
-$\dfrac{di}{dt}$ looks nicer: $L\:\dfrac{di}{dt}$. Table~\ref{cap:Spaces-in-math mode}
-shows a list of all commands for horizontal space which can be used
-in math mode. The ``space{}'' is seen ``between{}'' the boxed a
-and b. For all examples a is \verb+\boxed{a}+ and
-b is \verb+\boxed{b}+. The short forms for some
-\mPar{\CMD{hspace}\\
-\CMD{hphantom}\\
-\CMD{kern}} 
-spaces may cause problems with other packages. In this case use the
-long form of the commands.
-
-\subsection{Problems}\label{space:problems}
-Using \CIndex{hphantom} in mathmode depends to on object. \CIndex{hphantom} 
-reserves only the space of
-the exact width without any additional space. In the following example the second line is
-wrong: \verb+& \hphantom{\rightarrow} b\\+. It does not reserve any additional space.
-
-\begin{LTXexample}[width=0.15\linewidth,wide]
-\begin{align*}
-a & \rightarrow b\\
-  & \hphantom{\rightarrow} b\\
-  & \mkern\thickmuskip\hphantom{\rightarrow}\mkern\thickmuskip b\\
-  & \mathrel{\hphantom{\rightarrow}} b
-\end{align*}
-\end{LTXexample}
-
-This only works when the math symbol is a mathrel one, otherwise you have to change the
-horizontal space to \CIndex{medmuskip} or \CIndex{thinmuskip} or to use an empty group after
-the \CIndex{hphantom} command. For more informations
-about the math objects look into \verb+fontmath.ltx+ or \PIndex{amssymb} or use the \CIndex{show}
-macro, which prints out the type of the mathsymbol, \eg \verb+\show\rightarrow+ with the
-output:
-
-\begin{lstlisting}
-> \rightarrow=\mathchar"3221.
-l.20 \show\rightarrow
-\end{lstlisting}
-
-The first digit represents the type:
-
-\begin{tabular}{l@{ : }l}
-0 & ordinary\\
-1 & large operator\\
-2 & binary operation\\ 
-3 & relation\\
-4 & opening\\
-5 & closing\\
-6 & punctuation\\ 
-7 & variable family
-\end{tabular}
-
-
-%\iffalse
-\begingroup
-\thinmuskip=3mu
-\medmuskip=4mu plus 2mu minus 4mu
-\thickmuskip=5mu plus 5mu
-
-\medskip
-Grouping a math symbol can change the behaviour in horizontal spacing. Compare
-$50\mkern\thinmuskip\times\mkern\thinmuskip10^{12}$ and $50{\times}10^{12}$, the first one is typeset with 
-\verb+$50\times10^{12}$+ and the second one with \verb+$50{\times}10^{12}$+.
-\endgroup
-%\fi
-Another possibilty is to use the \PIndex{numprint} package.\footnote{%
-\href{ftp://ftp.dante.de/tex-archive/macros/latex/contrib/numprint/}%
-{CTAN://macros/latex/contrib/numprint/}}
-
-\subsection{Dot versus comma}\label{subsec:dot-comma}
-\mPar{\CMD{mathpunct}\\\CMD{mathord}}%
-In difference to a \Index{decimal point} and a \Index{comma} as a marker of thousands a lot of
-countries prefer it vice versa. To get the same behaviour the meaning of \Index{dot} and
-comma has to be changed:
-
-
-\begin{align}
-1,234,567.89 & \text{ default}\\
-1.234.567,89 & \text{ vice versa, wrong spacing}\label{eq:comma}\\
-1\mathpunct{.}234\mathpunct{.}567{,}89 & \text{ correct spacing}
-\end{align}
-
-
-\begin{lstlisting}
-%\usepackage{amsmath}
-1,234,567.89 & \text{ default}\\
-1.234.567,89 & \text{ vice versa, wrong spacing}\\
-1\mathpunct{.}234\mathpunct{.}567{,}89 & \text{ correct spacing}
-\end{lstlisting}
-
-The original definitions from \verb+fontmath.ltx+\footnote{%
-Located in \url{texmf/tex/latex/base/}} are
-
-\begin{verbatim}
-\DeclareMathSymbol{,}{\mathpunct}{letters}{"3B}
-\DeclareMathSymbol{.}{\mathord}{letters}{"3A}
-\end{verbatim}
-
-\noindent\CIndex{mathord} and \CIndex{mathpunct} 
-can be changed for a documentwide other behaviour. In the above equation~\ref{eq:comma} 
-the comma is only set in a pair of braces \verb+{,}+, which is the same as writing 
-\verb+\mathord{,}+ because \LaTeX{} handles everything
-inside of parenthises as a formula, which gets the same spacing. 
-
-It is also possible to use the package \PIndex{icomma}\footnote{%
-\href{ftp://ftp.dante.de/tex-archive/macros/latex/contrib/was/}%
-{CTAN:// macros/latex/contrib/was/}} for a documentwide
-correct spacing.
-
-\subsection{Vertical whitespace}\label{subsec:vwhitespace}
-\subsubsection{Before/after math expressions}\label{subsubsec:displayskip}
-
-There are four predefined lengths, which control the vertical whitespace
-of displayed formulas:
-\begin{verbatim}
-\abovedisplayskip=12pt plus 3pt minus 9pt
-\abovedisplayshortskip=0pt plus 3pt
-\belowdisplayskip=12pt plus 3pt minus 9pt
-\belowdisplayshortskip=7pt plus 3pt minus 4pt
-\end{verbatim}
-\index{abovedisplayskip@\textbackslash abovedisplayskip}
-\index{abovedisplayshortskip@\textbackslash abovedisplayshortskip}
-\index{belowdisplayskip@\textbackslash belowdisplayskip}
-\index{belowdisplayshortskip@\textbackslash belowdisplayshortskip}
-The short skips are used if the formula starts behind the end of the foregoing
-last line. Only for demonstration the shortskips
-are set to \verb|0pt| in the following examples and the normal skips to 
-\verb|20pt| without any glue:
-
-\medskip
-\noindent\fbox{\begin{minipage}{\linewidth-2\fboxsep-2\fboxrule}
-\abovedisplayshortskip=0pt
-\belowdisplayshortskip=0pt
-\abovedisplayskip=20pt
-\belowdisplayskip=20pt
-\noindent The line ends before.
-\begin{equation}
-f(x) =  \int\frac{\sin x}{x}\,\mathrm{d}x
-\end{equation}
-\noindent The line doesn't end before the formula.
-\begin{equation}
-f(x) =  \int\frac{\sin x}{x}\,\mathrm{d}x
-\end{equation}
-\noindent And the next line starts as usual with some text ...
-\end{minipage}}
-
-\medskip
-\begin{lstlisting}
-\abovedisplayshortskip=0pt
-\belowdisplayshortskip=0pt
-\abovedisplayskip=20pt
-\belowdisplayskip=20pt
-\noindent The line ends before.
-\begin{equation}
-	f(x) =  \int\frac{\sin x}{x}\,\mathrm{d}x
-\end{equation}
-\noindent The line doesn't end before the formula.
-\begin{equation}
-	f(x) =  \int\frac{\sin x}{x}\,\mathrm{d}x
-\end{equation}
-\noindent And the next line starts as usual with some text ...
-\end{lstlisting}
-%$
-
-
-\mPar{\texttt{fleqn} class option}%
-When using the \verb+fleqn+\index{fleqn@\texttt{fleqn}} classoption for left
-aligned equations the math environments \uIndex{equation} 
-and \CIndex{[}\ldots\CIndex{]} are typeset as a list. This is the reason why the
-vertical space is defined by the length registers for a list, especially
-\LIndex{topsep}, instead of \LIndex{abovedisplayskip} and \LIndex{belowdisplayskip}.
-This doesn't effect the \UIndex{eqnarray}. 
-
-
-\subsubsection{Inside math expressions}\label{subsec:vspacing}
-
-\paragraph{\CMD{\textbackslash [<length>]}}
-This works inside the math mode in the same way as in the text mode.
-
-
-\paragraph{\CMD{jot}}\mPar{\CMD{jot}}
-The vertical space between the lines for all math expressions which allow multiple
-lines  can be changed with the length \LIndex{jot}, which is predefined as
-
-\begin{verbatim}
-\newdimen\jot \jot=3pt
-\end{verbatim}
-
-The following three formulas show this for the default value, \verb|\setlength\jot{0pt}|  
-and \verb|\setlength\jot{10pt}|.
-
-\begin{minipage}{0.3\linewidth}
-\begin{eqnarray*}
-	y & = & d\\
-	y & = & c\frac{1}{x}+d\\
-	y & = & b\frac{1}{x^{2}}+cx+d\\
-\end{eqnarray*}
-\end{minipage}\hfill
-\begin{minipage}{0.3\linewidth}
-\setlength\jot{0pt}
-\begin{eqnarray*}
-	y & = & d\\
-	y & = & c\frac{1}{x}+d\\
-	y & = & b\frac{1}{x^{2}}+cx+d\\
-\end{eqnarray*}
-\end{minipage}\hfill
-\begin{minipage}{0.3\linewidth}
-\setlength\jot{10pt}
-\begin{eqnarray*}
-	y & = & d\\
-	y & = & c\frac{1}{x}+d\\
-	y & = & b\frac{1}{x^{2}}+cx+d\\
-\end{eqnarray*}
-\end{minipage}
-
-Defining a new environment with a parameter makes things easier, because changes to the
-length are locally.
-\begin{lstlisting}
-\newenvironment{mathspace}[1]{%
-  \setlength{\jot}{#1}%
-  \ignorespaces%
-}{%
-  \ignorespacesafterend%
-}
-\end{lstlisting}
-
-\paragraph{\CMD{arraystretch}}\cIndex{arraystretch}
-\mPar{\CMD{arraystretch}}%
-The vertical space between the lines for all math expressions which contain an
-\UIndex{array} can be changed with the command
-\CIndex{arraystretch}, which is predefined
-as
-\begin{verbatim}
-\renewcommand\arraystretch{1}
-\end{verbatim}
-
-Renewing this definition is global to all following math expressions, so it should be used
-in the same way as \LIndex{jot}.
-
-\paragraph{\CMD{vskip}}\index{Vertical spacing}\index{Spacing!vertical}
-Another spacing for single lines is possible with the \CIndex{vskip} macro:
-
-\begin{LTXexample}[width=0.4\linewidth]
-\[
-\begin{pmatrix}
-0 & 1 & 1 & 0 & 0 & 1 \\
-1 & 0 & 0 & 1 & 1 & 0 \\
-\noalign{\vskip2pt}
-0 & 1 & 1 & 0 & \dfrac{1}{\sqrt{2}} & 1\\
-\noalign{\vskip2pt}
-1 & 0 & 1 & 0 & 1 & 0 \\
-0 & 1 & 0 & 1 & 0 & 1 \\
-\end{pmatrix}
-\]
-\end{LTXexample}
-
-
-
-\paragraph{Package \texttt{setspace}}
-To have all formulas with another vertical spacing, one can choose
-the package \PIndex{setspace} and redefining some of the math macros, \eg
-
-\begingroup
-\newcommand*\Array[2][1]{\setstretch{#1}\array{#2}}
-\let\endArray\endarray
-
-\begin{lstlisting}
-\newcommand*\Array[2][1]{\setstretch{#1}\array{#2}}
-\let\endArray\endarray
-\end{lstlisting}
-
-\begin{LTXexample}[width=0.25\linewidth]
-\[
-\begin{Array}[2]{cc}
-a =&b\\
-a =&b\\
-a =&b
-\end{Array}
-\]
-
-text $\begin{Array}{cc}
-a =&b\\
-a =&b\\
-a =&b
-\end{Array}$ text
-\end{LTXexample}
-\endgroup
-
-\section{Styles}\label{sec:Styles}
-
-\begin{table}[htb]
-\newlength\formula
-\settowidth{\formula}{$f(t)=\frac{T}{2\pi }\int \frac{1}{\sin \frac{\omega }{t}}dt$}
-\begin{tabular}{l|ll}
-Mode & Inline & Displayed\\\hline
-default & $f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt$&
-\begin{minipage}{\formula}\[
-f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt\]
-\end{minipage}\\
-\CMD{displaystyle} &
-${\displaystyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$&
-\begin{minipage}{\formula}\[
-{\displaystyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\]
-\end{minipage}\\
-\CMD{scriptstyle} &
-${\scriptstyle {\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}}$&
-\begin{minipage}{\formula}\[
-{\textstyle {\scriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}}\]
-\end{minipage}\tabularnewline
-\CMD{scriptscriptstyle} &
-${\scriptscriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$&
-\begin{minipage}{\formula}\[
-{\scriptscriptstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\]
-\end{minipage}\tabularnewline
-\CMD{textstyle} &
-${\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}$&
-\begin{minipage}{\formula}\[
-{\textstyle f(t)=\frac{T}{2\pi}\int\frac{1}{\sin\frac{\omega}{t}}dt}\]
-\end{minipage}
-\end{tabular}
-\caption{Math styles}\label{cap:Mathstyles}
-\end{table}
-%$
-\makeatletter
-\newenvironment{smallequation}[1]{%
-  \skip@=\baselineskip
-  #1%
-  \baselineskip=\skip@
-  \equation
-}{\endequation \ignorespacesafterend}
-\makeatother
-
-This depends on the environment in which they are used. An inline
-formula has a default math %
-\mPar{\CMD{textstyle}\\
-\CMD{displaystyle}\\
-\CMD{scriptstyle}\\
-\CMD{scripscriptstyle}} fontsize called \CIndex{textstyle},
-which is smaller than the one for a display formula (see section~\ref{display}), which is called
-\CIndex{displaystyle}.
-Beside this predefinition there are two other special fontstyles for
-math, \CIndex{scriptstyle} and \CIndex{scriptscriptstyle}.
-They are called ``style{}'' in difference to ``size{}'', because
-they have a dynamic character, their real fontsize belongs to the
-environment in which they are used. A fraction for example is by default in scriptstyle when it is in an
-inline formula like this $\frac{a}{b}$, which can be changed to
-${\displaystyle \frac{a}{b}}$.
-This may be in some cases useful but it looks in general ugly because
-the line spacing is too big.
-These four styles\index{Style} are predefined and together in a
-logical relationship. It is no problem to use the other styles like
-\Index{large}, \CIndex{Large}, \ldots\ \textbf{outside} the math environment. 
-For example a fraction written with \CIndex{Huge}: {\Huge$\frac{a}{b}$}
-(\verb|\Huge$\frac{a}{b}$|). This may cause some problems when you want to write
-a displayed formula in another fontsize\index{Fontsize}, because it also affects the interline spacing of
-the preceding part of the paragraph.
-If you end the paragraph, you get problems with spacing and page breaking
-above the equations.  So it is better to declare the font size and then
-restore the baselines:
-\begin{smallequation}{\tiny}
-\int_1^2\,\frac{1}{x^2}\,\mathrm{d}x=0.5
-\end{smallequation}
-\begin{lstlisting}
-\makeatletter
-\newenvironment{smallequation}[1]{%
-  \skip@=\baselineskip
-  #1%
-  \baselineskip=\skip@
-  \equation
-}{\endequation \ignorespacesafterend}
-\makeatother
-
-\begin{smallequation}{\tiny}
-\int_1^2\,\frac{1}{x^2}\,\mathrm{d}x=0.5
-\end{smallequation}
-\end{lstlisting}
-If you use this the other way round for huge fontsizes, don't forget to load package
-\PIndex{exscale} (see section~\vref{sec:exscale}). Also see this section for diffent symbol sizes.
-
-
-
-\section{Dots\label{sec:Dots}}
-
-\mPar{\CMD{cdots}\\
-\CMD{dots}\\
-\CMD{dotsb}\\
-\CMD{dotsc}\\
-\CMD{dotsi}\\
-\CMD{dotsm}\\
-\CMD{dotso}\\
-\CMD{ldots}\\
-\CMD{vdots}}%
-In addition to the above decorations there are some more different
-dots which are single commands and not by default over/under a letter.
-It is not easy to see the differences between some of them. Dots from
-lower left to upper right are possible with 
-\verb|\reflectbox{$\ddots$}|\index{reflectbox@\textbackslash reflectbox}
-\reflectbox{$\ddots$}
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{*{5}{rc}}
-\CMD{cdots}\index{cdots@\textbackslash cdots}&$\cdots$ &
-\CMD{ddots}\index{ddots@\textbackslash ddots}&$\ddots$ &
-\CMD{dotsb}\index{dotsb@\textbackslash dotsb}&$\dotsb$ &
-\CMD{dotsc}\index{dotsc@\textbackslash dotsc}&$\dotsc$ &
-\CMD{dotsi}\index{dotsi@\textbackslash dotsi}&$\dotsi$ \\\hline
-\CMD{dotsm}\index{dotsm@\textbackslash dotsm}&$\dotsm$ &
-\CMD{dotso}\index{dotso@\textbackslash dotso}&$\dotso$ &
-\CMD{ldots}\index{ldots@\textbackslash ldots}&$\ldots$ &
-\CMD{vdots}\index{vdots@\textbackslash vdots}&$\vdots$
-\end{tabular}
-\caption{Dots in math mode}
-\end{table}
-
-
-
-\section{Accents}\label{sec:Accents}
-
-The letter ``a{}'' is only for demonstration.  The table \ref{cap:Accents-in-math mode}
-shows all in standard \LaTeX{} available accents and also the ones placed under a character.
-With package \PIndex{amssymb} it is easy to define new accents. For
-more information see section~\vref{amssymb}  or
-other possibilities at section \vref{sec:package-accent}.
-
-
-\begin{table}[htb]
-\makebox[\textwidth]{%
-\begin{tabular}{rc|rc|rc}
-\CIndex{acute}\index{acute@\textbackslash acute} &$\acute{a}$&
-\CIndex{bar}\index{bar@\textbackslash bar}&$\bar{a}$&
-\CIndex{breve}\index{breve@\textbackslash breve} & $\breve{a}$\\
-\CIndex{bar}\index{bar@\textbackslash bar}&$\bar{a}$&
-\CIndex{breve}\index{breve@\textbackslash breve} &$\breve{a}$\tabularnewline
-\CIndex{check}\index{check@\textbackslash check} &$\check{a}$&
-\CIndex{dddot} \index{dddot@\textbackslash dddot}&$\dddot{a}$&
-\CIndex{ddot}\index{ddot@\textbackslash ddot}&$\ddot{a}$\tabularnewline
-\CIndex{dot}\index{dot@\textbackslash dot}&$\dot{a}$&
-\CIndex{grave}\index{grave@\textbackslash grave}&$\grave{a}$&
-\CIndex{hat}\index{hat@\textbackslash hat}&$\hat{a}$\tabularnewline
-\CIndex{mathring}\index{mathring@\textbackslash mathring}&$\mathring{a}$&
-\CIndex{overbrace}\index{overbrace@\textbackslash overbrace}&$\overbrace{a}$&
-\CIndex{overleftarrow}\index{overleftarrow@\textbackslash overleftarrow}&$\overleftarrow{a}$\tabularnewline
-\CIndex{overleftrightarrow}\index{overleftrightarrow@\textbackslash overleftrightarrow}&$\overleftrightarrow{a}$&
-\CIndex{overline}\index{overline@\textbackslash overline}&$\overline{a}$&
-\CIndex{overrightarrow}\index{overrightarrow@\textbackslash overrightarrow}&$\overrightarrow{a}$\tabularnewline
-\CIndex{tilde}\index{tilde@\textbackslash tilde}&$\tilde{a}$&
-\CIndex{underbar}\index{underbar@\textbackslash underbar}&$\underbar{a}$&
-\CIndex{underbrace}\index{underbrace@\textbackslash underbrace}&$\underbrace{a}$\tabularnewline
-\CIndex{underleftarrow}\index{underleftarrow@\textbackslash underleftarrow}&$\underleftarrow{a}$&
-\CIndex{underleftrightarrow}\index{underleftrightarrow@\textbackslash underleftrightarrow}&
-$\underleftrightarrow{a}$&
-\CIndex{underline}\index{underline@\textbackslash underline}&$\underline{a}$\tabularnewline
-\CIndex{underrightarrow}\index{underrightarrow@\textbackslash underrightarrow}&$\underrightarrow{a}$&
-\CIndex{vec}\index{vec@\textbackslash vec}&$\vec{a}$&
-\CIndex{widehat}\index{widehat@\textbackslash widehat}&$\widehat{a}$\tabularnewline
-\CIndex{widetilde}\index{widetilde@\textbackslash widetilde}&$\widetilde{a}$ & & & &
-\end{tabular}%
-}
-\caption{Accents in math mode}\label{cap:Accents-in-math mode}
-\end{table}
-
-The letters \verb+i+ and \verb+j+ can be substituted with the macros \CIndex{imath}
-and \CIndex{jmath} when an accents is placed over these letters and the dot should
-disappear: $\vec{\imath}\ \dddot{\jmath}$ (\verb+$\vec{\imath}\ \dddot{\jmath}$+).
-
-Accents can be used in different ways, \eg strike a single character with a horizontal line like
-\verb+$\mathaccent`-A$+: $\mathaccent`-A$ or \verb+$\mathaccent\mathcode`-A$+: $\mathaccent\mathcode`-A$.
-In section~\vref{cancel.sty} is a better solution for more than one character.
-
-\subsection{Over- and underbrackets}
-There are no \CIndex{underbracket} and \CIndex{overbracket}
-commands in the list of accents. They can be defined in the preamble
-with the following code.
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1cm]
-\makeatletter
-\def\underbracket{%
-	\@ifnextchar[{\@underbracket}{\@underbracket [\@bracketheight]}%
-}
-\def\@underbracket[#1]{%
-	\@ifnextchar[{\@under@bracket[#1]}{\@under@bracket[#1][0.4em]}%
-}
-\def\@under@bracket[#1][#2]#3{%\message {Underbracket: #1,#2,#3}
-	\mathop{\vtop{\m@th \ialign {##\crcr $\hfil \displaystyle {#3}\hfil $%
-	\crcr \noalign {\kern 3\p@ \nointerlineskip }\upbracketfill {#1}{#2}
-     \crcr \noalign {\kern 3\p@ }}}}\limits}
-\def\upbracketfill#1#2{$\m@th \setbox \z@ \hbox {$\braceld$}
-                  \edef\@bracketheight{\the\ht\z@}\bracketend{#1}{#2}
-                  \leaders \vrule \@height #1 \@depth \z@ \hfill
-                  \leaders \vrule \@height #1 \@depth \z@ \hfill \bracketend{#1}{#2}$}
-\def\bracketend#1#2{\vrule height #2 width #1\relax}
-\makeatother
-\end{lstlisting}
-%$
-\begin{enumerate}
-\item \verb/\underbrace{...}/ is an often used command:
-\begin{eqnarray}
-\underbrace{{x^{2}+2x+1}} & = & f(x)\\
-\left(x+1\right)^{2}\,\,\,\nonumber
-\end{eqnarray}
-
-\item Sometimes an under\textbf{bracket} is needed, which can be used in
-	more ways than \verb/\underbrace{...}/.  An example for \verb/\underbracket{...}/:
-
-
-\begin{eqnarray*}
-\textrm{Hate Science  }& \underbracket[0.5pt]{1\rightarrow2\rightarrow3\rightarrow4}
-    \underbracket[0.75pt][0.75em]{\rightarrow5\rightarrow6\rightarrow7}
-    \underbracket[1pt][1em]{\rightarrow8\rightarrow9\rightarrow10} & \textrm{Love Science}\\
- & \textrm{low}\hspace{1.5cm}\textrm{medium}\hspace{1.5cm}\textrm{high}
- \end{eqnarray*}
-
-
-\end{enumerate}
-
-\subsubsection{Use of \CMD{underbracket\{...\}}}
-
-The \verb/\underbracket{...}/ command has two optional parameters:
-
-\begin{itemize}
-\item the line thickness in any valid latex unit, \eg \verb/1pt/
-\item the height of the edge brackets, \eg \verb/1em/
-\end{itemize}
-using without any parameters gives the same values for thickness and
-height as predefined for the \CIndex{underbrace} command.
-
-
-\vspace{0.3cm}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline
-1.& \verb/$\underbracket{foo~bar}$/ & $\underbracket{foo~bar}$ \tabularnewline\hline
-2.& \verb/$\underbracket[2pt]{foo~bar}$/ & $\underbracket[2pt]{foo~bar}$ \tabularnewline\hline
-3.& \verb/$\underbracket[2pt][1em] {foo~bar}$/& $\underbracket[2pt][1em] {foo~bar}$\tabularnewline\hline
-\end{tabular}
-\end{center}
-
-
-\subsubsection{Overbracket}
-
-In addition to the underbracket an overbracket is also useful, which can be used in
-more ways than \verb/\overbrace{...}/. For example:
-
-
-\begin{eqnarray*}
-\textrm{Hate Science  }& \overbracket[0.5pt]{1\rightarrow2\rightarrow3\rightarrow4}
-    \overbracket[0.75pt][0.75em]{\rightarrow5\rightarrow6\rightarrow7}
-    \overbracket[1pt][1em]{\rightarrow8\rightarrow9\rightarrow10} & \textrm{Love Science}\\
- & \textrm{low}\hspace{1.5cm}\textrm{medium}\hspace{1.5cm}\textrm{high}\nonumber
- \end{eqnarray*}
-
-
-The \verb/\overbracket{...}/ command has two optional parameters:
-
-\begin{itemize}
-\item the line thickness in any valid latex unit, \eg \verb/1pt/
-\item the height of the edge brackets, \eg \verb/1em/
-\end{itemize}
-using without any parameters gives the same values for thickness and
-height as predefined for the \CIndex{overbrace} command.
-
-
-\vspace{0.3cm}
-\begin{center}\begin{tabular}{|c|c|c|}
-\hline
-1.&\verb/$\overbracket {foo\ bar}$/ & $\overbracket {foo\ bar}$ \tabularnewline\hline
-2.&\verb/$\overbracket[2pt] {foo\ bar}$/ &$\overbracket[2pt] {foo\ bar}$ \tabularnewline\hline
-3.&\verb/$\overbracket[2pt] [1em] {foo\ bar}$/&$\overbracket[2pt] [1em] {foo\ bar}$\tabularnewline\hline
-\end{tabular}
-\end{center}
-
-%$
-\subsection{Vectors}
-
-Especially for vectors\index{Vector} there is the package \PIndex{esvect}%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/esvect/}%
-	{CTAN://macros/latex/contrib/esvect/}} package, which looks better than the
-\CMD{overrightarrow}\index{overrightarrow@\textbackslash overrightarrow}, \eg
-
-\begin{table}[!htb]
-\centering
-\begin{tabular}{c|c}
-\textbackslash{}vv\{...\}&\textbackslash{}overrightarrow\{...\}\tabularnewline\hline
-$\vv{a}$ & $\overrightarrow{a}$\tabularnewline
-$\vv{abc}$ & $\overrightarrow{abc}$\tabularnewline
-$\vv{\imath}$ & $\overrightarrow{\imath}$\tabularnewline
-$\vv*{A}{x}$ & $\overrightarrow{A}_{x}$\tabularnewline
-\end{tabular}
-\caption[Vectors with package \texttt{esvect}]%
-    {Vectors with package \texttt{esvect} (in the right column the default one from \LaTeX{})}
-\end{table}
-
-
-Look into the documentation for more details about the package \PIndex{esvect}.
-
-%$
-\section{Exponents and indices}\label{sec:exponents}
-The two active characters \verb|_| and \verb|^| can only be used in math mode. The
-\textbf{following} character will be printed as an index (\verb|$y=a_1x+a_0$|: $y=a_1x+a_0$)
-or as an exponent (\verb|$x^2+y^2=r^2$|: $x^2+y^2=r^2$). For more than the next character
-put it inside of \verb|{}|, like \verb|$a_{i-1}+a_{i+1}<a_i$|: $a_{i-1}+a_{i+1}<a_i$.
-
-Especially for multiple exponents \index{Multiple exponents}
-there are several possibilities. For example:
-\begin{equation}
-((x^2)^3)^4 = {({(x^2)}^3)}^4 = {\left({\left(x^2\right)}^3\right)}^4
-\end{equation}
-
-\begin{lstlisting}
-((x^2)^3)^4 =
-{({(x^2)}^3)}^4 =
-{\left({\left(x^2\right)}^3\right)}^4
-\end{lstlisting}
-
-\index{Upright letters}
-For variables with both exponent\index{Exponent} and indice index\index{Indice} 
-the order is not important, \verb|$a_1^2$| is
-exactly the same than \verb|$a^2_1$|: $a_1^2=a^2_1$. By default all exponents and indices
-are set as italic characters. It is possible to change this behaviour 
-to get upright characters. The following example shows this for the indices.
-
-\bgroup
-\begin{LTXexample}[width=4.5cm,preset=\raggedright]
-$A_{abc_{xyz}123def}^{abc123def}aa$
-
-\makeatletter
-\catcode`\_\active
-\def_#1{\sb{\operator@font#1}}
-\makeatother
-
-$A_{abc_{xyz}123def}^{abc123def}aa$
-\end{LTXexample}
-\egroup
-
-\section{Operators}\label{sec:ltxOperators}
-
-They are written in upright font shape and are placed with some additional
-space before and after for a better typesetting. With the \AmSmath
-package it is possible to define one's own operators\index{Operator} (see
-section~\vref{OperatorNames}). Table~\vref{tab:operator} and \vref{tab:operator2} show a list of
-the predefined ones for standard \LaTeX{}.
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{llllll}
-\verb+\coprod+  &$\coprod$  &\verb+\bigvee+   &$\bigvee$   &\verb+\bigwedge+&$\bigwedge$\\
-\verb+\biguplus+&$\biguplus$&\verb+\bigcap+   &$\bigcap$   &\verb+\bigcup+  &$\bigcup$   \\
-\verb+\intop+   &$\intop$   &\verb+\int+      &$\int$      &\verb+\prod+    &$\prod$ \\
-\verb+\sum+     &$\sum$     &\verb+\bigotimes+&$\bigotimes$&\verb+\bigoplus+&$\bigoplus$\\
-\verb+\bigodot+ &$\bigodot$ &\verb+\ointop+   &$\ointop$   &\verb+\oint+    &$\oint$\\
-\verb+\bigsqcup+&$\bigsqcup$&\verb+\smallint+ &$\smallint$
-\end{tabular}
-\caption{The predefined operators of \texttt{fontmath.ltx}}\label{tab:operator}
-\end{table}
-The difference between \CIndex{intop} and \CIndex{int} is that the first one has by default
-over/under limits and the second subscript/superscript limits. Both can be changed
-with the \CIndex{limits} or \CIndex{nolimits} command. The same behaviour happens to the
-\CIndex{ointop} and \CIndex{oint} Symbols.
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{llllll}
-\verb+\log+   & $\log$    &\verb+\lg+     & $\lg$      &\verb+\ln+     & $\ln$     \\
-\verb+\lim+   & $\lim$    &\verb+\limsup+ & $\limsup$  &\verb+\liminf+ & $\liminf$ \\
-\verb+\sin+   & $\sin$    &\verb+\arcsin+ & $\arcsin$  &\verb+\sinh+   & $\sinh$   \\
-\verb+\cos+   & $\cos$    &\verb+\arccos+ & $\arccos$  &\verb+\cosh+   & $\cosh$   \\
-\verb+\tan+   & $\tan$    &\verb+\arctan+ & $\arctan$  &\verb+\tanh+   & $\tanh$   \\
-\verb+\cot+   & $\cot$    &\verb+\coth+   & $\coth$    &\verb+\sec+    & $\sec$    \\
-\verb+\csc+   & $\csc$    &\verb+\max+    & $\max$     &\verb+\min+    & $\min$    \\
-\verb+\sup+   & $\sup$    &\verb+\inf+    & $\inf$     &\verb+\arg+    & $\arg$    \\
-\verb+\ker+   & $\ker$    &\verb+\dim+    & $\dim$     &\verb+\hom+    & $\hom$    \\
-\verb+\det+   & $\det$    &\verb+\exp+    & $\exp$     &\verb+\Pr+     & $\Pr$     \\
-\verb+\gcd+   & $\gcd$    &\verb+\deg+    & $\deg$     &\verb+\bmod+   & $\bmod$   \\
-\verb+\pmod{a}+& $\pmod{a}$
-\end{tabular}
-\caption{The predefined operators of \texttt{latex.ltx}}\label{tab:operator2}
-\end{table}
-
-
-\makeatletter
-\newcommand\foo{\mathop{\operator@font foo}\nolimits}
-\makeatother
-For more predefined operator names see table~\vref{tab:amsopn}. It is easy 
-to define a new operator with
-%
-\begin{lstlisting}
-\makeatletter
-\newcommand\foo{\mathop{\operator@font foo}\nolimits}
-\makeatother
-\end{lstlisting}
-
-Now you can use \verb|\foo| in the usual way:
-%
-\begin{LTXexample}[width=4cm]
-\[ \foo_1^2 = x^2 \]
-\end{LTXexample}
-In this example \verb|\foo| is defined with \verb|\nolimits|, means 
-that limits\index{Limits} are placed in
-superscript/subscript mode and not over under. This is still possible with \verb|\limits| in the
-definition or the equation:
-\begin{LTXexample}[width=4cm]
-\[ \foo\limits_1^2 = x^2 \]
-\end{LTXexample}
-
-\AmSmath has an own macro for a definition, have a look at section~\vref{OperatorNames}.
-
-
-\section{Greek letters}\label{sec:greek}
-The \AmSmath package simulates a bold font for the greek letters, it writes a 
-greek character twice with a small kerning.  The \verb|\mathbf{<character>}| 
-doesn't work with lower greek character. See
-section \vref{sec:greek-AMS} for the \CIndex{pmb} macro, which makes it possible 
-to print bold lower greek\index{Greek} letters. Not all upper case letters have 
-own macro names. If there is no difference to the roman font, then the default 
-letter is used, \eg A for the upper case of
-$\alpha$. Table \ref{tab:greek-letters} shows only those upper case letters 
-which have own macro names. Some of the lower case letters have an additional 
-\verb|var| option for an alternative.
-
-\bgroup
-\tabcolsep=3pt
-\begin{longtable}{lclccc}
-lower & default &  upper & default & \verb|\mathbf| & \verb|\mathit|\\\hline
-\endhead
-\verb|\alpha| & $\alpha$ \\
-\verb|\beta|  & $\beta$  \\
-\verb|\gamma| & $\gamma$
-	& \verb|\Gamma| & $\Gamma$ & $\mathbf{\Gamma}$ & $\mathit{\Gamma}$\\
-\verb|\delta| & $\delta$
-	& \verb|\Delta| & $\Delta$ & $\mathbf{\Delta}$ & $\mathit{\Delta}$\\
-\verb|\epsilon|  & $\epsilon$\\
-\verb|\varepsilon|  & $\varepsilon$\\
-\verb|\zeta|  & $\zeta$\\
-\verb|\eta|  & $\eta$ \\
-\verb|\theta|  & $\theta$
-	& \verb|\Theta| & $\Theta$ & $\mathbf{\Theta}$ & $\mathit{\Theta}$\\
-\verb|\vartheta|  & $\vartheta$\\
-\verb|\iota|  & $\iota$\\
-\verb|\kappa|  & $\kappa$\\
-\verb|\lambda| & $\lambda$
-	& \verb|\Lambda| & $\Lambda$ & $\mathbf{\Lambda}$ & $\mathit{\Lambda}$\\
-\verb|\mu|  & $\mu$ \\
-\verb|\nu|  & $\nu$\\
-\verb|\xi|  & $\xi$
-	& \verb|\Xi| & $\Xi$ & $\mathbf{\Xi}$ & $\mathit{\Xi}$\\
-\verb|\pi|  & $\pi$
-	& \verb|\Pi| & $\Pi$ & $\mathbf{\Pi}$ & $\mathit{\Pi}$\\
-\verb|\varpi|  & $\varpi$ \\
-\verb|\rho|  & $\rho$\\
-\verb|\varrho|  & $\varrho$\\
-\verb|\sigma| & $\sigma$
-	& \verb|\Sigma| & $\Sigma$ & $\mathbf{\Sigma}$ & $\mathit{\Sigma}$\\
-\verb|\varsigma| & $\varsigma$\\
-\verb|\tau|  & $\tau$\\
-\verb|\upsilon|  & $\upsilon$
-	& \verb|\Upsilon| & $\Upsilon$ & $\mathbf{\Upsilon}$ & $\mathit{\Upsilon}$\\
-\verb|\phi|  & $\phi$
-	& \verb|\Phi| & $\Phi$ & $\mathbf{\Phi}$ & $\mathit{\Phi}$\\
-\verb|\varphi|  & $\varphi$\\
-\verb|\chi|  & $\chi$ \\
-\verb|\psi|  & $\psi$
-	& \verb|\Psi| & $\Psi$ & $\mathbf{\Psi}$ & $\mathit{\Psi}$\\
-\verb|\omega| & $\omega$
-	& \verb|\Omega| & $\Omega$ & $\mathbf{\Omega}$ & $\mathit{\Omega}$\\[5pt]
-\caption{The greek letters}\label{tab:greek-letters}\\
-\end{longtable}
-\egroup
-
-Bold \Index{greek} letters are possible with the package \PIndex{bm} (see section~\vref{sec:bm})
-and if they should also be upright with the package \PIndex{upgreek}:
-\index{greek!upright}\index{greek!bold}
-
-\medskip
-\verb+$\bm{\upalpha}, \bm{\upbeta} ... $+ $ \bm{\upalpha}, \bm{\upbeta} ... $
-
-A useful definition maybe:
-
-\begin{lstlisting}
-\usepackage{upgreek}
-\makeatletter
-\newcommand{\bfgreek}[1]{\bm{\@nameuse{up#1}}}
-\makeatother
-\end{lstlisting}
-
-\makeatletter
-\newcommand{\bfgreek}[1]{\bm{\@nameuse{up#1}}}
-\makeatother
-Then 
-\verb|$\bfgreek{mu}$| will allow you to type $\bfgreek{mu}$ to obtain an upright boldface $\mu$.
-
-
-
-\section{Pagebreaks}
-\mPar{\CMD{allowdisplaybreaks}}By default a displayed formula cannot 
-have a pagebreak. This makes some sense, but sometimes it gives a better 
-typesetting when a pagebreak is possible.
-
-\begin{verbatim}
-\allowdisplaybreaks
-\end{verbatim}
-
-\CIndex{allowdisplaybreaks} enables \TeX{} to insert pagebreaks into 
-displayed formulas whenever a newline command appears.\index{Pagebreak} 
-With the command \CIndex{displaybreak} it is also possible to insert a 
-pagebreak at any place.
-
-\section{\CMD{stackrel}}
-
-\CIndex{stackrel} puts a character on top of another one which may be important if a
-used symbol is not predefined. For example ``$\stackrel{\wedge}{=}$''
-(\verb|\stackrel{\wedge}{=}|). \mPar{\CMD{stackrel}}
-The syntax is
-
-\begin{lstlisting}
-\stackrel{top}{base}
-\end{lstlisting}
-
-Such symbols may be often needed so that a macro  definition in the preamble makes some sense:
-
-\begin{lstlisting}
-\newcommand{\eqdef}{%
- \ensuremath{\mathrel{\stackrel{\mathrm{def}}{=}}}}
-\end{lstlisting}
-%
-With the \CIndex{ensuremath} command we can use the new \CIndex{eqdef} command in text
-and in math mode, \LaTeX{} switches automatically in math mode, which
-saves some keystrokes like the following command, which is written
-without the delimiters (\texttt{\$...\$}) for the math mode \eqdef ,
-only \CMD{eqdef} with a space at the end. In math mode
-together with another material it may look like 
-$\vec{x}\eqdef\left(x_{1},\ldots,x_{n}\right)$ and as command sequence
-
-\begin{lstlisting}
-$\vec{x}\eqdef\left(x_{1},\ldots,x_{n}\right)$
-\end{lstlisting}
-
-The fontsize of the top is one size smaller than the one from the
-base, but it is no problem to get both the same size, just increase the
-top or decrease the base.
-
-\section{\CMD{choose}}
-
-\CIndex{choose}\index{Binom} is like \CIndex{atop}
-with delimiters or like \CIndex{frac}
-without the fraction line and also with delimiters. It is often used
-for binomial coefficients and has the following syntax:\mPar{\CMD{choose}}
-
-\begin{lstlisting}
-{above \choose below}
-\end{lstlisting}
-The two braces are not really important but it is safe to use them.
-
-\begin{equation}
-{{m+1 \choose n}}={{m \choose n}}+{{m \choose k-1}}\label{eq:choose}
-\end{equation}
-
-\begin{lstlisting}
-{{m+1 \choose n}}={{m \choose n}}+{{m \choose k-1}}\label{eq:choose}
-\end{lstlisting}
-
-
-See section~\vref{sub:Binoms} for the \AmSmath equivalents and enhancements.
-
-\section{Color in math expressions}\label{sec:color}
-\index{Color}There is no difference in using colored text and colored math expressions. With
-\begin{verbatim}
-\usepackage{color}
-\end{verbatim}
-
-\noindent in the preamble the macro \verb|\textcolor{<color>}{<text or math>}| exists.
-\begin{equation}
-\textcolor{blue}{f(x)} = \int\limits_1^{\infty}\textcolor{red}{\frac{1}{x^2}}\,\mathrm{d}x=1
-\end{equation}
-\mPar{\CMD{textcolor}}
-\begin{lstlisting}
-\begin{equation}
-\textcolor{blue}{f(x)} = \int\limits_1^{\infty}\textcolor{red}{\frac{1}{x^2}}\,\mathrm{d}x=1
-\end{equation}
-\end{lstlisting}
-
-If all math expressions should be printed in the same color, then it is better
-to use the \verb+everydisplay+ macro (section~\vref{sec:other}).
-
-
-\section{Boldmath}\label{sec:boldmath}
-
-\mPar{\CMD{mathversion}\\\CMD{boldmath}\\\CMD{unboldmath}}%
-Writing a whole formula in bold\index{boldmath@\textbackslash boldmath} is possible with the command sequence
-\CMD{boldmath} \ldots\ \CMD{unboldmath}, which itself must be written in textmode (outside the
-formula) or with the command \verb+{\mathversion{bold} ... }+.
-\index{mathversion@\textbackslash mathversion}\index{boldmath@\textbackslash
-boldmath}\index{unboldmath@\textbackslash unboldmath}
-
-\noindent\begin{minipage}{0.49\linewidth}
-\[
-\sum_{%
-	\makebox[0pt]{$%
-		{{\scriptscriptstyle 1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}}%
-	$}%
-	}a_{ij}b_{jk}c_{ki}
-\]
-\end{minipage}\hfill
-\begin{minipage}{0.49\linewidth}
-\boldmath
-\[
-\sum_{%
-	\makebox[0pt]{$%
-		{{\scriptscriptstyle 1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}}%
-	$}%
-	}a_{ij}b_{jk}c_{ki}
-\]
-\unboldmath
-\end{minipage}
-
-\medskip
-\begin{lstlisting}
-\boldmath
-\[
-\sum_{%
-	\makebox[0pt]{$%
-		{{\scriptscriptstyle 1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}}%
-	$}%
-	}a_{ij}b_{jk}c_{ki}
-\]
-\unboldmath
-\end{lstlisting}
-
-The \verb+\mathversion+ macro defines a math style which is valid for all following
-math expressions. If you want to have all math in bold then use this macro instead of
-\CIndex{boldmath}. But it is no problem to put \CIndex{mathversion} inside a group to hold
-the changes locally.
-
-{\mathversion{bold}%
-\begin{equation}
-y(x) = ax^3+bx^2+cx+d
-\end{equation}}
-
-\begin{lstlisting}
-{\mathversion{bold}%
-\begin{equation}
-y(x) = ax^3+bx^2+cx+d
-\end{equation}}
-\end{lstlisting}
-
-
-Single characters inside a formula can be written in bold with \CIndex{mathbf}, 
-but only in upright mode, which is in general not useful as shown in 
-equation~\ref{eq:bold}. It is better
-to use package \PIndex{bm} (see section~\vref{sec:bm}).
-
-\begin{equation}\label{eq:bold}
-\sum_{%
-	\makebox[0pt]{$%
-		{{\scriptscriptstyle 1\le j\le p\atop {%
-		{1\le j\le q\atop 1\le k\le r}}}}%
-	$}%
-	}a_{ij}\mathbf{b_{jk}}c_{ki}
-\end{equation}
-
-\subsection[Bold math titles and items]{Bold math expressions as part of titles and items}\label{sec:titleItem}
-By default the titles in sections, subsections, a.s.o. are printed in bold. Same for the
-\verb|description| environment. The problem is that a math expression in one of these
-environments is printed in default font shape, like the following example for a \verb|section| and
-\UIndex{description}:
-
-\medskip
-\fbox{%
-\begin{minipage}{.75\linewidth}
-\section*{\thesection\ Function $f(x)=x^2$}
-\begin{description}
-\item[This is $y=f(x)$] Only a demonstration.
-\item[And $z=f(x,y)$] Another demonstration.
-\end{description}
-\end{minipage}%
-}
-
-\medskip
-With a redefinition of the \CIndex{section} and 
-\CIndex{item} macros it is possible to get everything in bold font.
-
-\medskip
-\fbox{%
-\begin{minipage}{.75\linewidth}
-\let\itemOld\item
-\makeatletter
-\renewcommand\item[1][]{%
-    \def\@tempa{#1}
-    \ifx\@tempa\@empty\itemOld\else\boldmath\itemOld[#1]\unboldmath\fi%
-}
-\makeatother
-\section*{\thesection\ \boldmath Function $f(x)=x^2$\unboldmath}
-\begin{description}
-\item[This is $y=f(x)$] Only a demonstration.
-\item[And $z=f(x,y)$] Another demonstration.
-\end{description}
-\end{minipage}%
-}
-
-
-\medskip
-\begin{lstlisting}
-\let\itemOld\item
-\makeatletter
-\renewcommand\item[1][]{%
-    \def\@tempa{#1}
-    \ifx\@tempa\@empty\itemOld\else\boldmath\itemOld[#1]\unboldmath\fi%
-}
-\makeatother
-\let\sectionOld\section
-\renewcommand\section[2][\empty]{%
-	\boldmath\sectionOld[#1]{#2}\unboldmath%
-}
-\end{lstlisting}
-
-\section{Multiplying numbers}
-When the dot is used as the decimal marker as in the United States, the preferred sign
-for the multiplication of
-numbers or values of quantities is a cross (\verb|\times| $\times$ ), not a half-high and
-centered dot (\verb|\cdot| $\cdot$ ).
-
-When the comma is used as the decimal marker as in Europe, the preferred sign for the
-multiplication of
-numbers is the half-high dot. The multiplication of quantity symbols (or numbers in
-parentheses or values of
-quantities in parentheses) may be indicated in one of the following ways: $ab$,
-$a\cdot b$, $a\times b$.
-
-For more information see ``Nist Guide to SI Units -More on Printing and Using Symbols and
-Numbers in Scientific and
-Technical Documents''\footnote{\url{http://physics.nist.gov/Pubs/SP811/sec10.html}} or
-the German DIN 1304, Teil 1.
-
-
-\section{Other macros}\label{sec:other}
-\mPar{\CMD{everymath}\\\CMD{everydisplay}\\\CMD{underline}}%
-There are some other macros which are not mentioned in the foregoing text. Here comes
-a not really complete list of these macros.
-\begin{description}
-\item[\CMD{everymath}] \index{everymath@\textbackslash everymath} puts the argument before
-any inlined math expression, \eg \verb+\everymath{\displaysize}+. Using this macro doesn't really
-make sense, when one is using footnotes because the footnote number is printed as superscript in
-inline mathmode and an \CMD{everymath} will be valid, too.
-\item[\CMD{everydisplay}] \index{everydisplay@\textbackslash everydisplay} puts  the
-argument before any displayed math expression, \eg \verb+\everydisplay{\color{blue}}+.
-\item[\CMD{underline}] \index{underline@\textbackslash underline} underlines a math
-expression and has to be used inside the math mode.
-\[
-\underline{F(x)=\int f(x)\,\mathrm{d}x}
-\]
-\end{description}
-
-
-
-\part{\texorpdfstring{\AmSmath}{amsmath} package}\label{par:AMSmath-package}
-
-In general the \AmS packages are at least a collection of three different ones:
-\begin{enumerate}
-\item \verb|amsmath.sty|
-\item \verb|amssymb.sty|
-\item \verb|amsfonts.sty|
-\end{enumerate}
-In the following only the first one is described in detail.
-
-The \AmSmath has the following options:
-
-\bigskip\noindent
-\begin{tabularx}{\linewidth}{@{}lX@{}}
-\verb+centertags+\index{centertags} & (default) For a split equation, place
-equation numbers vertically centered on the total height of the equation.\\\hline
-\verb+tbtags+\index{tbtags} & `Top-or-bottom tags' For a split equation,
-place equation numbers level with the last (resp. first) line, if
-numbers are on the right (resp. left).\\\hline
-\verb+sumlimits+\index{sumlimits} & (default) Place the subscripts and superscripts
-of summation symbols above and below, in displayed equations. This
-option also affects other symbols of the same type -- $\prod$, $\coprod$,
-$\bigotimes$, $\bigoplus$, and so forth -- but excluding integrals
-(see below).\\\hline
-\verb+nosumlimits+\index{nosumlimits} & Always place the subscripts and
-superscripts of summation-type symbols to the side, even in displayed
-equations.\\\hline
-\verb+intlimits+\index{intlimits} & Like sumlimits, but for integral symbols.\\\hline
-\verb+nointlimits+\index{nointlimits} & (default) Opposite of intlimits.\\\hline
-\verb+namelimits+\index{namelimits} & (default) Like sumlimits, but for
-certain `operator names' such as \verb+det+, \verb+inf+, \verb+lim+, \verb+max+, \verb+min+, that traditionally
-have subscripts placed underneath when they occur in a displayed equation.\\\hline
-\verb+nonamelimits+\index{nonamelimits} & Opposite of namelimits.\\\hline
-\end{tabularx}
-\bigskip
-
-To use one of these package options, put the option name in the optional
-argument, \eg
-\verb|\usepackage[intlimits]{amsmath}|. The   %%% ----- Martin -----
-\AmSmath also recognises the following options which are normally
-selected (implicitly or explicitly) through the \verb|documentclass|
-command, and thus need not be repeated in the option list of the \verb|\usepackage{amsmath}| statement.    %%% ----- Martin -----
-
-\bigskip\noindent
-\begin{tabularx}{\linewidth}{@{}lX@{}}
-\verb+leqno+\index{leqno} & Place equation numbers on the left.\\\hline
-\verb+reqno+\index{reqno} & (default) Place equation numbers on the right.\\\hline
-\verb+fleqn+\index{fleqn} & Position equations at a fixed indent from the
-left margin rather than centered in the text column. \AmSmath defines the
-length \CMD{mathindent} and uses it when the equations have only one
-tabbing character (\verb+&+).\index{mathindent@\textbackslash mathindent}\\\hline
-\end{tabularx}
-
-\bigskip\noindent All math environments are displayed ones, so  there is no special inline
-math.
-
-\section{\texttt{align} environments}
-
-There are four different align environments, described in the following
-subsections. Their behaviour is shown in table \ref{cap:align}. The symbolic
-code for all align environments is:
-
-\begin{lstlisting}
-\begin{<name>}
-   <name> &= x & x &= x\\
-   <name> &= x & x &= x
-\end{<name>}
-\end{lstlisting}
-
-\begin{table}[htb]
-\caption[Comparison between the different align environments]{Comparison between the different align environments
-with the same code, where the first three can have an equation number}\label{cap:align}
-\begin{align*}
-\framebox[0.125\columnwidth]{align} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x}&= \framebox[0.125\columnwidth]{x}\\
-\framebox[0.125\columnwidth]{align}&= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x}
-\end{align*}
-
-\begin{alignat*}{2}
-\framebox[0.125\columnwidth]{alignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\
-\framebox[0.125\columnwidth]{alignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x}
-\end{alignat*}
-
-\begin{flalign*}
-\framebox[0.125\columnwidth]{flalign} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\
-\framebox[0.125\columnwidth]{flalign} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x}
-\end{flalign*}
-
-\begin{xalignat*}{2}
-\framebox[0.125\columnwidth]{xalignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\
-\framebox[0.125\columnwidth]{xalignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x}
-\end{xalignat*}
-
-\begin{xxalignat}{2}
-\framebox[0.125\columnwidth]{xxalignat} &= \framebox[0.125\columnwidth]{x} & \framebox[0.125\columnwidth]{x} &= \framebox[0.125\columnwidth]{x}\\
-\framebox[0.125\columnwidth]{xxalignat} &= \framebox[0.1\columnwidth]{x} & \framebox[0.1\columnwidth]{x} &= \framebox[0.1\columnwidth]{x}
-\end{xxalignat}
-
-\end{table}
-
-In difference to the \UIndex{eqnarray} from standard \LaTeX{} 
-(section~\ref{display:eqnarray}),  the ``three'' parts
-of one equation \verb+expr.-symbol-expr.+ are divided by only one ampersand    %%% ----- Martin -----
-in two parts. In general the ampersand should be before the symbol to get the right spacing, 
-\eg \verb+y &= x+. Compare the following three equations, the second one has a wrong spacing.    %%% ----- Martin -----
-
-
-\noindent
-~\hfill\includegraphics{amsalign}
-
-\iffalse
-\begin{minipage}{0.4\linewidth}
-\begin{align}
-\rnode[lt]{a}{y} &= \rnode[rt]{A}{x}
-\end{align}
-\vspace*{-3\abovedisplayskip}
-\begin{align}
-y =& x
-\end{align}
-\vspace*{-3\abovedisplayskip}
-\begin{align}
-\rnode[lb]{b}{y} ={}& \rnode[rb]{B}{x}
-\end{align}
-\ncline[nodesep=-10pt,linewidth=0.1pt]{A}{B}
-\ncline[nodesepA=-11pt,nodesepB=-10pt,linewidth=0.1pt]{a}{b}
-\end{minipage}
-\hfill\begin{minipage}{0.4\linewidth}
-\begin{lstlisting}
-  y &= x
-  y =& x
-  y ={}& x
-\end{lstlisting}
-\end{minipage}
-\fi
-
-\subsection{The default \texttt{align} environment}
-
-The \texttt{eqnarray} environment has a not so good spacing between
-the cells. Writing the equations no. \ref{eq:2} to \ref{eq:5} with
-the \texttt{align} environment gives:
-
-\begin{align}
-	y & =d\label{eq:IntoSection}\\
-	y & =cx+d\\
-	y_{12} & =bx^{2}+cx+d\\
-	y(x) & =ax^{3}+bx^{2}+cx+d
-\end{align}
-
-\noindent The code looks like:
-\begin{lstlisting}
-\begin{align}
-	y & =d\label{eq:IntoSection}\\
-	y & =cx+d\\
-	y_{12} & =bx^{2}+cx+d\\
-	y(x) & =ax^{3}+bx^{2}+cx+d
-\end{align}
-\end{lstlisting}
-
-\begin{itemize}
-\item The \texttt{align} environment has an implicit \textbf{\{rlrl...\}}
-horizontal alignment with a vertical column-alignment, \eg
-\begin{LTXexample}[width=0.5\linewidth]
-\begin{align*}
-  1 & 2 & 3
-\end{align*}
-\end{LTXexample}
-
-\item A nonumber-version \texttt{\small \textbackslash{}begin\{align{*}\}...\textbackslash{}end\{align{*}\}}
-exists.
-\item Unnumbered single rows are possible with \CMD{nonumber}.    %%% ----- Martin -----
-\item The \texttt{align} environment takes the whole horizontal space if
-you have more than two columns:
-\begin{align}
-y & =d & z & =1\\
-y & =cx+d & z & =x+1\\
-y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\
-y(x) & =ax^{3}+bx^{2}+cx+d & z & =x^{3}+x^{2}+x+1
-\end{align}
-
-\end{itemize}
-The code for this example looks like%
-\begin{lstlisting}
-\begin{align}
-	y & =d & z & =1\\
-	y & =cx+d & z & =x+1\\
-	y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\
-	y(x) & =ax^{3}+bx^{2}+cx+d & z & =x^{3}+x^{2}+x+1
-\end{align}
-\end{lstlisting}
-
-\subsection{\texttt{alignat} environment\label{sec:alignat environment}}
-\mPar{\CMD{begin\{align\}\\...\\\CMD{end\{align\}}}}
-\renewcommand{\theequation}{%
-  \thepart-\arabic{equation}%
-}
-
-\begin{leftbar}
->From now the counting of the equation changes. It is introduced with a foregoing command,
-which doesn't really make sense, it is only for demonstration:\\
-\verb|\renewcommand{\theequation}{\thepart-\arabic{equation}}|.
-\end{leftbar}
-
-
-This means  ``align at several places{}'' and is something like
-more than two \verb+align+ environment side by side.
-Parameter is the number of the \verb+align+ environments, which
-is not important for the user. The
-above last \verb+align+ example looks like:
-
-\begin{alignat}{2}
-y & =d & z & =1\label{eq:newCounting}\\
-y & =cx+d & z & =x+1\\
-y_{12} & =bx^{2}+cx+d & z & =x^{2}+x+1\nonumber \\
-y(x) & =ax^{3}+bx^{2}+cx+d\quad & z & =x^{3}+x^{2}+x+1\end{alignat}
-
-
-The parameter was 2 and it is 3 for the following example:    %%% ----- Martin -----
-
-\begin{alignat}{3}
-i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\
-i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\
-i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11}\end{alignat}
-
-
-For this example the code is:
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{alignat}{3}
-  i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\
-  i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\
-  i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11}
-\end{alignat}
-\end{lstlisting}
-
-With the \verb+alignat+ environment one can easily align equations vertically
-at more than one marker:
-
-\begin{alignat}{3}
-   abc &= xxx             &&= xxxxxxxxxxxx &&= aaaaaaaaa \\
-   ab  &= yyyyyyyyyyyyyyy &&= yyyy         &&= ab
-\end{alignat}
-\begin{lstlisting}
-\begin{alignat}{3}
-   abc &= xxx             &&= xxxxxxxxxxxx &&= aaaaaaaaa \\
-   ab  &= yyyyyyyyyyyyyyy &&= yyyy         &&= ab
-\end{alignat}
-\end{lstlisting}
-
-
-
-
-\begin{itemize}
-\item The \texttt{alignat} environment has an implicit \{rlrl...rlrl\}
-horizontal alignment with a vertical column alignment.
-\item A nonumber-version \texttt{\small
-\textbackslash{}begin\{alignat{*}\}...\textbackslash{}end\{alignat{*}\}}
-exists.
-\item Unnumbered single rows are possible with \CMD{nonumber}.    %%% ----- Martin -----
-\end{itemize}
-
-\subsection{\texttt{flalign} environment}\label{ams:flalign}
-\mPar{\CMD{begin\{flalign\}\\...\\\CMD{end\{flalign\}}}}This is the new replacement for the \texttt{xalignat} and \texttt{xxalignat}
-environments. It is nearly the same as the  \texttt{xalignat} environment, only
-more ``out spaced'' and ``left aligned''. 
-
-\begin{LTXexample}[width=0.5\linewidth]
-\begin{flalign}
-i_{11} & =0.25\nonumber \\
-i_{21} & =\frac{1}{3}i_{11}\\
-i_{31} & =0.33i_{22}
-\end{flalign}
-\end{LTXexample}
-
-\medskip
-As seen, the equations are not really left aligned, when they have only one
-ampersand. In this case \verb+flalign+ has the same behaviour as the \verb+align+
-environment.\index{Alignment!left}\index{Indentation}
-
-
-When there are more than one tabbing characters (\verb+&+), then the equations are
-really left aligned. This is also an easy way to get an equation with only one
-ampersand left aligned, see equation \ref{eq:leftaligned} below.
-\begin{flalign}
-i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\
-i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\
-i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11}
-\end{flalign}
-The code looks like:
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{flalign}
-  i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\
-  i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\
-  i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11}
-\end{flalign}
-\end{lstlisting}
-
-\medskip
-This environment can be used to mix centered and left aligned\index{Left aligned}
-equations without
-using the document wide valid option \verb|fleqn|.
-\begin{align}\label{eq:centered}
-	f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x
-\end{align}
-
-\begin{flalign}\label{eq:leftaligned}
-	f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x &
-\end{flalign}
-Equation \ref{eq:leftaligned} is left aligned in fact of the second tabbing
-character \verb|&|.
-
-\begin{lstlisting}
-\begin{align}\label{eq:centered}
-	f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x
-\end{align}
-
-\begin{flalign}\label{eq:leftaligned}
-	f(x) & = \int\frac{1}{x^2}\,\mathrm{d}x &
-\end{flalign}
-\end{lstlisting}
-
-Another case is placing text left aligned, whereas the formulas should be right aligned.
-
-\begin{flalign*}
-                && 12(x-1)+20(y-3)+14(z-2) &= 0\\
-\text{same as } &&               6x+10y+7z &= 0
-\end{flalign*}
-
-\begin{lstlisting}
-\begin{flalign*}
-                && 12(x-1)+20(y-3)+14(z-2) &= 0\\
-\text{same as } &&               6x+10y+7z &= 0
-\end{flalign*}
-\end{lstlisting}
-
-
-\subsection{\texttt{xalignat} environment}
-\mPar{\CMD{begin\{xalignat\}\\...\\\CMD{end\{xalignat\}}}}%
-This is an obsolete macro but still supported by the \AmSmath package.
-Same as \texttt{alignat} environment, only a little more ``out spaced{}''.
-\begin{xalignat}{3}
-i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber \\
-i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\
-i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11}
-\end{xalignat}
-The same code looks like:
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{xalignat}{3}
-  i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\
-  i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\
-  i_{31} & =0.33i_{22}\quad & i_{32} & =0.15i_{32}\quad & i_{33} & =i_{11}
-\end{xalignat}
-\end{lstlisting}
-
-\subsection{\texttt{xxalignat} environment}
-\mPar{\CMD{begin\{xxalignat\}\\...\\\CMD{end\{xxalignat\}}}}%
-Like \texttt{xalignat}  an obsolete macro but still supported by the \AmSmath package.
-Same as \texttt{align} environment, only extremely ``out spaced{}'',
-therefore no equation number!
-\begin{xxalignat}{3}
-i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\\
-i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12} & i_{23} & =i_{31}\\
-i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11}
-\end{xxalignat}
-The same code looks like:
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{xxalignat}{3}
-  i_{11} & =0.25 & i_{12} & =i_{21} & i_{13} & =i_{23}\nonumber\\
-  i_{21} & =\frac{1}{3}i_{11} & i_{22} & =0.5i_{12}& i_{23} & =i_{31}\\
-  i_{31} & =0.33i_{22} & i_{32} & =0.15i_{32} & i_{33} & =i_{11}
-\end{xxalignat}
-\end{lstlisting}
-
-
-\subsection{\texttt{aligned} environment}\label{sec:aligned}
-
-\mPar{\CMD{begin\{aligned\}\\...\\\CMD{end\{aligned\}}}}In difference to the 
-\verb|split| environment (section \vref{split})\index{Split equation}, the 
-\verb|aligned| environment allows more than one horizontal alignment but has 
-also only one equation number:
-%
-\begin{equation}
-\begin{aligned}
-    2x+3 &= 7  &     2x+3-3 &=7-3    \\
-    2x   &= 4  & \frac{2x}2 &=\frac42\\
-    x    &= 2
-\end{aligned}
-\end{equation}
-
-\begin{lstlisting}
-\begin{equation}
-\begin{aligned}
-    2x+3 &= 7  &     2x+3-3 &= 7-3    \\
-    2x   &= 4  & \frac{2x}2 &= \frac42\\
-    x    &= 2
-\end{aligned}
-\end{equation}
-\end{lstlisting}
-
-The \verb|aligned| environment is similar to the \verb|array|\index{array} 
-environment, there exists no
-starred version and it has only one equation number and has to be part of 
-another math environment, which should be \verb|equation| environment. 
-The advantage of \verb|aligned| is the much
- better horizontal and vertical spacing.    %%% ----- Martin -----
-
-
-\subsection{Problems}
-When using one of the \verb+align+ environments, there should be no \verb+\\+ at the
-end of the last line, otherwise you'll get another equation number for this  
-``empty{}'' line:    %%% ----- Martin -----
-
-\begin{LTXexample}[width=0.65\linewidth]
-\begin{align}
-    2x+3 &= 7\\
-\end{align}
-\end{LTXexample}
-
-\begin{LTXexample}[width=0.65\linewidth]
-\begin{align}
-    2x+3 &= 7
-\end{align}
-\end{LTXexample}
-\section{Other environments}
-
-
-\subsection{\texttt{gather} environment}
-
-\mPar{\CMD{begin\{gather\}\\...\\\CMD{end\{gather\}}}}
-This is like a multi line environment with no special horizontal alignment.
-All rows are centered and can have an own equation number:
-%
-\begin{gather}
-i_{11}=0.25\\
-i_{21}=\frac{1}{3}i_{11}\nonumber \\
-i_{31}=0.33i_{22}
-\end{gather}
-%
-For this example the code looks like:
-\begin{lstlisting}
-\begin{gather}
-  i_{11} = 0.25\\
-  i_{21} = \frac{1}{3}i_{11}\nonumber\\
-  i_{31} =0.33i_{22}
-\end{gather}
-\end{lstlisting}
-
-\begin{itemize}
-\item The \texttt{gather}\index{gather} environment has an implicit \texttt{\{c\}}
-horizontal alignment with no vertical column alignment. It is just
-like an one column array/table.
-\item A nonumber-version \texttt{\small \textbackslash{}begin\{gather{*}\}...\textbackslash{}end\{gather{*}\}}
-exists.
-Look at section \vref{split} for an example.
-\end{itemize}
-
-\subsection{\texttt{gathered} environment}
-\mPar{\CMD{begin\{gathered\}[c]\\...\\\CMD{end\{gathered\}}}}
-
-The \verb+gathered+ environment is like the \verb+aligned+ or \verb+alignat+
-\index{gathered}\index{aligned}\index{alignat}
-environment. They use only so much horizontal space as the widest line needs.
-In difference to the \verb+gather+ environment it must be itself inside the
-math mode.
-%
-\begin{align}
-\rule{2cm}{1pt}
-\begin{gathered}
-\quad i_{11}=0.25\\
-\quad i_{21}=\frac{1}{3}i_{11}\\
-\quad i_{31}=0.33i_{22}
-\end{gathered}
-\rule{2cm}{1pt}
-\end{align}
-
-%
-\begin{lstlisting}
-\begin{align}
-\rule{2cm}{1pt}
-\begin{gathered}
-\quad i_{11}=0.25\\
-\quad i_{21}=\frac{1}{3}i_{11}\\
-\quad i_{31}=0.33i_{22}
-\end{gathered}
-\rule{2cm}{1pt}
-\end{align}
-\end{lstlisting}
-%
-
-The optional argument can be used for setting the vertical alignment which is
-by default c (centered). It can also be t for top or b for bottom.
-
-\begin{align}
-\rule{1cm}{1pt}
-\begin{gathered}[t]
-\quad A=a\\
-\quad B=b\\
-\quad C=c
-\end{gathered}
-%
-\begin{gathered}[c]
-\quad A=a\\
-\quad B=b\\
-\quad C=c
-\end{gathered}
-%
-\begin{gathered}[b]
-\quad A=a\\
-\quad B=b\\
-\quad C=c
-\end{gathered}
-\ \rule{1cm}{1pt}
-\end{align}
-
-\begin{lstlisting}
-\begin{align}
-\rule{1cm}{1pt}
-\begin{gathered}[t]
-\quad A=a\\
-\quad B=b\\
-\quad C=c
-\end{gathered}
-%
-\begin{gathered}[c]
-\quad A=a\\
-\quad B=b\\
-\quad C=c
-\end{gathered}
-%
-\begin{gathered}[b]
-\quad A=a\\
-\quad B=b\\
-\quad C=c
-\end{gathered}
-\ \rule{1cm}{1pt}
-\end{align}
-\end{lstlisting}
-
-
-When using a square bracket as first character inside the environment, then 
-everything is ignored by \AmS until a following closing bracket, because \AmS takes this
-as an optional argument:
-%
-\begin{align}
-\begin{gathered}
-[A]\quad A=a\\
-[B]\quad B=b\\
-[C]\quad C=c
-\end{gathered}
-\end{align}
-%
-\begin{lstlisting}
-\begin{align}
-\begin{gathered}
-[A]\quad A=a\\
-[B]\quad B=b\\
-[C]\quad C=c
-\end{gathered}
-\end{align}
-\end{lstlisting}
-%
-The \verb+[A]+ is completely ignored, which can be avoided by using the
-optional argument \verb+[c]+ or at least an empty one directly
-after the \verb+\begin{gather}+. Another possibility is using the package \verb+empheq+,
-which fixes this behaviour by default.
-%
-\begin{align}
-\begin{gathered}[]
-[A]\quad A=a\\
-[B]\quad B=b\\
-[C]\quad C=c
-\end{gathered}
-\end{align}
-%
-\begin{lstlisting}
-\begin{align}
-\begin{gathered}[]
-[A]\quad A=a\\
-[B]\quad B=b\\
-[C]\quad C=c
-\end{gathered}
-\end{align}
-\end{lstlisting}
-%
-
-
-\subsection{\texttt{multline} environment}
-\mPar{\CMD{begin\{multline\}\\...\\\CMD{end\{multline\}}}}
-This is also like a multi line%
-\footnote{It is no typo, the name of the environment is \texttt{multline}, no
-missing i here!} environment with a special vertical alignment. The \textbf{first}
-row is \textbf{left aligned}, the second and all following ones except
-the last one are \textbf{centered} and the \textbf{last} line is \textbf{right
-aligned}. It is often used to write extremely long formulas:
-
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{multline}
-  A = \lim _{n\rightarrow \infty }\Delta x\left( a^{2}+\left( a^{2}+2a\Delta x
-          +\left( \Delta x\right) ^{2}\right)\right.\\
-  +\left( a^{2}+2\cdot 2a\Delta x+2^{2}\left( \Delta x\right) ^{2}\right)\\
-  +\left( a^{2}+2\cdot 3a\Delta x+3^{2}\left( \Delta x\right) ^{2}\right)\\
-  + \ldots\\
-  \left.+\left( a^{2}+2\cdot (n-1)a\Delta x +(n-1)^{2}\left( \Delta x\right) ^{2}\right) \right)\\
-  = \frac{1}{3}\left( b^{3}-a^{3}\right)
-\end{multline}
-\end{lstlisting}
-\begin{multline}
-A=\lim_{n\rightarrow\infty}\Delta x\left(a^{2}+\left(a^{2}+2a\Delta x+\left(\Delta x\right)^{2}\right)\right.\label{eq:reset}\\
-+\left(a^{2}+2\cdot2a\Delta x+2^{2}\left(\Delta x\right)^{2}\right)\\
-+\left(a^{2}+2\cdot3a\Delta x+3^{2}\left(\Delta x\right)^{2}\right)\\
-+\ldots\\
-\left.+\left(a^{2}+2\cdot(n-1)a\Delta x+(n-1)^{2}\left(\Delta x\right)^{2}\right)\right)\\
-=\frac{1}{3}\left(b^{3}-a^{3}\right)
-\end{multline}
-
-
-\begin{figure}[htb]
-\begin{multline}
-\framebox[0.5\columnwidth]{x}\\
-\framebox[0.5\columnwidth]{x}\\
-\framebox[0.5\columnwidth]{x}\\
-\shoveright{\framebox[0.5\columnwidth]{x}}\\
-\framebox[0.5\columnwidth]{x}\\
-\framebox[0.5\columnwidth]{x}
-\end{multline}
-\caption{\texttt{multline} Alignment demo
-(the fourth row is shifted to the right with \CMD{shoveright})}
-\label{cap:multline-Alignment-Demo}
-\end{figure}
-
-\begin{figure}[htb]
-\begin{minipage}[c]{0.45\textwidth}%
-\fbox{\parbox{\columnwidth}{\begin{multline}
-\framebox[0.5\columnwidth]{\textrm{\textbackslash multlinegap=}}\\
-\framebox[0.5\columnwidth]{\the\multlinegap}\end{multline}
-}}
-\end{minipage}%
-\hfill{}\begin{minipage}[c]{0.45\textwidth}%
-{\setlength{\multlinegap}{0pt}\fbox{\parbox{\columnwidth}{\begin{multline}
-\framebox[0.5\columnwidth]{\textbackslash\textrm{multlinegap=}}\\
-\framebox[0.5\columnwidth]{\the\multlinegap}\end{multline}
-}}}
-\end{minipage}%
-\caption{\label{cap:multlinegap}Demonstration of \CMD{multlinegap} (default is 0pt)}
-\end{figure}
-
-
-
-\begin{itemize}
-\item A nonumber-version \CMD{begin\{multline{*}\}...}\CMD{end\{multline{*}\}}
-exists.
-\item By default only the last line (for right equation numbers) or the
-first line (for left equation numbers) gets a number, the others can't.
-\item The alignment of a single line can be changed with the command
-\CMD{shoveright}\index{shoveright@\textbackslash shoveright} (figure \vref{cap:multline-Alignment-Demo})
-\item The first line and the last line have a small gap to the text border.%
-\footnote{When the first (numbers left) or last line (numbers right) has an
-equation number then \CMD{multlinegap} is not used
-for these ones, only for the line without a number.} See figure \ref{cap:multlinegap}, where the length of \CMD{multlinegap}\index{multlinegap@\textbackslash multlinegap}
-is set to \texttt{0pt} for the right one.
-\end{itemize}
-
-\subsubsection{Examples for \texttt{multline}}\label{sec:Specials-for-multline}
-
-With the multline environment the equation~\vref{eq:braces} looks like:
-
-\begin{multline}
-\frac{1}{2}\Delta(f_{ij}f^{ij})=2\left(\sum_{i<j}\chi_{ij}(\sigma_{i}-\sigma_{j})^{2}
-  +f^{ij}\nabla_{j}\nabla_{i}(\Delta f)+\right.\\
-+\left.\nabla_{k}f_{ij}\nabla^{k}f^{ij}+f^{ij}f^{k}\left[2\nabla_{i}R_{jk}-\nabla_{k}R_{ij}
- \right]\right)
-\end{multline}
-%
-which is again a bad typesetting because of the two unequal parentheses.
-Each one has a size which is correct for the line but not for the
-whole formula. \LaTeX{} accepts only pairs of parentheses for one
-line and has an ``empty{}'' parentheses, the dot ``\texttt{\textbackslash{}left.}''
-or ``\texttt{\textbackslash{}right.}''{} to get only one of the ``pair{}''.
-There are different solutions to get the right size of the parentheses.
-One of them is to use the \CMD{vphantom} command,
-which reserves the vertical space without any horizontal one, like
-a vertical rule without any thickness. The sum symbol from the first
-line is the biggest one and responsible for the height, so this one is
-the argument of \CMD{vphantom} which has to be
-placed anywhere.
-
-\begin{multline}
-\frac{1}{2}\Delta(f_{ij}f^{ij})=
-	2\left(\sum_{i<j}\chi_{ij}(\sigma_{i}-
-	\sigma_{j})^{2}+f^{ij}\nabla_{j}\nabla_{i}(\Delta f)+\right.\\
-	\left.+\nabla_{k}f_{ij}\nabla^{k}f^{ij}+
-	f^{ij}f^{k}\left[2\nabla_{i}R_{jk}-
-	\nabla_{k}R_{ij}\right]\vphantom{\sum_{i<j}}\right)
-\end{multline}
-%
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{multline}
-\frac{1}{2}\Delta(f_{ij}f^{ij})=
-	2\left(\sum_{i<j}\chi_{ij}(\sigma_{i}-
-	\sigma_{j})^{2}+f^{ij}\nabla_{j}\nabla_{i}(\Delta f)+\right.\\
-	\left.+\nabla_{k}f_{ij}\nabla^{k}f^{ij}+
-	f^{ij}f^{k}\left[2\nabla_{i}R_{jk}-
-	\nabla_{k}R_{ij}\right]\vphantom{\sum_{i<j}}\right)
-\end{multline}
-\end{lstlisting}
-%
-Instead of using the \CMD{vphantom} command it is
-also possible to use fixed-width parentheses, which is described in
-section \vref{sec:Brackets,-Braces-and}.
-
-
-A math expression with a very long fraction like the following one, which runs out 
-of the margin
-could be written as a multiplication to avoid the fraction line.
-%
-%\begin{LTXexample}[pos=t,xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{equation}
-\frac{\mathrm{d}G_\infty}{\mathrm{d}n}=\frac{\left[1-e^{-pn}\right] 
-  \left[Q\left(n\right)-pR\left(n\right)+R'\left(n\right)\right]e^{-pn}
-  -\left[-\frac{Q \left(n\right)e^{-pn}}{p}+\frac{Q\left(0\right)}{p}+R
-  \left(n\right)e^{-pn} - A\right] pe^{-pn}}{\left({1-e^{-pn}}\right)^2} = 0
-\end{equation}
-%\end{LTXexample}
-%
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{equation}
-\frac{\mathrm{d}G_\infty}{\mathrm{d}n}=\frac{\left[1-e^{-pn}\right] 
-  \left[Q\left(n\right)-pR\left(n\right)+R'\left(n\right)\right]e^{-pn}
-  -\left[-\frac{Q \left(n\right)e^{-pn}}{p}+\frac{Q\left(0\right)}{p}+R
-  \left(n\right)e^{-pn} - A\right] pe^{-pn}}{\left({1-e^{-pn}}\right)^2} = 0
-\end{equation}
-\end{lstlisting}
-%
-With the \verb+multline+ environment it can then be split into two or more parts:
-%
-\begin{LTXexample}[pos=t,xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{multline}
-\frac{\mathrm{d}G_\infty}{\mathrm{d}n} = 
-      \frac{1}{\left( {1-e^{-pn}} \right)^2 }\cdot
-      \left\{\vphantom{\frac{Q}{p}}% >>>> to get the correct height <<<<<
-      \left[ 1-e^{-pn} \right] \left[ Q \left( n \right) - pR 
-      \left( n \right) + R'\left( n \right) \right]e^{-pn}\right.\\
-    - \left.\left[-\frac{Q \left( n \right) e^{-pn}}{p} + 
-    \frac{Q \left( 0 \right)}{p} + R \left( n \right) e^{-pn} 
-    - A\right] pe^{-pn}\right\} = 0
-\end{multline}
-\end{LTXexample}
-
-
-
-\subsection{\texttt{split} environment}\label{split}
-
-\mPar{\CMD{begin\{split\}\\...\\\CMD{end\{split\}}}}%
-\makeatletter
-\@removefromreset{equation}{section}
-\makeatother
-%
-\begin{leftbar}
-\noindent From now on the counting of the equations changes. It is introduced with a 
-foregoing command, which doesn't really make sense, it is only 
-for demonstration: 
-\begin{lstlisting}
-\makeatletter
-\@removefromreset{equation}{section}
-\makeatother
-\end{lstlisting}
-\end{leftbar}
-
-
-The \verb|split| environment is like the \verb|multline|\index{multline}
-or \verb|array| environment for equations longer than the column
-width. Just like the array environment and in contrast to \verb|multline|,
-\verb|split| can only be used as \textbf{part of another environment}.
-\verb|split| itself has no own numbering, this is given by the other
-environment. Without an ampersand all lines in the split environment
-are right-aligned and can be aligned at a special point by using an
-ampersand. In difference to the \verb|aligned| environment (section \vref{sec:aligned}), the \verb|split| 
-environment don't permit more than one horizontal alignment.
-
-It is important that the split environment has another behaviour when used inside one of the    %%% ----- Martin -----
-``old'' \LaTeX{} environments \verb+\[...\]+ or \verb+\begin{equation}+ \verb+...+\verb+ \end{equation}+, in this
-case more than one horizontal alignment tabs are possible.
-
-\hspace*{-\marginparwidth}%
-\begin{minipage}{0.5\columnwidth}
-\[
-\begin{split}
-   \framebox[0.35\columnwidth]{x}\\
-   \framebox[0.75\columnwidth]{x}\\
-   \framebox[0.65\columnwidth]{x}\\
-   \framebox[0.95\columnwidth]{x}
-\end{split}
-\]
-\end{minipage}\hfill%
-\begin{minipage}{0.5\columnwidth}
-\footnotesize\begin{verbatim}
-\[
-\begin{split}
-   \framebox[0.35\columnwidth]{x}\\
-   \framebox[0.75\columnwidth]{x}\\
-   \framebox[0.65\columnwidth]{x}\\
-   \framebox[0.95\columnwidth]{x}
-\end{split}
-\]
-\end{verbatim}
-\end{minipage}
-\vspace{2ex}
-
-\hspace*{-\marginparwidth}%
-\begin{minipage}{0.5\columnwidth}
-\[
-\begin{split}
-   \vec{a} = {}&\framebox[0.35\columnwidth]{x}\\
-             &\framebox[0.75\columnwidth]{x}\\
-             &\framebox[0.65\columnwidth]{x}\\
-             &\framebox[0.95\columnwidth]{x}
-\end{split}
-\]
-\end{minipage}\hspace{1cm}%
-\begin{minipage}{0.5\columnwidth}
-\footnotesize%
-\begin{verbatim}
-\[
-\begin{split}
-   \vec{a} = {}&\framebox[0.35\columnwidth]{x}\\
-               &\framebox[0.75\columnwidth]{x}\\
-               &\framebox[0.65\columnwidth]{x}\\
-               &\framebox[0.95\columnwidth]{x}
-\end{split}
-\]
-\end{verbatim}
-\end{minipage}
-\vspace{1ex}
-
-The following example shows the \texttt{split} environment as part
-of the \texttt{equation} environment:
-
-\begin{equation}
-\begin{split}A_{1} & =\left|\int_{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right|+\left|\int_{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right|\\
- & =\left|\int_{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right|+\left|\int_{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right|\\
- & =\left|\frac{x^{3}}{3}-\frac{3}{2}x^{2}\right|_{0}^{1}+\left|\frac{x^{3}}{3}-\frac{5}{2}x^{2}+6x\right|_{1}^{2}\\
- & =\left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}-\frac{5}{2}+6\right)\right|\\
- & =\left|-\frac{7}{6}\right|+\left|\frac{14}{3}-\frac{23}{6}\right|=\frac{7}{6}+\frac{5}{6}=2\,\textrm{FE}\end{split}
-\label{eq:Beispiel-Integral}\end{equation}
-
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{equation}
-  \begin{split}
-    A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left|
-			\int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\
-          & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left|
-			\int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\
-          & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+
-			\left| \frac{x^{3}}{3}-
-                \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\
-          & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left|
-			\frac{8}{3}-\frac{20}{2}+12-
-                \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\
-          & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6}
-			\right| =\frac{7}{6}+\frac{5}{6}=2\, \textrm{FE}
-  \end{split}
-\end{equation}
-\end{lstlisting}
-
-\bigskip{}
-The same using the \verb|array| environment with \verb|{rl}|-alignment
-instead of \verb|split| gives same horizontal alignment, but another    %%% ----- Martin -----
-vertical spacing%
-\footnote{Can be changed with \texttt{\textbackslash renewcommand\textbackslash arraystretch\{1.5\}}} and the
-symbols are only in scriptsize and not textsize:\footnote{See section \vref{sec:Styles}}    %%% ----- Martin -----
-
-\begin{equation}
-\begin{array}{rl}
-A_{1} & =\left|\int_{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right|+\left|\int_{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right|\\
- & =\left|\int_{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right|+\left|\int_{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right|\\
- & =\left|\frac{x^{3}}{3}-\frac{3}{2}x^{2}\right|_{0}^{1}+\left|\frac{x^{3}}{3}-\frac{5}{2}x^{2}+6x\right|_{1}^{2}\\
- & =\left|\frac{1}{3}-\frac{3}{2}\right|+\left|\frac{8}{3}-\frac{20}{2}+12-\left(\frac{1}{3}-\frac{5}{2}+6\right)\right|\\
- & =\left|-\frac{7}{6}\right|+\left|\frac{14}{3}-\frac{23}{6}\right|=\frac{7}{6}+\frac{5}{6}=2\,\textrm{FE}
- \end{array}
- \end{equation}
-
-Compare the following two examples for typesetting the minus sign. In the first case it
-is typeset similiar to the plus character, and in the second example it is typeset
-without the additional space for a binary math atom.  
-
-\begin{minipage}{0.49\linewidth}
-\begin{align}
-\begin{split}
-a = {} & -b + c \\
-       & -d + e
-\end{split}
-\end{align}
-%
-\begin{align}
-\begin{split}
-a = {} & {-}b + c \\
-       & {-}d + e
-\end{split}
-\end{align}
-\end{minipage}\hfill
-\begin{minipage}{0.49\linewidth}
-\begin{lstlisting}
-\begin{align}
-\begin{split}
-a = {} & -b + c \\
-       & -d + e
-\end{split}
-\end{align}
-%
-\begin{align}
-\begin{split}
-a = {} & {-}b + c \\
-       & {-}d + e
-\end{split}
-\end{align}
-\end{lstlisting}
-\end{minipage}
-
-\begin{itemize}
-\item There exists no starred version (\texttt{\textbackslash{}begin\{split{*}\}})    %%% ----- Martin -----
-of the \texttt{split} environment.
-\end{itemize}
-
-
-\subsection{\texttt{cases} environment }
-
-This gives support for an often used mathematical construct.\index{cases@\textbackslash cases}
-You can also choose the more than once described way to convert some
-text into math, like
-{\footnotesize\begin{verbatim}
-$x=\begin{cases}
- 0 & \text{if A=...}\\
- 1 & \text{if B=...}\\
- x & \textrm{this runs with as much text as you like,
-      but without an automatic linebreak, it runs out
-      of page....}
-\end{cases}$
-\end{verbatim}}
-\noindent which gives equation~\vref{eq:cases}. It is obvious what the problem
-is.
-
-\begin{eqnarray}
-x & = & \begin{cases}
-0 & \text{if A=...}\\
-1 & \text{if B=...}\\
-x & \textrm{this runs with as much text as you like, but without a linebreak, it runs out of page....}\end{cases}\label{eq:cases}\end{eqnarray}
-
-
-In this case it is better to use a parbox\index{parbox@\textbackslash parbox}
-for the text part with a \texttt{flushleft} command for a better view.
-
-\begin{equation}
-x=\begin{cases}
-0 & \text{if A=...}\\
-1 & \text{if B=...}\\
-x & \parbox{5cm}{\flushleft this runs with as much text as you like, but without an automatic linebreak, it runs out of page....}\end{cases}\end{equation}
-
-
-
-\begin{lstlisting}
-\begin{equation}
-x=\begin{cases}
-  0 & \text{if A=...}\\
-  1 & \text{if B=...}\\
-  x & \parbox{5cm}{%
-      \flushleft%
-      this runs with as much text as you like,
-      but without an automatic linebreak,
-      it runs out of page....}%
-\end{cases}
-\end{equation}
-\end{lstlisting}
-
-\begin{leftbar}
-\noindent From now on the counting of the equations changes. It is introduced 
-with a foregoing command, which doesn't really make sense, it is only for 
-demonstration: 
-\begin{lstlisting}
-\renewcommand\theequation{\arabic{equation}}
-\end{lstlisting}
-\end{leftbar}
-
-\renewcommand\theequation{\arabic{equation}}
-
-
-\subsection{Matrix environments}\label{sec:ams-matrix}
-%
-\begin{table}[htb]
-\centering\begin{tabular}{rcrcrc}
-\textbackslash{}Vmatrix\index{Vmatrix@\textbackslash Vmatrix}&
-$\begin{Vmatrix}a & b\\
-c & d\end{Vmatrix}$&
-\textbackslash{}Bmatrix\index{Bmatrix@\textbackslash Bmatrix}&
-$\begin{Bmatrix}a & b\\
-c & d\end{Bmatrix}$&
-\textbackslash{}matrix\index{matrix@\textbackslash matrix}&
-$\begin{matrix}a & b\\
-c & d\end{matrix}$\tabularnewline
-\rule{0pt}{0.85cm}\textbackslash{}vmatrix\index{vmatrix@\textbackslash vmatrix}&
-$\begin{vmatrix}a & b\\
-c & d\end{vmatrix}$&
-\textbackslash{}bmatrix\index{bmatrix@\textbackslash bmatrix}&
-$\begin{bmatrix}a & b\\
-c & d\end{bmatrix}$&
-\textbackslash{}pmatrix\index{pmatrix@\textbackslash pmatrix}&
-$\begin{pmatrix}a & b\\
-c & d\end{pmatrix}$\tabularnewline[10pt]
-&&&&\textbackslash{}smallmatrix\index{smallmatrix@\textbackslash smallmatrix}&
-$\begin{smallmatrix}a & b\\
-c & d\end{smallmatrix}$
-\end{tabular}
-\caption{Matrix environments}
-\end{table}
-
-All matrix environments can be nested and an element may also contain
-any other math environment, so that very complex structures are possible.
-By default all cells have a centered alignment, which is often not the best
-when having different decimal numbers or plus/minus values. Changing the
-alignment to right (not for the \verb+smallmatrix+) is possible with
-\mPar{%
-\texttt{matrix}\\
-\texttt{vmatrix}\\
-\texttt{Vmatrix}\\
-\texttt{bmatrix}\\
-\texttt{Bmatrix}\\
-\texttt{pmatrix}\\
-\texttt{smallmatrix}%
-}%
-
-\begin{lstlisting}
-\makeatletter
-\def\env@matrix{\hskip -\arraycolsep
-  \let\@ifnextchar\new@ifnextchar
-  \array{*\c@MaxMatrixCols r}}
-\makeatother
-\end{lstlisting}
-
-The special matrix environment \verb+smallmatrix+, which decreases
-horizontal and vertical space is typeset in scriptstyle. The \verb|smallmatrix|
-\index{smallmatrix@\textbackslash smallmatrix} environment makes some sense
-in the inline mode to decrease the line height.
-For dots over several columns look for \CMD{hdotsfor} in the following section.
-
-
-
-\section{Vertical whitespace}\label{sec:ams-whitespace}
-See section~\vref{subsec:vwhitespace} for the lengths which control the
-vertical whitespace. There is no difference to \AmSmath.
-
-\section{Dots}\label{sec:ams-dots}
-
-In addition to section~\vref{sec:Dots} \AmSmath has two more commands
-for dots: \CMD{dddot}\{...\}\footnote{already mentioned in section \ref{sec:Accents}} and \CMD{ddddot}\{...\}
-\index{dddot@\textbackslash dddot}\index{ddddot@\textbackslash ddddot}
-
-\verb|$\dddot{y}$|: $\dddot{y}$
-
-\verb|$\ddddot{y}$|: $\ddddot{y}$
-
-
-Another interesting dot command is \CMD{hdotsfor}\index{hdotsfor@\textbackslash hdotsfor}
-with the syntax:
-
-\begin{lstlisting}
-\hdotsfor[<spacing factor>]{<number of columns>}
-\end{lstlisting}
-
-With the spacing factor the width of the dots can be stretched or
-shrinked. The number of columns allows a continuing dotted line over
-more columns. Equation \ref{eq:tridiagonal} shows the definition
-of a tridiagonal matrix.
-
-\begin{equation}
-\underline{A}=\left[\begin{array}{ccccccc}
-a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0\\
-a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0\\
-0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0\\
-\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
-\hdotsfor{7}\cr\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
-0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0\\
-0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n}\\
-0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn}
-\end{array}\right]\label{eq:tridiagonal}
-\end{equation}
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{equation}
-\underline{A}=\left[\begin{array}{ccccccc}
-a_{11} & a_{12} & 0 & \ldots & \ldots & \ldots & 0\\
-a_{21} & a_{22} & a_{23} & 0 & \ldots & \ldots & 0\\
-0 & a_{32} & a_{33} & a_{34} & 0 & \ldots & 0\\
-\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
-\hdotsfor{7}\cr\vdots & \vdots & \vdots & \vdots & \vdots & \vdots & \vdots\\
-0 & \ldots & 0 & a_{n-2,n-3} & a_{n-2,n-2} & a_{n-2,n-1} & 0\\
-0 & \ldots & \ldots & 0 & q_{n-1,n-2} & a_{n-1,n-1} & a_{n-1,n}\\
-0 & \ldots & \ldots & \ldots & 0 & a_{n,n-1} & a_{nn}
-\end{array}\right]
-\end{equation}
-\end{lstlisting}
-
-
-\section{\texttt{fraction} commands}\label{sec:ams-fraction}
-
-
-\subsection{Standard}
-
-Additional to the font size problem described in subsection~\vref{sub:fraction command}
-\AmSmath supports some more commands for fractions\index{Fraction}. The \CMD{frac} command
-described in \cite{MathGuide}, does no more exist in \AmSmath.    %%% ----- Martin -----
-
-\begin{itemize}
-\item The global fraction definition has five parameters\index{genfrac@\textbackslash genfrac}
-\index{fraction@\textbackslash frac}
-\begin{lstlisting}[xleftmargin=-1em,xrightmargin=-1em]
-\genfrac{<left delim>}{<right  delim>}{<thickness>}{<mathstyle>}{<nominator>}{<denominator>}
-\end{lstlisting}
-where thickness can have any length with a valid unit like \\
-\verb|genfrac{}{}{1pt}{}{x^2+x+1}{3x-2}|
-$\rightarrow\genfrac{}{}{1pt}{}{x^2+x+1}{3x-2}$
-\item \CMD{cfrac}\index{cfrac@\textbackslash cfrac} (continued fraction) which is
-by default set in the display mathstyle and useful for fractions like
-\begin{equation}
-\cfrac{1}{\sqrt{2}+\cfrac{1}{\sqrt{3}+\cfrac{1}{\sqrt{4}+\cfrac{1}{\ldots}}}}\label{cfrac}
-\end{equation}
-which looks with the default \CMD{frac} command like
-\begin{equation}
-	\frac{1}{\sqrt{2}+\frac{1}{\sqrt{3}+\frac{1}{\sqrt{4}+\frac{1}{\ldots}}}}
-\end{equation}
-where the mathstyle decreases for every new level in the fraction.
-The \CMD{cfrac} command can be called with an optional
-parameter which defines the placing of the nominator, which can be
-\texttt{[l]}eft, \texttt{[r]}ight or \texttt{[c]}enter (the default - see
-equation~\ref{cfrac}):\\
-\begin{minipage}[c]{0.40\textwidth}%
-\[
-\cfrac[l]{1}{\sqrt{2}+\cfrac[l]{1}{\sqrt{3}+\cfrac[l]{1}{\sqrt{4}+\cfrac[l]{1}{\ldots}}}}
-\]
-\end{minipage}%
-\hfill{}\begin{minipage}[c]{0.40\textwidth}%
-\[\cfrac[r]{1}{\sqrt{2}+\cfrac[r]{1}{\sqrt{3}+\cfrac[r]{1}{\sqrt{4}+\cfrac[r]{1}{\ldots}}}}\]
-\end{minipage}%
-
-\item \CMD{dfrac}\index{dfrac@\textbackslash dfrac}
-which takes by default the displaystyle\index{displaystyle@\textbackslash displaystyle}, so that
-fractions in inline mode $\dfrac{1}{2}$ have the same size than in
-display mode.
-\item \CMD{tfrac}\index{tfrac@\textbackslash tfrac} (vice versa to \CMD{dfrac}) which takes by default
-the scriptstyle\index{scriptstyle@\textbackslash scriptstyle}, so that fractions in display
-mode have the same size than in inline mode.
-\end{itemize}
-
-\[\tfrac{2}{3} \text{\hspace{0.5cm}\CMD{tfrac\{2\}\{3\}}} \]
-\[\frac{2}{3} \text{\hspace{0.5cm}\CMD{frac\{2\}\{3\}}} \]
-
-
-\subsection{Binoms}\label{sub:Binoms}
-
-\mPar{\CMD{binom}\\\CMD{dbinom}\\\CMD{tbinom}}They are like fractions without a rule and its syntax is different
-to the \CMD{choose} command from standard \LaTeX{}
-(see section \vref{sub:fraction command}). \AmSmath{} provides three
-different commands for binoms just like the ones for fractions.
-
-\begin{table}[htb]
-\centering%
-\begin{tabular}{lcl}
-Command & Inlinemath & Displaymath\tabularnewline
-\hline
-\texttt{\textbackslash{}binom\{m\}\{n\}} & $\binom{m}{n}$&
-${\displaystyle \binom{m}{n}}$\tabularnewline
-\texttt{\rule{0pt}{0.75cm}\textbackslash{}dbinom\{m\}\{n\}}&
-$\dbinom{m}{n}$&
-${\displaystyle \dbinom{m}{n}}$\tabularnewline
-\texttt{\rule{0pt}{0.5cm}\textbackslash{}tbinom\{m\}\{n\}}&
-$\tbinom{m}{n}$&
-${\displaystyle \tbinom{m}{n}}$\tabularnewline
-\end{tabular}
-\caption{binom commands}
-\end{table}
-
-
-\section{Roots}\label{sec:Roots-ams}
-
-The typesetting for roots\index{uproot@\textbackslash uproot} is sometimes not
-the best. Some solutions for better typesetting are %
-\mPar{\CMD{leftroot}\\\CMD{uproot}}%
-described in section~\vref{sec:Roots} for standard \LaTeX{}. \AmSmath
-has some more commands for the $n$-th root:
-
-\begin{lstlisting}
-\sqrt[\leftroot{<number>}\uproot{<number>}<root>]{< ... >}
-\end{lstlisting}
-
-\noindent \verb+<number>+ indicates a value for the points%
-\footnote{In PostScript units (bp -- Big Points).} of which the root can be
-adjusted to the left and/or to the top, \eg
-$\sqrt[k_n]{a}$ (\verb+$\sqrt[k_n]{a}$+) has a too deep exponent, whereas $\sqrt[\uproot{2}k_n]{a}$ \verb+$\sqrt[\uproot{2}k_n]{a}$+ looks nicer.
-
-
-
-\subsection{Roots with \CMD{smash} command}
-
-\mPar{\CMD{smash}}The default for a root\index{Root} with $\lambda_{k_{i}}$ as root
-argument looks like $\sqrt{\lambda_{k_{i}}}$, which may be not the    %%% ----- Martin -----
-best typesetting. It is possible to reduce the lowest point of the root
-to the baseline with the \CMD{smash} command: $\sqrt{\lambda_{k_{i}}}\xrightarrow{\text{with \textbackslash smash}}\sqrt{\smash[b]{\lambda_{k_{i}}}}$
-
-
-The syntax of the \CMD{smash} command%
-\footnote{In \texttt{latex.ltx} \CMD{smash} is defined without an optional argument.} renewed by the \AmSmath  package is    %%% ----- Martin -----
-
-\begin{lstlisting}
-\smash[<position>]{<argument>}
-\end{lstlisting}
-The optional argument for the position can be:
-
-\begin{description}
-\item [t]keeps the bottom and annihilates the top
-\item [b]keeps the top and annihilates the bottom
-\item [tb]annihilates top and bottom (the default)
-\end{description}
-
-\section{Accents}\label{amssymb}
-
-With the macro \verb|\mathaccent| it is easy to define new accent types, for example
-
-\begin{lstlisting}
-\def\dotcup{$\mathaccent\cdot\cup$}
-\end{lstlisting}
-
-$\mathaccent\cdot\cup$
-
-\def\curvearrowleftright{%
-	\ensuremath{%
-		\mathaccent\curvearrowright{\mkern-5mu\curvearrowleft}%
-	}%
-}
-
-Overwriting of two symbols is also possible:
-
-{\huge
-$\curvearrowleft\curvearrowright\curvearrowleftright$}
-
-In this case the second symbol has to be shifted to the left for a length    %%% ----- Martin -----
-of $5mu$ (mu: math unit\index{Math unit}).
-
-\begin{lstlisting}
-\def\curvearrowleftright{%
-	\ensuremath{%
-		\mathaccent\curvearrowright{\mkern-5mu\curvearrowleft}%
-	}%
-}
-\end{lstlisting}
-
-For other possibilities to define new accents see section \vref{sec:package-accent}.    %%% ----- Martin -----
-
-\section{\CMD{mod} command}
-
-In standard \LaTeX{} the modulo command is not an operator, though    %%% ----- Martin -----
-it is often used in formulas. \AmSmath provides two (three) different
-commands for modulo, which are listed in tabular~\vref{cap:The-modulo commands}.
-
-\begin{itemize}
-\item They all insert some useful space before and behind the mod-operator.
-\end{itemize}
-
-\begin{table}[htb]
-\centering\begin{tabular}{rrl}
-a\textbackslash{}mod\{n\^{}2\}=b&
-$\rightarrow$&
-$a\mod{n^{2}}=b$\tabularnewline
-a\textbackslash{}pmod\{n\^{}2\}=b&
-$\rightarrow$&
-$a\pmod{n^{2}}=b$\tabularnewline
-a\textbackslash{}pod\{n\^{}2\}=b&
-$\rightarrow$&
-$a\pod{n^{2}}=b$\tabularnewline
-\end{tabular}
-\caption{\label{cap:The-modulo commands}The modulo commands and their meaning}
-\end{table}
-
-
-
-\section{Equation numbering\label{sec:Equation-numbering}}
-
-See section \vref{sub:Equationnumbering} for equation numbering\index{Equation!numbering}.
-It is mostly the %
-\mPar{\textbackslash{}numberwithin%
-}same, only one command is new to \AmSmath. If you want
-a numbering like ``\ref{eq:IntoSection}{}'' then write either in the preamble    %%% ----- Martin -----
-or like this example anywhere in your doc:
-
-\begin{lstlisting}
-\numberwithin{equation}{section}
-\end{lstlisting}
-
-\begin{leftbar}
-\numberwithin{equation}{section}From now on the numbering looks like    %%% ----- Martin -----
-equation \vref{eq:IntoSection}. For the book-class you can get the
-same for chapters.
-\end{leftbar}
-
-If you want to get rid of the parentheses then write in the preamble:    %%% ----- Martin -----
-
-\begin{lstlisting}
-\makeatletter
-\def\tagform@#1{\maketag@@@{\ignorespaces#1\unskip\@@italiccorr}}
-\makeatother
-\end{lstlisting}
-
-Now the following four subequation numbers have no parentheses.
-
-
-
-
-\makeatletter
-\let\oldTagForm\tagform@
-\def\tagform@#1{\maketag@@@{\ignorespaces#1\unskip\@@italiccorr}}
-\makeatother
-
-\subsection{Subequations}\label{ams:subeqn}
-
-Amsmath supports this with the environment \verb|subequation|\index{Subequations}.
-For example:
-\begin{subequations}
-\begin{align}
-y & =  d\\
-y & =  cx+d\\
-y & =  bx^{2}+cx+d\\
-y & =  ax^{3}+bx^{2}+cx+d
-\end{align}
-\end{subequations}
-
-\begin{lstlisting}
-\begin{subequations}
-\begin{align}
-y & =  d\\
-y & =  cx+d\\
-y & =  bx^{2}+cx+d\\
-y & =  ax^{3}+bx^{2}+cx+d
-\end{align}
-\end{subequations}
-\end{lstlisting}
-
-\makeatletter
-\let\tagform@\oldTagForm
-\makeatother
-
-
-Inside of subequations only complete other environments (\texttt{\textbackslash{}begin\{...\}
-... \textbackslash{}end\{...\}}) are possible.
-
-\begin{lstlisting}
-\renewcommand{\theequation}{%
-  \theparentequation{}-\arabic{equation}%
-}
-\end{lstlisting}
-
-\begin{subequations}
-\renewcommand{\theequation}{%
-  \theparentequation -\arabic{equation}%
-}%
-\begin{align}
-y & =  d\\
-y & =  cx+d\label{eq:subequation-neu}\\
-y & =  bx^{2}+cx+d\\
-y & =  ax^{3}+bx^{2}+cx+d
-\end{align}
-\end{subequations}
-
-A ref to a subequation is possible like the one to equation \ref{eq:subequation-neu}.
-The environment chooses the same counter ``\texttt{equation}''
-but saves the old value into ``\texttt{parentequation}''.
-
-\newcounter{mySubCounter}
-\newcommand{\twocoleqn}[2]{
-    \setcounter{mySubCounter}{0}%
-    \let\OldTheEquation\theequation%
-    \renewcommand{\theequation}{\OldTheEquation\alph{mySubCounter}}%
-    \noindent%
-    \begin{minipage}{.49\textwidth}
-          \begin{equation}\refstepcounter{mySubCounter}
-            #1
-        \end{equation}
-    \end{minipage}\hfill%
-    \addtocounter{equation}{-1}%
-    \begin{minipage}{.49\textwidth}
-        \begin{equation}\refstepcounter{mySubCounter}
-            #2
-        \end{equation}
-    \end{minipage}
-    \let\theequation\OldTheEquation
-}
-
-It is also possible to place two equations side by side with counting as subfigures:
-
-\twocoleqn{y=f(x)}{y=f(z)}
-
-\vspace{1ex}
-In this case, the \AmSmath internal subfigure counter cannot be used and an own
-counter has to be defined:
-
-\begin{lstlisting}
-\newcounter{mySubCounter}
-\newcommand{\twocoleqn}[2]{
-    \setcounter{mySubCounter}{0}%
-    \let\OldTheEquation\theequation%
-    \renewcommand{\theequation}{\OldTheEquation\alph{mySubCounter}}%
-    \noindent%
-    \begin{minipage}{.49\textwidth}
-          \begin{equation}\refstepcounter{mySubCounter}
-            #1
-        \end{equation}
-    \end{minipage}\hfill%
-    \addtocounter{equation}{-1}%
-    \begin{minipage}{.49\textwidth}
-        \begin{equation}\refstepcounter{mySubCounter}
-            #2
-        \end{equation}
-    \end{minipage}%
-    \let\theequation\OldTheEquation
-}
-[ ... ]
-\twocoleqn{y=f(x)}{y=f(z)}
-\end{lstlisting}
-
-
-\section{Labels and tags}\label{sec:Labels-and-Tags}
-
-For the \CMD{label} command\index{label@\textbackslash label} \mPar{\textbackslash{}tag%
-}
-see section \vref{sec:Labels}, it is just the same behaviour. \AmSmath
-allows to define own single ``equation numbers\index{Equation number}''
-with the \CMD{tag} command. 
-\begin{align}
-f(x) & =a\tag{linear}\label{eq:linear}\\
-g(x) & =\,\mathrm{d}x^{2}+cx+b\tag{quadratic}\label{eq:quadratic}\\
-h(x) & =\sin x\tag*{trigonometric}
-\end{align}
-
-\begin{lstlisting}
-\begin{align}
-f(x) & =a\tag{linear}\label{eq:linear}\\
-g(x) & =\,\mathrm{d}x^{2}+cx+b\tag{quadratic}\label{eq:quadratic}\\
-h(x) & =\sin x\tag*{trigonometric}
-\end{align}
-\end{lstlisting}
-
-\begin{itemize}
-\item The \CMD{tag} command is also possible for unnumbered
-equations, \LaTeX{} changes the behaviour when a tag is detected.
-\item There exists a starred version \verb|\tag{*}{...}|,    %%% ----- Martin -----
-which supresses any annotations like parentheses for equation numbers\index{Equation!number}.
-\item There exist two package options for tags, \verb|ctagsplit|\index{ctagsplit}    %%% ----- Martin -----
-and \verb|righttag|\index{righttag} (look at the beginning of this
-part on page~\pageref{par:AMSmath-package}).
-\end{itemize}
-
-
-\section{Limits}\label{sec:limit-AMS}
-
-By default the sum/prod has the limits above/below and the integral
-at the side. To get the same behaviour for all symbols which can have
-limits load the package \AmSmath in the preamble as    %%% ----- Martin -----
-
-\begin{lstlisting}
-\usepackage[sumlimits,intlimits]{amsmath}
-\end{lstlisting}
-
-There exist also options for the vice versa (see page~\pageref{par:AMSmath-package}).    %%% ----- Martin -----
-See also Section~\ref{sec:misc-AMS} for the additional commands \CMD{underset} and \CMD{overset}.
-
-
-
-\subsection{Multiple limits}
-
-For general information about limits\index{Limits} read section
-\vref{sub:Limits-Inline}. Standard \LaTeX{} provides the \texttt{\textbackslash{}atop}\index{atop@\textbackslash atop} command
-for multiple limits (section \vref{sub:Multiple-Limits}). \AmSmath \mPar{\textbackslash{}substack%
-}
-has an additional command for that, which
-can have several lines with the following syntax:
-\mPar{\CMD{begin\{Sb\}}\\...\\\CMD{end\{Sb\}}\\\CMD{begin\{Sp\}}\\...\\\CMD{end\{Sp\}}%
-}
-
-\begin{lstlisting}
-\substack{...\\...\\...}
-\end{lstlisting}
-
-The environments described in \cite{MathGuide}
-
-\begin{lstlisting}
-\begin{Sb} ... \end{Sb}
-\begin{Sp} ... \end{Sp}
-\end{lstlisting}
-are obsolete and no more part of \AmSmath.
-
-The example equation \vref{eq:atop} with the \CMD{substack}\index{substack@\textbackslash substack} command
-looks like:
-
-\begin{equation}\label{eq:multlimits}
-\sum_{\substack{1\le i\le p\\
-1\le j\le q\\
-1\le k\le r}
-}a_{ij}b_{jk}c_{ki}
-\end{equation}
-
-
-Insert these limits in the following way:
-\begin{lstlisting}
-\begin{equation}
-	\sum_{%
-		\substack{1\le i\le p\\
-			1\le j\le q\\
-			1\le k\le r}
-		}%
-	a_{ij}b_{jk}c_{ki}
-\end{equation}
-\end{lstlisting}
-
-\subsection{Problems}\label{subsec:ams-limits}
-
-There are still some problems with limits and the following math
-expression. For example:
-
-\[
-X = \sum_{1\le i\le j\le n}X_{ij}
-\]
-\begin{lstlisting}
-\[
-X = \sum_{1\le i\le j\le n}X_{ij}
-\]
-\end{lstlisting}
-
-\noindent does not look nice because of the long limit. Using a
-\CMD{makebox} also does not really solve the problem, because
-\CMD{makebox} is in \TeX{} horizontal mode and knows nothing about
-the appropriate math font size, because limits have a smaller font size.
-It is better to define a \CMD{mathclap}\index{mathclap@\textbackslash mathclap} macro, similiar to the two
-macros \CMD{llap} and \CMD{rlap} and uses the also new defined \CMD{mathclap} macro\index{clap@\textbackslash clap}:
-
-\begin{lstlisting}
-\def\mathllap{\mathpalette\mathllapinternal}
-\def\mathllapinternal#1#2{%
-	\llap{$\mathsurround=0pt#1{#2}$}% $
-}
-\def\clap#1{\hbox to 0pt{\hss#1\hss}}
-\def\mathclap{\mathpalette\mathclapinternal}
-\def\mathclapinternal#1#2{%
-	\clap{$\mathsurround=0pt#1{#2}$}%
-}
-\def\mathrlap{\mathpalette\mathrlapinternal}
-\def\mathrlapinternal#1#2{%
-	\rlap{$\mathsurround=0pt#1{#2}$}% $
-}
-\end{lstlisting}
-
-
-Now we can write limits which have a boxwidth of 0pt and the right font
-size and the following math expression appears just behind the symbol:
-
-\[
-X = \sum_{\mathclap{1\le i\le j\le n}}X_{ij}
-\]
-\begin{lstlisting}
-\[
-X = \sum_{\mathclap{1\le i\le j\le n}}X_{ij}
-\]
-\end{lstlisting}
-
-Another problem occurs when having operators with stacked limits in braces:\index{substack@\textbackslash substack}
-\index{Braces!Problems}
-\index{Stacked limits}
-\begin{align}
-\left[\sum_{\substack{i,j\\i>j}} \dots \right]
-\end{align}
-
-This case is not easy to handle when some other math expressions are around the braces
-which should be on the same baseline. However, the following may help in some cases
-to get better looking braces.
-
-\begin{LTXexample}[width=0.45\linewidth,wide]
-\begin{align}
-foo \left[\begin{array}{@{}c@{}}
-    \displaystyle\sum_{\substack{i,j\\i>j}} \dots
-  \end{array}\right] bar
-\end{align}
-\end{LTXexample}
-
-
-\subsection{\CMD{sideset}}
-
-This is a command for a very special purpose, to combine over/under
-limits with superscript/subscripts for \mPar{\CMD{sideset}}the
-sum-symbol. For example: it is not possible to place the prime
-for the equation \ref{eq:sideset} near to the sum\index{sum@\textbackslash sum} symbol,
-because it becomes an upper limit when writing without an preceeding \verb|{}|.
-\begin{equation}
-\sum_{n<k\atop n\ \textrm{odd}}{}'nE_{n}\label{eq:sideset}
-\end{equation}
-
-The command \CMD{sideset}\index{sideset@\textbackslash sideset}
-has the syntax
-
-\begin{lstlisting}
-\sideset{<before>}{<behind>}
-\end{lstlisting}
-
-It can place characters on all four corners of the sum-symbol:
-\[
-\sideset{_{LowerLeft}^{UpperLeft}}{_{LowerRight}^{UpperRight}}\sum_{B}^{T}
-\]
-
-\begin{lstlisting}
-\[
-\sideset{_{LowerLeft}^{UpperLeft}}{_{LowerRight}^{UpperRight}}\sum_{B}^{T}
-\]
-\end{lstlisting}
-
-Now it is possible to write the equation \ref{eq:sideset} in a proper
-way with the command \verb|\sideset{}{'}| before
-the sum symbol:
-\begin{equation}
-\sideset{}{'}\sum_{n<k\atop n\ \textrm{odd}}nE_{n}
-\end{equation}
-
-
-\section{Operator names}\label{OperatorNames}
-
-\mPar{\CMD{operatorname}}%
-By default variables are written in italic\index{Italic} and operator
-names\index{Operator!names} in upright mode, like $y=\sin(x)$.%
-\footnote{See section \vref{sec:ltxOperators}, where all the standard \LaTeX{}    %%% ----- Martin -----
-known operator names are listed. Package \AmSmath has
-some more (see documentation).} This happens only for the known operator names, but creating a new
-one is very easy with:
-
-\begin{lstlisting}
-\newcommand{\mysin}{\operatorname{mysin}}
-\end{lstlisting}
-
-Now \CMD{mysin} is also written in upright mode
-$y=\mysin(x)$ and with some additional space before and behind.
-
-It is obvious, that only those names can be defined as new operator
-names which are not commands in another way. Instead of using the
-new definition as an operator, it is also possible to use the text
-mode. But it is better to have all operators of the same type, so that
-changing the style will have an effect for all operators.
-
-\mPar{\CMD{operatornamewithlimits}}%
-The new defined operator names cannot have limits\index{Limits}, only
-superscript/subscript is possible. \verb+amsopn.sty+ has an additional command
-\CMD{operatornamewithlimits}\index{operatornamewithlimits@\textbackslash operatornamewithlimits},
-which supports over/under limits like the one from \CMD{int}
-or \CMD{sum}.
-
-\mPar{\CMD{mathop}}
-It is also possible to use the macro \verb+\mathop+ to declare anything
-as operator, like
-\[ \sideset{_1}{}{\mathop{\mathrm{B}}} \]
-\begin{lstlisting}
-\[ \sideset{_1}{}{\mathop{\mathrm{B}}} \]
-\end{lstlisting}
-With this definition it is possible to use \CMD{sideset} for a forgoing index, which
-is only possible for an operator.
-
-For a real \LaTeX{} definition have a look at section \vref{sec:ltxOperators}.
-
-
-\section{Text in math mode}\label{sec:Text-in-math mode}
-
-If you need complex structures between formulas, look also at section \ref{sec:verticalAlignment}.
-
-\subsection{\CMD{text} command}
-\mPar{%
-\CMD{text}\\
-\CMD{mbox}\\
-\CMD{textnormal}\\
-\CMD{mathrm}%
-}%
-This is the equivalent command to \CMD{mathrm}\index{mathrm@\textbackslash mathrm}
-or \CMD{mbox}\index{mbox@\textbackslash mbox}
-from the standard \LaTeX{} (section~\vref{sec:Text}) with the exception, that \CMD{mathrm}
-always uses the roman font and \CMD{text} the actual one and that the font size is different
-when used in super- and subscript. 
-
-For example: $\boxed{f(x)=x\quad\text{this was math}}$.
-
-\bigskip
-{\sffamily\huge
-$A^{\mbox{text}}_{\mbox{text}}$\quad
-$A^{\text{text}}_{\text{text}}$\quad
-$A^{\textnormal{text}}_{\textnormal{text}}$\quad
-$A^{\mathrm{text}}_{\mathrm{text}}$
-}
-\medskip
-\begin{lstlisting}
-$\boxed{f(x)=x\quad\text{this was math}}$
-
-{\sffamily\huge
-$A^{\mbox{text}}_{\mbox{text}}$\quad
-$A^{\text{text}}_{\text{text}}$\quad
-$A^{\textnormal{text}}_{\textnormal{text}}$\quad
-$A^{\mathrm{text}}_{\mathrm{text}}$ 
-}
-\end{lstlisting}
-
-The \verb+\text+ macro can be used at any place and can be in some cases a better
-solution as \verb+\intertext+ (see section~\ref{subsec:intertext}).
-
-\begin{flalign*}
-             && 12(x-1) + 20(y-3) + 14(z-2) & = 0 &&\\
-  \text{and} &&               6x + 10y + 7z & = 0  &&
-\end{flalign*}
-
-\begin{align}
-            && 12(x-1) + 20(y-3) + 14(z-2) & = 0\\
-  \text{and} &&               6x + 10y + 7z & = 0 
-\end{align}
-
-\begin{lstlisting}
-\begin{flalign*}
-             && 12(x-1) + 20(y-3) + 14(z-2) & = 0 &&\\
-  \text{and} &&               6x + 10y + 7z & = 0  &&
-\end{flalign*}
-
-\begin{align}
-            && 12(x-1) + 20(y-3) + 14(z-2) & = 0\\
-  \text{and} &&               6x + 10y + 7z & = 0 
-\end{align}
-\end{lstlisting}
-
-
-
-\subsection{\CMD{intertext} command}\label{subsec:intertext}
-
-This is useful when you want to place some text between two parts
-of math stuff without leaving the math mode, like the name
-``intertext\index{intertext@\textbackslash intertext}''    %%% ----- Martin -----
-says. For example we write the equation~\vref{eq:Beispiel-Integral}
-with an additional command after the second line.
-
-\[
-  \begin{split}
-    A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left| \int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\
-          & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left| \int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\
-          \intertext{Now the limits of the integrals are used}
-          & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+\left| \frac{x^{3}}{3}-
-                \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\
-          & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left| \frac{8}{3}-\frac{20}{2}+12-
-                \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\
-          & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6}\right| =\frac{7}{6}+
-                \frac{5}{6}=2\, \textrm{FE}
-  \end{split}
-\]
-
-The code looks like:\\
-
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\begin{equation}
-  \begin{split}
-    A_{1} & = \left| \int _{0}^{1}(f(x)-g(x))\,\mathrm{d}x\right| +\left| \int _{1}^{2}(g(x)-h(x))\,\mathrm{d}x\right| \\
-          & = \left| \int _{0}^{1}(x^{2}-3x)\,\mathrm{d}x\right| +\left| \int _{1}^{2}(x^{2}-5x+6)\,\mathrm{d}x\right| \\
-          \intertext{Now the limits of the integrals are used}
-          & = \left| \frac{x^{3}}{3}-\frac{3}{2}x^{2}\right| _{0}^{1}+\left| \frac{x^{3}}{3}-
-                \frac{5}{2}x^{2}+6x\right| _{1}^{2}\\
-          & = \left| \frac{1}{3}-\frac{3}{2}\right| +\left| \frac{8}{3}-\frac{20}{2}+12-
-                \left( \frac{1}{3}-\frac{5}{2}+6\right) \right| \\
-          & = \left| -\frac{7}{6}\right| +\left| \frac{14}{3}-\frac{23}{6}\right| =\frac{7}{6}+
-                \frac{5}{6}=2\, \textrm{FE}
-  \end{split}
-\end{equation}
-\end{lstlisting}
-
-Writing very long text is possible by using a \verb+parbox+, see section~\vref{sec:Text} for    %%% ----- Martin -----
-an example with \verb+\textrm+, which behaves in the same way as \verb+\text+.
-
-
-
-
-\section{Extensible arrows}
-\mPar{%
-  \CMD{xrightarrow}\\
-  \CMD{xleftarrow}\\
-  \CMD{xmapsto}}To write something like $\xrightarrow[\text{below}]{\text{above the arrow}}$ you can use the following macro
-
-\begin{verbatim}
-$\xrightarrow[\text{below}]{\text{above the arrow}}$
-\end{verbatim}
-\index{Arrows}\index{Extensible arrows}
-
-\noindent and the same with \verb|\xleftarrow|. You can define your own extensible arrow macros
-if you need other than these two predefined ones. To get a doublelined extensible
-arrow like \verb|$\Longleftrightarrow$| ($\Longleftrightarrow$) but with the same
-behaviour as an extensible one, write in the preamble    %%% ----- Martin -----
-
-\begin{lstlisting}
-\newcommand\xLongLeftRightArrow[2][]{%
-    \ext@arrow 0055{\LongLeftRightArrowfill@}{#1}{#2}}
-\def\LongLeftRightArrowfill@{%
-	\arrowfill@\Leftarrow\Relbar\Rightarrow}
-\newcommand\xlongleftrightarrow[2][]{%
-    \ext@arrow 0055{\longleftrightarrowfill@}{#1}{#2}}
-\def\longleftrightarrowfill@{%
-	\arrowfill@\leftarrow\relbar\rightarrow}
-\end{lstlisting}
-
-The three parts \verb|\Leftarrow\Relbar\Rightarrow| define left|middle|right of the
-arrow, where the middle part would be stretched in a way that the arrow is at least
-as long as the text above and/or below it. This macro has one optional and one
-standard parameter. The optional one is written below and the standard one above this    %%% ----- Martin -----
-arrow. Now we can write
-
-\begin{verbatim}
-$\xLongLeftRightArrow[\text{below}]{\text{above the arrow}}$
-$\xlongleftrightarrow[\text{below}]{\text{above the arrow}}$
-\end{verbatim}
-
-\noindent to get $\xLongLeftRightArrow[\text{below}]{\text{above the arrow}}$ or
-$\xlongleftrightarrow[\text{below}]{\text{above the arrow}}$. 
-The ``number'' $0055$ after \verb+\ext@arrow+ defines the position relative to the extended arrow and is
-not a number but four parameters for additional space in the math unit \verb+mu+.
-\index{mapstofill@\CMD{mapstofill}}
-
-\makeatletter
-\def\mapstofill@{%
-  \arrowfill@{\mapstochar\relbar}\relbar\rightarrow}
-\renewcommand*\xmapsto[6][]{%
-  \ext@arrow #3#4#5#6\mapstofill@{#1}{#2}}
-\makeatother
-\begin{lstlisting}
-\def\mapstofill@{%
-  \arrowfill@{\mapstochar\relbar}\relbar\rightarrow}
-\newcommand*\xmapsto[2][]{%
-  \ext@arrow <four digits>\mapstofill@{#1}{#2}}
-\end{lstlisting}
-
-{\fboxsep=0pt
-\verb+$\ext@arrow 0000$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0000$}
-
-\verb+$\ext@arrow 9000$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}9000$}
-
-\verb+$\ext@arrow 0900$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0900$}
-
-\verb+$\ext@arrow 0009$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0009$}
-
-\verb+$\ext@arrow 0090$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0090$}
-
-\verb+$\ext@arrow 0099$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}0099$}
-
-\verb+$\ext@arrow 9999$+\quad{\huge $\xmapsto[\fbox{under}]{\fbox{over}}9999$}
-}
-
-% $
-\begin{itemize}
-\item 1st digit: space left
-\item 2nd digit: space right
-\item 3rd digit: space left and right
-\item 4th digit: space relativ to the tip of the ``arrow''
-\end{itemize}
-
-The two macros \verb+\xrightarrow+ and \verb+\xleftarrow+ are defined as:
-\begin{lstlisting}
-\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}}
-\newcommand{\xleftarrow}[2][]{\ext@arrow 3095\leftarrowfill@{#1}{#2}}
-\end{lstlisting}
-
-
-
-\section{Frames}\label{sec:ams-frames}
-\mPar{\CMD{boxed}}%
-\AmSmath knows the macro \verb|\boxed|\index{boxed@\textbackslash boxed} which can
-be used for inline $a\boxed{b+c}$ and displayed math expressions:
-
-\begin{align}
-\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1}
-\end{align}
-
-\begin{lstlisting}
-\begin{align}
-\boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1}
-\end{align}
-\end{lstlisting}
-
-For coloured boxes use package \verb|empheq|. For an example see section \vref{sec:empheq}.
-
-\section{Greek letters}\label{sec:greek-AMS}
-\mPar{\CMD{pmb}\\\CMD{boldsymbol}}%
-The \AmSmath package simulates a bold font for the greek letters by writing a greek    %%% ----- Martin -----
-character twice with a small kerning. This is done with the macro
-\verb|\pmb{<letter>}|\index{pmb@\textbackslash pmb}\index{Bold greek letters}. The
-\verb|\mathbf{<character>}| doesn't work with lower greek character. However,
-using the \CMD{boldsymbol} macro from \AmSmath{} is the better way when the font
-has a bold symbol. 
-\index{boldsymbol@\CMD{boldsymbol}}
-
-Uppercase greek letters are by default in upright mode. \AmSmath\ supports also
-such letters in italic mode with a preceeding \verb+var+ e.g., \verb+\varGamma+
-
-\medskip
-\begin{tabular}{ccc|cc}
-\emph{letter} & \CMD{pmb}\verb+{letter}+ & \CMD{boldsymbol}\verb+{letter}+ & \emph{letter} & \emph{italic}\\
-$\alpha$ & $\pmb{\alpha}$ & $\boldsymbol{\alpha}$ & $\Gamma$ & $\varGamma$\\
-$\beta$ & $\pmb{\beta}$ & $\boldsymbol{\beta}$ & $\Delta$ & $\varDelta$\\
-$\gamma$ & $\pmb{\gamma}$ & $\boldsymbol{\gamma}$ & $\Theta$ & $\varTheta$\\
-$\delta$ & $\pmb{\delta}$ & $\boldsymbol{\delta}$ & $\Lambda$ & $\varLambda$\\
-$\epsilon$ & $\pmb{\epsilon}$ & $\boldsymbol{\epsilon}$ & $\Xi$ & $\varXi$\\
-$\varepsilon$ & $\pmb{\varepsilon}$ & $\boldsymbol{\varepsilon}$ & $\Pi$ & $\varPi$\\
-$\zeta$ & $\pmb{\zeta}$ & $\boldsymbol{\zeta}$ & $\Sigma$ & $\varSigma$\\
-$\eta$ & $\pmb{\eta}$ & $\boldsymbol{\eta}$ & $\Upsilon$ & $\varUpsilon$\\
-$\theta$ & $\pmb{\theta}$ & $\boldsymbol{\theta}$ & $\Phi$ & $\varPhi$\\
-$\vartheta$ & $\pmb{\vartheta}$ & $\boldsymbol{\vartheta}$ & $\Psi$ & $\varPsi$\\
-$\iota$ & $\pmb{\iota}$ & $\boldsymbol{\iota}$ & $\Omega$ & $\varOmega$\\
-$\ldots$   & $\ldots$ & $\ldots$ 
-\end{tabular}
-
-
-\section{Miscellaneous commands}\label{sec:misc-AMS}
-
-There are several commands which can be used in math mode:\mPar{\CMD{overset}\\\CMD{underset}}
-
-Some examples are shown in table~\vref{cap:Different-Mathcommands-supported-AMS}.
-
-\begin{table}[htb]
-\centering
-{\renewcommand{\arraystretch}{2}
-\begin{tabular}{r|>{\raggedright}p{2cm}}
-\verb|$\underset{under}{baseline}$| \index{underset@\textbackslash underset} &
-$\underset{under}{baseline}$\tabularnewline
-\verb|$\overset{over}{baseline}$| \index{overset@\textbackslash overset} &
-$\overset{over}{baseline}$\tabularnewline
-\verb+\boldsymbol{\Omega}+ & $\boldsymbol{\Omega}$
-\end{tabular}}
-\caption{Different mathcommands}\label{cap:Different-Mathcommands-supported-AMS}
-\end{table}
-
-\CMD{underset} is a useful macro for having limits under non-operators 
-(see page~\pageref{sec:amsopn}).    %%% ----- Martin -----
-\CMD{boldsymbol} can be used for a math symbol that remains unaffected by
-\CMD{mathbf} if the current math font set includes a bold version of that symbol. 
-
-
-\section{Problems with \texttt{amsmath}}
-\AmSmath{} is an excellent package with some ``funny features''. 
-When using an \verb+align+ environment inside a \verb+gather+ environment, it should
-be centered just like the other lines. This is only true, when there is a number/tag or
-an additional ampersand:
-
-
-%\begin{LTXexample}[pos=t]
-\begin{gather*}
-  \begin{align*}
-    m_2 &=  m_2' + m_2''\\
-        &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''}
-  \end{align*}\\
-  \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\
-\end{gather*}
-\begin{gather*}
-  \begin{align*}
-    m_2 &=  m_2' + m_2''\\
-        &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} & %<<<====
-  \end{align*}\\
-  \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\
-\end{gather*}
-%\end{LTXexample}
-
-\begin{lstlisting}
-\begin{gather*}
-  \begin{align*}
-    m_2 &=  m_2' + m_2''\\
-        &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''}
-  \end{align*}\\
-  \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\
-\end{gather*}
-\begin{gather*}
-  \begin{align*}
-    m_2 &=  m_2' + m_2''\\
-        &= \frac{V_2'}{v_2'} + \frac{V_2''}{v_2''} & %<<<====
-  \end{align*}\\
-  \Rightarrow m_2 v_2' = V - V_2'' + V_2''\frac{v_2'}{v_2''}\\
-\end{gather*}
-\end{lstlisting}
-
-
-This effect depends to the horizontal width, which is wrong in the first example,
-in fact of a missing tag or number the right whitespace is cut, but the left one
-is still there. The additional ampersand prevents \AmSmath{} to change the right
-margin. 
-
-Another kind of curiousity is the following example, which depends to the
-same problem of cutting whitespace only on one side.
-
-\bigskip\noindent%
-%\begin{LTXexample}[pos=t]
-\fbox{%
-\begin{minipage}{10cm}
-\begin{align*}
-  a&=b \\ c&=d
-\end{align*}
-\end{minipage}}
-
-\noindent\fbox{%
-\begin{minipage}{10cm}
-\noindent\begin{align*}
-  a&=b \\ c&=d
-\end{align*}
-\end{minipage}} 
-%\end{LTXexample}
-
-\bigskip
-\begin{lstlisting}
-\bigskip\noindent\fbox{%
-\begin{minipage}{10cm}
-\begin{align*}
-  a&=b \\ c&=d
-\end{align*}
-\end{minipage}}
-
-\noindent\fbox{%
-\begin{minipage}{10cm}
-\noindent\begin{align*}
-  a&=b \\ c&=d
-\end{align*}
-\end{minipage}} 
-\end{lstlisting}
-
-
-
-\part{\TeX{} and math}
-
-There is in general no need to use the \TeX{} macros, because the ones defined with \LaTeX{}
-or with \AmSmath{} are much more useful. Nevertheless there may be situations, where someone    %%% ----- Martin -----
-has to use one of the \TeX{} macros or special \TeX{} math length. One can not expect, that all
-macros work in the usual way, a lot of them are redefined by \LaTeX{}    %%% ----- Martin -----
-or \AmSmath{}. On the other hand some of these basic macros or length definitions are used
-in the \TeX{} way, so it might be interesting to have all declared in a short way for some
-information.
-
-\section{Length registers}
-
-\subsection{\CMD{abovedisplayshortskip}}
-\cIndex{abovedisplayshortskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example.
-
-\subsection{\CMD{abovedisplayskip}}
-\cIndex{abovedisplayskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example.
-
-\subsection{\CMD{belowdisplayshortskip}}
-\cIndex{belowdisplayshortskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example.
-
-\subsection{\CMD{belowdisplayskip}}
-\cIndex{belowdisplayskip}A length with glue, see section~\ref{subsubsec:displayskip} for an example.
-
-
-\subsection{\CMD{delimiterfactor}}
-\cIndex{delimiterfactor}The height of a delimiter is often not optimally calculated by \TeX{}. In some cases it is    %%% ----- Martin -----
-too short. With \verb+\delimiterfactor+ one can correct this height. The delimiterheight
-is $<\textrm{calculated height}>\cdot <\textrm{\#1}>/1000$ where \verb+#1+ is the parameter of
-\verb+\delimiterfactor+. The default value is $901$.
-
-\begin{LTXexample}[width=0.4\linewidth]
-\[
-y = \left\{%
- \begin{array}{ll}
-   x^2+2x  &\textrm{if }x<0,\\
-   x^3     &\textrm{if }0\le x<1,\\
-   x^2+x   &\textrm{if }1\le x<2,\\
-   x^3-x^2 &\textrm{if }2\le x.
- \end{array}%
-\right.
-\]
-\end{LTXexample}
-
-\begin{LTXexample}[width=0.4\linewidth]
-\[
-\delimiterfactor=1500
-y = \left\{%
- \begin{array}{ll}
-   x^2+2x  &\textrm{if }x<0,\\
-   x^3     &\textrm{if }0\le x<1,\\
-   x^2+x   &\textrm{if }1\le x<2,\\
-   x^3-x^2 &\textrm{if }2\le x.
- \end{array}%
-\right.
-\]
-\end{LTXexample}
-
-\subsection{\CMD{delimitershortfall}}
-\cIndex{delimitershortfall}Additionally to the forgoing \verb+\delimiterfactor+ one can modify the height of the
-delimiter with another value. \TeX{} makes the delimiter larger than the values of
-$<\textrm{calculated height}>\cdot <\textrm{delimiterfactor}>/1000$ and $<\textrm{calculated height}>-<\textrm{delimitershortfall}>$. This makes it possible to always get different heights    %%% ----- Martin -----
-of a sequence of delimiters. 
-
-\begin{LTXexample}[width=0.3\linewidth]
-$x\cdot\left(\left(x^2-y^2\right)-3\right)$\\[7pt]
-
-$
-\delimitershortfall-1pt
-x\cdot\left(\left(x^2-y^2\right)-3\right)$
-\end{LTXexample}
-
-\begin{LTXexample}[width=0.2\linewidth]
-$\left(\left(\left(A\right)\right)\right)$\\[7pt]
-
-$\delimitershortfall-1pt
-\left(\left(\left(A\right)\right)\right)$
-\end{LTXexample}
-
-
-\subsection{\CMD{displayindent}}
-\cIndex{displayindent}This is the left shift amount of a line holding displayed equation. 
-By default it is $0pt$ but
-gets the value of an indented paragraph when there is an environment like the quotation one.\index{Indentation}
-
-The following formula is typeset in the usual way without modifying anything.
-
-\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \]
-
-Now we start a quotation environment which sets \CIndex{labelwidth} to new values for a 
-greater    %%% ----- Martin -----
-left margin.
-
-\begin{itemize}
-\item The following formula is typeset in the usual way without modifying anything.
-
-\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \]
-
-\item Now we write the same equation, but now with modifying \Index{displayindent}, it is set to
-the negative \verb+\leftskip+:
-
-\[
-  \displayindent=-\labelwidth
-  f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x 
-\]
-\end{itemize}
-
-\begin{lstlisting}
-\[
-  \displayindent=-\leftskip 
-  f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x 
-\]
-\end{lstlisting}
-
-\subsection{\CMD{displaywidth}}
-\cIndex{displaywidth}The width of the line holding a displayed equation, which is by default 
-\verb+\linewidth+. In the
-second example the formula is centered for a display width of \verb+0.5\linewidth+.
-
-\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \]
-\[
-  \displaywidth=0.5\linewidth
-  f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x 
-\]
-\begin{lstlisting}
-\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \]
-\[
-  \displaywidth=0.5\linewidth
-  f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x 
-\]
-\end{lstlisting}
-
-\subsection{\CMD{mathsurround}}
-\cIndex{mathsurround}Extra space added when switching in and out of the 
-inline math mode (see section~\ref{subsec:whitespace}).
-
-\subsection{\CMD{medmuskip}}
-\cIndex{medmuskip}See section~\ref{subsec:mathskip} for an example.
-
-\subsection{\CMD{mkern}}
-\cIndex{mkern}Similiar to \verb+\kern+, but adds a math kern item to the current math list. Length must be a math unit.
-
-\subsection{\CMD{mskip}}
-\cIndex{mskip}Similiar to \verb+\skip+, but adds math glue to the current math list. Length must be a math unit.
-
-\subsection{\CMD{muskip}}
-\cIndex{muskip}Assigns a length with a math unit to one of the 256 \verb+\muskip+ register.
-
-\subsection{\CMD{muskipdef}}
-\cIndex{muskipdef}Defines a symbolic name for a \verb+\muskip+ register.
-
-\subsection{\CMD{nonscript}}
-\cIndex{nonscript}Ignores immediately following glue or kern in script and 
-scriptscript styles, which makes a redefinition of \verb+\mathchoice+ superfluous.
-
-\subsection{\CMD{nulldelimiterspace}}
-\cIndex{nulldelimiterspace}This is the width of a null or missing delimiter, 
-\eg \verb+\right.+ or for the left one.
-
-\subsection{\CMD{predisplaysize}}
-\cIndex{predisplaystyle}Is the effective width of the line preceeding a displayed equation, whether 
-\verb+\abovedisplayskip+ or \verb+abovedisplayshortskip+ is used for the vertical skip. 
-
-\subsection{\CMD{scriptspace}}
-\cIndex{scriptspace}The space inserted after an exponent or index, predefined as \verb+\scriptspace=0.5pt+    %%% ----- Martin -----
-
-\subsection{\CMD{thickmuskip}}
-\cIndex{thickmuskip}See section~\ref{subsec:mathskip}.
-
-\subsection{\CMD{thinmuskip}}
-\cIndex{thinmuskip}The short version for positive skip is defined as \verb+\def\,{\mskip\thinmuskip}+ and the one
-for a negative skip as \verb+\def\!{\mskip-\thinmuskip}+ (see also Section~\ref{subsec:mathskip}).
-
-
-\begin{LTXexample}[width=0.35\linewidth]
-$\sqrt 2 x$ -- $\sqrt 2\,x$\\
-$\sqrt{\log x}$ -- $\sqrt{\,\log x}$\\
-$P\left({1/\sqrt n}\right)$ -- $P\left({1/ \sqrt n}\,\right)$\\[8pt]
- $[0,1)$ -- $[\,0,1)$\\
-$x^2/2$ -- $x^2\!/2$\\
-\end{LTXexample}
-
-\begin{LTXexample}[width=0.35\linewidth]
-\[\int\int_D \mathrm{d}x\mathrm{d}y \quad 
-  \int\!\int_D \mathrm{d}x\,\mathrm{d}y\]
-\[\int\!\!\int_D \mathrm{d}x\,\,\mathrm{d}y \quad 
-  \int\!\!\!\int_D \mathrm{d}x\,\,\,\mathrm{d}y\]
-\[\int\!\!\!\!\int_D \mathrm{d}x\,\,\,\,\mathrm{d}y \quad 
-  \int\!\!\!\!\!\int_D \mathrm{d}x\,\,\,\,\,\mathrm{d}y\]
-\[\int\!\!\!\int_D \mathrm{d}x\,\mathrm{d}y\]
-\end{LTXexample}
-
-\subsection{\CMD{medmuskip}}
-See section~\ref{subsec:mathskip}.
-
-
-\section{Math font macros}
-\subsection{\CMD{delcode}}
-\cIndex{delcode}Each character has not only a \CIndex{catcode} and \CIndex{mathcode} but also 
-a \verb+\delcode+
-which defines for a single chracter how it should look when used as a math delimiter.
-
-\subsection{\CMD{delimiter}}
-\cIndex{delimiter}Every character can be declared as a delimiter, but \TeX{} 
-must know which characters
-should be used for the default and the big size. For \LaTeX{} 
-the macro \CIndex{DeclareMathDelimiter} should be used (see section~\vref{subsec:delim}). 
-
-In the following example \verb+\tdela+ is the character $0x22$ ($\uparrow$) from 
-font number $2$ (\verb+csmy+)  and character $0x78$ from font number $3$ (\verb+cmex+) 
-for the big version.  \verb+\tdelb+ is the same vice versa ($\downarrow$).
-\begin{LTXexample}[width=0.35\linewidth]
-\def\tdela{\delimiter"4222378\relax}
-\def\tdelb{\delimiter"5223379\relax}
-
-$\tdela x-y\tdelb(x+y)=x^2-y^2$
-
-\[\tdela\sum_{n=0}^\infty {1\over2^n}\tdelb^2 = 4\]
-
-\[\left\tdela\sum_{n=0}^\infty {1\over2^n}\right\tdelb^2 = 4\]
-\end{LTXexample}
-
-\subsection{\CMD{displaystyle}}
-\cIndex{displaystyle}See section~\ref{sec:Styles} for an example.
-
-\subsection{\CMD{fam}}
-\cIndex{fam}When \TeX{} switches into the math mode, it typesets everything using one of the 16 
-possible families of fonts. \verb+\fam+ is an internal register where other macros can check which font is the actual one. At the beginning \TeX{} starts with \verb+\fam=-1+.
-
-\bigskip
-\noindent
-\includegraphics{family}
-\iffalse
-
-\begin{center}
-\begin{tabular}{ll}
-\verb+\fam=-1+ & $\fam=-1 123abcABC\alpha\beta\gamma$\\
-\verb+\fam=0+  & $\fam=0 123abcABC\alpha\beta\gamma$\\
-\verb+\fam=1+  & $\fam=1 123abcABC\alpha\beta\gamma$\\
-\verb+\fam=2+  & $\fam=2 123abcABC\alpha\beta\gamma$\\
-\verb+\fam=3+  & $\fam=3 123abcABC\alpha\beta\gamma$\\
-\verb+\fam=4+  & $\fam=4 123abcABC\alpha\beta\gamma$\\
-\verb+\fam=5+  & $\fam=5 123abcABC\alpha\beta\gamma$
-\end{tabular}
-\end{center}
-
-
-\begin{LTXexample}[width=0.3\linewidth]
-$\mathrm{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt]
-$\mathbf{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt]
-$\mathit{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt]
-$\mathtt{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt]
-$\mathsf{123abcABC\alpha\beta\gamma (\the\fam)}$\\[5pt]
-$\mathnormal{123abcABC\alpha\beta\gamma (\the\fam)}$
-\end{LTXexample}
-\fi
-
-\subsection{\CMD{mathaccent}}
-\cIndex{mathaccent}Requires three parameter as one number, the class, the font family and the character.
-
-\begin{LTXexample}[width=0.3\linewidth]
-\def\dA{\mathaccent"7015\relax}
-{\Large $\dA{A}$}
-\end{LTXexample}
-
-\subsection{\CMD{mathbin}}
-\cIndex{mathbin}Declares a following character as a binary symbol with another 
-spacing before and behind such a symbol.
-
-\begin{LTXexample}[width=0.3\linewidth]
-{\Large 
-$a|b \quad a\mathbin| b$}
-\end{LTXexample}
-
-\subsection{\CMD{mathchar}}
-\cIndex{mathchar}Declares a math character by three integer numbers as Parameters, giving its class,     %%% ----- Martin -----
-font family, and font position. In the following example \verb+\mathchar+ defines a 
-character of class 1 (big operators), font family 3 (math extension font) and number
-58 (big sum character).
-
-\begin{LTXexample}[width=0.3\linewidth]
-{\Large 
-$a\sum\limits_{i=1}^{\infty} b \quad 
- a\mathchar"1358\limits_{i=1}^{\infty} b$}
-\end{LTXexample}
-
-\subsection{\CMD{mathchardef}}
-\cIndex{mathchardef}This is in principle the same as \CIndex{mathchar}, 
-it only allows to make such definitions permanent.  
-
-\begin{LTXexample}[width=0.25\linewidth]
-\bgroup
-\mathchardef\sum="1358
-$a\sum\limits_{i=1}^{\infty}\sqrt{i+1}$\\[5pt]
-\egroup
- 
-$a\sum\limits_{i=1}^{\infty}\sqrt{i+1}$ 
-\end{LTXexample}
-
-
-\subsection{\CMD{mathchoice}}
-\cIndex{mathchoice}Specifies specific subformula sizes for the 4 main styles: 
-\CIndex{displaystyle} -- \CIndex{textstyle} --
-\CIndex{scriptstyle} -- \CIndex{scriptscriptstyle}.
-
-\begin{LTXexample}[width=0.15\linewidth]
-\Large
-\def\myRule{{%
-  \color{red}%
-  \mathchoice{\rule{2pt}{20pt}}{\rule{1pt}{10pt}}%
-    {\rule{0.5pt}{5pt}}{\rule{0.25pt}{2.5pt}}%
-    \mkern2mu}}
-$\myRule\sum\limits_{\myRule i=1}^{\myRule\infty}%
- \myRule\frac{\myRule\sqrt{\myRule i+1}}{\myRule i^2}$
-\end{LTXexample}
-
-\subsection{\CMD{mathclose}}\label{subsec:mathclose}
-\cIndex{mathclose}Assigns class 5 (closing character) to the following 
-parameter, which can hold a single character or a subformula.
-
-\begin{LTXexample}[width=0.2\linewidth]
-{\large
-$A:\frac{B}{C}:D$\\[5pt]
-$A\mathopen:\frac{B}{C}\mathclose: D $}
-\end{LTXexample}
-
-
-\subsection{\CMD{mathcode}}
-\cIndex{mathcode}A math font is far different from a text font. A lot of the characters has to be defined with 
-\verb+\mathcode+, which defines the character with its class, font family and character number, \eg
-\verb+\mathcode`\<="313C+. It defines the character ``<''{} as a realtion symbol (class 3) from
-the font family 1 and the character number 0x3C, which is 60 decimal.
-
-\subsection{\CMD{mathop}}
-\cIndex{mathop}Assigns class 1 (large operator) to the parameter, which can be a single character or a subformula.
-
-\begin{LTXexample}[width=0.2\linewidth]
-\[ A_{i=1}^{\infty} \]
-\[ \mathop{A}_{i=1}^{\infty} \]
-\end{LTXexample}
-
-\subsection{\CMD{mathopen}}
-\cIndex{mathopen}Vice versa to \verb+\mathclose+ (see section~\ref{subsec:mathclose}).
-
-
-\subsection{\CMD{mathord}}
-\cIndex{mathord}Assigns class 0 (ordinary character) to the following parameter, which can be a single character 
-or a subformula.
-
-\begin{LTXexample}[width=0.2\linewidth]
-{\large
-$y = f(x)$\\[5pt]
-$y \mathord= f(x)$}
-\end{LTXexample}
-
-\subsection{\CMD{mathpunct}}
-\cIndex{mathpunct}Assigns class 6 (punctuation) to the following parameter, which can be a single character
-or a subformula (see section~\ref{subsec:dot-comma} for an example).
-
-\subsection{\CMD{mathrel}}
-\cIndex{mathrel}Assigns class 3 (relation) to the following parameter, which can be a single character
-or a subformula.
-
-\begin{LTXexample}[width=0.25\linewidth]
-{\large
-$x_1 o x_2 o x_3$\\[5pt]
-$x_1\mathrel o x_2\mathrel o x_3$}
-\end{LTXexample}
-
-
-\subsection{\CMD{scriptfont}}
-\cIndex{scriptfont}Specifies the scriptstyle font (used for super/subscript) for a family.
-
-\begin{LTXexample}[width=0.25\linewidth]
-$A_1$
-\font\tenxii=cmr12
-\scriptfont0=\tenxii
-$A_1$ 
-\end{LTXexample}
-
-
-\subsection{\CMD{scriptscriptfont}}
-\cIndex{scriptscriptfont}Specifies the scriptscriptstyle font for a family. 
-
-\subsection{\CMD{scriptscriptstyle}}
-\cIndex{scriptscriptstyle}Selects scriptscript style for the following characters.
-
-\subsection{\CMD{scriptstyle}}
-\cIndex{scriptstyle}Selects script style for the following characters.
-
-
-\subsection{\CMD{skew}}
-\cIndex{skew}Especially for italic characters double accents are often misplaced. \verb+\skew+ has three arguments
-\begin{description}
-\item[horizontal shift:] A value in math units for the additional shift of the accent.
-\item[the accent:] The symbol which is placed above the character.
-\item[the character:] This is in general a single character, but can also include itself an accent.
-\end{description}
-
-\AmSmath\ redefines the setting of double accents. This is the reason why there are only a few
-cases where someone has to use \verb+\skew+ when the package \PIndex{amsmath} is loaded, like
-in this document.
-
-\begin{LTXexample}[width=0.2\linewidth]
-\large
-$\tilde i$ \qquad $\tilde{A}$\\[5pt]
-$\skew{3}{\tilde}{i}$ \qquad $\skew{7}{\tilde}{A}$
-\end{LTXexample}
-
-\subsection{\CMD{skewchar}}
-\cIndex{skewchar}Is -1 or the character (reference symbol) used to fine-tune the positioning of math accents.
-
-\subsection{\CMD{textfont}}
-\cIndex{textfont}Specifies the text font for a family.
-
-\subsection{\CMD{textstyle}}
-\cIndex{textstyle}Selects the text style for the following characters.
-
-
-
-\section{Math macros}
-
-
-\subsection{\CMD{above}}
-\cIndex{above}
-\begin{LTXexample}[width=0.2\linewidth]
-$a\above0pt b$\\[8pt]
-
-${a\above1pt b}$\\[8pt]
-
-${a\above2.5pt b}$\\[8pt]
-
-$\displaystyle{a\above0pt b}$
-\end{LTXexample}
-
-
-
-\subsection{\CMD{abovewithdelims}}
-\cIndex{abovewithdelims}
-\begin{LTXexample}[width=0.2\linewidth]
-$a\abovewithdelims()0pt b$\\[8pt]
-
-\def\fdelimA{\abovewithdelims\{)1.0pt}
-${a\fdelimA b}$\\[8pt]
-
-\def\fdelimB{\abovewithdelims[]2.0pt}
-${a\fdelimB b}$\\[8pt]
-
-\def\fdelimC{\abovewithdelims\{.0pt}
-$\displaystyle{a\fdelimC b}$
-\end{LTXexample}
-
-\subsection{\CMD{atop}}
-\cIndex{atop}
-
-\begin{LTXexample}[width=0.2\linewidth]
-$a\atop b$\\[8pt]
-
-$({n \atop k}) = {n!\above1pt k!(n-k)!}$\\[8pt]
-
-$\displaystyle{a\atop b}$
-\end{LTXexample}
-
-
-\subsection{\CMD{atopwithdelims}}
-\cIndex{atopwithdelims}
-\begin{LTXexample}[width=0.2\linewidth]
-$a\atopwithdelims() b$\\[8pt]
-
-${n \atopwithdelims() k} = {n!\above1pt k!(n-k)!}$\\[8pt]
-
-$\displaystyle{a\atopwithdelims\{. b}$
-\end{LTXexample}
-
-\subsection{\CMD{displaylimits}}
-\cIndex{displaylimits}Resets the conventions for using limits with operators to the standard for the used environment.
-
-\subsection{\CMD{eqno}}\label{subsec:eqno}
-\cIndex{eqno}Puts an equation number at the right margin, the parameter can hold anything. \verb+\eqno+ places
-only the parameter, but doesn't increase any equation counter.
-
-\begin{LTXexample}[width=0.5\linewidth]
-\[ y=f(x) \eqno{(A12)} \]
-\end{LTXexample}
-
-\subsection{\CMD{everydisplay}}
-\cIndex{everydisplay}Inserts the parameter at the start of every switch to display math mode.
-
-\begin{LTXexample}[width=0.4\linewidth]
-\everydisplay{\color{red}
-}
-\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \]
-\[ g(x) = \int \frac{\sin^2 x}{x^2}\,\mathrm{d}x \]
-\end{LTXexample}
-
-\subsection{\CMD{everymath}}
-\cIndex{everymath}Same as \CIndex{everydisplay}, but now for the inline mode. 
-In the following example
-the displaystyle is used (besides using color red) for every inline math expression.
-
-\bgroup
-\begin{LTXexample}[width=0.45\linewidth]
-\everymath{\color{red}%
-  \displaystyle}
-\[ f(x) = \int \frac{\sin x}{x}\,\mathrm{d}x \]
-Instead of $\frac{\sin x}{x}$ 
-  now with $\frac{\cos x}{x}$:
-\[ g(x) = \int \frac{\cos x}{x}\,\mathrm{d}x \]
-\end{LTXexample}
-\egroup
-
-Pay attention for side effects on footnotes and other macros which use the math mode for superscript
-and other math related modes. In this case you'll get the footnotes also in red.
-
-\subsection{\CMD{left}}
-\cIndex{left}\TeX{} calculates the size of the following delimiter needed at the left side of a formula.
-Requires an additional \verb+right+.
-
-\subsection{\CMD{leqno}}
-\cIndex{leqno}Vice versa to \verb+\eqno+ (see section~\vref{subsec:eqno}).
-
-\subsection{\CMD{limits}}
-\cIndex{limits}Typesets limits above and/or below operators (see section~\vref{sec:limits}).
-
-\subsection{\CMD{mathinner}}
-\cIndex{mathinner}Defines the following parameter as subformula.
-
-\subsection{\CMD{nolimits}}
-\cIndex{nolimits}The opposite of \CIndex{limits}, instead of above/below limits are placed to the right of large 
-operators (class 1).
-
-
-\subsection{\CMD{over}}
-\cIndex{over}Is equivalent to the fraction macro of \LaTeX{} and equivalent to the 
-\verb+\overwithdelims+, see section~\vref{subsec:overwithdelims}.
-
-\begin{LTXexample}[width=0.2\linewidth]
-$ {a\over b} \qquad {{m\over n}\over{a+b}} $
-\[ {m\over n}\over{a+b} \]
-\end{LTXexample}
-
-
-\subsection{\CMD{overline}}
-\cIndex{overline}Puts a line over the following character or subformula and has the same problems with different
-heights as underlines (see section~\ref{subsec:underline}).
-
-\begin{LTXexample}[width=0.2\linewidth]
-$\overline{x}+\overline{y}=\overline{z}$\\
-\let\ol\overline
-$ \ol{x} + \ol{A} = \ol{z} $\\[5pt]
-\def\yPh{\vphantom{A}}
-$ \ol{x\yPh} + \ol{A} = \ol{z\yPh} $
-\end{LTXexample}
-
-\subsection{\CMD{overwithdelims}}\label{subsec:overwithdelims}
-\cIndex{overwithdelims}Is a generalized fraction command with preset fraction bar thickness.    %%% ----- Martin -----
-
-\begin{LTXexample}[width=0.25\linewidth]
-$ {a\overwithdelims() b} \qquad {{m\over n}\overwithdelims[]{a+b}} $
-\[ {m\over n}\overwithdelims\{.{a+b} \]
-\end{LTXexample}
-
-
-\subsection{\CMD{radical}}
-\cIndex{radical}Makes a radical atom from the delimiter (27-bit number) and the math field.
-
-\begin{LTXexample}[width=0.2\linewidth]
-\def\mySqrt{\radical"0270371\relax}
-$ \mySqrt{\frac{1}{7}} $\\[5pt]
-
-\def\mySqrt{\radical"0270372\relax}
-$ \mySqrt{\frac{1}{7}} $\\[5pt]
-
-\def\mySqrt{\radical"0270373\relax}
-$ \mySqrt{\frac{1}{7}} $\\[5pt]
-
-\def\mySqrt{\radical"0270374\relax}
-$ \mySqrt{\frac{1}{7}} $\\[5pt]
-\end{LTXexample}
-
-\subsection{\CMD{right}}
-\cIndex{right}Opposite to \verb+\left+, makes \TeX{} calculate the size of the 
-delimiter needed at the right of a formula.
-
-\subsection{\CMD{underline}}\label{subsec:underline}
-\cIndex{underline}When there is a combination of variables with and without an index, the underlines are typeset    %%% ----- Martin -----
-with a different depth. Using \verb+\vphantom+ in this case is a good choice. 
-
-\begin{LTXexample}[width=0.2\linewidth]
-$\underline{x}+\underline{y}=\underline{z}$\\
-
-\let\ul\underline
-\def\yPh{\vphantom{y}}
-$ \ul{x\yPh} + \ul{y} = \ul{z\yPh} $\\
-
-$ \ul{x_1} + \ul{y_2} = \ul{z_3} $
-\end{LTXexample}
-
-\subsection{\CMD{vcenter}}
-\cIndex{vcenter}Centers vertical material with respect to the axis.
-
-
-\section{Math penalties}
-
-\subsection{\CMD{binoppenalty}}
-\cIndex{binoppenalty}A penalty for  breaking math expressions between lines in a paragraph. TeX breaks lines only
-when the binary symbol is not the last one and when the penalty is below 10,000.
-
-\subsection{\CMD{displaywidowpenalty}}
-\cIndex{displaywidowpenalty}The penalty which is added after the penultimate line immediately preceeding a display math formula.
-
-\subsection{\CMD{postdisplaypenalty}}
-\cIndex{postdisplaypenalty}Is added immediately after a math display ends.
-
-\subsection{\CMD{predisplaypenalty}}
-\cIndex{predisplaypenalty}Is added immediately before a math display starts.
-
-\subsection{\CMD{relpenalty}}
-\cIndex{relpenalty}The penalty for a line break after a relation symbol (if a break is possible).
-
-
-\part{Other packages}
-The following sections are not a replacement for the package documentation!
-\section{List of available math packages}
-\markboth{Math packages}{Math packages}
-
-\begin{center}
-\noindent
-\begin{tabular}{llll}
-\href{http://www.dante.de/CTAN/help/Catalogue/entries/accents.html}{accents}&
-\href{http://www.dante.de/CTAN/help/Catalogue/entries/alphalph.html}{alphalph}&
-\href{http://www.dante.de/CTAN/help/Catalogue/entries/amsart.html}{amsart}&
-\href{http://www.dante.de/CTAN/help/Catalogue/entries/amsbook.html}{amsbook}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsbsy.html}{amsbsy}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amscd.html}{amscd}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amscls.html}{amscls}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsfonts.html}{amsfonts}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amslatex.html}{amslatex}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsltx11.html}{amsltx11}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsmath.html}{amsmath}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsppt.html}{amsppt}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsppt1.html}{amsppt1}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsproc.html}{amsproc}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amssym.html}{amssym (plain TeX)}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amssymb.html}{amssymb (LaTeX)}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amstex.html}{amstex (Plain TeX)}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amstext.html}{amstext}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/amsthm.html}{amsthm}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/bez123.html}{bez123}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/bitfield.html}{bitfield}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/brclc.html}{brclc}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/breqn.html}{breqn}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/cancel.html}{cancel}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/cases.html}{cases}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/comma.html}{comma}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/datenumber.html}{datenumber}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/diagxy.html}{diagxy}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/doublestroke.html}{doublestroke}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/easyeqn.html}{easyeqn}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/easybmat.html}{easybmat}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/easymat.html}{easymat}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/eqnarray.html}{eqnarray}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/esvect.html}{esvect}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/fixmath.html}{fixmath}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/fltpoint.html}{ftlpoint}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/icomma.html}{icomma}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/leftidx.html}{leftidx}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathdots.html}{mathdots}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathtools.html}{mathtools}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/mathematica.html}{mathematica}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/mil3.html}{mil3}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/mtbe.html}{mtbe}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/nath.html}{Nath}\\
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/numprint.html}{numprint}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/random.html}{random}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/romannum.html}{romannum}&
-\href{http://www.dante.de/CTAN//help/Catalogue/entries/texaide.html}{TeXaide}
-\end{tabular}
-\end{center}
-
-The following examples depend on the listed versions of the packages:    %%% ----- Martin -----
-
-{\small
-\begin{verbatim}
-  amsopn.sty    1999/12/14 v2.01 operator names
-      bm.sty    1999/07/05 v1.0g Bold Symbol Support (DPC/FMi)
-  empheq.sty    2007/12/03 v2.12 Emphasizing equations (MH)
-   amscd.sty    1999/11/29 v2.0
- accents.sty    2000/08/06 v1.2 Math Accent Tools
-  framed.sty    2007/10/04 v 0.95: framed or shaded text with page breaks
-pstricks.sty    2004/05/06 v0.2k LaTeX wrapper for `PSTricks' (RN,HV)
-pstricks.tex    2003/03/07 v97 patch 15 `PSTricks' (tvz)
-pst-node.tex    2008/11/26 v1.01 PSTricks package for nodes (tvz,hv)
-delarray.sty    1994/03/14 v1.01 array delimiter package (DPC)
-   xypic.sty    1999/02/16 Xy-pic version 3.7
- exscale.eps    Graphic file (type veps)
-\end{verbatim}
-}
-
-
-\subsection{\texttt{accents}}\label{sec:package-accent}
-If you want to write for example an underlined M, then you can do it by    %%% ----- Martin -----
-
-\medskip
-\begin{tabular}{ll}
-\verb|\underline{$M$}| & \underline{$M$}\\
-\verb|\underbar{$M$}|  & \underbar{$M$}\\
-\verb|\underaccent{\bar}{M}| & $\underaccent{\bar}{M}$
-\end{tabular}
-\medskip
-
-As seen, there is no difference between \CMD{underline} and \CMD{underbar}. For    %%% ----- Martin -----
-some reasons it may be better to use the \PIndex{accent} package with the
-\CMD{underaccents} macro.
-
-\subsection{\texttt{amscd} -- commutative diagrams}
-
-The \PIndex{amscd} package is part of the \AmSmath bundle
-or available at CTAN%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/amscd.dtx}%
-{CTAN://macros/latex/required/amslatex/math/amscd.dtx}} and has no options for the
-\verb|\usepackage| command.
-\texttt{amscd} does not support diagonal arrows but is much     %%% ----- Martin -----
-easier to handle than the complex \PIndex{pstricks} package or
-the \PIndex{xypic} package. On the other hand simple diagrams
-can be written with the \UIndex{array} or look at \cite{taylor00}.
-
-\[
-\begin{CD}
-  R\times S\times T @>\text{restriction}>> S\times T \\
-        @VprojVV                            @VVprojV \\
-  R\times S         @<<\text{inclusion}<        S
-\end{CD}
-\]
-
-\begin{lstlisting}
-\[
-\begin{CD}
-  R\times S\times T @>\text{restriction}>> S\times T \\
-        @VprojVV                            @VVprojV \\
-  R\times S         @<<\text{inclusion}<        S
-\end{CD}
-\]
-\end{lstlisting}
-
-
-\subsection{\texttt{amsopn}}\label{sec:amsopn}
-With the \PIndex{amsopn} package it is very easy to declare new math operators, which are written in
-upright mode:
-
-$\underset{s=p}{Res}\quad\text{versus}\quad\underset{s=p}{\Res}$
-
-\medskip
-\begin{lstlisting}
-\documentclass[10pt]{article}
-\usepackage{amsmath}
-\usepackage{amsopn}
-\DeclareMathOperator{\Res}{Res}
-\begin{document}
-$\underset{s=p}{Res}\quad\underset{s=p}{\Res}$
-\end{document}
-\end{lstlisting}
-
-Table~\ref{tab:amsopn} shows the predefined operatornames of \verb+amsopn+.
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{llllll}
-\verb+\arccos+ & $\arccos$ & \verb+\arcsin+ & $\arcsin$ & \verb+\arctan+ & $\arctan$\\
-\verb+\arg+    & $\arg$    & \verb+\cos+    & $\cos$    & \verb+\cosh+   & $\cosh$\\
-\verb+\cot+    & $\cot$    & \verb+\coth+   & $\coth$   & \verb+\csc+    & $\csc$\\
-\verb+\deg+    & $\deg$    & \verb+\det+    & $\det$    & \verb+\dim+    & $\dim$\\
-\verb+\exp+    & $\exp$    & \verb+\gcd+    & $\gcd$    & \verb+\hom+    & $\hom$\\
-\verb+\inf+    & $\inf$    & \verb+\injlim+ & $\injlim$ & \verb+\ker+    & $\ker$\\
-\verb+\lg+     & $\lg$     & \verb+\lim+    & $\lim$    & \verb+\liminf+ & $\liminf$\\
-\verb+\limsup+ & $\limsup$ & \verb+\ln+     & $\ln$     & \verb+\log+    & $\log$\\
-\verb+\max+    & $\max$    & \verb+\min+    & $\min$    & \verb+\Pr+     & $\Pr$\\
-\verb+\projlim+& $\projlim$& \verb+\sec+    & $\sec$    & \verb+\sin+    & $\sin$\\
-\verb+\sinh+   & $\sinh$   & \verb+\sup+    & $\sup$    & \verb+\tan+    & $\tan$\\
-\verb+\tanh+   & $\tanh$
-\end{tabular}
-\caption{The predefined operators of \texttt{amsopn.sty}}\label{tab:amsopn}
-\end{table}
-
-
-\subsection{\texttt{bigdel}}\label{sec:bigdelim}
-This is a very useful package together with the \PIndex{multirow} package.
-In the following example we need additional parentheses for a different
-number of rows. This is also possible with the \UIndex{array},
-but not as easy as with the \PIndex{bigdelim} package. The trick is that you need one
-separate column for a big delimiter, but with empty cells in all rows, which
-the delimiter spans. 
-
-\[
-  \begin{pmatrix}
-     & x_{11} & x_{12} & \dots & x_{1p} & \rdelim\}{4}{3cm}[some text]\\
-     \ldelim[{5}{1cm}[text] & x_{21} & x_{22} & \dots & x_{2p} \\
-     & \vdots\\
-     & x_{n_1 1}& x_{n_1 2} & \dots & x_{n_1 p}\\
-     & x_{n_1+1,1}&x_{n_1+1,2} & \dots & x_{n_1+1, p} &
-         \rdelim\}{3}{3cm}[some more text]\\
-     & \vdots\\
-     & x_{n_1+n_2, 1} & x_{n_1+n_2,2} & \dots & x_{n_1+n_2,p}\\
-     & \vdots \\
-  \end{pmatrix}
-\]
-
-\begin{lstlisting}[xleftmargin=-1cm,xrightmargin=-1.5cm]
-\[
-  \begin{pmatrix}
-     & x_{11} & x_{12} & \dots & x_{1p} & \rdelim\}{4}{3cm}[some text]\\
-     \ldelim[{5}{1cm}[text] & x_{21} & x_{22} & \dots & x_{2p} \\
-     & \vdots\\
-     & x_{n_1 1}& x_{n_1 2} & \dots & x_{n_1 p}\\
-     & x_{n_1+1,1}&x_{n_1+1,2} & \dots & x_{n_1+1, p} &
-         \rdelim\}{3}{3cm}[some more text]\\
-     & \vdots\\
-     & x_{n_1+n_2, 1} & x_{n_1+n_2,2} & \dots & x_{n_1+n_2,p}\\
-     & \vdots \\
-  \end{pmatrix}
-\]
-\end{lstlisting}
-
-As seen in the above listing the left big delimiter is placed in the first
-column, all other rows start with second column. It is possible to use all
-columns above and below the delimiter. For the \UIndex{array}
-there must be two more columns defined, in case of a big delimiter left and
-right. The syntax of \CIndex{ldelim} and \CIndex{rdelim} is:
-%
-\begin{verbatim}
-\ldelim<delimiter>{<n rows>}{<added horizontal space>}[<text>]
-\rdelim<delimiter>{<n rows>}{<added horizontal space>}[<text>]
-\end{verbatim}
-
-Any delimiter which is possible for the \CIndex{left} or \CIndex{right} command
-is allowed, \eg ``\verb/()[]{}|/''. The text is an optional argument and 
-always typeset in text mode.
-
-\subsection{\texttt{bm}}\label{sec:bm}
-By default the math macro \CIndex{mathbf} writes everything in bold and in upright mode
-$\mathbf{y=f(x)}$  (\verb|$\mathbf{y=f(x)}$|), but it should be in italic mode especially
-for variables $\bm{y=f(x)}$ (\verb|$\bm{y=f(x)}$|), which is possible with the package \PIndex{bm}. 
-For writing a whole formula in bold have a look at section~\vref{sec:boldmath}.
-
-
-\subsection{\texttt{braket}}\label{sec:braket}
-It is available at
- \href{http://www.ctan.org/tex-archive/macros/latex/contrib/other/misc/braket.sty}%
-{CTAN://macros/latex/contrib/other/misc/braket.sty}
-and provides several styles for writing math expressions inside brakets. For example:
-
-\[ \left\{ x\in\mathbf{R} | 0<{|x|}<\frac{5}{3}\right\} \]
-
-\begin{lstlisting}
-\[ \left\{ x\in\mathbf{R} | 0<{|x|}<\frac{5}{3}\right\} \]
-\end{lstlisting}
-
-\noindent looks not quite right and it is not really easy to get the first vertical line in the same
-size as the outer braces. Some solution may be using \CIndex{vphantom}:
-
-\[
-\left\{\vphantom{\frac{5}{3}}x\in\mathbf{R} \right|\left. 0<{|x|}<\frac{5}{3}\right\}
-\]
-
-\begin{lstlisting}
-\[
-\left\{\vphantom{\frac{5}{3}}x\in\mathbf{R} \right|\left. 0<{|x|}<\frac{5}{3}\right\}
-\]
-\end{lstlisting}
-
-The package \PIndex{braket} has the macros
-
-\begin{lstlisting}
-\Bra{<math expression>}
-\Ket{<math expression>}
-\Braket{<math expression>}
-\Set{<math expression>}
-\end{lstlisting}
-
-\noindent and the same with a leading lower letter, which are not really interesting.
-
-\[ \Bra{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\[ \Ket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\[ \Braket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\[ \Braket{x\in\mathbf{R} | 0<\vert x\vert <\frac{5}{3}} \]
-\[ \Set{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-
-\begin{lstlisting}
-\[ \Bra{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\[ \Ket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\[ \Braket{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\[ \Braket{x\in\mathbf{R} | 0<\vert x\vert <\frac{5}{3}} \]
-\[ \Set{x\in\mathbf{R} | 0<|x|<\frac{5}{3}} \]
-\end{lstlisting}
-
-The difference between the \CIndex{Set} and the \CIndex{Braket} macro is the  handling of the
-vertical lines. In \CIndex{Set} only the first one gets the same size as the
-braces\index{Braces} and in \CIndex{Braket} all.
-
-\[  \Braket{ \phi | \frac{\partial^2}{\partial t^2} | \psi }\]
-\[  \Set{ \phi | \frac{\partial^2}{\partial t^2} | \psi }\]
-\begin{lstlisting}
-\[\Braket{\phi | \frac{\partial^2}{\partial t^2} | \psi}\]
-\[\Set{\phi | \frac{\partial^2}{\partial t^2} | \psi}\]
-\end{lstlisting}
-
-
-\CMD{Bra} and \CMD{Ket} do nothing with the inner vertical lines.
-
-
-\subsection{\texttt{cancel}}\label{cancel.sty}
-This is a nice package for canceling anything in mathmode with a slash, 
-backslash or a \verb+X+. To get
-a horizontal line we can define an additional macro called \CIndex{hcancel} 
-with an optional argument
-for the line color (requires package \PIndex{color}):
-%
-\begin{lstlisting}
-\newcommand\hcancel[2][black]{\setbox0=\hbox{#2}%
-	\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2}
-\end{lstlisting}
-
-It is no problem to redefine the \CIndex{cancel} macros to get also colored lines. 
-A horizontal line for
-single characters is also decribed in section~\vref{sec:Accents}.
-
-\medskip
-\noindent
-\verb+\cancel+: $f(x)=\dfrac{\left(x^2+1\right)\cancel{(x-1)}}{\cancel{(x-1)}(x+1)}$\\[0.5cm]
-\verb+\bcancel+: $\bcancel{3}\qquad\bcancel{1234567}$\\[0.5cm]
-\verb+\xcancel+: $\xcancel{3}\qquad\xcancel{1234567}$\\[0.5cm]
-\verb+\hcancel+: $\hcancel{3}\qquad\hcancel[red]{1234567}$
-
-\bigskip
-\begin{lstlisting}
-$f(x)=\dfrac{\left(x^2+1\right)\cancel{(x-1)}}{\cancel{(x-1)}(x+1)}$\\[0.5cm]
-$\bcancel{3}\qquad\bcancel{1234567}$\\[0.5cm]
-$\xcancel{3}\qquad\xcancel{1234567}$\\[0.5cm]
-$\hcancel{3}\qquad\hcancel[red]{1234567}$
-\end{lstlisting}
-
-
-\subsection{\texttt{cool}}\label{cool}
-The \PIndex{cool} package defines a lot of special mathematical expressions 
-to use them by the macro name. The following list shows only some of
-them, for more informations look at the example file, which comes with
-the package.  
-
-\bgroup
-\parindent=0pt
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{Sin}\verb|{x}|	& $\displaystyle \Sin{x}$\\
-\CIndex{Cos}\verb|{x}|	& $\displaystyle \Cos{x}$\\
-\CIndex{Tan}\verb|{x}|	& $\displaystyle \Tan{x}$\\
-\CIndex{Csc}\verb|{x}|	& $\displaystyle \Csc{x}$\\
-\CIndex{Sec}\verb|{x}|	& $\displaystyle \Sec{x}$\\
-\CIndex{Cot}\verb|{x}|	& $\displaystyle \Cot{x}$
-\end{tabular}
-
-\bigskip
-\Style{ArcTrig=inverse}%
-\CMD{Style\{ArcTrig=inverse\}} (default)
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{ArcSin}\verb|{x}|& $\displaystyle \ArcSin{x}$\\
-\CIndex{ArcCos}\verb|{x}|& $\displaystyle \ArcCos{x}$\\
-\CIndex{ArcTan}\verb|{x}|& $\displaystyle \ArcTan{x}$
-\end{tabular}
-
-\bigskip
-\Style{ArcTrig=arc}
-\CMD{Style\{ArcTrig=arc\}}
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{ArcSin}\verb|{x}| & $\displaystyle \ArcSin{x}$\\
-\CIndex{ArcCos}\verb|{x}| & $\displaystyle \ArcCos{x}$\\
-\CIndex{ArcTan}\verb|{x}| & $\displaystyle \ArcTan{x}$\\
-\CIndex{ArcCsc}\verb|{x}| & $\displaystyle \ArcCsc{x}$\\
-\CIndex{ArcSec}\verb|{x}| & $\displaystyle \ArcSec{x}$\\
-\CIndex{ArcCot}\verb|{x}| & $\displaystyle \ArcCot{x}$
-\end{tabular}
-
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{Factorial}\verb|{n}|	& $\displaystyle \Factorial{n}$\\
-\CIndex{DblFactorial}\verb|{n}|	& $\displaystyle \DblFactorial{n}$\\
-\CIndex{Binomial}\verb|{n}{k}|	& $\displaystyle \Binomial{n}{k}$\\
-\CIndex{Multinomial}\verb|{1,2,3,4}|& $\displaystyle \Multinomial{i_1,\ldots,i_n}$
-\end{tabular}
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{GammaFunc}\verb|{x}|	& $\displaystyle \GammaFunc{x}$\\
-\CIndex{IncGamma}\verb|{a}{x}|	& $\displaystyle \IncGamma{a}{x}$\\
-\CIndex{GenIncGamma}\verb|{a}{x}{y}|& $\displaystyle \GenIncGamma{a}{x}{y}$	\\
-\CIndex{RegIncGamma}\verb|{a}{x}|& $\displaystyle \RegIncGamma{a}{x}$	\\
-\CIndex{RegIncGammaInv}\verb|{a}{x}|& $\displaystyle \RegIncGammaInv{a}{x}$	\\
-\CIndex{GenRegIncGamma}\verb|{a}{x}{y}|	& $\displaystyle \GenRegIncGamma{a}{x}{y}$\\
-\CIndex{GenRegIncGammaInv}\verb|{a}{x}{y}|& $\displaystyle \GenRegIncGammaInv{a}{x}{y}$\\
-\CIndex{Pochhammer}\verb|{a}{n}|	& $\displaystyle \Pochhammer{a}{n}$	\\
-\CIndex{LogGamma}\verb|{x}|		& $\displaystyle \LogGamma{x}$
-\end{tabular}
-
-
-\bigskip
-
-\begin{tabular}{@{}ll@{}}
-\CIndex{Hypergeometric}\verb|{0}{0}{}{}{x}| & $\displaystyle \Hypergeometric{0}{0}{}{}{x}$\\
-\CIndex{Hypergeometric}\verb|{0}{1}{}{b}{x}|& $\displaystyle \Hypergeometric{0}{1}{}{b}{x}$
-\end{tabular}
-
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{RegHypergeometric}\verb|{0}{0}{}{}{x}| & $\displaystyle \RegHypergeometric{0}{0}{}{}{x}$\\
-\CIndex{RegHypergeometric}\verb|{0}{1}{}{b}{x}|& $\displaystyle \RegHypergeometric{0}{1}{}{b}{x}$
-\end{tabular}
-
-
-
-\bigskip
-\begin{tabular}{@{}l@{}}
-\CIndex{MeijerG}\verb|[a,b]{n}{p}{m}{q}{x}| \\
- \hspace*{2cm} $\displaystyle \MeijerG[a,b]{n}{p}{m}{q}{x}$ \\
-\CIndex{MeijerG}\verb|{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}| \\
- \hspace*{2cm} $\displaystyle \MeijerG{1,2,3,4}{5,6}{3,6,9}{12,15,18,21,24}{x}$
-\end{tabular}
-
-\index{Zeta!Functions}
-\index{Polylogarithm}
-\index{Zeta!Riemann}
-\index{Zeta!Hurwitz}
-\index{Zeta}
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{RiemannZeta}\verb|{s}|	& $\displaystyle \RiemannZeta{s}$\\
-\CIndex{Zeta}\verb|{s}|		& $\displaystyle \Zeta{s}$\\
-\CIndex{HurwitzZeta}\verb|{s}{a}|& $\displaystyle \HurwitzZeta{s}{a}$\\
-\CIndex{Zeta}\verb|{s,a}|	 & $\displaystyle \Zeta{s,a}$	\\
-\CIndex{RiemannSiegelTheta}\verb|{x}|& $\displaystyle \RiemannSiegelTheta{x}$	\\
-\CIndex{RiemannSiegelZ}\verb|{x}|	& $\displaystyle \RiemannSiegelZ{x}$		\\
-\CIndex{StieltjesGamma}\verb|{n}|	& $\displaystyle \StieltjesGamma{n}$
-\end{tabular}
-
-
-\index{Mathieu!Functions}
-\index{Mathieu!Characteristics}
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{MathieuC}\verb|{a}{q}{z}|	& $\displaystyle \MathieuC{a}{q}{z}$	\\
-\CIndex{MathieuS}\verb|{a}{q}{z}| 	& $\displaystyle \MathieuS{a}{q}{z}$
-\end{tabular}
-
-
-\bigskip
-\begin{tabular}{@{}ll@{}}
-\CIndex{MathieuCharacteristicA}\verb|{r}{q}|& $\displaystyle \MathieuCharacteristicA{r}{q}$	\\
-\CIndex{MathieuCharisticA}\verb|{r}{q}|	& $\displaystyle \MathieuCharisticA{r}{q}$	\\
-
-%%%%%%% Characteristic Value of Even Mathieu Fucntion b_r(q)
-\CIndex{MathieuCharacteristicB}\verb|{r}{q}|& $\displaystyle \MathieuCharacteristicB{r}{q}$	\\
-\CIndex{MathieuCharisticB}\verb|{r}{q}|& $\displaystyle \MathieuCharisticB{r}{q}$	\\
-				
-%%%%%%%% Characteristic Exponent of a Mathieu Fucntion r(a,q)
-\CIndex{MathieuCharacteristicExponent}\verb|{a}{q}|& $\displaystyle \MathieuCharacteristicExponent{a}{q}$\\
-\CIndex{MathieuCharisticExp}\verb|{a}{q}|& $\displaystyle \MathieuCharisticExp{a}{q}$
-\end{tabular}
-\egroup
-
-\subsection{\texttt{delarray}}\label{delarray}
-
-Package \PIndex{delarray}%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/required/tools/delarray.dtx}{CTAN://macros/latex/required/tools/delarray.dtx}%
-} supports different delimiters which are defined together with the
-beginning of an array:
-
-\begin{lstlisting}
-\begin{array}<delLeft>{cc}<delRight>
-...
-\end{lstlisting}
-
-\noindent defines an array with two centered columns and the delimiters\\
-``\texttt{<delLeft><delRight>}{}'', \eg ``\texttt{()}{}''.
-
-\medskip{}
-\begin{minipage}[c]{0.45\textwidth}%
-\begin{lstlisting}
-\[
-A=\begin{array}({cc})
-	a & b\\
-	c & d
-\end{array}
-\]
-\end{lstlisting}
-
-\end{minipage}%
-\hfill{}\begin{minipage}[c]{0.45\textwidth}%
-\[
-A=\begin{array}({cc})
-a & b \\
-c & d
-\end{array}
-\]
-\end{minipage}%
-
-\medskip{}
-
-The \PIndex{delarray} package expects a pair of delimiters. If you need only
-one (like the cases structure) then use the dot for an ``empty''
-delimiter, \eg
-
-\medskip{}
-\begin{minipage}[c]{0.45\textwidth}%
-\begin{lstlisting}
-\[
-A=\begin{array}\{{cc}.
-	a & b\\
-	c & d
-\end{array}
-\]
-\end{lstlisting}
-
-\end{minipage}%
-\hfill{}\begin{minipage}[c]{0.45\textwidth}%
-\[A=\begin{array}\{{cc}.
-a & b \\
-c & d
-\end{array}\]
-\end{minipage}%
-
-\medskip{}
-
-\noindent which is a useful command for a cases structure without the \AmSmath 
-package, which is described in the \AmSmath part.
-
-
-\subsection{\texttt{dotseqn}}\label{dotseqn}
-This package%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/dotseqn/}%
-{CTAN://macros/latex/contrib/dotseqn}} fills the space between the math 
-expression and the equation
-number with dots. Expect problems when using this package together with \AmSmath.
-
-\begingroup
-\makeatletter 
-% package couldn't be loaded, it redefines the math
-% environments
-\newcommand\EqnDots{\leaders\hbox{\kern4\p@ .\kern4\p@}\hfill}
-\@ifundefined{mathindent}{\newdimen\mathindent \mathindent\leftmargini}{}
-\renewcommand{\[}{\relax \ifmmode\@badmath \else
- \begin{trivlist}%
-  \@beginparpenalty\predisplaypenalty \@endparpenalty\postdisplaypenalty
-  \item[]\leavevmode \hbox to\linewidth\bgroup $\m@th\displaystyle %$
-  \hskip\mathindent\bgroup
- \fi}
-\renewcommand{\]}{\relax\ifmmode \egroup $\hfil% $
-    \egroup \end{trivlist}%
-  \else \@badmath \fi}
-\renewenvironment{equation}%
- {\@beginparpenalty\predisplaypenalty \@endparpenalty\postdisplaypenalty
-     \refstepcounter{equation}\trivlist \item[]\leavevmode
-       \hbox to\linewidth\bgroup $\m@th% $
-         \displaystyle \hskip\mathindent}%
- {$\EqnDots % $   Replace `\hfil' with dotted leaders `\EqnDots'.
-     \displaywidth\linewidth\hbox{\@eqnnum}\egroup \endtrivlist}
-\renewenvironment{eqnarray}{%
-   \stepcounter{equation}%
-   \def\@currentlabel{\p@equation\theequation}%
-   \global\@eqnswtrue \m@th \global\@eqcnt\z@  \tabskip\mathindent
-   \let\\\@eqncr \setlength\abovedisplayskip\topsep
-   \ifvmode \addtolength\abovedisplayskip\partopsep \fi
-   \addtolength\abovedisplayskip\parskip
-   \setlength\belowdisplayskip\abovedisplayskip
-   \setlength\belowdisplayshortskip\abovedisplayskip
-   \setlength\abovedisplayshortskip\abovedisplayskip
-   $$\everycr{}\halign to\linewidth% $$
-   \bgroup
-     \hskip\@centering
-     $\displaystyle\tabskip\z@skip{##}$\@eqnsel&%
-     \global\@eqcnt\@ne \hfil${\DEQ@acs##\DEQ@acs}$\hfil&%
-     \global\@eqcnt\tw@ $\displaystyle{##}$\hskip\@centering\cr%
- }% end of "\begin" part
- {\@@eqncr
-   \noalign{% vertical skip up to overlay phantom line
-      \penalty\@M \vskip-\prevdepth
-      \edef\@tempa{\omit\span\omit\span\omit   % span three columns
-        \vrule\@depth\the\prevdepth \@width\z@ % strut of proper depth
-        \kern-\mathindent \kern\linewidth}%    % full line width
-      \nointerlineskip \expandafter % use saved |\@tempa| outside group
-   }\@tempa\cr
-   \egroup
-   \global\advance\c@equation\m@ne$$% $$
-   \global\@ignoretrue
- }
-\def\@@eqncr{\let\reserved@a\@empty
-   \ifcase\@eqcnt \def\reserved@a{& &}\or \def\reserved@a{&}\fi
-   \reserved@a
-   \if@eqnsw \egroup $\EqnDots \@eqnnum $\bgroup \stepcounter{equation}%
-   \fi \global\@eqnswtrue\global\@eqcnt\z@\cr}
-\def\DEQ@acs{\hskip\tw@\arraycolsep}
-\makeatother
-\begin{eqnarray} 
-  F(x) &=& \int f(x)\,\mathrm{d}x + C 
-\end{eqnarray}
-%
-\begin{equation}
-  F(x)=\int f(x)\,\mathrm{d}x + C 
-\end{equation}
-\endgroup
-
-\begin{lstlisting}
-\begin{eqnarray} 
-  F(x) &=& \int f(x)\,\mathrm{d}x + C 
-\end{eqnarray}
-%
-\begin{equation}
-  F(x)=\int f(x)\,\mathrm{d}x + C 
-\end{equation}
-\end{lstlisting}
-
-
-\subsection{\texttt{empheq}}\label{sec:empheq}
-
-This package\footnote{The package is part of the \texttt{mh}-bundle 
-of Morten H\o gholm (\href{http://www.ctan.org/tex-archive/macros/latex/contrib/mh/}{CTAN://macros/latex/contrib/mh/}).} 
-supports different frames for math environments of the \AmSmath
-package. It doesn't support  all the environments from standard \LaTeX{} which 
-are not modified by \AmSmath, \eg \UIndex{eqnarray}.
-
-With the optional argument of the \UIndex{empheq} 
-the preferred box type
-can be specified. A simple one is \CIndex{fbox}
-
-\begin{empheq}[box=\fbox]{align}
-	f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1
-\end{empheq}
-
-\begin{lstlisting}
-\begin{empheq}[box=\fbox]{align}
-	f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1
-\end{empheq}
-\end{lstlisting}
-
-The same is possible with the macro \verb|\colorbox|:
-\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align}
-	f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1
-\end{empheq}
-
-\begin{lstlisting}
-\begin{empheq}[box={\fboxsep=10pt\colorbox{yellow}}]{align}
-	f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1
-\end{empheq}
-\end{lstlisting}
-
-The key \verb|box| can hold any possible \LaTeX{} command sequence. Boxing
-subequations is also no problem, the \UIndex{empheq} works in the same way:
-
-\begin{subequations}
-\begin{empheq}[box={\fboxsep=10pt\colorbox{cyan}}]{align}
-	f(x) & =\int_1^{\infty}\frac{1}{x^1}\,\mathrm{d}x=1\\
-	f(x) & =\int_2^{\infty}\frac{1}{x^2}\,\mathrm{d}x=0.25
-\end{empheq}
-\end{subequations}
-
-\begin{lstlisting}
-\begin{subequations}
-\begin{empheq}[box={\fboxsep=10pt\colorbox{cyan}}]{align}
-	f(x) & =\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1\\
-	f(x) & =\int_2^{\infty}\frac{1}{x^2}\,\mathrm{d}x=0.25
-\end{empheq}
-\end{subequations}
-\end{lstlisting}
-
-For more information on \PIndex{empheq} package have a look at the documentation of the package
-which is available at any CTAN server.
-
-\subsection{\texttt{esint}}\label{sec:esint}
-This is a very useful package when you want nice double or triple integral or curve
-integral symbols. The ones from the \PIndex{wasysym} package%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/wasysym/}%
-{CTAN://macros/latex/contrib/wasysym/}} are not the best.
-\verb|esint|\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/contrib/esint/}%
-{CTAN://macros/latex/contrib/esint/}
-\href{http://www.ctan.org/tex-archive/fonts/ps-type1/esint/}{CTAN://fonts/ps-type1/esint/}} supports the following symbols:
-
-\allowdisplaybreaks
-\begin{align}
-\text{\CMD{int}}      &: \int\\
-\text{\CMD{iint}}     &: \iint\\
-\text{\CMD{iiintop}}  &: \iiintop\\
-\text{\CMD{iiiintop}} &: \iiiintop\\
-\text{\CMD{dotsintop}}&: \dotsintop\\
-\text{\CMD{ointop}}   &: \ointop\\
-\text{\CMD{oiint}}    &: \oiint\\
-\text{\CMD{sqint}}    &: \sqint\\
-\text{\CMD{sqiint}}   &: \sqiint\\
-\text{\CMD{ointctrclockwise}}    &: \ointctrclockwise\\
-\text{\CMD{ointclockwise}}       &: \ointclockwise\\
-\text{\CMD{varointclockwise}}    &: \varointclockwise\\
-\text{\CMD{varointctrclockwise}} &: \varointctrclockwise\\
-\text{\CMD{fint}}        &: \fint\\
-\text{\CMD{varoiint}}    &: \varoiint\\
-\text{\CMD{landupint}}   &: \landupint\\
-\text{\CMD{landdownint}} &: \landdownint
-\end{align}
-
-
-\subsection{\texttt{eucal} and \texttt{euscript}}\label{sec:euscript.sty}
-
-These packages should be part of your local \TeX{} installation, because
-they come with the \AmSmath packages. Otherwise get them from CTAN%
-\footnote{\href{http://www.ctan.org/tex-archive/fonts/amsfonts/latex/euscript.sty}%
-{CTAN://fonts/amsfonts/latex/euscript.sty}}. They support a scriptwriting of only uppercase
-letters:
-
-\begin{center}
-\includegraphics{EuScript}
-%\texttt{\textbackslash{}mathscr\{...\}}\index{EuScript@\textbackslash EuScript}
-%{$\EuScript{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$}
-\end{center}
-
-Read the documentation for the interdependence to the    %%% ----- Martin -----
-\verb|\mathcal| command. For the above example the
-package \PIndex{eucal} was loaded with the option \verb|mathscr|.
-
-
-\subsection{\texttt{exscale}}\label{sec:exscale}
-
-The following formula is written with the default fontsize where everything
-looks more or less well:
-
-\[
-\int_{-1}^{+1}\frac{f(x)}{\sqrt{1-x^{2}}}\,%
-\,\mathrm{d}x\approx\frac{\pi}{n}\sum_{i=1}^{n}f\left(\cos\left(\frac{2i-1}{2n}\right)\right)\]
-
-
-Writing the same with the fontsize \CIndex{huge} gives
-a surprising result, which belongs to the historical development of
-\LaTeX{}, the \CIndex{int} and \CIndex{sum} symbols
-are not stretched. This extreme fontsize is often needed for slides
-and not only written ``just for fun{}''.
-
-\begin{center}
-\includegraphics{exscale}
-\end{center}
-
-Using the \PIndex{exscale} package%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/base/}%
-{CTAN://macros/latex/base/}} package, which should be part of any local \TeX{}
-installation, all symbols get the right size.
-
-\begin{minipage}[c]{1.0\textwidth}%
-\centering\huge\[
-\int_{-1}^{+1}\frac{f(x)}{\sqrt{1-x^{2}}}\,\mathrm{d}x\approx\frac{\pi}{n}%
-\sum_{i=1}^{n}f\left(\cos\left(\frac{2i-1}{2n}\right)\right)\]
-\end{minipage}%
-
-\subsection{\texttt{mathtools}}\label{sec:mathtools}
-This package comes with a lot of additional features for typesetting math code.
-Sometimes it is useful when only such equations are numbered which are
-referenced in the text. This is possible with the switch \verb+\showonlyrefs+.
-
-Matrices are set by default with a centered horizontal alignment, which is
-often not the best way. The \PIndex{mathtools} package provides a starred version of
-the matrix environments which allow an optional argument for the horizontal
-alignment:
-
-\[
-\begin{pmatrix*}[r]
-  1 & -1 &  0 \\
- -1 &  1 & -1 \\
-  1 & -1 &  0 \\
--11 & 11 &-11 \\
-\end{pmatrix*}
-\]
-
-\begin{lstlisting}
-\[
-\begin{pmatrix*}[r]
-  1 & -1 &  0 \\
- -1 &  1 & -1 \\
-  1 & -1 &  0 \\
--11 & 11 &-11 \\
-\end{pmatrix*}
-\]
-\end{lstlisting}
-
-\PIndex{mathtools} also provides some more environments for setting equations.
-Very interesting is the \UIndex{lgathered}, which allows to typeset a formula in
-the following way:
-
-\begin{LTXexample}[width=0.6\linewidth]
-\begin{align}
- x &= 
-  \begin{lgathered}[t]
-    a + b + c \\
-    d + e + 
-      \!\begin{gathered}[t]
-        f + g + h \\
-        i + j + k
-      \end{gathered}
-  \end{lgathered}
-\end{align}
-\end{LTXexample}
-
-The \CMD{!}\index{*@\textbackslash\char033} revokes the internal horizontal space 
-in front of the \UIndex{gathered}.
-
-
-
-\subsection{\texttt{nicefrac}}\label{sec:nicefrac}
-Typesetting fractions\index{Fraction} in the inline mode is often a bad choice, the vertical spacing
-increases in fact of the fraction. The \PIndex{nicefrac} package defines the macro
-\CIndex{nicefrac}, which is used in the same way as the \CIndex{frac} command, but it
-typesets the fraction with a less height: \nicefrac{2}{3} \lstinline|\nicefrac{2}{3}|. 
-The package is part of the \PIndex{units} package bundle and can be found in the
-directory of \PIndex{units}. 
-
-
-
-\subsection{\texttt{relsize}}\label{sec:relsize}
-Often consecutives math operators are used, like two sum symbols, \eg
-%
-\[  \sum\sum_{i=1}^n i^2 \]
-
-
-As seen the sums are of the same size. To increase the first operator size, someone
-can use the \CIndex{scalebox} macro from package \UIndex{graphicx} and write an own macro    %%% ----- Martin -----
-\verb+\Sum+, \eg \index{Operator!size}\index{Size!Operator}
-
-\begin{lstlisting}
-\def\Sum{\ensuremath\mathop{\scalebox{1.2}{$\displaystyle\sum$}}}
-\[ \Sum_{j=1}\sum_{i=1}^\infty i \]
-\end{lstlisting}
-
-\def\Sum{\ensuremath\mathop{\scalebox{1.2}{$\displaystyle\sum$}}}
-\[ \Sum_{j=1}\sum_{i=1}^\infty i \]
-
-Another solution is to use the \PIndex{relsize} package%
-\footnote{\href{http://www.ctan.org/tex-archive/macros/latex/ltxmisc/}{CTAN://macros/latex/ltxmisc/}} 
-together with the \PIndex{exscale} one. \PIndex{relsize} defines a useful macro \CIndex{mathlarger}:
-
-\begin{LTXexample}
-\[ \mathlarger{\sum}\sum_{i=1}^n i^2 \]
-\end{LTXexample}
-
-
-\subsection{\texttt{xypic}}\label{xypic.sty}
-
-The \CIndex{xymatrix} macro is part of the \PIndex{xypic} package%
-\footnote{\href{http://www.ctan.org/tex-archive/support/latex2html/}%
-{CTAN://macros/generic/diagrams/xypic/xy-3.7/}} which can be loaded with several options
-which are not so important here.%
-\footnote{For more information look at the package documentation or the
-package \PIndex{xy} itself, which is often saved in \texttt{/usr/share/texmf/tex/generic}}.
-
-\begin{equation}
-\xymatrix{A\POS[];[d]**\dir{~},[];[dr]**\dir{-} & B & C\\
-D & E\POS[];[l]**\dir{.},[];[r]**\dir{~} & F\POS[];[dl]**\dir{~}\\
-G & H & I}
-\label{eq:xymatrix}
-\end{equation}
-
-
-This matrix was created with
-
-\begin{lstlisting}
-\[
-\xymatrix{ A\POS [];[d]**\dir {~},[];[dr]**\dir {-} & B & C\\
- D & E\POS [];[l]**\dir {.},[];[r]**\dir {~} & F\POS [];[dl]**\dir {~}\\
- G & H & I}
-\]
-\end{lstlisting}
-
-
-
-
-\part{Math fonts}
-Typesetting text and math is far different. There exist a lot of free text fonts without
-additional math characters. This is the reason why we have to buy a commercial math font, e.\,g. 
-\Index{Palatino} (\PIndex{pamath}) or \Index{Helvetica} (\PIndex{hvmath}), or to 
-combine the free text font with another free math font.
-
-\section{Computer modern}
-This is the default font, designed by Knuth.\index{cmr}\index{Computer modern} For the PDF output
-the Type 1 fonts cm-super and BlueSky were used.
-
-\Mbox{cm-crop}
-
-\section{Latin modern}
-This is the new designed font which comes with an own Type 1 version.\FIndex{lm}\index{Latin modern} 
-
-\Mbox{lm-crop}
-
-\section{Palatino}
-There is a free package mathpazo.\PIndex{mathpazo}\index{Palatino} 
-
-\Mbox{pazo-crop}
-
-\section{Palatino -- microimp}
-There is the package \PIndex{pamath} for the nonfree palatino font.\PIndex{mathpazo}\index{Palatino} 
-
-\Mbox{pamath-crop}
-
-\section{cmbright}
-
-\Mbox{cmbright-crop}
-
-\section{minion}
-
-\Mbox{minionpro-crop}
-
-
-
-\part{Special symbols}
-
-In this section only those symbols are defined, which are not part of the    %%% ----- Martin -----
-list of all available symbols:
-\href{http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}%
-{CTAN://info/symbols/comprehensive/symbols-a4.pdf}. With
-\verb+fontmath.ltx+ \LaTeX{} itself defines the following special symbols for using inside math:    %%% ----- Martin -----
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{l|c}
-Name & Meaning\\\hline
-\verb+\mathparagraph+ & $\mathparagraph$\\
-\verb+\mathsection+ & $\mathsection$\\
-\verb+\mathdollar+ & $\mathdollar$\\
-\verb+\mathsterling+ & $\mathsterling$\\
-\verb+\mathunderscore+ & $\mathunderscore$\\
-\verb+\mathellipsis+ & $\mathellipsis$\\
-\end{tabular}
-\caption{Predefined math symbols from \texttt{fontmath.ltx}}\label{fontmath.ltx}
-\end{table}
-
-\section{Integral symbols}
-\index{Integral symbols}
-
-\def\Xint#1{\mathchoice
-   {\XXint\displaystyle\textstyle{#1}}%
-   {\XXint\textstyle\scriptstyle{#1}}%
-   {\XXint\scriptstyle\scriptscriptstyle{#1}}%
-   {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}%
-   \!\int}
-\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$}
-     \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}}
-\def\ddashint{\Xint=}
-\def\dashint{\Xint-}
-\def\clockint{\Xint\circlearrowright} % GOOD!
-\def\counterint{\Xint\rotcirclearrowleft} % Good for Computer Modern!
-\def\rotcirclearrowleft{\mathpalette{\RotLSymbol{-30}}\circlearrowleft}
-\def\RotLSymbol#1#2#3{\rotatebox[origin=c]{#1}{$#2#3$}}
-
-\begin{center}
-\begin{tabular}{lc}
-Name & Symbol\\\hline
-\verb|\dashint| & $\dashint$\\
-\verb|\ddashint| & $\ddashint$\\
-\verb|\clockint| & $\clockint$\\
-\verb|\counterint| & $\counterint$
-\end{tabular}
-\end{center}
-
-%$
-For all new integral symbols limits can be used in the usual way:
-
-\begin{equation}
-\ddashint_01=\dashint_10<\oint\limits_{-\infty}^\infty = \clockint\counterint_A
-\end{equation}
-
-\begin{lstlisting}
-\ddashint_01=\dashint_10<\oint\limits_{-\infty}^\infty = \clockint\counterint_A
-\end{lstlisting}
-
-Put the following definitions into the preamble to use one or all of these new
-integral symbols.
-
-\begin{lstlisting}
-\def\Xint#1{\mathchoice
-   {\XXint\displaystyle\textstyle{#1}}%
-   {\XXint\textstyle\scriptstyle{#1}}%
-   {\XXint\scriptstyle\scriptscriptstyle{#1}}%
-   {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}%
-   \!\int}
-\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$}
-     \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}}
-\def\ddashint{\Xint=}
-\def\dashint{\Xint-}
-\def\clockint{\Xint\circlearrowright} % GOOD!
-\def\counterint{\Xint\rotcirclearrowleft} % Good for Computer Modern!
-\def\rotcirclearrowleft{\mathpalette{\RotLSymbol{-30}}\circlearrowleft}
-\def\RotLSymbol#1#2#3{\rotatebox[origin=c]{#1}{$#2#3$}}
-\end{lstlisting}
-
-%\clearpage
-\section{Harpoons}
-\LaTeX{} knows no stretchable harpoon\index{Harpoon} symbols, like \verb|\xrightarrow|.
-The following code defines several harpoon symbols.%
-\index{xrightharpoondown@\textbackslash xrightharpoondown}
-\index{xrightharpoonup@\textbackslash xrightharpoonup}
-\index{xleftharpoondown@\textbackslash xleftharpoondown}
-\index{xleftharpoonup@\textbackslash xleftharpoonup}
-\index{xleftrightharpoons@\textbackslash xleftrightharpoons}
-\index{xrightleftharpoons@\textbackslash xrightleftharpoons}%
-%
-\mPar{\CMD{xrightharpoondown}\\%
-\CMD{xrightharpoonup}\\%
-\CMD{xleftharpoondown}\\%
-\CMD{xleftharpoonup}\\%
-\CMD{xleftrightharpoons}\\%
-\CMD{xrightleftharpoons}%
-}
-
-\begin{lstlisting}
-\def\rightharpoondownfill@{%
-	\arrowfill@\relbar\relbar\rightharpoondown}
-\def\rightharpoonupfill@{%
-	\arrowfill@\relbar\relbar\rightharpoonup}
-\def\leftharpoondownfill@{%
-	\arrowfill@\leftharpoondown\relbar\relbar}
-\def\leftharpoonupfill@{%
-	\arrowfill@\leftharpoonup\relbar\relbar}
-\newcommand{\xrightharpoondown}[2][]{%
-	\ext@arrow 0359\rightharpoondownfill@{#1}{#2}}
-\newcommand{\xrightharpoonup}[2][]{%
-	\ext@arrow 0359\rightharpoonupfill@{#1}{#2}}
-\newcommand{\xleftharpoondown}[2][]{%
-	\ext@arrow 3095\leftharpoondownfill@{#1}{#2}}
-\newcommand{\xleftharpoonup}[2][]{%
-	\ext@arrow 3095\leftharpoonupfill@{#1}{#2}}
-\newcommand{\xleftrightharpoons}[2][]{\mathrel{%
-	\raise.22ex\hbox{%
-		$\ext@arrow 3095\leftharpoonupfill@{\phantom{#1}}{#2}$}%
-	\setbox0=\hbox{%
-		$\ext@arrow 0359\rightharpoondownfill@{#1}{\phantom{#2}}$}%
-	\kern-\wd0 \lower.22ex\box0}%
-}
-\newcommand{\xrightleftharpoons}[2][]{\mathrel{%
-	\raise.22ex\hbox{%
-		$\ext@arrow 3095\rightharpoonupfill@{\phantom{#1}}{#2}$}%
-	\setbox0=\hbox{%
-		$\ext@arrow 0359\leftharpoondownfill@{#1}{\phantom{#2}}$}%
-	\kern-\wd0 \lower.22ex\box0}%
-}
-\end{lstlisting}
-
-\begin{tabular}{ll}
-\verb|\xrightharpoondown[under]{over}| & $\xrightharpoondown[under]{over}$\\[10pt]
-\verb|\xrightharpoonup[under]{over}|   & $\xrightharpoonup[under]{over}$ \\[10pt]
-\verb|\xleftharpoondown[under]{over}|  & $\xleftharpoondown[under]{over}$\\[10pt]
-\verb|\xleftharpoonup[under]{over}|    & $\xleftharpoonup[under]{over}$  \\[10pt]
-\verb|\xleftrightharpoons[under]{over}|& $\xleftrightharpoons[under]{over}$\\[10pt]
-\verb|\xrightleftharpoons[under]{over}|& $\xrightleftharpoons[under]{over}$
-\end{tabular}
-
-%$
-
-\section{Bijective mapping arrow}
-
-To get something like \bijmap~we can define:
-\begin{lstlisting}
-\def\bijmap{%
-	\ensuremath{%
-		\mathrlap{\rightarrowtail}\rightarrow%
-	}%
-}
-\end{lstlisting}
-
-This uses the \CIndex{mathrlap} definition from section~\vref{subsec:ams-limits}. With this
-definition a huge symbol is also possible: \verb+{\Huge\bijmap}+ {\Huge\bijmap}.
-
-\section{Stacked equal sign}
-There are several symbols stacked with an equal sign, \eg \CIndex{doteq}, \CIndex{equiv} or
-\CIndex{cong} ($\doteq$, $\equiv{}$, $\cong$ ). But there are still some missing, which are
-shown in table~\ref{tab:equal} and the following definitions.
-
-\begin{table}[htb]
-\centering
-\begin{tabular}{ll}
-\verb+\eqdef+ & \eqdef\\
-\verb+\eqexcl+ & \eqexcl\\
-\verb+\eqhat+ & \eqhat
-\end{tabular}
-\caption{New symbols in combination with the equal sign}\label{tab:equal}
-\end{table}
-
-\begin{lstlisting}
-\newcommand{\eqdef}{\ensuremath{\mathrel{\stackrel{\mathrm{def}}{=}}}}
-\newcommand{\eqexcl}{\ensuremath{\mathrel{\stackrel{\mathrm{!}}{=}}}}
-\newcommand{\eqhat}{\ensuremath{\mathrel{\widehat{=}}}}
-\end{lstlisting}
-
-\section{Other symbols}
-
-\begin{minipage}{0.7\linewidth}
-\begin{lstlisting}
-\newcommand*{\threesim}{%
-  \mathrel{\vcenter{\offinterlineskip
-  \hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}\vskip-.35ex\hbox{$\sim$}}}}
-$\threesim ABC$
-\end{lstlisting}%
-\end{minipage}\hfill
-\begin{minipage}{0.15\linewidth}
-$\threesim ABC$
-\end{minipage}
-
-
-\noindent
-\begin{minipage}{0.7\linewidth}
-\begin{lstlisting}
-\newcommand\Let{\mathrel{\mathop:\!\!=}}%  Upper case L!
-\newcommand\teL{\mathrel{=\!\!\mathop:}}
-$x\Let y$ $y\teL x$
-\end{lstlisting}%
-\end{minipage}\hfill
-\newcommand\Let{\mathrel{\mathop:\!\!=}}%  Upper case L!
-\newcommand\teL{\mathrel{=\!\!\mathop:}}
-$x\Let y$ $y\teL x$
-\begin{minipage}{0.15\linewidth}
-\end{minipage}
-
-
-%\lstset{xrightmargin=-\marginparwidth}
-
-\part{Examples}
-\section{Tuning math typesetting}
-Chapter 18 of the \TeX book is named ,,Fine Points of Mathematics Typing``~\cite{knuth86}
-and it 
-shows on 20 pages some more or less important facts when typesetting mathematical 
-expressions. Often inline formulas contain a \Index{punctuation} character like a
-\Index{dot}, \Index{comma}, \Index{colon}, \etc. It is a general rule to write
-those characters outside the math mode. Compare
-
-\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
-$a, b, c, d, e, \textrm{and }f$ \\[5pt]
-$a$, $b$, $c$, $d$, $e$, and $f$ 
-\end{LTXexample}
-
-Having such math as single expressions enables \TeX\ to insert a linebreak at several
-places (see Section~\vref{subsec:linebreak}). 
-
-Writing an \Index{ellipses} as three single dots, doesn't look very nice, one should
-always use the \CIndex{ldots} command:
-
-\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
-$1,...,10$\\[5pt]
-$1,\ldots,10$
-\end{LTXexample}
-
-This is correct as long as on the left and right are a comma as a separator.
-For sums the \CIndex{cdot} command should be used instead:
-
-\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
-$1+2+\cdots+10$\\[5pt]
-$x_n=x_{n-1}=\cdots=n_0=1$
-\end{LTXexample}
-
-For a multiplication it is important which character is used, in european countries
-often a centered dot. In such a case it is appropriate not to use the \CIndex{cdots}
-command for a ellipsis.
-
-For typesetting integrals\index{Integral} or differential equations\index{differential equation} 
-it makes sense to define the following short macros:
-
-\begin{lstlisting}
-\newcommand*{\diff}{\mathop{}\!\mathrm{d}}
-\newcommand*\dst{\,\frac{\diff s}{\diff t}
-\end{lstlisting}
-
-\newcommand*{\diff}{\mathop{}\!\mathrm{d}}
-
-
-\iffalse
-\newcommand*\dy{\,\mathrm{d}y}
-\newcommand*\dx{\,\mathrm{d}x}
-\newcommand*\dyx{\,\frac{\mathrm{d}y}{\mathrm{d}x}}
-\newcommand*\ds{\,\mathrm{d}s}
-\newcommand*\dt{\,\mathrm{d}t}
-\newcommand*\dst{\,\frac{\mathrm{d}s}{\mathrm{d}t}}
-\fi
-
-\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
-\begin{align*}
-F(x) &= \int\!f(x)\diff x\\
-v(t) &= \dst\\
-a(t) &= \frac{\diff{}^2s}{\diff t^2}
-\end{align*}
-\end{LTXexample}
-
-\begin{LTXexample}[preset=\raggedright,width=0.4\linewidth]
-\begin{align*}
-G(t)   &= \underbrace{\,\int\cdots\!\int\!\!}_D\;\diff x\diff y\ldots\\
-u_C(t) &= \int\!\,i_C(t)\diff t  
-\end{align*}
-\end{LTXexample}
-
-\bigskip
-\section{Matrix}
-\subsection{Identity matrix}
-
-There are several possibilities to write this matrix. Here is a solution
-with the default array environment.
-
-\begin{LTXexample}[width=0.4\linewidth]
-\[
-\left(
-  \begin{array}{ccccc}
-    1\\
-     & 1 &  & \text{{\huge{0}}}\\
-     &  & 1\\
-     & \text{{\huge{0}}} &  & 1\\
-     &  &  &  & 1
-  \end{array}
-\right) 
-\]
-\end{LTXexample}
-
-\subsection{System of linear equations}
-
-\begin{LTXexample}[pos=t]
-\[
-\begin{array}{l@{\:=\:}*{5}{l@{\:+\:}}l}
-y_1 & a_{11}x_1 & a_{12}x_2 & a_{13}x_3 & \dots & a_{1(n-1)}x_{n-1} & a_{1n}x_n \\
-y_2 & a_{21}x_1 & a_{22}x_2 & a_{23}x_3 & \dots & a_{2(n-1)}x_{n-1} & a_{2n}x_n \\
-\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots &\ \vdots\\
-y_{n-1} & a_{(n-1)1}x_1 & a_{(n-1)2}x_2 & a_{(n-1)3}x_3 & \dots & a_{(n-1)(n-1)}x_{n-1} & a_{(n-1)n}x_n\\
-y_n & a_{n1}x_1 & a_{n2}x_2 & a_{n3}x_3 & \dots & a_{(n)(n-1)}x_{n-1} & a_{nn}x_n
-\end{array} 
-\]
-\end{LTXexample}
-
-\subsection{Matrix with comments on top}
-
-
-\begin{LTXexample}[width=0.35\linewidth]
-\def\rb#1{\rotatebox{90}{$\xleftarrow{#1}$}}
-\begin{tabular}{c}
-$\begin{matrix}
-\rb{text1}&\rb{text1}&\rb{text1}&\rb{text1}\\
-\end{matrix}$\\
-$\begin{bmatrix}
-X_x & Y_x & Z_x & T_x \\
-X_y & Y_y & Z_y & T_y \\
-X_z & Y_z & Z_z & T_z \\
-0   & 0   & 0   & 1
-\end{bmatrix}$
-\end{tabular}
-\end{LTXexample}
-
-%$
-
-
-
-
-\section{Cases structure}
-
-\index{Cases!numbered lines}Sometimes it is better to use the array environment instead of amsmath's    %%% ----- Martin -----
-cases environment. To get optimal horizontal spacing for the conditions,
-there are two matrixes in series, one $3\times 1$ followed by $3\times 3$ matrix.
-To minimize the horizontal space around the variable $z$ a
-
-\begin{lstlisting}
-\addtolength{\arraycolsep}{-3pt}
-\end{lstlisting}
-is a useful command.
-
-\begin{equation}
-\addtolength{\arraycolsep}{-3pt}
-I(z)=\delta_{0}\left\{%
-	\begin{array}{lcrcl}
-		D+z & \quad & -D & \le z\le & -p\\
-		D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right)%
-			 & \quad & -p & \le z\le & \phantom{-}p\\
-		D-z & \quad & p & \le z\le & \phantom{-}D
-	\end{array}\right.
-\end{equation}
-
-\begin{lstlisting}
-\begin{equation}
-\addtolength{\arraycolsep}{-3pt}
-I(z)=\delta_{0}\left\{%
-  \begin{array}{lcrcl}
-    D+z & \quad & -D & \le z\le & -p\\
-    D-\frac{1}{2}\left(p-\frac{z^{2}}{p}\right)%
-	 & \quad & -p & \le z\le & \phantom{-}p\\
-    D-z & \quad & p & \le z\le & \phantom{-}D
-  \end{array}\right.
-\end{equation}
-\end{lstlisting}
-
-
-The \CMD{phantom}\index{phantom@\textbackslash phantom} command
-replaces exactly that place with whitespace which the argument needs.
-
-\subsection{Cases with numbered lines}
-This is not possible in an easy way, because \verb+cases+ uses the array
-environment for typesetting which has by default no numbering. However, there
-are some tricky ways to get numbered lines. The following three examples
-use the \verb+tabular+, the \verb+tabularx+ and the \verb+array+ environment.   
-
-\bigskip\noindent
-\begin{tabular}{rc}
-\ldelim\{{2}{2.75cm}[some text here] &      %%% ----- Martin -----
-   \parbox{{\linewidth-3cm-4\tabcolsep}}{
-   \vspace*{1ex}
-   \begin{flalign}
-     x & = 2\quad\text{if }y >2 &\\
-     x & = 3\quad\text{if }y \le 2&
-   \end{flalign}}
-\end{tabular}
-
-\bigskip
-\begin{lstlisting}
-\begin{tabular}{rc}
-\ldelim\{{2}{2.75cm}[some text here] & 
-   \parbox{{\linewidth-3cm-4\tabcolsep}}{
-   \vspace*{1ex}
-   \begin{flalign}
-     x & = 2\quad\text{if }y >2 &\\
-     x & = 3\quad\text{if }y \le 2&
-   \end{flalign}}
-\end{tabular}
-\end{lstlisting}
-
-
-\bigskip\noindent
-\begin{tabularx}{\linewidth}{rXc}
-\ldelim\{{2}{2.75cm}[some text here]     %%% ----- Martin -----
-  & $ x = 2\quad\text{if }y > 2  $ & \refstepcounter{equation}(\theequation)\\
-  & $ x = 3\quad\text{if }y \le 2$ &\refstepcounter{equation}(\theequation)
-\end{tabularx}
-
-\bigskip
-\begin{lstlisting}
-\begin{tabularx}{\linewidth}{rXc}
-\ldelim\{{2}{2.75cm}[some text here] 
-  & $x=2\quad\text{if }y>2$ &\refstepcounter{equation}(\theequation)\\
-  & $x=3\quad\text{if }y\le2$&\refstepcounter{equation}(\theequation)
-\end{tabularx}
-\end{lstlisting}
-
-
-\bigskip
-\[
-\begin{array}{rc@{\qquad}c}
-\ldelim\{{2}{2.75cm}[some text here]     %%% ----- Martin -----
-  & x = 2\quad\text{if }y > 2  & \refstepcounter{equation}(\theequation)\\
-  & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation)
-\end{array}
-\]
-
-
-\bigskip
-\begin{lstlisting}
-\[
-\begin{array}{rc@{\qquad}c}
-\ldelim\{{2}{2.75cm}[some text here] 
-  & x = 2\quad\text{if }y > 2  & \refstepcounter{equation}(\theequation)\\
-  & x = 3\quad\text{if }y \le 2& \refstepcounter{equation}(\theequation)
-\end{array}
-\]
-\end{lstlisting}
-
-%$
-
-\section{Arrays}
-
-There is a general rule that a lot of mathematical stuff should be
-divided in smaller pieces. But sometimes it is difficult to get a nice
-horizontal alignment when splitting a formula. The following ones
-uses the \texttt{array} environment to get a proper alignment.
-
-
-\subsection{Quadratic equation}
-
-\begin{equation}
-\begin{array}{rcll}
-y & = & x^{2}+bx+c\\
-  & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\
-  & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle%
- \left(\frac{b}{2}\right)^{2}+c}\\
- &  & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\
- & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle%
- \frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle%
- \frac{b}{2}}\right)^{2}-c\right.\\
-y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle%
- \frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\
-y-y_{S} & = & (x-x_{S})^{2}\\
-S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle%
- \frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right)
-\end{array}
-\end{equation}
-
-\begin{lstlisting}[xrightmargin=-\marginparwidth]
-\begin{equation}
-\begin{array}{rcll}
-y & = & x^{2}+bx+c\\
-  & = & x^{2}+2\cdot{\displaystyle\frac{b}{2}x+c}\\
-  & = & \underbrace{x^{2}+2\cdot\frac{b}{2}x+\left(\frac{b}{2}\right)^{2}}-{\displaystyle%
- \left(\frac{b}{2}\right)^{2}+c}\\
- &  & \qquad\left(x+{\displaystyle \frac{b}{2}}\right)^{2}\\
- & = & \left(x+{\displaystyle \frac{b}{2}}\right)^{2}-\left({\displaystyle%
-\frac{b}{2}}\right)^{2}+c & \left|+\left({\displaystyle%
-\frac{b}{2}}\right)^{2}-c\right.\\
-y+\left({\displaystyle \frac{b}{2}}\right)^{2}-c & = & \left(x+{\displaystyle%
-\frac{b}{2}}\right)^{2} & \left|(\textrm{Scheitelpunktform})\right.\\
-y-y_{S} & = & (x-x_{S})^{2}\\
-S(x_{S};y_{S}) & \,\textrm{bzw.}\, & S\left(-{\displaystyle%
-\frac{b}{2};\,\left({\displaystyle \frac{b}{2}}\right)^{2}-c}\right)
-\end{array}
-\end{equation}
-\end{lstlisting}
-
-
-
-\subsection{Vectors and matrices}
-\index{Vector}
-\begin{equation}
-\begin{array}{rcl}
-\underline{RS} & = & \left(\begin{array}{cccccccc}
-01 & a4 & 55 & 87 & 5a & 58 & db & 9e\\
-a4 & 56 & 82 & f3 & 1e & c6 & 68 & e5\\
-02 & a1 & fc & c1 & 47 & ae & 3d & 19\\
-a4 & 55 & 87 & 5a & 58 & db & 9e & 03\end{array}\right)\\
-\\
-\left(\begin{array}{c}
-	s_{i,0}\\
-	s_{i,1}\\
-	s_{i,2}\\
-	s_{i,3}
-\end{array}\right) & = & \underline{RS}\cdot%
-\left(\begin{array}{c}
-	m_{8i+0}\\
-	m_{8i+1}\\
-	\cdots\\
-	m_{8i+6}\\
-	m_{8i+7}
-\end{array}\right)\\
-\\
-S_{i} & = & \sum_{j=0}^{3}s_{i,j}\cdot2^{8j}\qquad i=0,1,...,k-1\\
-\\
-S & = & \left(S_{k-1},S_{k-2},...,S_{1},S_{0}\right)
-\end{array}
-\end{equation}
-
-\begin{lstlisting}
-\begin{equation}
-\begin{array}{rcl}
-\underline{RS} & = & \left(\begin{array}{cccccccc}
-01 & a4 & 55 & 87 & 5a & 58 & db & 9e\\
-a4 & 56 & 82 & f3 & 1e & c6 & 68 & e5\\
-02 & a1 & fc & c1 & 47 & ae & 3d & 19\\
-a4 & 55 & 87 & 5a & 58 & db & 9e & 03\end{array}\right)\\
-\\
-\left(\begin{array}{c}
-	s_{i,0}\\
-	s_{i,1}\\
-	s_{i,2}\\
-	s_{i,3}
-\end{array}\right) & = & \underline{RS}\cdot%
-\left(\begin{array}{c}
-	m_{8i+0}\\
-	m_{8i+1}\\
-	\cdots\\
-	m_{8i+6}\\
-	m_{8i+7}
-\end{array}\right)\\
-\\
-S_{i} & = & \sum_{j=0}^{3}s_{i,j}\cdot2^{8j}\qquad i=0,1,...,k-1\\
-\\
-S & = & \left(S_{k-1},S_{k-2},...,S_{1},S_{0}\right)
-\end{array}
-\end{equation}
-\end{lstlisting}
-
-
-\subsection{Cases with (eqn)array environment}
-
-This solution is important when \AmSmath can't be used.    %%% ----- Martin -----
-
-$\lim\limits_{n->\infty}q^{n}=\left\{%
-	\begin{array}{lc@{\kern2pt}c@{\kern2pt}r}
-		\textrm{divergent}\  & q & \le & -1\\
-		0 & |q| & < & 1\\
-		1 &  q  & = & 1\\
-		\infty  & q & > & 1
-	\end{array}\right.$
-
-\medskip
-\begin{lstlisting}
-$\lim\limits_{n->\infty}q^{n}=\left\{%
-  \begin{array}{lc@{\kern2pt}c@{\kern2pt}r}
-	\textrm{divergent}\  & q & \le & -1\\
-	0 & |q| & < & 1\\
-	1 &  q  & = & 1\\
-	\infty  & q & > & 1
-  \end{array}\right.$
-\end{lstlisting}
-%$
-
-\subsection{Arrays inside arrays}
-The array environment is a powerful one because it can be nested in several ways:
-
-\[
-\left(
-\begin{array}{c@{}c@{}c}
-\begin{array}{|cc|}
-\hline
-a_{11} & a_{12} \\
-a_{21} & a_{22} \\
-\hline
-\end{array} & 0 & 0 \\
-0 & \begin{array}{|ccc|}
-    \hline
-    b_{11} & b_{12} & b_{13}\\
-    b_{21} & b_{22} & b_{23}\\
-    b_{31} & b_{32} & b_{33}\\
-    \hline
-    \end{array} & 0 \\
-0 & 0 & \begin{array}{|cc|}
-        \hline
-        c_{11} & c_{12} \\
-        c_{21} & c_{22} \\
-        \hline
-        \end{array} \\
-\end{array}
-\right)
-\]
-
-\begin{lstlisting}
-\[
-\left(
-\begin{array}{c@{}c@{}c}
-	\begin{array}{|cc|}\hline
-		a_{11} & a_{12} \\
-		a_{21} & a_{22} \\\hline
-	\end{array} & \mathbf{0} & \mathbf{0} \\
-	\mathbf{0} &
-	\begin{array}{|ccc|}\hline
-		b_{11} & b_{12} & b_{13}\\
-		b_{21} & b_{22} & b_{23}\\
-		b_{31} & b_{32} & b_{33}\\\hline
-	\end{array} & \mathbf{0} \\
-	\mathbf{0} & \mathbf{0} &
-	\begin{array}{|cc|}\hline
-		c_{11} & c_{12} \\
-		c_{21} & c_{22} \\\hline
-	\end{array} \\
-\end{array}
-\right)
-\]
-\end{lstlisting}
-
-\[
-Y^1=
-\begin{array}{c}
-	\null\\[1ex]% kann weg
-	\left[\begin{array}{rrrr}
-		0 & 0 & 1 & 0\\
-		1 & 0 & 1 & 0\\
-		1 & 1 & 1 & 1
-	\end{array}\right]\\[3ex]\hline
-	\begin{array}{rrrr}
-%		\hdotsfor{4}\\% statt \\[3ex]\hline
-		2 & 1 &3 & 1
-	\end{array}
-\end{array}
-\]
-
-\begin{lstlisting}
-\[
-Y^1=
-\begin{array}{c}
-  \null\\[1ex]% only vor vertical alignment
-  \left[\begin{array}{rrrr}
-	0 & 0 & 1 & 0\\
-	1 & 0 & 1 & 0\\
-	1 & 1 & 1 & 1
-  \end{array}\right]\\[3ex]\hline
-  \begin{array}{rrrr}
-%	\hdotsfor{4}\\%( needs \AmSmath) instead of \\[3ex]\hline
-	2 & 1 &3 & 1
-  \end{array}
-\end{array}
-\]
-\end{lstlisting}
-
-\subsection{Colored cells}\label{sub:color}
-In general there is no difference in coloring tabular or array cells. The following example
-shows how one can put \index{color}colors in rows, columns and cells.
-\index{rowcolor@\textbackslash rowcolor}\index{columncolor@\textbackslash columncolor}
-
-\medskip\noindent
-\includegraphics[width=\columnwidth]{colArray}
-
-%\[
-%\left[\,
-%\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}}
-%  {h_{k,1,0}(n)} & {h_{k,1,1}(n)} & {h_{k,1,2}(n)} & \zero & \zero \\
-%  {h_{k,2,0}(n)} & {h_{k,2,1}(n)} & {h_{k,2,2}(n)} & \zero & \zero \\
-%  {h_{k,3,0}(n)} & {h_{k,3,1}(n)} & {h_{k,3,2}(n)} & \zero & \zero \\
-%  {h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & {h_{k,4,2}(n)} & \zero & \zero \\
-%  \zero & {h_{k,1,0}(n-1)} & {h_{k,1,1}(n-1)} & {h_{k,1,2}(n-1)} & \zero \\
-%  \zero & {h_{k,2,0}(n-1)} & {h_{k,2,1}(n-1)} & {h_{k,2,2}(n-1)} & \zero \\
-%  \zero & {h_{k,3,0}(n-1)} & {h_{k,3,1}(n-1)} & {h_{k,3,2}(n-1)} & \zero \\
-%  \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & {h_{k,4,1}(n-1)} & {h_{k,4,2}(n-1)} & \zero \\
-%  \zero & \zero & {h_{k,1,0}(n-2)} & {h_{k,1,1}(n-2)} & {h_{k,1,2}(n-2)}\\
-%  \rowcolor[gray]{0.75}%
-%  \zero & \zero & {h_{k,2,0}(n-2)} & {h_{k,2,1}(n-2)} & {h_{k,2,2}(n-2)}\\
-%  \zero & \zero & {h_{k,3,0}(n-2)} & {h_{k,3,1}(n-2)} & {h_{k,3,2}(n-2)}\\
-%  \zero & \zero & {h_{k,4,0}(n-2)} & {h_{k,4,1}(n-2)} & {h_{k,4,2}(n-2)}
-%\end{array} \,\right]
-%\end]
-
-
-\medskip
-\begin{lstlisting}[xrightmargin=-\marginparwidth]
-...
-\usepackage{array}
-\usepackage{colortbl}
-\definecolor{umbra}{rgb}{0.8,0.8,0.5}
-\def\zero{\multicolumn{1}{>{\columncolor{white}}c}{0}}
-\def\colCell#1#2{\multicolumn{1}{>{\columncolor{#1}}c}{#2}}
-\begin{document}
-\[\left[\,
-\begin{array}{*{5}{>{\columncolor[gray]{0.95}}c}}
-  h_{k,1,0}(n) & h_{k,1,1}(n) & h_{k,1,2}(n) & \zero & \zero\\
-  h_{k,2,0}(n) & h_{k,2,1}(n) & h_{k,2,2}(n) & \zero & \zero\\
-  h_{k,3,0}(n) & h_{k,3,1}(n) & h_{k,3,2}(n) & \zero & \zero\\
-  h_{k,4,0}(n)} & \colCell{umbra}{h_{k,4,1}(n)} & h_{k,4,2}(n) & \zero & \zero\\
-  \zero & h_{k,1,0}(n-1) & h_{k,1,1}(n-1) & h_{k,1,2}(n-1) & \zero\\
-  \zero & h_{k,2,0}(n-1) & h_{k,2,1}(n-1) & h_{k,2,2}(n-1) & \zero\\
-  \zero & h_{k,3,0}(n-1) & h_{k,3,1}(n-1) & h_{k,3,2}(n-1) & \zero\\
-  \zero & \colCell{umbra}{h_{k,4,0}(n-1)} & h_{k,4,1}(n-1) & h_{k,4,2}(n-1) & \zero\\
-  \zero & \zero & h_{k,1,0}(n-2) & h_{k,1,1}(n-2) & h_{k,1,2}(n-2)\\
-  \zero & \zero & h_{k,2,0}(n-2) & h_{k,2,1}(n-2) & h_{k,2,2}(n-2)\\
-  \zero & \zero & h_{k,3,0}(n-2) & h_{k,3,1}(n-2) & h_{k,3,2}(n-2)\\
-  \zero & \zero & h_{k,4,0}(n-2) & h_{k,4,1}(n-2) & h_{k,4,2}(n-2)
-\end{array} \,\right]_{12\times 5}\]
-...
-\end{lstlisting}
-
-
-\subsection{Boxed rows and columns}
-
-\begin{LTXexample}[width=0.35\linewidth]
-\[
-\overrightarrow{A}=\left[
-    \begin{array}{cccc}
-	1 & 2 & 3 & 4\\
-	1 & 2 & 3 & 4\\\hline
-	\multicolumn{1}{|c}{1} & 2 & 3 & 
-	\multicolumn{1}{c|}{4}\\\hline
-	1 & 2 & 3 & 4
-    \end{array}\right]
-\]
-\end{LTXexample}
-
-
-\begin{LTXexample}[width=0.35\linewidth]
-\[
-\overrightarrow{A}=\left[
-    \begin{array}{cc|c|c}\cline{3-3}
-	1 & 2 & 3 & 4\\
-	1 & 2 & 3 & 4\\
-	1 & 2 & 3 & 4\\
-	1 & 2 & 3 & 4\\\cline{3-3}
-    \end{array}\right]
-\]
-\end{LTXexample}
-
-\begin{LTXexample}[width=0.35\linewidth]
-\[
-\overrightarrow{A}=\left[
-    \begin{array}{cc|c|c}\cline{3-3}
-	1 & 2 & 3 & 4\\
-	1 & 2 & 3 & 4\\\hline
-	\multicolumn{1}{|c}{1} & 2 & 3 & 
-	\multicolumn{1}{c|}{4}\\\hline
-	1 & 2 & 3 & 4\\\cline{3-3}
-    \end{array}\right]
-\]
-\end{LTXexample}
-
-
-
-\section{Over- and underbraces}
-\subsection{Braces and roots}
-To put an underbrace in a root without enlarging the root symbol is possible with
-the \verb+\makebox+ macro:
-
-\[ z =\;\;\underbrace{\makebox[\widthof{~$x^2+y^2$}][r]{$\sqrt{x^2+y^2}$}}_{=z^2} \]
-
-\begin{lstlisting}
-\[
-z =\;\;\underbrace{%
-  \makebox[\widthof{~$x^2+y^2$}][r]{%
-     $\sqrt{x^2+y^2}$}}_{=z^2}
-\]
-\end{lstlisting}
-
-
-
-\subsection{Overlapping braces}
-Overlapping under- and overbraces like%
-\parbox{10em}{\begin{align*}
-\qquad\overbrace{\qquad\qquad}^o\qquad\\[-16pt]
-\underbrace{\qquad\qquad}_{u1}\underbrace{\qquad\qquad}_{u2}
-\end{align*}} needs some tricky code, because we cannot have parts of the argument inside
-\verb+overbrace+\index{overbrace@\textbackslash overbrace} and also \verb+underbrace+.
-\index{underbrace@\textbackslash underbrace} The following equation~\vref{eq:pqFormel}
-is an example for such a construction:
-
-\begin{align}\label{eq:pqFormel}
-y &= 2x^2 -3x +5\nonumber\\
-  & \hphantom{= \ 2\left(x^2-\frac{3}{2}\,x\right. }%
-         \textcolor{blue}{%
-              \overbrace{\hphantom{+\left(\frac{3}{4}\right)^2- %
-                  \left(\frac{3}{4}\right)^2}}^{=0}}\nonumber\\[-11pt]
-  &= 2\left(\textcolor{red}{%
-     \underbrace{%
-         x^2-\frac{3}{2}\,x + \left(\frac{3}{4}\right)^2}%
-     }%
-     \underbrace{%
-        - \left(\frac{3}{4}\right)^2 + \frac{5}{2}}%
-     \right)\\
-  &= 2\left(\qquad\textcolor{red}{\left(x-\frac{3}{4}\right)^2}
-     \qquad + \ \frac{31}{16}\qquad\right)\nonumber\\
-y\textcolor{blue}{-\frac{31}{8}}
-  &= 2\left(x\textcolor{cyan}{-\frac{3}{4}}\right)^2\nonumber
-\end{align}
-
-\medskip%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\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}
-%[xrightmargin=-\marginparwidth]
-\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+:
-
-\[ \binom{x_R}{y_R} = %
-    \kern-10pt\underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\kern-10pt%
-    \cdot\underbrace{%
-      \begin{pmatrix}
-        \sin \gamma & -\cos \gamma \\
-        \cos \gamma & \sin \gamma \\
-      \end{pmatrix}%
-    }_{\text{Rotation}}
-  \binom{x_K}{y_K} +\kern-5pt%
-  \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} \]
-%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\[ \binom{x_R}{y_R} = %
-    \kern-10pt\underbrace{r\vphantom{\binom{A}{B}}}_{\text{Skaling}}\kern-10pt%
-    \cdot\underbrace{%
-      \begin{pmatrix}
-        \sin \gamma & -\cos \gamma \\
-        \cos \gamma & \sin \gamma \\
-      \end{pmatrix}%
-    }_{\text{Rotation}}
-  \binom{x_K}{y_K} +\kern-5pt%
-  \underbrace{\binom{t_x}{t_y}}_{\text{Translation}} \]
-\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}
-
-%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\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:
-
-%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\[
-\underset{\mathcal{G}\quad}\iiint\!%
-  \left[u\nabla^{2}v+\left(\nabla u,\nabla v\right)\right]\mathrm{d}^{3}V%
-  =\underset{\mathcal{S}\quad}\oiint u\,\Q{v}{n}\,\,\mathrm{d}^{2}A
-\]
-\end{lstlisting}
-
-\noindent with the following definition in the preamble for the partial derivation:
-
-\begin{lstlisting}
-\def\Q#1#2{\frac{\partial#1}{\partial #2}}
-\end{lstlisting}
-
-\noindent which makes things easier to write.
-
-%--------------------------------------------------------------------------
-\section{Horizontal alignment}\label{sec:verticalAlignment}
-%--------------------------------------------------------------------------
-\subsection{Over more than one page}
-%--------------------------------------------------------------------------
-Sometimes it may be useful to have a vertical alignment over the whole page with a mix of    %%% ----- Martin -----
-formulas and text. Section \ref{sec:Text-in-math mode} shows the use of \CMD{intertext}.
-There is another trick to get all formulas vertical aligned.  Let's have the following
-formulas distributed over the whole page:
-%
-\begin{align*}
-     f(x) &= a\\
-     g(x) &= x^2-4x\\
-f(x)-g(x) &= x^2+x^3+x\\
-     g(x) &= x^2+x^3+x^4+x^5+b
-\end{align*}
-%
-They all have a different length of the left and right side. Now we want to write some
-text and other objects between them, but let the alignment untouched. We choose the
-longest left and the longest right side and take them for scaling with the \CMD{hphantom}
-command:
-
-\begin{verbatim}
-\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}
-\end{verbatim}
-
-This is the first (empty) line in every equation where now all other lines are aligned to
-this one. For example:
-
-\bgroup
-\medskip\noindent
-\rule{\columnwidth}{1pt}
-\newcommand\x{blah blah blah blah blah blah blah blah }
-\addtolength\abovedisplayshortskip{-.5cm}% decrease the skip
-\addtolength\abovedisplayskip{-.5cm}
-\x\x\x
-\begin{align}
-\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\
-f(x) &= a\\
-g(x) &= x^2-4x
-\end{align}
-%
-\x\x\x
-\begin{align}
-\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\
-f(x)-g(x) &= x^2+x^3+x
-\end{align}
-\x\x\x
-%
-\begin{align}
-\hphantom{\mbox{$f(x)-g(x)$}} & \hphantom{\mbox{$= x^2+x^3+x^4+x^5+b$}}\nonumber\\
-g(x) &= x^2+x^3+x^4+x^5+b
-\end{align}
-\x\x\x
-
-\noindent
-\rule{\columnwidth}{1pt}
-\egroup
-\medskip
-
-The phantom line is empty but leaves the vertical space for a line. This could be
-corrected with decreasing the \CMD{abovedisplayshortskip} length and done all
-inside a group.
-
-%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\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}
-
-%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\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.
-
-%[xrightmargin=-\marginparwidth]
-\begin{lstlisting}
-\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
-%,xrightmargin=-\marginparwidth
-\begin{lstlisting}[tabsize=4]
-\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}
-
-%,xrightmargin=-\marginparwidth
-\begin{lstlisting}[tabsize=4]
-\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:
-
-%,xrightmargin=-\marginparwidth
-\begin{lstlisting}[tabsize=4]
-\usepackage{amsmath}
-\newcounter{subequation}
-\newlength\mtabskip\mtabskip=-1.25cm
-\newcommand\eqnCnt[1][]{%
-	\refstepcounter{subequation}%
-	\begin{align}#1\end{align}%
-	\addtocounter{equation}{-1}}
-\def\mtabLong{long}
-\makeatletter
-\newenvironment{mtabular}[2][\empty]{%
-	\def\@xarraycr{%
-		\stepcounter{equation}%
-		\setcounter{subequation}{0}%
-		\@ifnextchar[\@argarraycr{\@argarraycr[\mtabskip]}}
-	\let\theoldequation\theequation%
-	\renewcommand\theequation{\theoldequation.\alph{subequation}}
-	\edef\mtabOption{#1}
-	\setcounter{subequation}{0}%
-	\tabcolsep=0pt
-	\ifx\mtabOption\mtabLong\longtable{#2}\else\tabular{#2}\fi%
-}{%
-	\ifx\mtabOption\mtabLong\endlongtable\else\endtabular\fi%
-	\let\theequation\theoldequation%
-	\stepcounter{equation}}
-\makeatother
-\end{lstlisting}
-
-
-As seen in equation~\ref{blub} and equation~\ref{blah}, everything of the table contents is 
-nonsense~\ldots And the following tabular is defined as a \Index{longtable} to enable pagebreaks.
-%which is the reason for the following big skip, to show that it works.
-
-
-%\vspace*{3cm}
-%\begin{framed}
-\begin{mtabular}[long]{*{2}{m{0.35\linewidth}m{0.15\linewidth}}}
-\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt %
-	& \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\
-\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt %
-	& \begin{align*} b = 1 \end{align*} & \eqnCnt\\
-\begin{align*} c =1 \end{align*} & \eqnCnt
-	& \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\
-\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt %
-	& \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\
-\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt %
-	& \begin{align*} b = 1 \end{align*} & \eqnCnt\\
-\begin{align*} c =1 \end{align*} & \eqnCnt
-	& \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\
-\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt %
-	& \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt[\label{blah2}]\\
-\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt %
-	& \begin{align*} b = 1 \end{align*} & \eqnCnt\\
-\begin{align*} c =1 \end{align*} & \eqnCnt[\label{blub2}]
-	& \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\
-\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt %
-	& \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\
-\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt %
-	& \begin{align*} b = 1 \end{align*} & \eqnCnt\\
-\begin{align*} c =1 \end{align*} & \eqnCnt
-	& \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt
-\end{mtabular}
-%\end{framed}
-
-As seen in equation~\ref{blub2} and equation~\ref{blah2}, everything is nonsense ...
-
-
-And again a default display equation:
-\begin{align}
-F(x) &= \int_0^\infty\dfrac{1}{x}\,\mathrm{d}x
-\end{align}
-
-\begin{lstlisting}[tabsize=4]
-\begin{mtabular}[long]{*{2}{m{0.375\linewidth}m{0.125\linewidth}}}
-\begin{align*} \oint E ds=0 \end{align*} & \eqnCnt %
-	& \begin{align*} \nabla\cdot B=0 \end{align*} & \eqnCnt\\
-\begin{align*} a =\frac{c}{d} \end{align*} & \eqnCnt %
-	& \begin{align*} b = 1 \end{align*} & \eqnCnt\\
-\begin{align*} c =1 \end{align*} & \eqnCnt
-	& \begin{align*} \int 2x \,\mathrm{d}x = x^2+C \end{align*} & \eqnCnt\\
-
-[ ... ]
-\end{lstlisting}
-
-%-----------------------------------------------------------------------------
-\subsection[Itemize environment]{Formulas inside an itemize enviroment}\label{sec:itemize}
-%-----------------------------------------------------------------------------
-Without any modification it is not possible to get a numbered equation
-at the same height as the symbol of the itemize environment\index{itemize@\texttt{itemize}}. This depends on    %%% ----- Martin -----
-the \LIndex{abovedisplayskip}. The formula has to be raised up for exactly this length.
-
-\begin{lstlisting}
-\def\itemMath#1{%
-    \raisebox{-\abovedisplayshortskip}{%
-        \parbox{0.75\linewidth}{%
-            \begin{equation}#1\end{equation}}}}
-%
-\begin{itemize}
-\item \itemMath{ f = l }
-\item \itemMath{ g(x) = \int f(x)\,\mathrm{d}x }
-\end{itemize}
-\end{lstlisting}
-
-\def\itemMath#1{%
-    \raisebox{-\abovedisplayshortskip}{%
-        \parbox{0.75\linewidth}{%
-            \begin{equation}#1\end{equation}}}}
-%
-\begin{itemize}
-\item \itemMath{ f = l }
-\item \itemMath{ g(x) = \int f(x)\,\mathrm{d}x }
-\end{itemize}
-
-
-\section{Roots}
-There exists no special symbol for roots\index{Root} which are longer than one line. In such
-cases the root should be split into two or more one, like $\sqrt{a\cdot b\cdot c}=\sqrt{a}\cdot\sqrt{a}\cdot\sqrt{b}\cdot\sqrt{c}$
-if possible. If nothing helps one can use \CMD{overline}\cIndex{overline} for 
-following lines of the root. The following example uses the \verb+multline+ environment
-to get only one equation number:
-
-\begin{multline}
-d(P,Q)|_{Stat.,Dependent}=\\
-  \sqrt{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+
-     \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+} \\
-  \overline{\rule{0pt}{2.5ex}
-     \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13}
-        (x_{1}-y_{1})(x_{3}-y_{3}) + \right.}\\  
-  \overline{\rule{0pt}{2.5ex}
-     \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]}
-\end{multline}
-
-
-\begin{lstlisting}
-\begin{multline}
-d(P,Q)|_{Stat.,Dependent}=\\
-  \sqrt{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+
-     \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+} \\
-  \overline{\rule{0pt}{2.5ex}
-     \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13}
-        (x_{1}-y_{1})(x_{3}-y_{3}) + \right.}\\  
-  \overline{\rule{0pt}{2.5ex}
-     \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]}
-\end{multline}
-\end{lstlisting}
-
-
-Alternative:
-
-\begin{multline}
-d(P,Q)|_{Stat.,Dependent}=\\
-  \Big(\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+
-     \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+ \\
-     \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13}
-        (x_{1}-y_{1})(x_{3}-y_{3}) + \right.\\  
-     \left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]\Big)^{1/2}
-\end{multline}
-
-
-\begin{lstlisting}
-\begin{multline}
-d(P,Q)|_{Stat.,Dependent}=\\
-  \left\{\left[a_{11}(x_{1}-y_{1})^{2}+a_{22}(x_{2}-y_{2})^{2}+
-     \ldots+a_{pp}(x_{p}-y_{p})^{2}\right]+\right. \\
-     \left[2a_{12}(x_{1}-y_{1})(x_{2}-y_{2})+2a_{13}
-        (x_{1}-y_{1})(x_{3}-y_{3}) + \right.\\  
-     \left.\left.\ldots +2a_{p-1,p}(x_{p-1}-y_{p-1})(x_{p}-y_{p})\right]\right\}^{1/2}
-\end{multline}
-\end{lstlisting}
-
-
-
-\part{Lists, bibliography and index}
-\bgroup
-\lhead{}\rhead{}
-\clearpage\phantomsection\addcontentsline{toc}{section}{List of Figures}
-\listoffigures
-\clearpage\phantomsection\addcontentsline{toc}{section}{List of Tables}
-\listoftables
-\clearpage\phantomsection\addcontentsline{toc}{section}{Bibliography}
-
-{\nocite{*}
-\raggedright
-\bibliography{Mathmode}
-\bibliographystyle{plain}
-}
-\clearpage\addcontentsline{toc}{section}{Index}
-{\let\BSL\textbackslash
-\renewcommand\textbackslash{{\ttfamily\BSL}}
-\printindex{}
-}
-\egroup
-
-
-\appendix
-\section*{Appendix}
-\section{Filelist}
-This document was build with
-
-\begin{lstlisting}[breaklines,xrightmargin=-\marginparwidth]
-This is pdfTeXk, Version 3.1415926-1.40.9 (Web2C 7.5.7) (format=pdflatex 2008.10.24)  30 OCT 2008 10:19
-\end{lstlisting}
-
-and with the following file and package versions:
-
-
-\begin{lstlisting}[breaklines,xrightmargin=-\marginparwidth]
- *File List*
- article.cls    2005/09/16 v1.4f Standard LaTeX document class
-  size11.clo    2005/09/16 v1.4f Standard LaTeX file (size option)
-fixltx2e.sty    2006/03/24 v1.1n fixes to LaTeX
- fontenc.sty
-   t1enc.def    2005/09/27 v1.99g Standard LaTeX file
-inputenc.sty    2006/05/05 v1.1b Input encoding file
-  latin1.def    2006/05/05 v1.1b Input encoding file
-    bera.sty    2004/01/31 (WaS)
- fontenc.sty
-   t1enc.def    2005/09/27 v1.99g Standard LaTeX file
-textcomp.sty    2005/09/27 v1.99g Standard LaTeX package
-  ts1enc.def    2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file
-beraserif.sty    2004/01/30 (WaS)
-  keyval.sty    1999/03/16 v1.13 key=value parser (DPC)
-   t1fve.fd    2004/09/07 scalable font definitions for T1/fve.
-berasans.sty    2004/01/30 (WaS)
-beramono.sty    2004/01/31 (WaS)
-   ifpdf.sty    2007/12/12 v1.6 Provides the ifpdf switch (HO)
-  ifvtex.sty    2007/09/09 v1.3 Switches for detecting VTeX and its modes (HO)
- comment.sty    
-graphicx.sty    1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
-graphics.sty    2006/02/20 v1.0o Standard LaTeX Graphics (DPC,SPQR)
-    trig.sty    1999/03/16 v1.09 sin cos tan (DPC)
-graphics.cfg    2007/01/18 v1.5 graphics configuration of teTeX/TeXLive
-  pdftex.def    2008/09/08 v0.04l Graphics/color for pdfTeX
-varwidth.sty    2003/03/10 ver 0.9a;  Variable-width minipages
-   array.sty    2005/08/23 v2.4b Tabular extension package (FMi)
-delarray.sty    1994/03/14 v1.01 array delimiter package (DPC)
-tabularx.sty    1999/01/07 v2.07 `tabularx' package (DPC)
- amsmath.sty    2000/07/18 v2.13 AMS math features
- amstext.sty    2000/06/29 v2.01
-  amsgen.sty    1999/11/30 v2.0
-  amsbsy.sty    1999/11/29 v1.2d
-  amsopn.sty    1999/12/14 v2.01 operator names
- amssymb.sty    2002/01/22 v2.2d
-amsfonts.sty    2001/10/25 v2.2f
-      bm.sty    2004/02/26 v1.1c Bold Symbol Support (DPC/FMi)
- upgreek.sty    2003/02/12 v2.0 (WaS)
-  cancel.sty    2000/03/12 v2.1 Cancel math terms
-   amscd.sty    1999/11/29 v1.2d
- accents.sty    2006/05/12 v1.3 Math Accent Tools
-  dsfont.sty    1995/08/01 v0.1 Double stroke roman fonts
-multirow.sty    
-bigdelim.sty    
-  framed.sty    2007/10/04 v 0.95: framed or shaded text with page breaks
-longtable.sty    2004/02/01 v4.11 Multi-page Table package (DPC)
-varioref.sty    2006/05/13 v1.4p package for extended references (FMi)
-  xcolor.sty    2007/01/21 v2.11 LaTeX color extensions (UK)
-   color.cfg    2007/01/18 v1.5 color configuration of teTeX/TeXLive
- makeidx.sty    2000/03/29 v1.0m Standard LaTeX package
-     url.sty    2006/04/12  ver 3.3  Verb mode for urls, etc.
-setspace.sty    2000/12/01 6.7 Contributed and Supported LaTeX2e package
-  empheq.sty    2007/12/03 v2.12 Emphasizing equations (MH)
- mhsetup.sty    2007/12/03 v1.2 programming setup (MH)
-mathtools.sty    2008/08/01 v1.06 mathematical typesetting tools (MH)
-    calc.sty    2005/08/06 v4.2 Infix arithmetic (KKT,FJ)
-nicefrac.sty    1998/08/04 v0.9b Nice fractions
-  ifthen.sty    2001/05/26 v1.1c Standard LaTeX ifthen package (DPC)
- exscale.sty    1997/06/16 v2.1g Standard LaTeX package exscale
- relsize.sty    2003/07/04 ver 3.1
-  xspace.sty    2006/05/08 v1.12 Space after command names (DPC,MH)
-   eucal.sty    2001/10/01 v2.2d Euler Script fonts
-footmisc.sty    2007/06/12 v5.4a a miscellany of footnote facilities
-   esint.sty    
-  esvect.sty    
-remreset.sty    
-    cool.sty    2006/12/29 v1.35 COntent Oriented LaTeX
-coollist.sty    2007/10/06 v1.2 COntent Oriented LaTeX Lists
- coolstr.sty    2007/01/08 v2.1 COntent Oriented LaTeX Strings
- forloop.sty    2006/09/18 v3.0 For Loops for LaTeX
-     bbm.sty    1999/03/15 V 1.2 provides fonts for set symbols - TH
-   xypic.sty    1999/02/16 Xy-pic version 3.7
-      xy.sty
-fancyhdr.sty    
-showexpl.sty    2007/02/03 v0.3h Typesetting example code (RN)
-listings.sty    2007/02/22 1.4 (Carsten Heinz)
- lstmisc.sty    2007/02/22 1.4 (Carsten Heinz)
-listings.cfg    2007/02/22 1.4 listings configuration
- lstmisc.sty    2007/02/22 1.4 (Carsten Heinz)
-showexpl.cfg    2005/06/30 v0.02 Definitions for the showexpl package (hv)
-lstlang1.sty    2004/09/05 1.3 listings language file
-lstlang2.sty    2004/09/05 1.3 listings language file
-lstlang3.sty    2004/09/05 1.3 listings language file
-lstlang1.sty    2004/09/05 1.3 listings language file
-lstlang2.sty    2004/09/05 1.3 listings language file
-lstlang3.sty    2004/09/05 1.3 listings language file
-lstlang1.sty    2004/09/05 1.3 listings language file
-lstlang2.sty    2004/09/05 1.3 listings language file
-lstlang3.sty    2004/09/05 1.3 listings language file
-lstlang1.sty    2004/09/05 1.3 listings language file
-lstlang2.sty    2004/09/05 1.3 listings language file
-lstlang3.sty    2004/09/05 1.3 listings language file
- lstmisc.sty    2007/02/22 1.4 (Carsten Heinz)
-microtype.sty    2008/06/04 v2.3b Micro-typography with pdfTeX (RS)
-microtype.cfg    2008/06/04 v2.3b microtype main configuration file (RS)
-hyperref.sty    2008/09/29 v6.78l Hypertext links for LaTeX
- ifxetex.sty    2008/09/18 v0.4 Provides ifxetex conditional
- hycolor.sty    2008/09/08 v1.4 Code for color options of hyperref/bookmark (HO
-)
-xcolor-patch.sty    2008/09/08 xcolor patch
-  pd1enc.def    2008/09/29 v6.78l Hyperref: PDFDocEncoding definition (HO)
-etexcmds.sty    2007/12/12 v1.2 Prefix for e-TeX command names (HO)
-infwarerr.sty    2007/09/09 v1.2 Providing info/warning/message (HO)
-hyperref.cfg    2002/06/06 v1.2 hyperref configuration of TeXLive
-kvoptions.sty    2007/10/18 v3.0 Keyval support for LaTeX options (HO)
-  bitset.sty    2007/09/28 v1.0 Data type bit set (HO)
- intcalc.sty    2007/09/27 v1.1 Expandable integer calculations (HO)
-bigintcalc.sty    2007/11/11 v1.1 Expandable big integer calculations (HO)
-pdftexcmds.sty    2007/12/12 v0.3 LuaTeX support for pdfTeX utility functions (
-HO)
-kvsetkeys.sty    2007/09/29 v1.3 Key value parser with default handler support 
-(HO)
-atbegshi.sty    2008/07/31 v1.9 At begin shipout hook (HO)
- hpdftex.def    2008/09/29 v6.78l Hyperref driver for pdfTeX
-  hypcap.sty    2008/09/08 v1.10 Adjusting anchors of captions (HO)
-   babel.sty    2008/07/06 v3.8l The Babel package
- english.ldf    2005/03/30 v3.3o English support from the babel system
-  braket.sty    
-  ts1cmr.fd    1999/05/25 v2.5h Standard LaTeX font definitions
-supp-pdf.tex
- nameref.sty    2007/05/29 v2.31 Cross-referencing by name of section
-refcount.sty    2008/08/11 v3.1 Data extraction from references (HO)
-Mathmode.out
-Mathmode.out
-Mathmode.tex
-  mt-cmr.cfg    2008/02/29 v1.9a microtype config. file: Computer Modern Roman 
-(RS)
-    umsa.fd    2002/01/19 v2.2g AMS font definitions
-  mt-msa.cfg    2006/02/04 v1.1 microtype config. file: AMS symbols (a) (RS)
-    umsb.fd    2002/01/19 v2.2g AMS font definitions
-  mt-msb.cfg    2005/06/01 v1.0 microtype config. file: AMS symbols (b) (RS)
-  mt-eur.cfg    2006/07/31 v1.1 microtype config. file: AMS Euler Roman (RS)
-  uesint.fd    
- uesvect.fd    
-  ts1fve.fd    2004/09/07 scalable font definitions for TS1/fve.
-   t1fvm.fd    2004/09/07 scalable font definitions for T1/fvm.
-images/styles.pdf
-images/amsalign.pdf
-   t1fvs.fd    2004/09/07 scalable font definitions for T1/fvs.
-images/family.pdf
-images/EuScript.pdf
-images/exscale.pdf
-images/cm-crop.pdf
-images/lm-crop.pdf
-images/pazo-crop.pdf
-images/pamath-crop.pdf
-images/cmbright-crop.pdf
-images/minionpro-crop.pdf
-images/colArray.pdf
-images/node.pdf
-Mathmode.bbl
-Mathmode.ind
-\end{lstlisting}
-
-%\clearpage
-%\layout
-\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/README b/Master/texmf-dist/doc/latex/voss-mathmode/README
deleted file mode 100644
index d9ef4f6d5c6..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/README
+++ /dev/null
@@ -1,9 +0,0 @@
-Mathmode.pdf      : math in TeX/LaTeX; package amsmath.sty
-                    needs package showexpl.
-Mathmode.ltx	  : main source file (preamble)
-Mathmode.tex	  : document source
-Mathmode.bib	  : BibTeX data
-Mathmode.ist	  : index style file
-showexpl.cfg      : config file for the showexpl package
-                    save it together with showexpl.sty
-images/           : subdir for all pdf|eps images
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/EuScript.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/EuScript.pdf
deleted file mode 100644
index 8ba3a8e1fdc..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/EuScript.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/amsalign.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/amsalign.pdf
deleted file mode 100644
index 08194ee4508..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/amsalign.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/cm-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/cm-crop.pdf
deleted file mode 100644
index 97a6aaa084d..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/cm-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/cmbright-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/cmbright-crop.pdf
deleted file mode 100644
index ea5117d91a7..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/cmbright-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.pdf
deleted file mode 100644
index 5cfbbb8bb50..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/colArray.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/exscale.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/exscale.pdf
deleted file mode 100644
index 3c674f79488..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/exscale.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/family.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/family.pdf
deleted file mode 100644
index 4e0c6192d4c..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/family.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/family0.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/family0.pdf
deleted file mode 100644
index d3d3d9a0d9c..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/family0.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/family1.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/family1.pdf
deleted file mode 100644
index eb52309ebcd..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/family1.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/lm-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/lm-crop.pdf
deleted file mode 100644
index f47326fe8f0..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/lm-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/minionpro-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/minionpro-crop.pdf
deleted file mode 100644
index 052b2053f21..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/minionpro-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/node.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/node.pdf
deleted file mode 100644
index d3d448e9735..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/node.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.pdf
deleted file mode 100644
index 3f9fc5e13e8..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/pamath-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.pdf
deleted file mode 100644
index a9ec41a9245..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/pazo-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.pdf
deleted file mode 100644
index c98539d9e0d..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/styles.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/images/test-crop.pdf b/Master/texmf-dist/doc/latex/voss-mathmode/images/test-crop.pdf
deleted file mode 100644
index c98539d9e0d..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/images/test-crop.pdf
+++ /dev/null
diff --git a/Master/texmf-dist/doc/latex/voss-mathmode/showexpl.cfg b/Master/texmf-dist/doc/latex/voss-mathmode/showexpl.cfg
deleted file mode 100644
index b7fc416afb7..00000000000
--- a/Master/texmf-dist/doc/latex/voss-mathmode/showexpl.cfg
+++ /dev/null
@@ -1,48 +0,0 @@
-% config file for showexpl.sty
-%
-% Copyright Herbert Voss, 2005
-% Licence: LPPL.
-
-\ProvidesFile{showexpl.cfg}
-  [2005/06/30 v0.02 Definitions for the showexpl package (hv)]
-%
-\definecolor{hellgelb}{rgb}{1,1,0.85}
-\definecolor{colKeys}{rgb}{0,0,1}
-\definecolor{colIdentifier}{rgb}{0,0,0}
-\definecolor{colComments}{rgb}{1,0,0}
-\definecolor{colString}{rgb}{0,0.5,0}
-
-\lstset{%
-     preset=\centering,%
-     explpreset={numbersep=1em,numbers=left,numberstyle=\tiny\ttfamily,vsep=\bigskipamount},
-     rframe={},%
-     language=[AlLaTeX]TeX,%
-     float=hbp,%
-     basicstyle=\footnotesize\ttfamily,%
-     identifierstyle=\color{colIdentifier},%
-     keywordstyle=\color{colKeys},%
-     stringstyle=\color{colString},%
-     commentstyle=\itshape\color{colComments},%
-%    columns=flexible,%
-%    columns=fullflexible,%
-     columns=fixed,
-     tabsize=4,%
-     frame=single,%
-     extendedchars=true,%
-     showspaces=false,%
-     showstringspaces=false,%
-     breaklines=true,%
-     breakindent=10pt,%
-     backgroundcolor=\color{hellgelb},%
-     breakautoindent=true,%
-     captionpos=t,%
-     xleftmargin=1.5em,%
-     xrightmargin=\fboxsep,%
-     numbersep=1em,
-     numbers=left,
-     numberstyle=\tiny\ttfamily, 
-     xrightmargin=-1cm,% 
-%     relwidth=0.5,%
-%     columnsep=10pt%
-}
-\renewcommand*\SX@Info{}%
author	Karl Berry <karl@freefriends.org>	2016-10-08 23:42:01 +0000
committer	Karl Berry <karl@freefriends.org>	2016-10-08 23:42:01 +0000
commit	dbc5c99e61c0ecccf7a954d6317c35a00228e97f (patch)
tree	1777af887a7f3006e8fd3ede503c0d8613f55807 /Master/texmf-dist/doc/latex
parent	8cfd90f7861d3ed698bafaa2dcdf6e17897aef37 (diff)