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+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 1999 American Mathematical Society.
+% Copyright (C) 2016-2019 LaTeX3 Project and American Mathematical Society.
+%
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3c
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% https://www.latex-project.org/lppl.txt
+% and version 1.3c or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is the LaTeX3 Project.
+%
+% \fi
+%
+%\iffalse
+%<*driver>
+\documentclass{amsdtx}
+\def\MaintainedByLaTeXTeam#1{%
+\begin{center}%
+\fbox{\fbox{\begin{tabular}{@{}l@{}}%
+This file is maintained by the \LaTeX{} Project team.\\%
+Bug reports can be opened (category \texttt{#1}) at\\%
+\url{https://latex-project.org/bugs/}.\end{tabular}}}\end{center}}
+\usepackage{amscd}
+\GetFileInfo{amscd.sty}
+% Dummy citation to avoid error in an example.
+\bibcite{fre:cichon}{C}
+\begin{document}
+\title{The \pkg{amscd} package}
+\author{Frank Mittelbach\and Rainer Sch\"opf\and Michael Downes}
+\date{Version \fileversion, \filedate}
+\DocInput{amscd.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+% \newcommand{\operatorname}[1]{\mathop{\mathrm{#1}}}
+% \newcommand{\per}{\operatorname{per}}
+% \newcommand{\cov}{\operatorname{cov}}
+% \newcommand{\non}{\operatorname{non}}
+% \newcommand{\cf}{\operatorname{cf}}
+% \newcommand{\add}{\operatorname{add}}
+% \newcommand{\End}{\operatorname{End}}
+%
+% \section{Introduction}
+%
+% The \pkg{amscd} package provides a \env{CD} environment that
+% emulates the commutative diagram capabilities of \amstex/ version
+% 2.x. This means that only simple rectangular diagrams are
+% supported, with no diagonal arrows or more exotic features. Many
+% users will be better served by one of the more powerful diagram
+% packages such as \pkg{diagram}, \pkg{xypic}, or \pkg{kuvio}.
+%
+% Example:
+% \begin{equation}\begin{CD}
+% S^{{\mathcal{W}}_\Lambda}\otimes T @>j>> T\\
+% @VVV @VV{\End P}V\\
+% (S\otimes T)/I @= (Z\otimes T)/J
+% \end{CD}\end{equation}
+% \begin{verbatim}
+% \begin{equation}\begin{CD}
+% S^{{\mathcal{W}}_\Lambda}\otimes T @>j>> T\\
+% @VVV @VV{\End P}V\\
+% (S\otimes T)/I @= (Z\otimes T)/J
+% \end{CD}\end{equation}
+% \end{verbatim}
+% (assuming \cn{End} is defined as an `operator name'.
+%
+% Another example:
+%
+% We will make liberal use of Cichon's Diagram \cite{fre:cichon}:
+% \begin{equation}
+% \begin{CD}
+% \cov(\mathcal{L}) @>>> \non(\mathcal{K}) @>>> \cf(\mathcal{K}) @>>>
+% \cf(\mathcal{L})\\
+% @VVV @AAA @AAA @VVV\\
+% \add(\mathcal{L}) @>>> \add(\mathcal{K}) @>>> \cov(\mathcal{K}) @>>>
+% \non(\mathcal{L})
+% \end{CD}\end{equation}
+% \begin{verbatim}
+% \begin{equation}\begin{CD}
+% \cov(\mathcal{L}) @>>> \non(\mathcal{K}) @>>> \cf(\mathcal{K}) @>>>
+% \cf(\mathcal{L})\\
+% @VVV @AAA @AAA @VVV\\
+% \add(\mathcal{L}) @>>> \add(\mathcal{K}) @>>> \cov(\mathcal{K}) @>>>
+% \non(\mathcal{L})
+% \end{CD}\end{equation}
+% \end{verbatim}
+%
+% \StopEventually{}
+%
+% Standard package info.
+% \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must December 1994 or later
+\ProvidesPackage{amscd}[2017/04/14 v2.1 AMS Commutative Diagrams]
+% \end{macrocode}
+% \begin{macrocode}
+\RequirePackage{amsgen}
+% \end{macrocode}
+% Better not to redefine \verb|\math@cr| if it is already defined,
+% because for CD use only we want to omit the part of the code
+% related to \verb|\dspbrk@lvl| (see \fn{amsmath.sty}).
+%
+% [mjd,1999/11/04] These definitions have gone somewhat obsolete; but
+% we had probably better leave them as they are for backward
+% compatibility.
+% \begin{macrocode}
+\@ifundefined{math@cr}{%
+ \def\math@cr{{\ifnum0=`}\fi
+ \@ifstar{\global\@eqpen\@M\math@cr@}%
+ {\global\@eqpen\interdisplaylinepenalty \math@cr@}}
+% \end{macrocode}
+% The following section merely duplicates some code from the
+% \pkg{amsmath} package, in case the \pkg{amscd} package is used by
+% itself. For documentation of the code refer to \fn{amsmath.dtx}.
+% \begin{macrocode}
+ \def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
+ \def\math@cr@@[#1]{\ifnum0=`{\fi}\math@cr@@@
+ \noalign{\vskip#1\relax}}
+ \def\restore@math@cr{\def\math@cr@@@{\cr}}
+}{}
+\restore@math@cr
+% \end{macrocode}
+% [mjd,1999/11/04] These definitions too are somewhat obsolete;
+% but we had probably better leave them as they are for backward
+% compatibility.
+% \begin{macrocode}
+\@ifundefined{rightarrowfill@}{
+ \def\rightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
+ $#1\copy\z@\mkern-6mu\cleaders
+ \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+ \mkern-6mu\mathord\rightarrow$}
+ \def\leftarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
+ $#1\mathord\leftarrow\mkern-6mu\cleaders
+ \hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
+ \mkern-6mu\box\z@$}
+ \def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1-$}\ht\z@\z@
+ $#1\mathord\leftarrow\mkern-6mu\cleaders
+ \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
+ \mkern-6mu\mathord\rightarrow$}
+}{}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}
+\@ifundefined{Iat}{%
+ \DeclareRobustCommand{\Iat}{\FN@\at@}
+}{}
+\begingroup \catcode`\@=\active
+% \end{macrocode}
+% Define math \qc{\@} to replicate its mathcode-dictated behavior.
+% This is in case \qc{\@} occurs outside of \env{CD}.
+% \begin{macrocode}
+\csname if\string @compatibility\endcsname
+\else \fam=\mathcode`\@
+ \xdef @{\mathchar\number\fam\space }
+\fi
+\gdef\CDat{\let @=\Iat}
+\endgroup
+\mathcode`\@="8000 % make @ pseudo-active in math
+\def\at@{\let\next@\at@@
+ \ifcat\noexpand\next a\else
+ \ifcat\noexpand\next0\else
+ \ifcat\noexpand\next\relax\else
+ \let\next@\at@@@\fi\fi\fi\next@}
+\def\at@@#1{\expandafter
+ \ifx\csname\space @\string#1\endcsname\relax
+ \DN@{\at@@@#1}%
+ \else
+ \DN@{\csname\space @\string#1\endcsname}%
+ \fi\next@}%
+% \end{macrocode}
+% The following items should be defined only if they are not
+% already defined, either to leave the package name untouched (in
+% the case of \cs{PackageError}) or to avoid redundant allocation
+% of token or dimen registers.
+% \begin{macrocode}
+\@ifundefined{default@tag}{%
+ \def\default@tag{%
+ \def\tag{\PackageError{amscd}{\protect\tag\space not allowed
+ here}\@eha}}%
+}{}%
+\@ifundefined{at@@@}{%
+ \def\at@@@{\PackageError{amscd}{\Invalid@@ @}{\the\athelp@}\char64\relax}
+}{}
+\@ifundefined{athelp@}{\csname newhelp\endcsname\athelp@
+{Only certain combinations beginning with @ make sense to me.^^J%
+I'll assume you wanted @@ for a printed @.}}{}
+\@ifundefined{minaw@}{\newdimen\minaw@}{}
+\@ifundefined{bigaw@}{\newdimen\bigaw@}{}
+% \end{macrocode}
+%
+% Assignment of a couple of dimensions, and initialization of
+% \verb=\ampersand@=. We check to see if we need to define
+% \verb=\minaw@= and \verb=\bigaw@=.
+% \begin{macrocode}
+\minaw@11.111pt
+\newdimen\minCDarrowwidth
+\minCDarrowwidth2.5pc
+\newif\ifCD@
+\let\ampersand@\relax
+% \end{macrocode}
+%
+% Added \verb|\restore@math@cr\default@tag| to fix line numbering
+% problems, 7-JUN-1991. Suggested by I.~Zakharevich.
+% \begin{macrocode}
+\newenvironment{CD}{%
+ \CDat
+ \bgroup\relax\iffalse{\fi\let\ampersand@&\iffalse}\fi
+ \CD@true\vcenter\bgroup\let\\\math@cr\restore@math@cr\default@tag
+ \tabskip\z@skip\baselineskip20\ex@
+ \lineskip3\ex@\lineskiplimit3\ex@\halign\bgroup
+ &\hfill$\m@th##$\hfill\crcr
+}{%
+ \crcr\egroup\egroup\egroup
+}
+% \end{macrocode}
+%
+% \begin{macro}{\CD@check}
+% This check is used by all macros that must not appear outside the
+% \env{CD} environment. The first argument is the symbol to be used
+% after \verb+@+, the second one the action to be performed.
+%
+% Once again we use the trick of defining a temporary control
+% sequence \verb+\next@+ and calling it after the final \verb+\fi+.
+% This is not absolutely necessary, but it ensures that the
+% conditional text is processed in one and the same column
+% of the enclosing alignment.
+% \begin{macrocode}
+\def\CD@check#1#2{\ifCD@\DN@{#2}\else
+ \DN@{\PackageError{amscd}{@\protect#1 not
+ allowed outside of the CD environment}\@eha}%
+ \fi\next@}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+\atdef@>#1>#2>{\ampersand@
+ \ifCD@ \global\bigaw@\minCDarrowwidth \else \global\bigaw@\minaw@ \fi
+ \setboxz@h{$\m@th\scriptstyle\;{#1}\;\;$}%
+ \ifdim\wdz@>\bigaw@\global\bigaw@\wdz@\fi
+% \end{macrocode}
+% If \verb|#2| is empty we can save some work.
+% \begin{macrocode}
+ \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%
+ \ifdim\wd\@ne>\bigaw@\global\bigaw@\wd\@ne\fi}%
+ \ifCD@\enskip\fi
+ \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill@\displaystyle}}%
+ \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
+ \ifCD@\enskip\fi \ampersand@}
+%
+\atdef@<#1<#2<{\ampersand@
+ \ifCD@ \global\bigaw@\minCDarrowwidth \else \global\bigaw@\minaw@ \fi
+ \setboxz@h{$\m@th\scriptstyle\;\;{#1}\;$}%
+ \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
+ \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;\;{#2}\;$}%
+ \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
+ \ifCD@\enskip\fi
+ \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill@\displaystyle}}%
+ \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
+ \ifCD@\enskip\fi \ampersand@}
+% \end{macrocode}
+%
+% Variants of the above two arrows, using \verb|(| and \verb|)|
+% characters instead of \verb|<| and \verb|>| characters, are
+% provided for those whose keyboards don't have the latter.
+% \begin{macrocode}
+\begingroup \catcode`\~=\active \lccode`\~=`\@
+\lowercase{%
+ \global\atdef@)#1)#2){~>#1>#2>}
+ \global\atdef@(#1(#2({~<#1<#2<}
+}% end lowercase
+\endgroup
+% \end{macrocode}
+%
+% \begin{macrocode}
+\atdef@ A#1A#2A{\CD@check{A..A..A}{\llap{$\m@th\vcenter{\hbox
+ {$\scriptstyle#1$}}$}\Big\uparrow
+ \rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
+%
+\atdef@ V#1V#2V{\CD@check{V..V..V}{\llap{$\m@th\vcenter{\hbox
+ {$\scriptstyle#1$}}$}\Big\downarrow
+ \rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
+%
+\atdef@={\CD@check={&\enskip\mathrel
+ {\vbox{\hrule\@width\minCDarrowwidth\vskip2\ex@\hrule\@width
+ \minCDarrowwidth}}\enskip&}}
+%
+\atdef@|{\CD@check|{\Big\Vert&&}}
+%
+\atdef@\vert{\CD@check\vert{\Big\Vert&&}}
+%
+\atdef@.{\CD@check.{&&}}
+% \end{macrocode}
+%
+% The \cn{pretend} command has weird syntax that doesn't fit well
+% with standard \latex/ syntax so we leave it undone, at least for
+% now. [mjd,1994/10/27]
+% \begin{macrocode}
+%\def\pretend#1\haswidth#2{\setboxz@h{$\m@th\scriptstyle{#2}$}\hbox
+% to\wdz@{\hfill$\m@th\scriptstyle{#1}$\hfill}}
+% \end{macrocode}
+%
+% The usual \cs{endinput} to ensure that random garbage at the end of
+% the file doesn't get copied by \fn{docstrip}.
+% \begin{macrocode}
+\endinput
+% \end{macrocode}
+%
+% \CheckSum{459}
+% \Finale