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|
%
% \iffalse meta-comment
%
% Copyright 1995, 1999 American Mathematical Society.
% Copyright 2016-2017 LaTeX3 Project and American Mathematical Society.
% Copyright 2019 Martin Vermeer.
%
% 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 Martin Vermeer.
%
% \fi
%
%\iffalse
%<*driver>
\documentclass{amsdtx}
\usepackage{amscdx,amsmath,xcolor,calc,graphicx}
\GetFileInfo{amscdx.sty}
% Dummy citation to avoid error in an example.
\bibcite{fre:cichon}{C}
\begin{document}
\title{The \pkg{amscd\textcolor[RGB]{255,0,0}{x}} package}
\author{\textcolor{red}{Martin Vermeer}\thanks{firstname.lastname$@$aalto.fi},\\
based on \pkg{amscd} by\\
Frank Mittelbach, Rainer Sch\"opf and Michael Downes}
\date{Version \fileversion, \filedate}
\DocInput{amscdx.dtx}
\end{document}
%</driver>
%\fi
%
% \maketitle
% This file is maintained by Martin Vermeer.\\%
%
% \MakeShortVerb\|
% \renewcommand{\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}}
%
% \renewcommand{\labelitemi}{$\circ$}
%
% \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}, \pkg{xymatrix},
% \pkg{kuvio}, or \pkg{tikz-cd}.
%
% 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}
%
% \section{\color[RGB]{255,0,0}Enhancements in amscdx}
% We implemented double ("fat") and dashed arrows in both directions,
% and color attributes for arrows and their annotations.
% Naming scheme:
% \begin{itemize}
% \item The left-right double arrow \verb+@ZZZ+
% \item The up-down double arrow \verb+@XXX+.
% \end{itemize}
%
% The color, a defined \verb+xcolor+ color name, can be added to an arrow by
% inserting \verb+\CDlor{<+\textit{color}\verb+>}+ into the diagram before, i.e.,
% to the immediate left of, the arrow that you wish to color. The command
% affects all arrows following it, so cancel it by the command
% \verb+\CDlor{black}+. If you want to change the color of all the arrows, you
% can place the color command outside and before the \verb+CD+ environment.
%
% Double arrows are obtained by inserting \verb+\CDfattrue+ into the diagram
% before, i.e., to the immediate left of, the arrow that you wish to be
% doubled. The command only affects the arrow immediately following it. To
% change the whole diagram to double arrows, place the \verb+\CDfattrue+ command
% outside and before the \verb+CD+ environment. If you do that, you can exempt
% individual arrows, i.e., make them single again, by the command
% \verb+\CDfatfalse+.
%
% A similar technique applies for obtaining dashed arrows, but with the
% boolean (flag) \verb+\CDash+, i.e., the command \verb+\CDashtrue+ will give
% a dashed arrow, while \verb+\CDashfalse+ will turn it off. \verb+\CDash+
% will only work if the state of the \verb+\CDfat+ flag be false. If both
% \verb+\CDfat+ and \verb+\CDash+ are true, the \verb+CDfat+ flag takes
% precedence.
%
% A demonstration of some of the new capabilities (yes, this looks tacky):
% \begin{equation}
% \CDfattrue
% \CDlor{green}
% \begin{CD}
% \text{Left header} @. \text{Right header} \\
% TL @>\text{Atop}>{\hspace{4cm}}> TR \\
% \CDfatfalse @X\text{Left}X{N_x}X
% \CDfatfalse \CDashtrue
% \CDlor{brown} @A{\scriptsize\begin{array}{r}\text{Right}\\
% \text{column}\end{array}}A{N^x}A \\
% ML \CDfatfalse \CDashtrue \CDlor{lime} @<{xyz}<{pqr}< MR \\
% \CDlor{red} @A{M^2}A\scriptsize\begin{array}{l}\text{Left}\\
% \text{column}\end{array}A @V+V{N_y}V \\
% BL \CDlor{purple} @Z\text{above}Z\text{below}Z BR \\
% \end{CD}
% \end{equation}
% \begin{verbatim}
% \begin{equation}
% \CDfattrue
% \CDlor{green}
% \begin{CD}
% \text{Left header} @. \text{Right header} \\
% TL @>\text{Atop}>{\hspace{4cm}}> TR \\
% \CDfatfalse @X\text{Left}X{N_x}X
% \CDfatfalse \CDashtrue
% \CDlor{brown} @A{\scriptsize\begin{array}{r}\text{Right}\\
% \text{column}\end{array}}A{N^x}A \\
% ML \CDfatfalse \CDashtrue \CDlor{lime} @<{xyz}<{pqr}< MR \\
% \CDlor{red} @A{M^2}A\scriptsize\begin{array}{l}\text{Left}\\
% \text{column}\end{array}A @V+V{N_y}V \\
% BL \CDlor{purple} @Z\text{above}Z\text{below}Z BR \\
% \end{CD}
% \end{equation}
% \end{verbatim}
% \hrule
% \bigskip
%
% \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{amscdx}[2019/06/04 v2.1x 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{amscdx} 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}
%
\def\clap#1{\hbox to 0pt{\hss#1\hss}}
%
\newif\ifCDfat
\newif\ifCDash
\def\dye@{black}
\def\CDlor#1{\gdef\dye@{#1}} % must be gdef
%
%
\@ifundefined{rightarrowfill@}{
\def\rightarrowfill@#1{%
\m@th\setboxz@h{$#1\relbar$}\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{$#1\relbar$}\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{$#1\relbar$}\ht\z@\z@
$#1\mathord\leftarrow\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
\mkern-6mu\mathord\rightarrow$}
}{}
% \end{macrocode}
%
% Added double arrows
%
% \begin{macrocode}
\def\Rightarrowfill@#1{%
\m@th\setboxz@h{$#1\Relbar$}\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{$#1\Relbar$}\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{$#1\Relbar$}\ht\z@\z@
$#1\mathord\Leftarrow\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
\mkern-6mu\mathord\Rightarrow$}
%
\def\rightdasharrowfill@#1{%
\m@th\setboxz@h{$#1\,\relbar\,$}\ht\z@\z@
$#1\copy\z@\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
\mkern-6mu\mathord\rightarrow$}
\def\leftdasharrowfill@#1{%
\m@th\setboxz@h{$#1\,\relbar\,$}\ht\z@\z@
$#1\mathord\leftarrow\mkern-6mu\cleaders%
\hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
\mkern-6mu\box\z@$}
\def\leftrightdasharrowfill@#1{%
\m@th\setboxz@h{$#1\,\relbar\,$}\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{amscdx}{\protect\tag\space not allowed
here}\@eha}}%
}{}%
\@ifundefined{at@@@}{%
\def\at@@@{\PackageError{amscdx}{\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{amscdx}{@\protect#1 not
allowed outside of the CD environment}\@eha}%
\fi\next@}
% \end{macrocode}
% \end{macro}
%
% The boolean \verb+\ifCDfat+ has scope only within a table cell:
%
% \begin{macrocode}
\atdef@>#1>#2>{%
\ifCDfat\gdef\ar@{\Rightarrowfill@}\else\ifCDash\gdef\ar@{\rightdasharrowfill@}\else\gdef\ar@{\rightarrowfill@}\fi\fi
\gdef\before@{\dye@}
\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
\color{\before@}\mathrel{\mathop{\hbox to\bigaw@{\ar@\displaystyle}}%
\limits^{#1}\@ifnotempty{#2}{_{#2}}}%
\ifCD@\enskip\fi \ampersand@}
%
\atdef@<#1<#2<{%
\ifCDfat\gdef\ar@{\Leftarrowfill@}\else\ifCDash\gdef\ar@{\leftdasharrowfill@}\else\gdef\ar@{\leftarrowfill@}\fi\fi
\gdef\before@{\dye@}
\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
\color{\before@}\mathrel{\mathop{\hbox to\bigaw@{\ar@\displaystyle}}%
\limits^{#1}\@ifnotempty{#2}{_{#2}}}%
\ifCD@\enskip\fi \ampersand@}
% \end{macrocode}
%
% \begin{macrocode}
\atdef@ Z#1Z#2Z{\CD@check{x..x..x}{%
\ifCDfat\gdef\ar@{\Leftrightarrowfill@}\else\ifCDash\gdef\ar@{\leftrightdasharrowfill@}\else\gdef\ar@{\leftrightarrowfill@}\fi\fi
\gdef\before@{\dye@}
\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
\color{\before@}\mathrel{\mathop{\hbox to\bigaw@{\ar@\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}{\color{\dye@}\llap{$\m@th\vcenter{\hbox
{$\scriptstyle#1$}}$}
\ifCDfat \Big\Uparrow \else
\ifCDash \vphantom{\Bigg\Updownarrow}\text{\rotatebox{90}{\clap{$\mkern8mu\mathop-\mathop-\mkern-2mu\rightarrow$}}}
\else \Big\uparrow \fi \fi
\rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
%
\atdef@ V#1V#2V{\CD@check{V..V..V}{\color{\dye@}\llap{$\m@th\vcenter{\hbox
{$\scriptstyle#1$}}$}
\ifCDfat \Big\Downarrow \else
\ifCDash \vphantom{\Bigg\Updownarrow}\text{\rotatebox{270}{\clap{$\mkern-8mu\mathop-\mathop-\mkern-2mu\rightarrow$}}}
\else \Big\downarrow \fi \fi
\rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
%
\atdef@ X#1X#2X{\CD@check{X..X..X}{\color{\dye@}\llap{$\m@th\vcenter{\hbox
{$\scriptstyle#1$}}$}
\ifCDfat \Big\Updownarrow \else
\ifCDash \vphantom{\Bigg\Updownarrow}\text{\rotatebox{90}{\clap{$\mkern8mu\leftarrow\mkern-2mu\mathop-\mkern-2mu\rightarrow$}}}
\else \Big\updownarrow \fi \fi
\rlap{$\m@th\vcenter{\hbox{$\scriptstyle#2$}}$}&&}}
%
\atdef@={\CD@check={\gdef\before@{\dye@}&\color{\before@}\enskip\mathrel
{\vbox{\hrule\@width\minCDarrowwidth\vskip2\ex@\hrule\@width
\minCDarrowwidth}}\enskip&}}
%
\atdef@|{\CD@check|{\color{\dye@}\Big\Vert&&}}
%
\atdef@\vert{\CD@check\vert{\color{\dye@}\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{814}
% \Finale
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