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authorNorbert Preining <norbert@preining.info>2019-09-15 03:00:57 +0000
committerNorbert Preining <norbert@preining.info>2019-09-15 03:00:57 +0000
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+%
+% \iffalse meta-comment
+%
+% Copyright (C) 1995, 2000, 2013 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}}
+\raggedbottom
+\let\savedarg\arg
+\usepackage{amsmath}
+\let\arg\savedarg
+\GetFileInfo{amsmath.sty}
+\begin{document}
+\title{The \pkg{amsmath} package}
+\author{Frank Mittelbach\and Rainer Sch\"opf\and Michael Downes\and
+ David M. Jones\and David Carlisle}
+\date{Version \fileversion, \filedate}
+\providecommand{\histnote}{}
+\renewenvironment{histnote}{%
+ \trivlist\item[\hspace{\labelsep}\bfseries Historical Note:]%
+}{%
+ \endtrivlist
+}
+\DocInput{amsmath.dtx}
+\end{document}
+%</driver>
+%\fi
+%
+% \maketitle
+% \MaintainedByLaTeXTeam{amslatex}
+%
+% \MakeShortVerb\|
+%
+% \section{Introduction}
+%
+% A \latex/ package named \pkg{amstex} was created in 1988--1989 by
+% adapting \fn{amstex.tex} for use within \latex/. The \pkg{amsmath}
+% package is the successor of the \pkg{amstex} package. It was
+% substantially overhauled to integrate it with \latex/2e, which
+% arrived on the scene in 1994. It provides more or less the same
+% features, but there are quite a few organizational differences as
+% well as some new features and bug fixes. For example, the
+% \pkg{amstex} package automatically loaded the \pkg{amsfonts}
+% package, but the \pkg{amsmath} package does not. At the present
+% time (November 1999) user-level documentation of the commands
+% provided here is found in the AMSmath Users' Guide,
+% \fn{amsldoc.tex}.
+%
+% \StopEventually{}
+%
+% Standard file identification.
+% \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
+[1994/12/01]% LaTeX date must be December 1994 or later
+% \end{macrocode}
+%
+% Providing a rollback to earlier version(s)
+% \begin{macrocode}
+\providecommand\DeclareRelease[3]{}
+\providecommand\DeclareCurrentRelease[2]{}
+%
+\DeclareRelease{}{2018-12-01}{amsmath-2018-12-01.sty}
+\DeclareCurrentRelease{}{2019-04-01}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\ProvidesPackage{amsmath}[2019/04/01 v2.17c AMS math features]
+% \end{macrocode}
+%
+% \section{Catcode defenses}
+%
+% Some packages change the catcode of characters that are essential
+% in low-level \tex/ syntax. Any package that does so does not
+% qualify as a PWWO package (\qq{Plays Well With Others}) because it
+% can cause other packages to fail if they are loaded later. \LaTeX{}
+% is partly to blame for this because it fails to provide adequate
+% built-in safeguards in the package loading mechanisms. In the
+% absence of such safeguards, we will provide them here.
+% \begin{macrocode}
+\edef\@temp{\catcode 96=\number\catcode 96 }
+\catcode\string `\`=12
+\def\do#1{\catcode\number`#1=\number\catcode`#1}
+\edef\@temp{%
+ \noexpand\AtEndOfPackage{%
+ \@temp
+ \do\"\do\'\do\(\do\)\do\*\do\+\do\,\do\-\do\.%
+ \do\/\do\<\do\=\do\>\do\[\do\]\do\^\do\_\relax
+ }%
+}
+\@temp
+\def\do#1{\catcode\number`#1=12 }
+\do\"\do\'\do\(\do\)\do\*\do\+\do\,\do\-\do\.
+\do\/\do\<\do\=\do\>\do\[\do\]
+\catcode`\^=7 \catcode`\_=8
+% \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Declare some options}
+%
+% Handling of limits on integrals, sums, operatornames.
+% \begin{macrocode}
+\DeclareOption{intlimits}{\let\ilimits@\displaylimits}
+\DeclareOption{nointlimits}{\let\ilimits@\nolimits}
+\DeclareOption{sumlimits}{\let\slimits@\displaylimits}
+\DeclareOption{nosumlimits}{\let\slimits@\nolimits}
+\DeclareOption{namelimits}{\PassOptionsToPackage{namelimits}{amsopn}}
+\DeclareOption{nonamelimits}{%
+ \PassOptionsToPackage{nonamelimits}{amsopn}}
+% \end{macrocode}
+%
+% The following two switches might have been defined already by the
+% documentclass, but it doesn't hurt to re-execute the \cs{newif}'s.
+% \begin{macrocode}
+\newif\ifctagsplit@
+\newif\iftagsleft@
+% \end{macrocode}
+% Right or left placement of equation numbers.
+% \begin{macrocode}
+\DeclareOption{leqno}{\tagsleft@true}
+\DeclareOption{reqno}{\tagsleft@false}
+\DeclareOption{centertags}{\ctagsplit@true}
+\DeclareOption{tbtags}{\ctagsplit@false}
+% \end{macrocode}
+%
+% The \opt{cmex10} option is an escape hatch for people who don't
+% happen to have sizes 7--9 of the \fn{cmex} fonts available to them
+% yet. (Strictly speaking they are considered part of a minimum
+% \latex/ distribution now, i.e., all \LaTeXe{} users should have
+% them, without needing to get the AMSFonts distrib.)
+% \begin{macrocode}
+\DeclareOption{cmex10}{%
+ \ifnum\cmex@opt=\@ne \def\cmex@opt{0}%
+ \else \def\cmex@opt{10}\fi
+}
+% \end{macrocode}
+% To help things work out better with various package loading orders
+% of \pkg{amsmath} and \pkg{amsfonts}, we establish a variable to
+% communicate the status of the cmex font definition. If the
+% \pkg{amsfonts} package was loaded first this variable might be
+% already defined, in which case we want to preserve its value.
+% \begin{macrocode}
+\@ifundefined{cmex@opt}{\def\cmex@opt{7}}{}
+% \end{macrocode}
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Flush-left equations [DMJ]}
+%
+% The left margin of math enviroments is controlled by
+% \cs{@mathmargin}. This can be set to \cs{@centering} to
+% implement the default behaviour, i.e., centered equations, and to
+% something else to implement the flushleft style.
+%
+% In theory, all that's needed to activate the flushleft mode
+% in the AMS document classes is something like this:
+% \begin{verbatim}
+% \DeclareOption{fleqn}{%
+% \AtBeginDocument{\@mathmargin30pt\relax}%
+% }
+% \end{verbatim}
+% (In fact, unless the document class wants to specify the
+% \cs{@mathmargin}, it doesn't need to do anything with the
+% \opt{fleqn} option.)
+% \begin{macrocode}
+\newif\if@fleqn
+%
+\newskip\@mathmargin
+\@mathmargin\@centering
+%
+\DeclareOption{fleqn}{%
+ \@fleqntrue
+ \@mathmargin = -1sp
+ \let\mathindent=\@mathmargin
+ \AtBeginDocument{%
+ \ifdim\@mathmargin= -1sp
+ \@mathmargin\leftmargini minus\leftmargini
+ \fi
+ }%
+}
+% \end{macrocode}
+%
+% DMJ: This ensures that \cs{@mathmargin} is given some sort of
+% sensible default if the class doesn't specify one, while still
+% allowing a user to override the default value in their document
+% preamble. (Incidentally, I'm initializing \cs{@mathmargin} to
+% \cs{leftmargini} for compatibility with \fn{fleqn.clo}, but I'm
+% not at all convinced that's the right thing to do.)
+%
+% The next question is what happens when amsmath is used with
+% one of the standard classes. Unfortunately, \latex/ implements
+% \opt{fleqn} somewhat clumsily; instead of paramaterizing the
+% definitions of the math structures (as I've attempted to do
+% here), \fn{fleqn.clo} declares a dimen \cn{mathindent} that is
+% much like my \cs{@mathmargin} and then redefines \cn\[, \cn\],
+% \cn{equation}, and \cn{eqnarray}. This means that things could
+% get rather messy in 2.09 compatibility mode, since \fn{fleqn.clo}
+% might be loaded after \fn{amsmath.sty}, which could cause a real
+% mess.
+%
+% [mjd,1999/07/07]: Let \cs{mathindent} = \cs{@mathmargin} as
+% envisioned by DMJ. Compatibility-mode documents will all use the
+% \pkg{amstex} package, not \pkg{amsmath}. There is a remote chance
+% of a problem if someone makes an assignment to \cs{mathindent} in a
+% way that implicitly assumes it is a dimen register (inasmuch as it
+% has now become a skip register), and the string ``plus'' follows in
+% the input stream, but if someone's document croaks in that way, I
+% think they will just have to bite the bullet and fix it. The
+% alternative is to penalize a lot of other users with a known
+% handicap.
+%
+% \section{Spacing around \cn{aligned} and \cn{gathered}}
+%
+% [dpc, 2016] Option to control the space to the left of aligned and gathered.
+%
+% Previously \cn{aligned} and \cn{gathered} inserted a thin space on
+% their left but not their right, there is no good reason for this
+% that anyone can remember, it has just always been that way
+% inherited from amstex. The usual advice to authors has been to use
+% |\!\begin{aligned}| to get better spacing.
+%
+% Here introduce:
+%
+% \opt{alignedleftspaceyes} to keep the behaviour of adding this space.
+%
+% \opt{alignedleftspaceno} to disable adding this space.
+%
+% \opt{alignedleftspaceyesifneg} the new default behaviour, do not add
+% the space unless the environment is preceded by a negative skip or
+% kern, so that |\!\begin{aligned}| works as before.
+%
+% \changes{v2.16a}{2016/11/05}{New options to control aligned spacing}
+% \begin{macrocode}
+\DeclareOption{alignedleftspaceyes}{\def\alignedspace@left{\null\,}}
+\DeclareOption{alignedleftspaceno}{\def\alignedspace@left{\null}}
+\DeclareOption{alignedleftspaceyesifneg}{%
+\def\alignedspace@left{%
+ \edef\@tempa{\expandafter\@car\the\lastskip\@nil}%
+ \if-\@tempa\null\,%
+ \else
+ \edef\@tempa{\expandafter\@car\the\lastkern\@nil}%
+ \if-\@tempa\null\,%
+ \else\null
+ \fi
+ \fi}%
+}
+% \end{macrocode}
+%
+%
+% \begin{macrocode}
+\DeclareOption{?}{}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\ExecuteOptions{%
+ nointlimits,sumlimits,namelimits,centertags,alignedleftspaceyesifneg}
+% \end{macrocode}
+% The \cs{par} after \cs{ProcessOptions} is to ensure the correct
+% line number on screen if an error occurs during option processing;
+% otherwise the lookahead for a \qc{\*} option would result in \tex/
+% showing the following line instead.
+% \begin{macrocode}
+\ProcessOptions\par
+% \end{macrocode}
+%
+% \begin{macrocode}
+\@ifpackagewith{amsmath}{?}{%
+ \typeout{^^J%
+Documentation for the amsmath package is found in amsldoc.dvi^^J%
+(or .pdf or .tex).^^J%
+^^J%
+See also https://www.ams.org/tex/amslatex.html.^^J%
+^^J%
+Note: Using the first edition of The LaTeX Companion (1994) without^^J%
+errata as a guide for amsmath use is not recommended.^^J%
+ }%
+}{%
+ \typeout{%
+For additional information on amsmath, use the \lq ?\rq\space option.%
+ }%
+}
+% \end{macrocode}
+%
+% Processing to handle the \opt{cmex10} option is a little tricky
+% because of different possible loading orders for \pkg{amsmath} and
+% \pkg{amsfonts}. The package \pkg{amsmath} sets the \cs{cmex@opt}
+% flag to 7 or 10, and the package \pkg{amsfonts} sets the flag to 1
+% or 0.
+% \begin{macrocode}
+\ifnum\cmex@opt=7 \relax
+ \DeclareFontShape{OMX}{cmex}{m}{n}{%
+ <-8>cmex7<8>cmex8<9>cmex9%
+ <10><10.95><12><14.4><17.28><20.74><24.88>cmex10%
+ }{}%
+ \expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
+\else
+ \ifnum\cmex@opt=\z@ % need to override cmex7 fontdef from amsfonts
+% \end{macrocode}
+% Force reloading of the OMX/cmex font definition file.
+% \begin{macrocode}
+ \begingroup
+ \fontencoding{OMX}\fontfamily{cmex}%
+ \expandafter\let\csname OMX+cmex\endcsname\relax
+ \try@load@fontshape
+ \endgroup
+% \end{macrocode}
+% The \fn{cmex10} font gets special preload handling in the building
+% of the \latex/ format file, need an extra bit here to work around
+% that.
+% \begin{macrocode}
+ \expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
+ \def\cmex@opt{10}%
+ \fi
+\fi
+% \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Call some other packages}
+%
+% The \pkg{amstext} package provides the \cn{text} command. The
+% \pkg{amsbsy} package provides \cn{boldsymbol} and \cn{pmb}. (Since
+% 1997 it is usually better to use the \pkg{bm} package instead; but
+% I think we have to keep \pkg{amsbsy} here for backward
+% compatibility [mjd,1999/11/19].) The \pkg{amsopn} package provides
+% \cn{DeclareMathOperator}.
+% \begin{macrocode}
+\RequirePackage{amstext}[1995/01/25]
+\RequirePackage{amsbsy}[1995/01/20]
+\RequirePackage{amsopn}[1995/01/20]
+% \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Miscellaneous}
+%
+% \begin{macro}{\ams@newcommand}
+% Where \pkg{stix} and \pkg{amsmath} define the same control
+% sequences, we want to avoid inadvertently overriding \pkg{stix}'s
+% definitions. If \pkg{stix} is loaded before \pkg{amsmath}, the
+% following conditional takes care of the problem. There is
+% similar code in the \pkg{stix} package in case \pkg{amsmath} is
+% loaded first.
+% \begin{macrocode}
+\@ifpackageloaded{stix}{%
+ \let\ams@newcommand\providecommand
+ \let\ams@renewcommand\providecommand
+ \let\ams@def\providecommand
+ \let\ams@DeclareRobustCommand\providecommand
+}{%
+ \let\ams@newcommand\newcommand
+ \let\ams@renewcommand\renewcommand
+ \let\ams@def\def
+ \let\ams@DeclareRobustCommand\DeclareRobustCommand
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@amsmath@err}
+% Defining this error function saves main mem.
+% \begin{macrocode}
+\def\@amsmath@err{\PackageError{amsmath}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\AmS}
+% The \cs{AmS} prefix can be used to construct the combination
+% |\AmS-\LaTeX|.
+% \begin{macrocode}
+\providecommand{\AmS}{{\protect\AmSfont
+ A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
+% \end{macrocode}
+% In \cn{AmSfont} we call cmsy directly in lieu of trying to access
+% it through the math fonts setup (e.g. |\the\textfont2|) because
+% math fonts can't be relied on to be properly set up if we are not
+% inside a math formula. This means that if this command is used in a
+% document where CM fonts are not wanted, then a font substitution
+% will need to be declared, e.g.:
+% \begin{verbatim}
+% \DeclareFontShape{OMS}{cmsy}{m}{n}{ <-> sub * xxx/m/n }{}
+% \end{verbatim}
+% where |xxx| is some alternate font family.
+% Taking the first letter of \cs{f@series} will produce |b| or |m|
+% for the most common values (|b,bx,m|). It may produce nonsense for
+% more unusual values of \cs{f@series}, so for safety's sake we have
+% an additional \cs{if} test. We want to avoid setting the series to
+% |bx| because in a standard \latex/ installation the combination
+% |cmsy/bx/n| does not have a font definition, and the user
+% would get a font substitution warning on screen.
+% \begin{macrocode}
+\newcommand{\AmSfont}{%
+ \usefont{OMS}{cmsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@mathmeasure}
+% The function |\@mathmeasure| takes three arguments; the third arg
+% is typeset as a math formula in an hbox, using arg |#2| as the
+% mathstyle, and the result is left in the box named by the first
+% arg. It is assumed that we are already in math mode, so we can turn
+% off |\everymath| (in particular, |\check@mathfonts|).
+%
+% As of 2018/12 release we don't turn off |\evermath| as this
+% optimization can be harmful.
+% \changes{v2.17b}{2018/12/01}{Don't drop \cs{frozen@everymath}}
+% \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined % kernel is < 2018/12
+\def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
+ \m@th$#2#3$}}
+\else
+\def\@mathmeasure#1#2#3{\setbox#1\hbox{%
+ \m@th$#2#3$}}
+\fi
+% \end{macrocode}
+% \end{macro}
+%
+% The \cs{inf@bad} constant is for testing overfull boxes.
+% \begin{macrocode}
+\@ifundefined{inf@bad}{%
+ \newcount\inf@bad \inf@bad=1000000 \relax
+}{}
+% \end{macrocode}
+%
+%\subsection{Math spacing commands}
+%
+% \begin{macro}{\tmspace}
+% \begin{macro}{\,}
+% \begin{macro}{\thinspace}
+% \begin{macro}{\!}
+% \begin{macro}{\negthinspace}
+% \begin{macro}{\:}
+% \begin{macro}{\medspace}
+% \begin{macro}{\negmedspace}
+% \begin{macro}{\;}
+% \begin{macro}{\thickspace}
+% \begin{macro}{\negthickspace}
+% Here we fill in some gaps in the set of spacing commands, and make them
+% all work equally well in or out of math.
+% We want all these commands to be robust but declaring them all with
+% \cs{DeclareRobustCommand} uses up an control sequence name per
+% command; to avoid this, we define a common command \cs{tmspace}
+% (text-or-math space) which carries the robustness burden for all of
+% them. The standard \cs{relax} before the \cs{ifmmode} is not
+% necessary because of the \cs{protect} added by
+% \cs{DeclareRobustCommand}.
+% \changes{v2.17b}{2018/12/01}{Start LR-mode for \cs{thinspace} and
+% friends if necessary (github/49)}
+% \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined
+\DeclareRobustCommand{\tmspace}[3]{%
+ \ifmmode\mskip#1#2\else\kern#1#3\fi\relax}
+\else
+\DeclareRobustCommand{\tmspace}[3]{%
+ \ifmmode\mskip#1#2\else\leavevmode@ifvmode\kern#1#3\fi\relax}
+\fi
+\renewcommand{\,}{\tmspace+\thinmuskip{.1667em}}
+\let\thinspace\,
+\renewcommand{\!}{\tmspace-\thinmuskip{.1667em}}
+\let\negthinspace\!
+\renewcommand{\:}{\tmspace+\medmuskip{.2222em}}
+\let\medspace\:
+\newcommand{\negmedspace}{\tmspace-\medmuskip{.2222em}}
+\renewcommand{\;}{\tmspace+\thickmuskip{.2777em}}
+\let\thickspace\;
+\newcommand{\negthickspace}{\tmspace-\thickmuskip{.2777em}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\mspace}
+% And while we're at it, why don't we provide an equivalent of
+% \cn{hspace} for math mode use. This allows use of |mu| units in
+% (for example) constructing compound math symbols.
+% \begin{macrocode}
+\newcommand{\mspace}[1]{\mskip#1\relax}
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Vertical bar symbols}
+% \begin{macro}{\lvert}
+% \begin{macro}{\rvert}
+% \begin{macro}{\lVert}
+% \begin{macro}{\rVert}
+% Add left/right specific versions of \cn{vert}, \cn{Vert}. Don't
+% assume the delimiter codes are the CM defaults.
+% \begin{macrocode}
+\def\@tempa#1#2\@nil{%
+ \ifx\delimiter#1\@tempcnta#2\relax\else\@tempcnta\z@\fi
+}
+\@xp\@tempa\vert\@empty\@nil
+\ifnum\@tempcnta>\z@
+ \advance\@tempcnta "4000000
+ \xdef\lvert{\delimiter\number\@tempcnta\space }
+ \advance\@tempcnta "1000000
+ \xdef\rvert{\delimiter\number\@tempcnta\space }
+\else
+ \ifx\@@undefined\lvert
+ % Fall back to cmex encoding since we don't know what else to do.
+ \DeclareMathDelimiter{\lvert}
+ {\mathopen}{symbols}{"6A}{largesymbols}{"0C}
+ \DeclareMathDelimiter{\rvert}
+ {\mathclose}{symbols}{"6A}{largesymbols}{"0C}
+ \fi
+\fi
+\@xp\@tempa\Vert\@empty\@nil
+\ifnum\@tempcnta>\z@
+ \advance\@tempcnta "4000000
+ \xdef\lVert{\delimiter\number\@tempcnta\space }
+ \advance\@tempcnta "1000000
+ \xdef\rVert{\delimiter\number\@tempcnta\space }
+\else
+ \ifx\@@undefined\lVert
+ \DeclareMathDelimiter{\lVert}
+ {\mathopen}{symbols}{"6B}{largesymbols}{"0D}
+ \DeclareMathDelimiter{\rVert}
+ {\mathclose}{symbols}{"6B}{largesymbols}{"0D}
+ \fi
+\fi
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Fractions}
+% Bury the generalized fraction primitives \cs{over}, \cs{atop},
+% etc., because of their bizarre syntax, which is decidedly out of
+% place in a \latex/ document.
+% \begin{macrocode}
+\@saveprimitive\over\@@over
+\@saveprimitive\atop\@@atop
+\@saveprimitive\above\@@above
+\@saveprimitive\overwithdelims\@@overwithdelims
+\@saveprimitive\atopwithdelims\@@atopwithdelims
+\@saveprimitive\abovewithdelims\@@abovewithdelims
+% \end{macrocode}
+%
+% \begin{macro}{\primfrac}
+% If someone insists on using \cs{over}, give a warning the first
+% time and then resurrect the old definition. Laissez-faire policy.
+% \begin{macrocode}
+\DeclareRobustCommand{\primfrac}[1]{%
+ \PackageWarning{amsmath}{%
+Foreign command \@backslashchar#1;\MessageBreak
+\protect\frac\space or \protect\genfrac\space should be used instead%
+\MessageBreak
+ }
+ \global\@xp\let\csname#1\@xp\endcsname\csname @@#1\endcsname
+ \csname#1\endcsname
+}
+% \end{macrocode}
+% \end{macro}
+% \begin{macrocode}
+\renewcommand{\over}{\primfrac{over}}
+\renewcommand{\atop}{\primfrac{atop}}
+\renewcommand{\above}{\primfrac{above}}
+\renewcommand{\overwithdelims}{\primfrac{overwithdelims}}
+\renewcommand{\atopwithdelims}{\primfrac{atopwithdelims}}
+\renewcommand{\abovewithdelims}{\primfrac{abovewithdelims}}
+% \end{macrocode}
+%
+% \cn{frac} calls \cn{@@over} directly instead of via \cn{genfrac}, for
+% better speed because it is so common. \cn{tfrac} and \cn{dfrac} are
+% abbreviations for some commonly needed mathstyle overrides. To
+% conserve csnames we avoid making \cn{dfrac} and \cn{tfrac} robust
+% (\cn{genfrac} is itself robust).
+% \begin{macrocode}
+\DeclareRobustCommand{\frac}[2]{{\begingroup#1\endgroup\@@over#2}}
+\newcommand{\dfrac}{\genfrac{}{}{}0}
+\newcommand{\tfrac}{\genfrac{}{}{}1}
+% \end{macrocode}
+% The \cn{binom} command for binomial notation works like \cn{frac}
+% and has similar variants. Note that we do not use \cs{z@} in
+% \cn{dbinom} and \cn{tbinom} because they are not top-level robust
+% like \cn{binom}, and so the \cs{z@} with the potentially
+% problematic \qc{\@} character would become visible when writing one
+% of those commands to a \fn{.toc} file.
+% \begin{macrocode}
+\DeclareRobustCommand{\binom}{\genfrac()\z@{}}
+\newcommand{\dbinom}{\genfrac(){0pt}0}
+\newcommand{\tbinom}{\genfrac(){0pt}1}
+% \end{macrocode}
+%
+% \begin{macro}{\genfrac}
+% \changes{v2.16a}{2016/11/05}{New genfrac implementation for extended
+% TeXs}
+% This command provides access to \tex/'s generalized fraction
+% primitives. Args: \arg{1} left delim, \arg{2} right delim, \arg{3}
+% line thickness, \arg{4} mathstyle override, \arg{5} numerator,
+% \arg{6} denominator. But we only read the first four args at first,
+% in order to give us a moment to select the proper generalized
+% fraction primitive. Any of those four args could be empty, and when
+% empty the obvious defaults are selected (no delimiters, default
+% line thickness (normally .4pt), and no mathstyle override).
+%
+% the |withdelims| primitives do not work in xetex with OpenType
+% fonts, and the relevant font dimen parameters are often not set
+% in luatex as theer are no matching values in the OpenType Math
+% table, so here we use variants that use the font parameters if
+% they are set, but scale using |\left\right| rather than the
+% |withdelims| primitives.
+%
+% \begin{macrocode}
+\ifx\directlua\@undefined
+% \end{macrocode}
+%
+% \begin{macrocode}
+\ifx\XeTeXcharclass\@undefined
+% \end{macrocode}
+% Classic version
+% \begin{macrocode}
+\DeclareRobustCommand{\genfrac}[4]{%
+ \def\@tempa{#1#2}%
+ \edef\@tempb{\@nx\@genfrac\@mathstyle{#4}%
+ \csname @@\ifx @#3@over\else above\fi
+ \ifx\@tempa\@empty \else withdelims\fi\endcsname}
+ \@tempb{#1#2#3}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\else
+% \end{macrocode}
+% XeTeX version
+% \begin{macrocode}
+\def\genfrac@rule#1#2#3#4{%
+\hbox{$\left#1\vcenter{\hrule \@width\z@
+ \@height
+ \ifdim\fontdimen#2#3\tw@=\z@
+ #4\fontdimen6#3\tw@
+ \else
+ \fontdimen#2#3\tw@
+ \fi
+ }\right.$}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\genfrac@choice#1#2{%
+\ifx @#2@\else
+% \end{macrocode}
+% \changes{v2.17a}{2017/09/02}{move \cs{nulldelimiterspace} correction}
+% \begin{macrocode}
+\ifx c#1\kern-\nulldelimiterspace\fi
+{\delimitershortfall\z@\delimiterfactor\@m
+ \mathsurround\z@\nulldelimiterspace\z@
+\mathchoice
+{\genfrac@rule{#2}{20}\textfont{2.39}}%
+{\genfrac@rule{#2}{21}\textfont{1}}%
+{\genfrac@rule{#2}{21}\scriptfont{1.45}}%
+{\genfrac@rule{#2}{21}\scriptscriptfont{1.35}}%
+}%
+\ifx o#1\kern-\nulldelimiterspace\fi
+\fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\DeclareRobustCommand{\genfrac}[6]{{%
+\@mathstyle{#4}%
+\genfrac@choice o{#1}%
+{\begingroup#5\endgroup\ifx @#3@\@@over\else\@@above\fi#3\relax#6}%
+\genfrac@choice c{#2}%
+}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\fi
+\else
+% \end{macrocode}
+% LuaTeX version
+% \begin{macrocode}
+\def\genfrac@rule#1#2#3{%
+\hbox{$\left#1\vcenter{\hrule \@width\z@
+ \@height
+ \ifdim\Umathfractiondelsize#2=\z@
+ #3\fontdimen6#3\tw@
+ \else
+ \Umathfractiondelsize#2%
+ \fi
+ }\right.$}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\genfrac@choice#1#2{%
+\ifx @#2@\else
+% \end{macrocode}
+% \changes{v2.17a}{2017/09/02}{move \cs{nulldelimiterspace} correction}
+% \begin{macrocode}
+\ifx c#1\kern-\nulldelimiterspace\fi
+{\delimitershortfall\z@\delimiterfactor\@m
+ \mathsurround\z@\nulldelimiterspace\z@
+\mathchoice
+{\genfrac@rule{#2}\displaystyle{2.39}}%
+{\genfrac@rule{#2}\textstyle{1}}%
+{\genfrac@rule{#2}\scriptstyle{1.45}}%
+{\genfrac@rule{#2}\scriptscriptstyle{1.35}}%
+}%
+\ifx o#1\kern-\nulldelimiterspace\fi
+\fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\DeclareRobustCommand{\genfrac}[6]{{%
+\@mathstyle{#4}%
+\genfrac@choice o{#1}%
+{\begingroup#5\endgroup\ifx @#3@\@@over\else\@@above\fi#3\relax#6}%
+\genfrac@choice c{#2}%
+}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\fi
+% \end{macrocode}
+%
+% End of test for Lua\TeX/Xe\TeX.
+%
+% \cs{@genfrac} takes the preceding arguments and reads the
+% numerator and denominator. Note that there's no convenient way to
+% make the numerator and denominator \emph{contents}
+% displaystyle, through this interface.
+%
+% Args: \arg{1} mathstyle, \arg{2} fraction primitive,
+% \arg{3} delimiters and rule thickness,
+% \arg{4} numerator, \arg{5} denominator.
+% \begin{macrocode}
+\def\@genfrac#1#2#3#4#5{{#1{\begingroup#4\endgroup#2#3\relax#5}}}
+% \end{macrocode}
+% \end{macro}
+%
+% Empty mathstyle arg: no change; 0 = displaystyle, 1 = textstyle, 2
+% = scriptstyle, 3 = scriptscriptstyle.
+% \begin{macrocode}
+\def\@mathstyle#1{%
+ \ifx\@empty#1\@empty\relax
+ \else\ifcase#1\displaystyle % case 0
+ \or\textstyle\or\scriptstyle\else\scriptscriptstyle\fi\fi}
+% \end{macrocode}
+%
+% \subsection{Sums and Integrals}
+% Default value for sum limits is \cs{displaylimits}, see option
+% `nosumlimits'.
+%
+% We redefine all the cumulative operator symbols to use
+% \cs{slimits@} so that switching between \cs{displaylimits} and
+% \cs{nolimits} can be controlled by package options. Also add
+% \cs{DOTSB} for the benefit of the dots lookahead. But we'd better
+% make sure \cn{coprod} and the others are simple mathchars; if not,
+% the attempted changes will probably fail miserably.
+%
+% \changes{v2.15}{2016/02/20}{Accept \cs{Umathchar}}
+% \begin{macrocode}
+\begingroup
+% \end{macrocode}
+% \begin{macrocode}
+\edef\@tempa{\string\mathchar"}
+\edef\@tempd{\string\Umathchar"}
+\def\@tempb#1"#2\@nil{#1"}
+\edef\@tempc{\expandafter\@tempb\meaning\coprod "\@nil}
+\ifx\@tempc\@tempd\let\@tempc\@tempa\fi
+% \end{macrocode}
+% \begin{macrocode}
+\ifx\@tempa\@tempc
+ \global\let\coprod@\coprod
+ \gdef\coprod{\DOTSB\coprod@\slimits@}
+ \global\let\bigvee@\bigvee
+ \gdef\bigvee{\DOTSB\bigvee@\slimits@}
+ \global\let\bigwedge@\bigwedge
+ \gdef\bigwedge{\DOTSB\bigwedge@\slimits@}
+ \global\let\biguplus@\biguplus
+ \gdef\biguplus{\DOTSB\biguplus@\slimits@}
+ \global\let\bigcap@\bigcap
+ \gdef\bigcap{\DOTSB\bigcap@\slimits@}
+ \global\let\bigcup@\bigcup
+ \gdef\bigcup{\DOTSB\bigcup@\slimits@}
+ \global\let\prod@\prod
+ \gdef\prod{\DOTSB\prod@\slimits@}
+ \global\let\sum@\sum
+ \gdef\sum{\DOTSB\sum@\slimits@}
+ \global\let\bigotimes@\bigotimes
+ \gdef\bigotimes{\DOTSB\bigotimes@\slimits@}
+ \global\let\bigoplus@\bigoplus
+ \gdef\bigoplus{\DOTSB\bigoplus@\slimits@}
+ \global\let\bigodot@\bigodot
+ \gdef\bigodot{\DOTSB\bigodot@\slimits@}
+ \global\let\bigsqcup@\bigsqcup
+ \gdef\bigsqcup{\DOTSB\bigsqcup@\slimits@}
+\fi
+\endgroup
+% \end{macrocode}
+%
+% \subsection{Roots and radicals}
+%
+% \begin{macro}{\root}
+% This root stuff needs syntax work and implementation work. Surely
+% something more compact can be done?? [mjd, 1994/09/05]
+% \begin{macrocode}
+\newcommand{\leftroot}{\@amsmath@err{\Invalid@@\leftroot}\@eha}
+\newcommand{\uproot}{\@amsmath@err{\Invalid@@\uproot}\@eha}
+\newcount\uproot@
+\newcount\leftroot@
+\renewcommand{\root}{\relaxnext@
+ \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
+ \ifx\@let@token\leftroot\let\next@\nextiii@\else
+ \let\next@\plainroot@\fi\fi\next@}%
+ \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
+ \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
+ \DN@.{\FN@\nextv@}\fi\next@.}%
+ \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
+ \let\next@\plainroot@\fi\next@}%
+ \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
+ \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
+ \def\nextvii@{\ifx\@let@token\@sptoken
+ \DN@. {\FN@\nextviii@}\else
+ \DN@.{\FN@\nextviii@}\fi\next@.}%
+ \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
+ \let\next@\plainroot@\fi\next@}%
+ \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
+ \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
+\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
+ $\m@th\scriptscriptstyle{#1}$}%
+ \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
+ {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
+% \end{macrocode}
+% \end{macro}
+%
+% \changes{v2.0}{1999/06/17}{Normalize @@sqrt to sqrtsign}
+
+% Name change from \cs{@@sqrt} to \cs{sqrtsign} happened in the
+% 1995/12/01 release of \latex/. If we were to assume that
+% \cs{sqrtsign} is defined then someone with the 1995/06/01 release
+% of \latex/ would have trouble using this package.
+% \begin{macrocode}
+\@ifundefined{sqrtsign}{\let\sqrtsign\@@sqrt}{}
+\def\r@@t#1#2{\setboxz@h{$\m@th#1\sqrtsign{#2}$}%
+ \dimen@\ht\z@\advance\dimen@-\dp\z@
+ \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
+ \advance\dimen@ by1.667\wd\@ne
+ \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
+ \mkern-10mu\mkern\leftroot@ mu\boxz@}
+% \end{macrocode}
+%
+% \subsection{Et cetera}
+%
+% \changes{v2.0}{1999/06/18}{Leave Greek cap letters unaltered}
+%
+% Specific names for the variant italic cap Greek letters are not
+% defined by \latex/. If no preceding package defined these, we will
+% define them now.
+% \begin{macrocode}
+\@ifundefined{varGamma}{%
+ \DeclareMathSymbol{\varGamma}{\mathord}{letters}{"00}
+ \DeclareMathSymbol{\varDelta}{\mathord}{letters}{"01}
+ \DeclareMathSymbol{\varTheta}{\mathord}{letters}{"02}
+ \DeclareMathSymbol{\varLambda}{\mathord}{letters}{"03}
+ \DeclareMathSymbol{\varXi}{\mathord}{letters}{"04}
+ \DeclareMathSymbol{\varPi}{\mathord}{letters}{"05}
+ \DeclareMathSymbol{\varSigma}{\mathord}{letters}{"06}
+ \DeclareMathSymbol{\varUpsilon}{\mathord}{letters}{"07}
+ \DeclareMathSymbol{\varPhi}{\mathord}{letters}{"08}
+ \DeclareMathSymbol{\varPsi}{\mathord}{letters}{"09}
+ \DeclareMathSymbol{\varOmega}{\mathord}{letters}{"0A}
+}{}
+% \end{macrocode}
+%
+% \begin{macro}{\overline}
+% \amstex/ redefines \cn{overline} as shown here, for reasons that
+% are probably less important in \latex/: Make it read its argument
+% as a macro argument rather than a ``math field'' (\emph{The
+% \tex/book}, Chapter 26), to avoid problems when something that is
+% apparently a single symbol is actually a non-simple macro (e.g.,
+% \cn{dag}) \emph{and} is given as a single-token argument without
+% enclosing braces.
+% \begin{macrocode}
+\@saveprimitive\overline\@@overline
+\DeclareRobustCommand{\overline}[1]{\@@overline{#1}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\boxed}
+% The \cs{boxed} command is specifically intended to put a box around
+% an equation or piece of an equation. (Not including the equation
+% number.) This isn't trivial for end-users to do it properly
+% with \cs{fbox} so we provide a command for them.
+% \begin{macrocode}
+\newcommand{\boxed}[1]{\fbox{\m@th$\displaystyle#1$}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\implies}
+% \begin{macro}{\impliedby}
+% \begin{macrocode}
+\newcommand{\implies}{\DOTSB\;\Longrightarrow\;}
+\newcommand{\impliedby}{\DOTSB\;\Longleftarrow\;}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\And}
+% \begin{macrocode}
+\def\And{\DOTSB\;\mathchar"3026 \;}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\nobreakdash}
+% The command \cn{nobreakdash} is designed only for use before a
+% hyphen or dash (|-|, |--|, or |---|).
+% Setting the hyphen in a box and then unboxing it means that the
+% normal penalty will not be added after it---and if the penalty is
+% not there a break will not be taken (unless an explicit penalty
+% or glue follows, thus the final \verb=\nobreak=).
+% \begin{macrocode}
+\newcommand{\nobreakdash}{\leavevmode
+ \toks@\@emptytoks \def\@tempa##1{\toks@\@xp{\the\toks@-}\FN@\next@}%
+ \DN@{\ifx\@let@token-\@xp\@tempa
+ \else\setboxz@h{\the\toks@\nobreak}\unhbox\z@\fi}%
+ \FN@\next@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\colon}
+% \cs{colon} is for a colon in math that resembles a text colon:
+% small space on the left, larger space on the right. The \qc{\:}
+% character by itself is treated as a \cs{mathrel} i.e. large, equal
+% spacing on both sides.
+% \begin{macrocode}
+\renewcommand{\colon}{\nobreak\mskip2mu\mathpunct{}\nonscript
+ \mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
+% \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Ellipsis dots}
+%
+% We can't use \cs{newif} for \cs{ifgtest@} because we want
+% to include \cs{global} in the definitions of
+% \cs{gtest@true} and \cs{gtest@false}.
+% \begin{macrocode}
+\let\ifgtest@\iffalse % initial value
+\def\gtest@true{\global\let\ifgtest@\iftrue}
+\def\gtest@false{\global\let\ifgtest@\iffalse}
+\let\DOTSI\relax
+\let\DOTSB\relax
+\let\DOTSX\relax
+{\uccode`7=`\\ \uccode`8=`m \uccode`9=`a \uccode`0=`t \uccode`!=`h
+ \uppercase{%
+ \gdef\math@#1#2#3#4#5#6\math@{\gtest@false\ifx 7#1\ifx 8#2%
+ \ifx 9#3\ifx 0#4\ifx !#5\xdef\meaning@{#6}\gtest@true
+ \fi\fi\fi\fi\fi}}}
+{\uccode`7=`c \uccode`8=`h \uccode`9=`\"
+ \uppercase{\gdef\mathch@#1#2#3#4#5#6\mathch@{\gtest@false
+ \ifx 7#1\ifx 8#2\ifx 9#5\gtest@true\xdef\meaning@{9#6}\fi\fi\fi}}}
+% \end{macrocode}
+% \changes{v2.15}{2016/02/20}{Accept \cs{Umathchar}}
+% \begin{macrocode}
+{\uccode`(=`U \uccode`)=`m
+ \uppercase{\gdef\Umathch@#1#2#3#4"#5"#6\Umathch@{\gtest@false
+ \ifx(#2\ifx)#3\gtest@true
+ \ifcase"#5 \or\or\gdef\thedots@{\dotsb@}\or\gdef\thedots@{\dotsb@}\fi
+ \fi\fi
+ }}}
+% \end{macrocode}
+% \changes{v2.15}{2016/02/20}{Decode the mathcode of character tokens for Unicode TeX}
+% For Unicode TeXs, if the next token is a character token look up the (U)mathcode. Do not do this for classic TeX for compatibility reasons.
+% \begin{macrocode}
+\ifx\Umathcharnumdef\@undefined
+\gdef\thecharacter@#1\thecharacter@{}
+\else
+{\uccode`(=`t \uccode`)=`c
+ \uppercase{\gdef\thecharacter@#1#2#3#4#5\thecharacter@{%
+ \ifx(#1\ifx)#4%
+ \@xp\getmathcode@\meaning@\getmathcode@
+ \fi\fi
+}}}
+\def\getmathcode@#1 #2 #3#4\getmathcode@{%
+ \Umathcharnumdef\@tempa\Umathcodenum`#3\relax
+ \edef\meaning@{\meaning\@tempa}%
+ \@xp\Umathch@\meaning@\Umathch@
+}
+\fi
+% \end{macrocode}
+% \begin{macrocode}
+\newcount\classnum@
+\def\getmathch@#1.#2\getmathch@{\classnum@#1 \divide\classnum@4096
+ \ifcase\number\classnum@\or\or\gdef\thedots@{\dotsb@}\or
+ \gdef\thedots@{\dotsb@}\fi}
+{\uccode`4=`b \uccode`5=`i \uccode`6=`n
+ \uppercase{\gdef\mathbin@#1#2#3{\relaxnext@
+ \def\nextii@##1\mathbin@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\mathbin@{}%
+ \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
+{\uccode`4=`r \uccode`5=`e \uccode`6=`l
+ \uppercase{\gdef\mathrel@#1#2#3{\relaxnext@
+ \def\nextii@##1\mathrel@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\mathrel@{}%
+ \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
+{\uccode`5=`m \uccode`6=`a \uccode`7=`c
+ \uppercase{\gdef\macro@#1#2#3#4\macro@{\gtest@false
+ \ifx 5#1\ifx 6#2\ifx 7#3\gtest@true
+ \xdef\meaning@{\macro@@#4\macro@@}\fi\fi\fi}}}
+\def\macro@@#1->#2\macro@@{#2}
+\newcount\DOTSCASE@
+{\uccode`6=`\\ \uccode`7=`D \uccode`8=`O \uccode`9=`T \uccode`0=`S
+ \uppercase{\gdef\DOTS@#1#2#3#4#5{\gtest@false\DN@##1\DOTS@{}%
+ \ifx 6#1\ifx 7#2\ifx 8#3\ifx 9#4\ifx 0#5\let\next@\DOTS@@
+ \fi\fi\fi\fi\fi
+ \next@}}}
+{\uccode`3=`B \uccode`4=`I \uccode`5=`X
+ \uppercase{\gdef\DOTS@@#1{\relaxnext@
+ \def\nextii@##1\DOTS@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \DN@{\FN@\nextii@}%
+ \ifx 3#1\global\DOTSCASE@\z@\else
+ \ifx 4#1\global\DOTSCASE@\@ne\else
+ \ifx 5#1\global\DOTSCASE@\tw@\else\DN@##1\DOTS@{}%
+ \fi\fi\fi\next@}}}
+{\uccode`5=`\\ \uccode`6=`n \uccode`7=`o \uccode`8=`t
+ \uppercase{\gdef\not@#1#2#3#4{\relaxnext@
+ \def\nextii@##1\not@{\ifx\@sptoken\@let@token\gtest@true\fi}%
+ \gtest@false\DN@##1\not@{}%
+ \ifx 5#1\ifx 6#2\ifx 7#3\ifx 8#4\DN@{\FN@\nextii@}\fi\fi\fi
+ \fi\next@}}}
+% \end{macrocode}
+% \changes{v2.15}{2016/02/20}{macro added to strip \cs{long} during tests}
+% \begin{macrocode}
+{\uccode`9=`\l %
+ \uppercase{\gdef\striplong@#1#2#3\relax{%
+ \ifx9#2 \@xp\@xp\@xp\zap@to@space\fi}}}
+\def\zap@to@space#1 {}
+% \end{macrocode}
+% \begin{macrocode}
+\def\keybin@{\gtest@true
+ \ifx\@let@token+\else\ifx\@let@token=\else
+ \ifx\@let@token<\else\ifx\@let@token>\else
+ \ifx\@let@token-\else\ifx\@let@token*\else\ifx\@let@token:\else
+ \gtest@false\fi\fi\fi\fi\fi\fi\fi}
+% \end{macrocode}
+% Patch to ensure \cs{@ldots} is defined. (Name changed to
+% \cn{mathellipsis} in Dec 94 release of \latex/.)
+% \begin{macrocode}
+\@ifundefined{@ldots}{\def\@ldots{\mathellipsis}}{}
+% \end{macrocode}
+% \begin{macro}{\ldots}
+% \begin{macro}{\dots}
+% Reiterate the standard definition of \cs{ldots} to keep it from
+% being clobbered by the redefinition of \cs{dots}.
+% \begin{macrocode}
+\DeclareRobustCommand{\ldots}{%
+ \ifmmode \mathellipsis \else \textellipsis \fi
+}
+\DeclareRobustCommand{\dots}{%
+ \ifmmode \@xp\mdots@\else \@xp\textellipsis \fi
+}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \begin{macrocode}
+\def\tdots@{\leavevmode\unskip\relaxnext@
+ \DN@{$\m@th\@ldots\,
+ \ifx\@let@token,\,$\else\ifx\@let@token.\,$\else
+ \ifx\@let@token;\,$\else\ifx\@let@token:\,$\else
+ \ifx\@let@token?\,$\else\ifx\@let@token!\,$\else
+ $ \fi\fi\fi\fi\fi\fi}%
+ \ \FN@\next@}
+\def\mdots@{\FN@\mdots@@}
+% \end{macrocode}
+% \changes{v2.15}{2016/02/20}{Indent \cs{mdots@@} for readability and add additional tests}
+% \begin{macrocode}
+\def\mdots@@{\gdef\thedots@{\dotso@}%
+ \ifx\@let@token\boldsymbol
+ \gdef\thedots@\boldsymbol{\boldsymboldots@}%
+ \else
+ \ifx,\@let@token \gdef\thedots@{\dotsc}%
+ \else
+ \ifx\not\@let@token
+ \gdef\thedots@{\dotsb@}%
+ \else
+ \keybin@
+ \ifgtest@ % if \keybin@ test
+ \gdef\thedots@{\dotsb@}%
+ \else
+% \end{macrocode}
+% \changes{v2.15d}{2016/06/28}{Add space token to prevent runaway argument error}
+% \begin{macrocode}
+ \xdef\meaning@{\meaning\@let@token. .........}%
+% \end{macrocode}
+% In previous versions \verb|\long| macros were not seen by the lokkahead.
+% That was bad as this file uses \verb|\(re)newcommand| for \verb|\implies| etc.
+% \begin{macrocode}
+ \xdef\meaning@@{\@xp\striplong@\meaning@\relax\meaning@}%
+% \end{macrocode}
+% \begin{macrocode}
+ \@xp\math@\meaning@\math@
+ \ifgtest@ % if \mathxxx test
+ \@xp\mathch@\meaning@\mathch@
+ \ifgtest@ % if \mathchar
+ \@xp\getmathch@\meaning@\getmathch@
+ \fi % end if \mathchar
+ \else % \not \mathxxx
+% \end{macrocode}
+% Test for \verb|\Umathchar| added.
+% \begin{macrocode}
+ \@xp\Umathch@\meaning@"0"\Umathch@
+ \ifgtest@ % if \Umathchar
+ \else % else not \Umathcar
+% \end{macrocode}
+% \begin{macrocode}
+ \@xp\macro@\meaning@@\macro@
+ \ifgtest@ % if macro test
+ \@xp\not@\meaning@\not@
+ \ifgtest@ % if macro starts \not test
+ \gdef\thedots@{\dotsb@}%
+ \else% else not \not
+ \@xp\DOTS@\meaning@\DOTS@
+ \ifgtest@ % \if DOTS
+ \ifcase\number\DOTSCASE@ %ifcase dots
+ \gdef\thedots@{\dotsb@}%
+ \or\gdef\thedots@{\dotsi}\else
+ \fi % endifcase dots
+ \else % not macro starts \DOTS
+ \@xp\math@\meaning@\math@
+ \ifgtest@ % \if macro starts \mathxxxx
+ \@xp\mathbin@\meaning@\mathbin@
+ \ifgtest@ % if macro starts \mathbin
+ \gdef\thedots@{\dotsb@}%
+ \else % not macro starting \mathbin
+ \@xp\mathrel@\meaning@\mathrel@
+ \ifgtest@ % if macro starts \mathrel
+ \gdef\thedots@{\dotsb@}%
+ \fi % endif macro starts \mathrel (no else)
+ \fi % endif macro starts \mathbin
+ \fi % endif macro starts with \mathxxx (no else)
+ \fi % endif macro starts \DOTS else
+ \fi % end macro starting \not \ifgtest@ test (no else)
+% \end{macrocode}
+% Additional test for a catcode 12 character.
+% \begin{macrocode}
+ \else
+ \@xp\thecharacter@\meaning@\thecharacter@
+% \end{macrocode}
+% \begin{macrocode}
+ \fi % end macro \ifgtest@ test (no else)
+ \fi % end if \Umathchar test
+ \fi % end \math@ \ifgtest@
+ \fi % end \keybin@ \ifgtest@ test (no else)
+ \fi % end if \not (no else)
+ \fi % end if comma (no else)
+ \fi % end if boldsymbol (no else)
+ \thedots@}
+% \end{macrocode}
+%
+% The \qc{\=} character is necessary in the two \cs{let} assignments
+% in \cs{boldsymboldots@}, because the symbol we are making
+% bold might be an \qc{\=} sign.
+% \begin{macrocode}
+\def\boldsymboldots@#1{%
+ \bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
+ \boldsymbol#1\bold@false}
+% \end{macrocode}
+%
+% The definition of \cs{@cdots} is merely the \fn{plain.tex}
+% definition of \cs{cdots}.
+% \begin{macrocode}
+\ams@def\@cdots{\mathinner{\cdotp\cdotp\cdotp}}
+\newcommand{\dotsi}{\!\@cdots}
+\let\dotsb@\@cdots
+% \end{macrocode}
+%
+% If any new right delimiters are defined, they would need to be
+% added to the definition of \cs{rightdelim@} in order for \cn{dots}
+% to work properly in all cases.
+% \begin{macrocode}
+\def\rightdelim@{\gtest@true
+ \ifx\@let@token)\else
+ \ifx\@let@token]\else
+ \ifx\@let@token\rbrack\else
+ \ifx\@let@token\}\else
+ \ifx\@let@token\rbrace\else
+ \ifx\@let@token\rangle\else
+ \ifx\@let@token\rceil\else
+ \ifx\@let@token\rfloor\else
+ \ifx\@let@token\rgroup\else
+ \ifx\@let@token\rmoustache\else
+ \ifx\@let@token\right\else
+ \ifx\@let@token\bigr\else
+ \ifx\@let@token\biggr\else
+ \ifx\@let@token\Bigr\else
+ \ifx\@let@token\Biggr\else\gtest@false
+ \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
+\def\extra@{%
+ \rightdelim@\ifgtest@
+ \else\ifx\@let@token$\gtest@true
+ \else\xdef\meaning@{\meaning\@let@token..........}%
+ \@xp\macro@\meaning@\macro@\ifgtest@
+ \@xp\DOTS@\meaning@\DOTS@
+ \ifgtest@
+ \ifnum\DOTSCASE@=\tw@\gtest@true\else\gtest@false
+ \fi\fi\fi\fi\fi}
+\newif\ifbold@
+\def\dotso@{\relaxnext@
+ \ifbold@
+ \let\@let@token\delayed@
+ \def\nextii@{\extra@\@ldots\ifgtest@\,\fi}%
+ \else
+ \def\nextii@{\DN@{\extra@\@ldots\ifgtest@\,\fi}\FN@\next@}%
+ \fi
+ \nextii@}
+% \end{macrocode}
+% Why not save some tokens? (space vs. time).
+% \begin{macrocode}
+\def\extrap@#1{%
+ \DN@{#1\,}%
+ \ifx\@let@token,\else
+ \ifx\@let@token;\else
+ \ifx\@let@token.\else\extra@
+ \ifgtest@\else
+ \let\next@#1\fi\fi\fi\fi\next@}
+% \end{macrocode}
+%
+% \begin{macro}{\cdots}
+% \begin{macro}{\dotsb}
+% \begin{macro}{\dotsm}
+% \begin{macro}{\dotso}
+% \begin{macro}{\dotsc}
+% The \cn{cdots} command.
+% \begin{macrocode}
+\ams@DeclareRobustCommand{\cdots}{\DN@{\extrap@\@cdots}\FN@\next@}
+\let\dotsb\cdots
+\let\dotsm\cdots
+\DeclareRobustCommand{\dotso}{\relax
+ \ifmmode \DN@{\extrap@\@ldots}%
+ \else \let\next@\tdots@\fi
+ \FN@\next@}
+\DeclareRobustCommand{\dotsc}{%
+ \DN@{\ifx\@let@token;\@ldots\,%
+ \else \ifx\@let@token.\@ldots\,%
+ \else \extra@\@ldots \ifgtest@\,\fi
+ \fi\fi}%
+ \FN@\next@}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\longrightarrow}
+% \begin{macro}{\Longrightarrow}
+% \begin{macro}{\longleftarrow}
+% \begin{macro}{\Longleftarrow}
+% \begin{macro}{\longleftrightarrow}
+% \begin{macro}{\Longleftrightarrow}
+% \begin{macro}{\mapsto}
+% \begin{macro}{\longmapsto}
+% \begin{macro}{\hookrightarrow}
+% \begin{macro}{\hookleftarrow}
+% \begin{macro}{\iff}
+% Various arrows.
+% \begin{macrocode}
+\renewcommand{\longrightarrow}{%
+ \DOTSB\protect\relbar\protect\joinrel\rightarrow}
+\renewcommand{\Longrightarrow}{%
+ \DOTSB\protect\Relbar\protect\joinrel\Rightarrow}
+\renewcommand{\longleftarrow}{%
+ \DOTSB\leftarrow\protect\joinrel\protect\relbar}
+\renewcommand{\Longleftarrow}{%
+ \DOTSB\Leftarrow\protect\joinrel\protect\Relbar}
+\renewcommand{\longleftrightarrow}{\DOTSB\leftarrow\joinrel\rightarrow}
+\renewcommand{\Longleftrightarrow}{\DOTSB\Leftarrow\joinrel\Rightarrow}
+\renewcommand{\mapsto}{\DOTSB\mapstochar\rightarrow}
+\renewcommand{\longmapsto}{\DOTSB\mapstochar\longrightarrow}
+\renewcommand{\hookrightarrow}{\DOTSB\lhook\joinrel\rightarrow}
+\renewcommand{\hookleftarrow}{\DOTSB\leftarrow\joinrel\rhook}
+\renewcommand{\iff}{\DOTSB\;\Longleftrightarrow\;}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \begin{macro}{\doteq}
+% The \cn{doteq} command formerly used \cs{buildrel}; we avoid that
+% because it requires `\cn{over}' as part of its syntax. Use 0pt
+% instead of \cs{z@} for robustitude.
+% \begin{macrocode}
+\renewcommand{\doteq}{%
+ \DOTSB\mathrel{\mathop{\kern0pt =}\limits^{\textstyle.}}}
+% \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Integral signs}
+%
+% \begin{macro}{\if@display}
+% The straightforward \cs{ifinner} test to see if the current math
+% context is non-display, fails if, for instance, we are typesetting
+% a multiline display within an \cs{halign}, with the pieces going
+% into constructions like
+% \begin{verbatim}
+% $\displaystyle...$
+% \end{verbatim}
+% So we need a better test to find out if we are `in a display'. We
+% therefore create \cs{if@display}.
+%
+% \begin{macrocode}
+\newif\if@display
+\everydisplay\@xp{\the\everydisplay \@displaytrue}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\int}
+% \begin{macro}{\oint}
+% \begin{macro}{\iint}
+% \begin{macro}{\iiint}
+% \begin{macro}{\iiiint}
+% \begin{macro}{\idotsint}
+% Default value for integral limits is \cs{nolimits}, see the
+% definition of the `nointlimits' option.
+% \begin{macrocode}
+\renewcommand{\int}{\DOTSI\intop\ilimits@}
+\renewcommand{\oint}{\DOTSI\ointop\ilimits@}
+\def\intkern@{\mkern-6mu\mathchoice{\mkern-3mu}{}{}{}}
+\def\intdots@{\mathchoice{\@cdots}%
+ {{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}%
+ {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}%
+ {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
+%
+\ams@newcommand{\iint}{\DOTSI\protect\MultiIntegral{2}}
+\ams@newcommand{\iiint}{\DOTSI\protect\MultiIntegral{3}}
+\ams@newcommand{\iiiint}{\DOTSI\protect\MultiIntegral{4}}
+\newcommand{\idotsint}{\DOTSI\protect\MultiIntegral{0}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\MultiIntegral}
+% If the \cs{limits} option is applied, use \cs{mathop} and fudge
+% the left-hand space a bit to make the subscript visually centered.
+%
+% \verb'#1' is the multiplicity.
+% \begin{macrocode}
+\newcommand{\MultiIntegral}[1]{%
+ \edef\ints@c{\noexpand\intop
+ \ifnum#1=\z@\noexpand\intdots@\else\noexpand\intkern@\fi
+ \ifnum#1>\tw@\noexpand\intop\noexpand\intkern@\fi
+ \ifnum#1>\thr@@\noexpand\intop\noexpand\intkern@\fi
+ \noexpand\intop
+ \noexpand\ilimits@
+ }%
+ \futurelet\@let@token\ints@a
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+\def\ints@a{%
+ \ifx\limits\@let@token \ints@b
+ \else \ifx\displaylimits\@let@token \ints@b
+ \else\ifx\ilimits@\displaylimits \ints@b
+ \fi\fi\fi
+ \ints@c
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\ints@b{%
+ \mkern-7mu\mathchoice{\mkern-2mu}{}{}{}%
+ \mathop\bgroup
+ \mkern7mu\mathchoice{\mkern2mu}{}{}{}%
+ \let\ilimits@\egroup
+}%
+% \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Size dependent definitions}
+%
+% We now define all stuff which has to change whenever a new math
+% size is to be activated. \latex/ provides a hook called
+% |\every@math@size| to support such a need. All assignments in the
+% |\every@math@size| hook that need to take outside effect should be
+% global.
+%
+% \subsection{Struts for math}
+%
+% The various kinds of struts could use some analysis and perhaps
+% consolidation.
+%
+% For example perhaps the \cn{bBigg} delimiters could use
+% \begin{verbatim}
+% 1.2\ht\strutbox (1.8, 2.4, 3.0)
+% \end{verbatim}
+% instead of
+% \begin{verbatim}
+% 1.0\big@size (1.5, 2.0, 2.5)
+% \end{verbatim}
+% since \cs{strut} is reset with every size change [mjd, 1994/10/07].
+% But this change would introduce the possibility of changed line
+% and page breaks in existing documents, so would need to be
+% handled with care.
+%
+% \begin{macro}{\Mathstrut@}
+% \begin{macro}{\Mathstrutbox@}
+% \begin{macro}{\resetMathstrut@}
+% Here comes the code for Spivak's |\Mathstrut@|.
+% \begin{macrocode}
+\newbox\Mathstrutbox@
+\setbox\Mathstrutbox@=\hbox{}
+\def\Mathstrut@{\copy\Mathstrutbox@}
+% \end{macrocode}
+% The setting of the height and depth of the |\Mathstrutbox@| is done
+% in the |\every@math@size| hook since it depends on the height of a
+% paren. As \cs{every@math@size} is triggered by |$| after a font
+% size change, we want to avoid using another math formula |$...$| to
+% measure the math paren height; instead we go through the mathcode
+% of the \qc{\(} character. We assume that the mathcode has a leading
+% hex digit 4 indicating `open delimiter'; this allows us to make a
+% relatively simple function to get the correct font and character
+% position.
+%
+% \changes{v2.15}{2016/02/20}{Modify \cs{resetMathstrut@} for Unicode \TeX}
+% \changes{v2.15b}{2016/03/10}{Modify \cs{resetMathstrut@} for classic \TeX\ to preserve box 0}
+% Original code assuming |\mathcode| is kept for 8bit \TeX. Unicode \TeX{}
+% uses |\Umathcharnumdef| which works for xetex and luatex, which use
+% different forms for |\mathchardef|. (New luatex always reports
+% definitions using |\Umathchardef| syntax even if |\mathchardef| used.)
+%
+% The unicode version uses e-tex |\fontcharht| to avoid boxing which
+% could also be done for pdftex, but not done here.
+% \begin{macrocode}
+\ifx\Umathcharnumdef\@undefined
+% \end{macrocode}
+% Original code
+% \begin{macrocode}
+\def\resetMathstrut@{%
+ \begingroup
+ \setbox\z@\hbox{%
+ \mathchardef\@tempa\mathcode`\(\relax
+ \def\@tempb##1"##2##3{\the\textfont"##3\char"}%
+ \expandafter\@tempb\meaning\@tempa \relax
+ }%
+ \edef\@tempa{%
+ \ht\Mathstrutbox@\the\ht\z@\relax
+ \dp\Mathstrutbox@\the\dp\z@\relax}%
+ \expandafter\endgroup\@tempa
+}
+\else
+% \end{macrocode}
+% xetex/luatex version
+% \changes{v2.15a}{2016/03/03}{missing percent added}
+% \begin{macrocode}
+\def\resetMathstrut@{%
+ \begingroup
+ \Umathcharnumdef\@tempa\Umathcodenum`\(\relax
+ \def\@tempb##1"##2"##3"##4\relax{%
+ \endgroup
+ \ht\Mathstrutbox@=\fontcharht\textfont"##3 "##4\relax
+ \dp\Mathstrutbox@=\fontchardp\textfont"##3 "##4\relax}%
+ \expandafter\@tempb\meaning\@tempa \relax
+}
+% \end{macrocode}
+% \begin{macrocode}
+\fi
+% \end{macrocode}
+% These height and depth assignments are implicitly global.
+% \begin{macrocode}
+\addto@hook\every@math@size{\resetMathstrut@}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\strut@}
+% \begin{macro}{\strutbox@}
+% Next follows a special internal strut which is supposed to match
+% the height and the depth of a normal |\strut| minus
+% |\normallineskiplimit| according to M. Spivak.
+%
+% This should really go into the definition of \cs{size@update}, and
+% then the box reset could be local; but \cs{size@update} doesn't
+% have any hook and is handled in such a way that it cannot even be
+% changed except by changing \cs{set@fontsize}. So instead we put
+% \cs{reset@strutbox@} into \cs{every@math@size} and make it global.
+% Then because of some complications in the way \cs{glb@settings} and
+% \cs{check@mathfonts} work, we have to re-invoke it at the beginning
+% of every environment that might use \cs{strut@}. Fortunately this
+% can be achieved (more or less) through the \cs{spread@equation}
+% hook. [mjd,2000/03/10]
+% \begin{macrocode}
+\newbox\strutbox@
+\def\strut@{\copy\strutbox@}
+\def\reset@strutbox@{%
+ \global\setbox\strutbox@\hbox{%
+ \lower.5\normallineskiplimit
+ \vbox{\kern-\normallineskiplimit\copy\strutbox}}}
+\addto@hook\every@math@size{\reset@strutbox@}
+\AtBeginDocument{\reset@strutbox@}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Big delimiters}
+%
+% We are now going to redefine the plain \tex/ commands \cn{big},
+% \cn{bigl}, etc., to produce different results in different sizes.
+% Actually we only have to define \cn{big}, \cn{Big}, etc., since
+% they are used to construct the directional versions \cn{bigl},
+% \cn{bigr}, and the rest.
+%
+% \begin{macro}{\big}
+% \begin{macro}{\Big}
+% \begin{macro}{\bigg}
+% \begin{macro}{\Bigg}
+% To save token space we put everything into the common macro
+% |\bBigg@|. The macros are now simply a call to |\bBigg@| with a
+% factor to determine the correct height of the delimiter as an
+% argument. This code should better go into a future version of
+% the \latex/ kernel; the macro |\n@space| is then superfluous (since
+% it is only used once) and should be removed to avoid wasting hash
+% table space unnecessarily.
+% \begin{macrocode}
+\renewcommand{\big}{\bBigg@\@ne}
+\renewcommand{\Big}{\bBigg@{1.5}}
+\renewcommand{\bigg}{\bBigg@\tw@}
+\renewcommand{\Bigg}{\bBigg@{2.5}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\bBigg@}
+% Now we tackle the macro which has to do the real work. It
+% actually has two arguments, the factor and the wanted delimiter.
+% \changes{v2.17b}{2018/12/01}{Start LR-mode for \cs{bigl} and
+% friends if necessary (github/49)}
+% \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined
+\def\bBigg@#1#2{%
+% \end{macrocode}
+% We start with an extra set of braces because we want
+% constructions like |\def\bigl{\mathopen\big}| to work without the
+% overhead of extra arguments.
+% \begin{macrocode}
+ {\@mathmeasure\z@{\nulldelimiterspace\z@}%
+ {\left#2\vcenter to#1\big@size{}\right.}%
+ \box\z@}}
+\else
+\def\bBigg@#1#2{\leavevmode@ifvmode
+ {\@mathmeasure\z@{\nulldelimiterspace\z@}%
+ {\left#2\vcenter to#1\big@size{}\right.}%
+ \box\z@}}
+\fi
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\big@size}
+% |\big@size| needs to be set to 1.2 times the height of a math
+% paren. This height is already recorded in |\Mathstrutbox@|.
+% \begin{macrocode}
+\addto@hook\every@math@size{%
+ \global\big@size 1.2\ht\Mathstrutbox@
+ \global\advance\big@size 1.2\dp\Mathstrutbox@ }
+\newdimen\big@size
+% \end{macrocode}
+% \end{macro}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Math accents}
+%
+% We want to change the leading digit of math accents to be
+% \cs{accentclass@} so that it can vary according to certain internal
+% purposes.
+% \begin{macrocode}
+\def\accentclass@{7}
+\def\noaccents@{\def\accentclass@{0}}
+% \end{macrocode}
+%
+% There are a few \meta{math alphabet}s in the standard fonts where
+% we have to change the extra macros because the standard definitions
+% don't account for these accent problems. The first is for the
+% \cs{mathit} command.
+% \begin{macrocode}
+\DeclareFontEncoding{OML}{}{\noaccents@}
+% \end{macrocode}
+% The next one corrects the \cs{cal} alphabet.
+% \begin{macrocode}
+\DeclareFontEncoding{OMS}{}{\noaccents@}
+% \end{macrocode}
+%
+% \begin{macro}{\dddot}
+% \begin{macro}{\ddddot}
+% Triple and quadruple dot accents.
+% \begin{macrocode}
+\ams@newcommand{\dddot}[1]{%
+ {\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont ...}\vss}}}}
+\ams@newcommand{\ddddot}[1]{%
+ {\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
+ \hbox{\normalfont....}\vss}}}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% The following code deals with support for compound accents.
+% By redefining \cs{set@mathaccent} we ensure that
+% \cn{DeclareMathAccent} will define accent commands to run our
+% \cs{mathaccentV} function instead of the primitive \cs{mathaccent}.
+% \begin{macrocode}
+\def\set@mathaccent#1#2#3#4{%
+ \xdef#2{\@nx\protect\@nx\mathaccentV
+ {\@xp\@gobble\string#2}\hexnumber@#1#4}%
+}
+% \end{macrocode}
+%
+% \begin{macro}{\hat}
+% \begin{macro}{\check}
+% \begin{macro}{\tilde}
+% \begin{macro}{\acute}
+% \begin{macro}{\grave}
+% \begin{macro}{\dot}
+% \begin{macro}{\ddot}
+% \begin{macro}{\breve}
+% \begin{macro}{\bar}
+% \begin{macro}{\vec}
+% \begin{macro}{\mathring}
+% We redefine the standard math accent commands to
+% call \cs{mathaccentV}, using the mathgroup/encoding-number
+% information embedded in their previous definitions. If the
+% definition of an accent command does not have the expected form, we
+% leave the accent command alone, but give a warning. For widehat and
+% widetilde, we need to avoid clobbering the definitions done by the
+% \pkg{amsfonts} package. Arbitrating the contention between
+% \pkg{amsmath} and \pkg{amsfonts} to allow doubling a widetilde
+% accent looks tricky, so for the time being [mjd,1999/07/19] we just
+% leave \cn{widehat} and \cn{widetilde} alone. As a result, if the
+% \pkg{amsmath} package is loaded on top of a vanilla \latex/
+% documentclass, everything runs through with no warnings. If a
+% Lucida Math or other math fonts package is loaded in addition to
+% \pkg{amsmath}, there are greater difficulties, but those are
+% addressed elsewhere.
+%
+%
+% \changes{v2.15}{2016/02/20}{Detect \cs{Umathaccent} on package load}
+% Adjust the test made at package load to recognise
+% |\Umathaccent|. Although currently it is just used to give a
+% modified warning that the accents will not be redefined.
+%
+% Note that the engines behave quite differently here, luatex
+% even without these definitions using the OpenType accent set up by
+% unicode-math stacks |\hat{hat{f}}| correctly but xetex acts like
+% classic tex and needs this adjustment. This difference is not
+% addressed here at all.
+%
+% This test is just at package loading and has no affect on the
+% definitions used in 8bit TeX.
+% \begin{macrocode}
+%\def\@tempa#1{\@xp\@tempb\meaning#1\@nil#1}
+% \end{macrocode}
+% The extended definition below tests if the accent is already
+% robust (as newer \LaTeX{} kernels do this by default) and if so
+% picks up the robust definition. However, as of
+% now it still redefines it to be non-robust.
+% \begin{macrocode}
+\def\@tempa#1{%
+ \@ifundefined{\@xp\@gobble\string#1\space}%
+ {\@xp\@tempb\meaning#1\@nil#1}%
+ {\@xp\@xp\@xp\@tempb\@xp\meaning
+ \csname\@xp\@gobble\string#1\space\endcsname\@nil#1}%
+}
+\def\@tempb#1>#2#3 #4\@nil#5{%
+ \@xp\ifx\csname#3\endcsname\mathaccent
+ \@tempc#4?"7777\@nil#5%
+ \else
+ \@xp\ifx\csname#3\endcsname\Umathaccent
+ \@tempd#4\@nil#5%
+ \else
+ \PackageWarningNoLine{amsmath}{%
+ Unable to redefine math accent \string#5}%
+ \fi\fi}
+\def\@tempc#1"#2#3#4#5#6\@nil#7{%
+ \chardef\@tempd="#3\relax\set@mathaccent\@tempd{#7}{#2}{#4#5}}
+\def\@tempd#1\@nil#2{%
+ \PackageWarningNoLine{amsmath}{%
+ Unable to redefine \string\Umathaccent\space\string#2}%
+}
+% \end{macrocode}
+% \begin{macrocode}
+\@tempa{\hat}
+\@tempa{\check}
+\@tempa{\tilde}
+\@tempa{\acute}
+\@tempa{\grave}
+\@tempa{\dot}
+\@tempa{\ddot}
+\@tempa{\breve}
+\@tempa{\bar}
+\@tempa{\vec}
+\@ifundefined{mathring}{%
+ \DeclareMathAccent{\mathring}{\mathalpha}{operators}{"17}
+}{%
+ \@tempa{\mathring}
+}
+%%\@tempa\widetilde
+%%\@tempa\widehat
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% Regression testing of amsmath 2.0 showed that in some documents
+% there occurred fragments of the form
+% \begin{verbatim}
+% \hat\mathcal{G}
+% \end{verbatim}
+% This is not at all correct syntax for the argument of a \latex/
+% command but it produced the intended result anyway because of the
+% internal syntax of the \cs{mathaccent} primitive. With
+% \cs{mathaccentV}, it will yield an error message. We therefore do a
+% special check for such syntax problems in order to make the error
+% message more informative. (dmj: ??????)
+% \begin{macrocode}
+\newcommand{\acc@check}{}
+\newcommand{\acc@error}{}
+\def\acc@check{\@ifnextchar\@empty\relax\acc@error}
+% \end{macrocode}
+% We put most of the tokens in a separate macro so they do not get
+% scanned unless they are actually needed.
+% \begin{macrocode}
+\def\acc@error{%
+ \@amsmath@err{%
+ Improper argument for math accent:\MessageBreak
+ Extra braces must be added to prevent wrong output%
+ }\@ehc
+}
+% \end{macrocode}
+%
+% For \cs{mathaccentV} part of the processing is dependent on the
+% depth of nesting of math accent commands. We introduce a dedicated
+% counter for this instead of using chardef because we want to
+% increment/decrement it during processing, and incrementing a
+% chardef integer is more work.
+% \begin{macrocode}
+\newcount\macc@depth
+% \end{macrocode}
+%
+% Provide this function in case it is not already available.
+% \begin{macrocode}
+\long\def\@gobblethree#1#2#3{}
+% \end{macrocode}
+%
+% The \cs{mathaccentV} function first counts the number of nested
+% math accents by setting the argument in a throw-away box. (This is
+% not as risky as such an operation would normally be because the
+% argument is generally either a simple math symbol or a nested math
+% accent call with a simple math symbol at the bottom of the
+% nesting.)
+%
+% There are two benefits from counting the nesting levels first
+% before doing anything else: (1) we can fall back to a simple
+% \cs{mathaccent} call if the nesting depth is 1, and (2) if the
+% nesting depth is greater than 1, we would like to be able to tell
+% when we have reached the lowest level, because at that point we
+% want to save the argument for later use and place an accent on top
+% of a phantom copy.
+%
+% When we have multiple accents, they will be placed on top of the
+% invisible box, followed by some suitable kerns, then a visible copy
+% of the nucleus. To see why, let us look at what goes wrong with a
+% double application of the \cs{mathaccent} primitive. The standard
+% definition of \cs{hat} is \verb'\mathaccent"705E', so
+% \verb'\hat{\hat{F}}' expands to
+%\begin{verbatim}
+%\mathaccent"705E{\mathaccent"705E{F}}
+%\end{verbatim}
+% The result of this operation is
+%\begin{verbatim}
+%\vbox(12.11111+0.0)x7.81946
+%.\hbox(6.94444+0.0)x0.0, shifted 1.40973
+%..\OT1/cmr/m/n/10 ^
+%.\kern-4.30554
+%.\vbox(9.47221+0.0)x7.81946
+%..\hbox(6.94444+0.0)x0.0, shifted 2.24309
+%...\OT1/cmr/m/n/10 ^
+%..\kern-4.30554
+%..\hbox(6.83331+0.0)x7.81946
+%...\OML/cmm/m/it/10 F
+%\end{verbatim}
+% \tex/ starts by constructing a vbox with the hat character on top
+% of the F. Then it puts another hat character on top of the vbox;
+% but without skew information, because that is only applied by
+% \cs{mathaccent} when the base object is a simple symbol. So the
+% first accent is skewed to the correct position but all later
+% accents are not. By the way, the actual width of the F in the above
+% example is less than 7.81946; the box in which it is packed was
+% automatically lengthened by the width of the F's italic correction
+% (without actually putting in a kern for it).
+%
+% To get the second accent shifted farther to the right we
+% artificially increase the width of the innermost box and add
+% a compensating kern afterward. Furthermore, to get proper placement
+% of a following subscript or superscript, we take the base symbol
+% out, leaving a phantom in its place, and print it by itself
+% following the kern. We then need to increase the kern amount to
+% move the base character backward under the accents again.
+% Here is what the results look like:
+%\begin{verbatim}
+%\vbox(12.11111+0.0)x9.48618
+%.\hbox(6.94444+0.0)x0.0, shifted 2.24309
+%..\OT1/cmr/m/n/10 ^
+%.\kern-4.30554
+%.\vbox(9.47221+0.0)x9.48618
+%..\hbox(6.94444+0.0)x0.0, shifted 2.24309
+%...\OT1/cmr/m/n/10 ^
+%..\kern-4.30554
+%..\hbox(6.83331+0.0)x9.48618
+%...\hbox(6.83331+0.0)x7.81946
+%...\kern 1.66672
+%\kern -9.48618
+%\OML/cmm/m/it/10 F
+%\end{verbatim}
+%
+% Much of this implementation is based on code from the \pkg{accents}
+% package of Javier Bezos. I added the test to revert to a simple
+% \cs{mathaccent} when accents are not nested, and some other
+% refinements to reduce the number of kerns used (to conserve box
+% memory) and the number of cycles through \cs{mathchoice} (to make
+% things run a little faster). It was all rather difficult and my
+% first two attempts had serious bugs but I hope and believe that
+% this version will do better. [mjd,2000/03/15]
+%
+% The \qq{V} in \cs{mathaccentV} is just an indication that it takes
+% five arguments. It is important that the name includes
+% \texttt{mathaccent}, otherwise \cs{DeclareMathAccent} will balk at
+% redefining one of our accent commands, for example when an
+% alternative math font package is loaded.
+% \begin{macrocode}
+\def\mathaccentV#1#2#3#4#5{%
+ \ifmmode
+ \gdef\macc@tmp{\macc@depth\@ne}%
+ \setbox\z@\hbox{%
+ \let\mathaccentV\macc@test
+ \let\use@mathgroup\@gobbletwo \let\select@group\@gobblethree
+ \frozen@everymath{}$#5$%
+ }%
+ \macc@tmp
+ \ifnum\macc@depth=\@ne
+ \global\let\macc@nucleus\@empty
+ \mathaccent"\accentclass@
+ \else
+ \@xp\macc@nested
+ \fi
+ #2#3#4{#5}%
+ \macc@nucleus
+ \else
+ \@xp\nonmatherr@\csname#1\endcsname
+ \fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\macc@test#1#2#3#4{\xdef\macc@tmp{\macc@tmp\advance\macc@depth\@ne}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\macc@group{-1}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\macc@nested#1#2#3#4{%
+ \begingroup
+ \let\math@bgroup\@empty \let\math@egroup\macc@set@skewchar
+ \mathsurround\z@ \frozen@everymath{\mathgroup\macc@group\relax}%
+ \macc@set@skewchar\relax
+ \let\mathaccentV\macc@nested@a
+ \macc@nested@a\relax#1#2#3{#4}%
+ \endgroup
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\macc@palette\mathpalette
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\macc@nested@a#1#2#3#4#5{%
+% \end{macrocode}
+% This test saves some work that would otherwise be always repeated
+% fourfold thanks to \cs{mathchoice}.
+% \begin{macrocode}
+ \ifnum\macc@group=\mathgroup
+ \else \macc@set@skewchar\relax \edef\macc@group{\the\mathgroup}%
+ \fi
+ \mathchardef\macc@code "\accentclass@ #2#3#4\relax
+ \macc@palette\macc@a{#5}%
+}
+% \end{macrocode}
+%
+% The reason that \cs{macc@set@skewchar} takes an argument is so that
+% it can serve as a direct substitute for \cs{math@egroup}, in
+% addition to being used separately.
+%
+% Setting a skewchar with this method works for symbols of variable
+% mathgroup (class 7, letters and numbers) but not necessarily for
+% special symbols like \cn{partial} or \cs{xi} whose mathgroup
+% doesn't change; fortunately the most commonly used ones come from
+% mathgroup one, which is the fall-back mathgroup for skewchar.
+% \begin{macrocode}
+\def\macc@set@skewchar#1{%
+ \begingroup
+ \ifnum\mathgroup=\m@ne \let\@tempa\@ne
+ \else
+ \ifnum\skewchar\textfont\mathgroup=\m@ne \let\@tempa\@ne
+ \else \let\@tempa\mathgroup
+ \fi
+ \fi
+ \count@=\skewchar\textfont\@tempa
+ \advance\count@"7100
+ \edef\@tempa{\endgroup
+ \mathchardef\noexpand\macc@skewchar=\number\count@\relax}%
+ \@tempa
+ #1%
+}
+% \end{macrocode}
+%
+% Arg1 is math-style, arg2 is accent base object. We assume that math
+% style doesn't change within the nested group of accents; this means
+% we can set \cs{macc@style} only once and redefine \cs{macc@palette}
+% to use it, in order to run \cs{mathchoice} only once instead of
+% multiplying the calls exponentially as the nesting level increases.
+% \begin{macrocode}
+\def\macc@a#1#2{%
+ \begingroup
+ \let\macc@style#1\relax
+ \def\macc@palette##1{##1\macc@style}%
+ \advance\macc@depth\m@ne
+ \ifnum\macc@depth=\z@
+ \gdef\macc@nucleus{#2}%
+% \end{macrocode}
+% Extra \cs{@empty} tokens are to prevent low-level \tex/ errors from
+% the potential syntactic error that \cs{acc@check} checks for.
+% \begin{macrocode}
+ \setbox\z@\hbox{$#1#2\@empty{}\macc@skewchar$}%
+ \setbox\tw@\hbox{$#1#2\@empty\macc@skewchar$}%
+ \dimen@\tw@\wd\tw@ \advance\dimen@-\tw@\wd\z@
+ \xdef\macc@kerna{\the\dimen@\relax}%
+ \setbox4\hbox{$#1#2\acc@check\@empty$}%
+ \global\setbox\@ne\hbox to\wd4{}%
+ \ht\@ne\ht4 \dp\@ne\dp4
+ \xdef\macc@kernb{\the\wd4\relax}%
+ \mathaccent\macc@code{\box\@ne\kern\macc@kerna}%
+ \else
+ \mathaccent\macc@code{\let\macc@adjust\@empty #1#2\@empty}%
+ \macc@adjust
+ \fi
+ \endgroup
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\macc@adjust{%
+ \dimen@\macc@kerna\advance\dimen@\macc@kernb
+ \kern-\dimen@
+}
+% \end{macrocode}
+%
+% The commands \cs{Hat}, \cs{Tilde}, \ldots, are supported as
+% synonyms of \cs{hat}, \cs{tilde}, \ldots, for backward
+% compatibility.
+% \begin{macrocode}
+\def\Hat{\hat}
+\def\Check{\check}
+\def\Tilde{\tilde}
+\def\Acute{\acute}
+\def\Grave{\grave}
+\def\Dot{\dot}
+\def\Ddot{\ddot}
+\def\Breve{\breve}
+\def\Bar{\bar}
+\def\Vec{\vec}
+% \end{macrocode}
+%
+% This error message about math mode is used several times so we make
+% an abbreviation for it.
+% \begin{macrocode}
+\def\nonmatherr@#1{\@amsmath@err{\protect
+ #1 allowed only in math mode}\@ehd}
+% \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Mods, continued fractions, etc.}
+%
+% \begin{macro}{\bmod}
+% \begin{macro}{\pmod}
+% \begin{macro}{\pod}
+% \begin{macro}{\mod}
+% The commands \cn{bmod}, \cn{pmod}, \cn{pod}, \cn{mod} aren't
+% currently robust. [mjd, 1994/09/05]
+% \begin{macrocode}
+\renewcommand{\bmod}{\nonscript\mskip-\medmuskip\mkern5mu\mathbin
+ {\operator@font mod}\penalty900
+ \mkern5mu\nonscript\mskip-\medmuskip}
+\newcommand{\pod}[1]{\allowbreak
+ \if@display\mkern18mu\else\mkern8mu\fi(#1)}
+\renewcommand{\pmod}[1]{\pod{{\operator@font mod}\mkern6mu#1}}
+\newcommand{\mod}[1]{\allowbreak\if@display\mkern18mu
+ \else\mkern12mu\fi{\operator@font mod}\,\,#1}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\cfrac}
+% Continued fractions. The optional arg l or r controls horizontal
+% placement of the numerators. The |\kern-\nulldelimiterspace|
+% is needed in the definition if we want the right-hand sides of the
+% fraction rules to line up. The \cs{strut} keeps the numerator of
+% a subsidiary cfrac from coming too close to the fraction rule above
+% it.
+% \begin{macrocode}
+\newcommand{\cfrac}[3][c]{{\displaystyle\frac{%
+ \strut\ifx r#1\hfill\fi#2\ifx l#1\hfill\fi}{#3}}%
+ \kern-\nulldelimiterspace}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\overset}
+% \begin{macro}{\underset}
+% \cn{overset} and \cn{underset} put symbols above, respectively
+% below, a symbol that is not a \cs{mathop} and therefore does not
+% naturally accept limits. \cs{binrel@@} uses information collected
+% by \cs{binrel@} to make the resulting construction be of type
+% mathrel or mathbin if the base symbol is either of those types.
+% \begin{macrocode}
+\newcommand{\overset}[2]{\binrel@{#2}%
+ \binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newcommand{\underset}[2]{\binrel@{#2}%
+ \binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \begin{macro}{\overunderset}
+% This is the combination of the previous two commands which is
+% something that is sometimes needed.
+% \changes{v2.17c}{FMi}{New command \cs{overunderset}}
+% \begin{macrocode}
+\newcommand{\overunderset}[3]{\binrel@{#3}%
+ \binrel@@{\mathop{\kern\z@#3}\limits^{#1}_{#2}}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\sideset}
+% \cn{sideset} allows placing `adscript' symbols at the four
+% corners of a \cs{mathop}, \emph{in addition to} limits. Left-side
+% adscripts go into arg \arg{1}, in the form |_{...}^{...}|, and
+% right-side adscripts go into arg \arg{2}.
+%
+% As currently written [mjd, 1995/01/21] this is pretty haphazard.
+% In order to really make it work properly in full generality we'd
+% have to read and measure the top and bottom limits and use
+% mathchoice to always get the right mathstyle for each piece,
+% etc., etc.
+% \begin{macrocode}
+\newcommand{\sideset}[3]{%
+ \@mathmeasure\z@\displaystyle{#3}%
+% \end{macrocode}
+% Use a global box assignment here since the depth override is
+% implicitly global. Then move the constructed box to a local box
+% register (2) to ensure it won't get destroyed during the next two
+% mathmeasure statements. This precaution may be more extreme than
+% necessary in practice.
+% \begin{macrocode}
+ \global\setbox\@ne\vbox to\ht\z@{}\dp\@ne\dp\z@
+ \setbox\tw@\box\@ne
+ \@mathmeasure4\displaystyle{\copy\tw@#1}%
+ \@mathmeasure6\displaystyle{#3\nolimits#2}%
+ \dimen@-\wd6 \advance\dimen@\wd4 \advance\dimen@\wd\z@
+ \hbox to\dimen@{}\mathop{\kern-\dimen@\box4\box6}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\smash}
+% We add to the \cn{smash} command an optional argument
+% denoting the part of the formula to be smashed.
+% \changes{v2.17b}{2018/12/01}{Start LR-mode for \cs{smash}
+% if necessary (github/49)}
+% \begin{macrocode}
+\ifx\leavevmode@ifvmode\@undefined
+\renewcommand{\smash}[1][tb]{%
+ \def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
+ \edef\finsm@sh{\csname mb@#1\endcsname\z@\z@\box\z@}%
+ \ifmmode \@xp\mathpalette\@xp\mathsm@sh
+ \else \@xp\makesm@sh
+ \fi
+}
+\else
+\renewcommand{\smash}[1][tb]{%
+ \def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
+ \edef\finsm@sh{\csname mb@#1\endcsname\z@\z@ \leavevmode@ifvmode\box\z@}%
+ \ifmmode \@xp\mathpalette\@xp\mathsm@sh
+ \else \@xp\makesm@sh
+ \fi
+}
+\fi
+% \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Extensible arrows}
+%
+% The minus sign used in constructing these arrow fills is smashed so
+% that superscripts above the arrows won't be too high. This
+% primarily affects the \cn{xleftarrow} and \cn{xrightarrow} arrows.
+%
+% \begin{macrocode}
+\mathchardef\std@minus\mathcode`\-\relax
+\mathchardef\std@equal\mathcode`\=\relax
+% \end{macrocode}
+% In case some alternative math fonts are loaded later:
+% \begin{macrocode}
+\AtBeginDocument{%
+ \mathchardef\std@minus\mathcode`\-\relax
+ \mathchardef\std@equal\mathcode`\=\relax
+}
+% \end{macrocode}
+%
+% \begin{macro}{\relbar}
+% \begin{macro}{\Relbar}
+% \begin{macrocode}
+\ams@def\relbar{\mathrel{\mathpalette\mathsm@sh\std@minus}}
+\ams@def\Relbar{\mathrel\std@equal}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macrocode}
+\def\arrowfill@#1#2#3#4{%
+ $\m@th\thickmuskip0mu\medmuskip\thickmuskip\thinmuskip\thickmuskip
+ \relax#4#1\mkern-7mu%
+ \cleaders\hbox{$#4\mkern-2mu#2\mkern-2mu$}\hfill
+ \mkern-7mu#3$%
+}
+\def\leftarrowfill@{\arrowfill@\leftarrow\relbar\relbar}
+\def\rightarrowfill@{\arrowfill@\relbar\relbar\rightarrow}
+\def\leftrightarrowfill@{\arrowfill@\leftarrow\relbar\rightarrow}
+\def\Leftarrowfill@{\arrowfill@\Leftarrow\Relbar\Relbar}
+\def\Rightarrowfill@{\arrowfill@\Relbar\Relbar\Rightarrow}
+\def\Leftrightarrowfill@{\arrowfill@\Leftarrow\Relbar\Rightarrow}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\overarrow@#1#2#3{\vbox{\ialign{##\crcr#1#2\crcr
+ \noalign{\nointerlineskip}$\m@th\hfil#2#3\hfil$\crcr}}}
+\ams@renewcommand{\overrightarrow}{%
+ \mathpalette{\overarrow@\rightarrowfill@}}
+\ams@renewcommand{\overleftarrow}{%
+ \mathpalette{\overarrow@\leftarrowfill@}}
+\ams@newcommand{\overleftrightarrow}{%
+ \mathpalette{\overarrow@\leftrightarrowfill@}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\underarrow@#1#2#3{%
+ \vtop{\ialign{##\crcr$\m@th\hfil#2#3\hfil$\crcr
+ \noalign{\nointerlineskip\kern1.3\ex@}#1#2\crcr}}}
+\ams@newcommand{\underrightarrow}{%
+ \mathpalette{\underarrow@\rightarrowfill@}}
+\ams@newcommand{\underleftarrow}{%
+ \mathpalette{\underarrow@\leftarrowfill@}}
+\ams@newcommand{\underleftrightarrow}{%
+ \mathpalette{\underarrow@\leftrightarrowfill@}}
+% \end{macrocode}
+%
+% \begin{macrocode}
+%\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}}
+\def\ext@arrow#1#2#3#4#5#6#7{%
+ \mathrel{\mathop{%
+% \end{macrocode}
+% Measure the superscript and subscript.
+% \begin{macrocode}
+ \setbox\z@\hbox{#5\displaystyle}%
+ \setbox\tw@\vbox{\m@th
+ \hbox{$\scriptstyle\mkern#3mu{#6}\mkern#4mu$}%
+ \hbox{$\scriptstyle\mkern#3mu{#7}\mkern#4mu$}%
+ \copy\z@
+ }%
+ \hbox to\wd\tw@{\unhbox\z@}}%
+% \end{macrocode}
+% We don't want to place an empty subscript since that will produce
+% too much blank space below the arrow.
+% \begin{macrocode}
+ \limits
+ \@ifnotempty{#7}{^{\if0#1\else\mkern#1mu\fi
+ #7\if0#2\else\mkern#2mu\fi}}%
+ \@ifnotempty{#6}{_{\if0#1\else\mkern#1mu\fi
+ #6\if0#2\else\mkern#2mu\fi}}}%
+}
+% \end{macrocode}
+%
+% Some extensible arrows to serve as mathrels and taking
+% sub/superscripts. These commands are robust because they take an
+% optional argument.
+% \begin{macrocode}
+\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}}
+\newcommand{\xleftarrow}[2][]{\ext@arrow 3095\leftarrowfill@{#1}{#2}}
+% \end{macrocode}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Array-related environments}
+% \subsection{Remarks}
+%
+% Because these environments can be nested within the equation
+% structures that allow \cn{tag}, there is some cross-influence in
+% the internal workings of the \cn{\\} command.
+%
+% \subsection{The \env{subarray} environment and \cn{substack} command}
+%
+% The \cn{substack} command can be used to set subscripts
+% and superscripts that consist of several lines. Usage:
+% \begin{verbatim}
+% X_{\substack{a=1\\b=2}}
+% \end{verbatim}
+%
+% \changes{v2.0}{1999/06/17}{Removed environment definitions: Sb, Sp}
+%
+% \begin{environment}{subarray}
+% The \env{subarray} environment makes a small-size array suitable
+% for use in a subscript or superscript. At the moment the supported
+% arguments are not the full possibilities of \env{array} but only
+% |c| or |l| for centered or left-aligned. And only one column.
+% \begin{macrocode}
+\newenvironment{subarray}[1]{%
+% \end{macrocode}
+% Note: The predecessors of \env{subarray} (\env{Sb} and \env{Sp},
+% inherited from \amstex/) used \cs{vbox} instead of \cs{vcenter}.
+% But when a multiline subscript is placed in \cs{limits} position
+% \cs{vcenter} is no worse than \cs{vbox}, and when it is placed
+% in the \cs{nolimits} position (e.g., for an integral), \cs{vcenter}
+% provides clearly better positioning than \cs{vbox}.
+% \begin{macrocode}
+ \vcenter\bgroup
+% \end{macrocode}
+% Use \cs{Let@} to set the proper meaning of the \cn{\\} and \cn{\\*}
+% commands. And restore the meaning of \cs{math@cr@@@} to \cs{cr}
+% (see above) in case \env{subarray} is used inside one of the more
+% complicated alignment macros where the meaning of \cs{math@cr@@@}
+% is different. Similarly, call \cs{default@tag} to ensure that a
+% line break here doesn't get an equation number!
+% \begin{macrocode}
+ \Let@ \restore@math@cr \default@tag
+% \end{macrocode}
+% Set the line spacing to be the same as \cs{atop} (when \cs{atop}
+% occurs in \cs{textstyle} or smaller), cf \textit{The \tex/book},
+% Appendix G.
+% \begin{macrocode}
+ \baselineskip\fontdimen10 \scriptfont\tw@
+ \advance\baselineskip\fontdimen12 \scriptfont\tw@
+ \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
+ \lineskiplimit\lineskip
+% \end{macrocode}
+% Start the \cs{vbox} \cs{halign} structure that encloses the
+% contents. Notice that we never get \cs{scriptscriptstyle}. That
+% would require a \cs{mathchoice} (ugh).
+% \begin{macrocode}
+ \ialign\bgroup\ifx c#1\hfil\fi
+ $\m@th\scriptstyle##$\hfil\crcr
+}{%
+ \crcr\egroup\egroup
+}
+% \end{macrocode}
+% \end{environment}
+%
+% \begin{macro}{\substack}
+% The \cn{substack} command is just an abbreviation for the
+% most common use of \env{subarray}.
+% \begin{macrocode}
+\newcommand{\substack}[1]{\subarray{c}#1\endsubarray}
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Matrices}
+%
+% \begin{environment}{smallmatrix}
+% \env{smallmatrix} is again an alignment, this time in a centered
+% box. The opening incantations are basically the same as those in
+% \cs{multilimits@}, followed by the alignment itself. A remark:
+% the baselineskip (|9\ex@|) used in \amstex/ is too large for
+% use in text with the usual baselineskip of $12$ or $13$ points; we
+% change it here to |6\ex@| and also adjust the \cs{lineskip}
+% and \cs{lineskiplimit} slightly to compensate. (MJD)
+% \begin{macrocode}
+\newenvironment{smallmatrix}{\null\,\vcenter\bgroup
+ \Let@\restore@math@cr\default@tag
+ \baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
+ \ialign\bgroup\hfil$\m@th\scriptstyle##$\hfil&&\thickspace\hfil
+ $\m@th\scriptstyle##$\hfil\crcr
+}{%
+ \crcr\egroup\egroup\,%
+}
+% \end{macrocode}
+% \end{environment}
+%
+% \begin{environment}{matrix}
+% The \env{matrix} environment is just an \env{array} that provides
+% up to ten centered columns, so that users don't have to give the
+% col-spec argument explicitly---unless they want some of the columns
+% noncentered, that is. The maximum number of columns is actually not
+% fixed at ten but given by the counter |MatrixCols|, and can
+% therefore be increased by changing that counter.
+%
+% The extra space of \cn{arraycolsep} that \env{array} adds on each
+% side is a waste so we remove it here (perhaps we should instead
+% remove it from \env{array} in general, but that's a harder task).
+%
+% TODO: Think about re-implementing \cn{matrix} to get rid of the
+% \cs{c@MatrixCols} limit and have hard-wired preamble that doesn't
+% have to be rebuilt each time.
+%
+% We must use \cn{renewenvironment} for \env{matrix} and
+% \env{pmatrix} because \latex/ doesn't kill the definitions found in
+% \fn{plain.tex}, even though it probably should because of their
+% foreign syntax.
+% \begin{macrocode}
+\renewenvironment{matrix}{%
+ \matrix@check\matrix\env@matrix
+}{%
+ \endarray \hskip -\arraycolsep
+}
+% \end{macrocode}
+% \end{environment}
+%
+% \begin{macro}{\env@matrix}
+%
+% \begin{macrocode}
+\def\env@matrix{\hskip -\arraycolsep
+ \let\@ifnextchar\new@ifnextchar
+ \array{*\c@MaxMatrixCols c}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\c@MaxMatrixCols}
+% \begin{macrocode}
+\newcount\c@MaxMatrixCols \c@MaxMatrixCols=10
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\matrix@check}
+% For various reasons, authors sometimes use the Plain \TeX{} form of
+% \cn{matrix} or \cn{pmatrix} in \LaTeX{} documents. If they later
+% add an invocation of the \pkg{amsmath} package to their document,
+% the Plain \TeX{} syntax would lead to rather unintelligible error
+% messages. The \cs{matrix@check} function does some checking to
+% forestall that problem.
+% \begin{macrocode}
+\def\matrix@check#1{%
+ \@xp\ifx\csname\@currenvir\endcsname#1%
+ \else\matrix@error#1%
+% \end{macrocode}
+% This error recovery is not that good but is better than the
+% infinite loop that can result from calling \cs{array} without a
+% matching \cs{endarray}. (The array setup leaves \cs{par} empty.)
+% \begin{macrocode}
+ \@xp\@gobble
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\matrix@error}
+%
+% \begin{macrocode}
+\def\matrix@error#1{%
+ \@amsmath@err{%
+Old form `\string#1' should be \string\begin{\@xp\@gobble\string#1}%
+ }{%
+`\string#1{...}' is old Plain-TeX syntax whose use is
+ill-advised in LaTeX.%
+ }%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macrocode}
+\renewenvironment{pmatrix}{%
+ \left(%
+ \matrix@check\pmatrix\env@matrix
+}{
+ \endmatrix\right)%
+}
+\newenvironment{bmatrix}{\left[\env@matrix}{\endmatrix\right]}
+\newenvironment{Bmatrix}{%
+ \left\lbrace\env@matrix
+}{%
+ \endmatrix\right\rbrace
+}
+\newenvironment{vmatrix}{\left\lvert\env@matrix}{\endmatrix\right\rvert}
+\newenvironment{Vmatrix}{\left\lVert\env@matrix}{\endmatrix\right\rVert}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\hdots\@ldots
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newcommand{\hdotsfor}[1]{%
+ \ifx[#1\@xp\shdots@for\else\hdots@for\@ne{#1}\fi}
+\newmuskip\dotsspace@
+\def\shdots@for#1]{\hdots@for{#1}}
+\def\hdots@for#1#2{\multicolumn{#2}c%
+ {\m@th\dotsspace@1.5mu\mkern-#1\dotsspace@
+ \xleaders\hbox{$\m@th\mkern#1\dotsspace@.\mkern#1\dotsspace@$}%
+ \hfill
+ \mkern-#1\dotsspace@}%
+ }
+% \end{macrocode}
+%
+% \begin{environment}{cases}
+% The easiest way to produce the \env{cases} environment is to base
+% it on the \env{array} environment. We must use
+% \cn{renewenvironment} to override the definition of \cn{cases} that
+% \latex/ (unwisely) leaves in place from \fn{plain.tex}.
+% \begin{macrocode}
+\renewenvironment{cases}{%
+ \matrix@check\cases\env@cases
+}{%
+ \endarray\right.%
+}
+\def\env@cases{%
+ \let\@ifnextchar\new@ifnextchar
+ \left\lbrace
+ \def\arraystretch{1.2}%
+ \array{@{}l@{\quad}l@{}}%
+}
+% \end{macrocode}
+% \end{environment}
+%
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Equation sub-numbering}
+%
+% \begin{macrocode}
+\newcounter{parentequation}% Counter for ``parent equation''.
+% \end{macrocode}
+%
+% We can't assume \cs{ignorespacesafterend} is defined since it was
+% not there in the earliest releases of \latex/ 2e. And we need to
+% include the \cs{global} for the same reason.
+% \begin{macrocode}
+\@ifundefined{ignorespacesafterend}{%
+ \def\ignorespacesafterend{\global\@ignoretrue}%
+}{}
+% \end{macrocode}
+%
+% \begin{environment}{subequations}
+% \begin{macrocode}
+\newenvironment{subequations}{%
+% \end{macrocode}
+% Before sending down the `equation' counter to the subordinate
+% level, add 1 using standard \cn{refstepcounter}.
+% \begin{macrocode}
+ \refstepcounter{equation}%
+% \end{macrocode}
+% Define \cn{theparentequation} equivalent to current
+% \cn{theequation}. \cn{edef} is necessary to expand the current
+% value of the equation counter. This might in rare cases cause
+% something to blow up, in which case the user needs to add
+% \cn{protect}.
+% \begin{macrocode}
+ \protected@edef\theparentequation{\theequation}%
+ \setcounter{parentequation}{\value{equation}}%
+% \end{macrocode}
+% And set the equation counter to 0, so that the normal incrementing
+% processes in the various equation environments will produce the
+% desired results.
+% \begin{macrocode}
+ \setcounter{equation}{0}%
+ \def\theequation{\theparentequation\alph{equation}}%
+ \ignorespaces
+}{%
+ \setcounter{equation}{\value{parentequation}}%
+ \ignorespacesafterend
+}
+% \end{macrocode}
+% \end{environment}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Equation numbering}
+%
+% In the multiline equation environments provided here, the task
+% of equation numbering is linked to the task of line breaking
+% in the sense that it is the \cn{\\} command that marks where an
+% equation number for the current line will be processed and added to
+% the page.
+%
+% \begin{macro}{\numberwithin}
+% Provide a convenient way to specify that equations should be
+% numbered within sections.
+% \begin{macrocode}
+\newcommand{\numberwithin}[3][\arabic]{%
+ \@ifundefined{c@#2}{\@nocounterr{#2}}{%
+ \@ifundefined{c@#3}{\@nocnterr{#3}}{%
+ \@addtoreset{#2}{#3}%
+ \@xp\xdef\csname the#2\endcsname{%
+ \@xp\@nx\csname the#3\endcsname .\@nx#1{#2}}}}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\eqref}
+% To make references to equation numbers easier, we provide
+% \cn{eqref}. We almost don't need \cn{textup}, except that
+% \cs{tagform@} doesn't supply the italic correction.
+% \begin{macrocode}
+\newcommand{\eqref}[1]{\textup{\tagform@{\ref{#1}}}}
+% \end{macrocode}
+% \end{macro}
+%
+% \subsection{Preliminary macros}
+%
+% The following macros implement the \latex/ syntax for the
+% \cn{\\} command, i.e. the possibility to add an asterisk to
+% inhibit a page break, or an optional argument to denote additional
+% vertical space. They are modelled more or less after the
+% corresponding macros for \latex/'s \env{eqnarray} and \env{array}
+% environments.
+%
+% [We can perhaps use the eqnarray mechanism if we change it so that
+% it also uses \cs{openup}.]
+%
+% \begin{macro}{\dspbrk@lvl}
+% We begin by defining the \cs{dspbrk@lvl} counter. This counter
+% records the desirability of a break after the current row, as a
+% number between $0$ and $4$. Its default value is $-1$ meaning that
+% no explicit \cn{displaybreak} command was given, and the default
+% \cs{interdisplaylinepenalty} is to be used.
+% \begin{macrocode}
+\newcount\dspbrk@lvl
+\dspbrk@lvl=-1
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\interdisplaylinepenalty}
+% We set the \cs{interdisplaylinepenalty} to $10000$.
+% \begin{macrocode}
+\interdisplaylinepenalty\@M
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\allowdisplaybreaks}
+% The \cn{allowdisplaybreaks} command. Since this is intended for use
+% outside displayed formulas (typically in the preamble), it does not
+% need to use \cs{new@ifnextchar}.
+% \begin{macrocode}
+\newcommand{\allowdisplaybreaks}[1][4]{%
+ \interdisplaylinepenalty\getdsp@pen{#1}\relax
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\getdsp@pen}
+% Modelled after \latex/'s \cs{@getpen}. We use higher numbers
+% than would normally be provided by \cs{@lowpenalty},
+% \cs{@medpenalty}, and \cs{@highpenalty}, since display
+% breaks are almost always less desirable.
+% \begin{macrocode}
+\def\getdsp@pen#1{%
+ \ifcase #1\@M \or 9999 \or 6999 \or 2999 \or \z@\fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\displaybreak}
+% \begin{macro}{\dspbrk@}
+% \begin{macro}{\dspbrk@context}
+% \begin{macro}{\nogood@displaybreak}
+% For breaks in a certain row of a alignment.
+% \begin{macrocode}
+\newcommand{\displaybreak}{\new@ifnextchar[\dspbrk@{\dspbrk@[4]}}
+\chardef\dspbrk@context=\sixt@@n
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\dspbrk@[#1]{%
+ \ifmeasuring@
+ \else
+ \ifcase\dspbrk@context % case 0 --- OK
+ \global\dspbrk@lvl #1\relax
+ \or % case 1 --- inside a box
+ \nogood@displaybreak
+ \else % other cases --- outside of a display
+ \@amsmath@err{\Invalid@@\displaybreak}\@eha
+ \fi
+ \fi
+}
+% \end{macrocode}
+%
+% This is the value of \cn{displaybreak} when it occurs inside some
+% structure where it will not work.
+% \begin{macrocode}
+\def\nogood@displaybreak{%
+ \@amsmath@err{\protect
+\displaybreak\space cannot be applied here}%
+{One of the enclosing environments creates an
+ unbreakable box\MessageBreak
+(e.g., split, aligned, gathered, ...).}%
+}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\math@cr}
+% The macro \cs{math@cr} ends a row inside one of the equation
+% environments, i.e., this is the internal name of the \cn{\\}
+% commands in these environments. As usual for this kind of macro
+% inside of alignments we insert a special brace into \tex/'s input
+% stream. The initial \cs{relax} is needed to trigger entry into the
+% \textit{u} template of the current column if the author ended the
+% current row with an empty column (i.e., the mathcr was immediately
+% preceded by an ampersand).
+% \begin{macrocode}
+\def\math@cr{\relax\iffalse{\fi\ifnum0=`}\fi
+% \end{macrocode}
+% The first step is now to check whether an asterisk follows.
+% \cs{@eqpen} is used to hold the penalty value to be put on
+% the vertical list.
+% Then we call up \cs{math@cr@} which performs the next step.
+% If an asterisk is read page breaking is inhibited.
+% \begin{macrocode}
+ \@ifstar{\global\@eqpen\@M\math@cr@}%
+% \end{macrocode}
+% Otherwise we have to check the \cs{dspbrk@lvl} value.
+% \begin{macrocode}
+ {\global\@eqpen
+ \ifnum\dspbrk@lvl <\z@ \interdisplaylinepenalty
+ \else -\@getpen\dspbrk@lvl \fi
+ \math@cr@}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@}
+% The purpose of \cs{math@cr@} is to check whether an optional
+% argument follows. If not it provides \cs{z@} as default
+% value.
+% \begin{macrocode}
+\def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@@}
+% \cs{math@cr@@} closes the special brace opened in
+% \cs{math@cr}, and calls \cs{math@cr@@@} which is supposed
+% the `real' row ending command. The meaning of this macro depends
+% on the environment in which it is used.
+% \begin{macrocode}
+\def\math@cr@@[#1]{\ifnum0=`{\fi \iffalse}\fi\math@cr@@@
+% \end{macrocode}
+% Finally we put the additional space onto the vertical list.
+% \begin{macrocode}
+ \noalign{\vskip#1\relax}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\Let@}
+% \cs{Let@} is called by all environments where \cn{\\}
+% ends a row of an alignment.
+% \begin{macrocode}
+\def\Let@{\let\\\math@cr}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\restore@math@cr}
+% We mentioned already that the exact meaning of \cs{math@cr@@@}
+% depends on the current environment. Since it is often a simple
+% \cs{cr} we provide \cs{restore@math@cr} to reset it.
+% \begin{macrocode}
+\def\restore@math@cr{\def\math@cr@@@{\cr}}
+% \end{macrocode}
+% This is also the default case.
+% \begin{macrocode}
+\restore@math@cr
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\intertext}
+% \begin{macro}{\intertext@}
+% The \cn{intertext} command is used for inserting text between the
+% rows of an alignment. It might better be done as an environment,
+% but the \cs{begingroup} from \cn{begin} would cause the
+% \cs{noalign} to fail.
+% \begin{macrocode}
+\newcommand{\intertext}{\@amsmath@err{\Invalid@@\intertext}\@eha}
+% \end{macrocode}
+% \cs{intertext@} is called by all environments that allow the use of
+% the \cn{intertext} command.
+% \begin{macrocode}
+\def\intertext@{%
+ \def\intertext##1{%
+% \end{macrocode}
+% If current mode is not vmode, the most likely reason is that the
+% writer forgot the \cn{\\} that is supposed to precede
+% \cn{intertext}. All right, then, let's try adding it our ownself.
+% But, to be slightly careful: \cn{\\} does a futurelet, and it's
+% slightly dangerous to allow a letted token to barge around loose in
+% our internal code when it has been let to a conditional token
+% like \cs{fi}. So let's interpose something in front of the \cs{fi}
+% for the futurelet to take instead. (And careful again: it has to be
+% something evanescent, not (e.g.) \cs{relax} which would cause the
+% next halign cell to fire up and keep \cs{noalign} from working.)
+% \begin{macrocode}
+ \ifvmode\else\\\@empty\fi
+ \noalign{%
+ \penalty\postdisplaypenalty\vskip\belowdisplayskip
+ \vbox{\normalbaselines
+% \end{macrocode}
+% We need to do something extra if the outside environment is a list
+% environment. I don't see offhand an elegant way to test ``are we
+% inside any list environment'' that is both easy and reliable (for
+% example, checking for zero \cs{@totalleftmargin} wouldn't catch the
+% case where \cs{@totalleftmargin} is zero but \cs{linewidth} is less
+% than \cs{columnwidth}), so it seems to me checking \cs{linewidth}
+% is the best practical solution.
+% \changes{v2.15c}{2016/05/23}{\cs{ignorespaces} at the start of the argument}
+% \begin{macrocode}
+ \ifdim\linewidth=\columnwidth
+ \else \parshape\@ne \@totalleftmargin \linewidth
+ \fi
+ \noindent\ignorespaces##1\par}%
+ \penalty\predisplaypenalty\vskip\abovedisplayskip%
+ }%
+}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{Implementing tags and labels}
+%
+% In this section we describe some of the macros needed to make the
+% \cn{tag} command work in various places. We start by defining a
+% help text to be used when a \cn{tag} command is used somewhere
+% it should not appear.
+%
+% \begin{macro}{\tag@help}
+% This is the default error help text provided when \cn{tag}
+% generates an error message.
+% Note that \cs{newhelp} generates a control sequence name
+% from the string given as its argument so that a leading
+% backslash is provided automatically.
+% \begin{macrocode}
+\newhelp\tag@help
+ {tag cannot be used at this point.\space
+ If you don't understand why^^Jyou should consult
+ the documentation.^^JBut don't worry: just continue, and I'll
+ forget what happened.}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\gobble@tag}
+% This macro is to be used when \cn{tag} should silently
+% skip its argument.
+% It is made to handle the \qc{\*}-form of \cn{tag} as well.
+% \begin{macrocode}
+\def\gobble@tag{\@ifstar\@gobble\@gobble}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\invalid@tag}
+% \cs{invalid@tag} is a macro that should be used whenever
+% \cn{tag} appears in an illegal place.
+% It sets up \cs{tag@help} (as defined above) as help message,
+% prints its argument as error message, and skips \cn{tag}'s
+% argument.
+% \begin{macrocode}
+\def\invalid@tag#1{\@amsmath@err{#1}{\the\tag@help}\gobble@tag}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\dft@tag}
+% \begin{macro}{\default@tag}
+% \cs{dft@tag} provides a convenient way to disallow the
+% use of \cn{tag} at certain points.
+% One simply has to write
+% \begin{verbatim}
+%\let\tag\dft@tag
+% \end{verbatim}
+% and the \cn{tag} command will produce an error message,
+% with a suitable error help text, and discard its argument.
+% \begin{macrocode}
+\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
+% \end{macrocode}
+% Since this is used several times we provide an abbreviation for
+% it.
+% \begin{macrocode}
+\def\default@tag{\let\tag\dft@tag}
+% \end{macrocode}
+% Since this is also the default, i.e.\ the \cn{tag} command
+% should not be used except in special places, we issue a
+% \cs{default@tag} command.
+% \begin{macrocode}
+\default@tag
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% Now that we have taken care of the case that \cn{tag} is not
+% allowed we will provide some macros to process tags appropriately.
+% As the user documentation states, a \cn{tag} command (without
+% the asterisk typesets its argument according to the document
+% styles' conventions, whereas a \cn{tag*} command typesets its
+% argument exactly as given. We define therefore the following
+% interface:
+%
+% \begin{macro}{\maketag@@}
+% \begin{macro}{\maketag@@@}
+% \begin{macro}{\tagform@}
+% \cn{tag} is supposed to call \cs{maketag@@} which checks
+% whether an asterisk follows. If this is the case it calls up
+% \cs{maketag@@@} which sets its argument `as is'. Otherwise
+% \cs{tagform@} is called to do the job. (This macro is to be
+% defined appropriately by the document style.)
+% \begin{macrocode}
+\def\maketag@@{\@ifstar\maketag@@@\tagform@}
+% \end{macrocode}
+% We define \cs{maketag@@@} to use the normal font of the document
+% text (since this is the usual practice for numbering of document
+% elements) and to put a box around the tag. Furthermore we use
+% \cs{m@th} for exceptional cases where the tag involves a
+% superscript or some such math. (Probably from an explicit use of
+% \cs{tag*} rather than from the automatic numbering.)
+% \begin{macrocode}
+\def\maketag@@@#1{\hbox{\m@th\normalfont#1}}
+% \end{macrocode}
+% We use the following default definition for \cs{tagform@}
+% that puts only parentheses around the tag.
+% \begin{macrocode}
+\def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip\@@italiccorr)}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% We need to insinuate \cs{tagform@} into \cs{@eqnnum} in case
+% \env{eqnarray} is used (probably in a document that was originally
+% written without use of the \pkg{amsmath} package).
+% \begin{macrocode}
+\iftagsleft@
+ \def\@eqnnum{\hbox to1sp{}\rlap{\normalfont\normalcolor
+ \hskip -\displaywidth\tagform@\theequation}}
+\else
+ \def\@eqnnum{{\normalfont\normalcolor \tagform@\theequation}}
+\fi
+% \end{macrocode}
+%
+% \begin{macro}{\thetag}
+% Sometimes one needs to set a literal tag according to the rules of
+% the document style. To achieve this we provide the \cn{thetag}
+% command. It typesets its argument by calling \cs{tagform@} on
+% it.
+% \begin{macrocode}
+\newcommand{\thetag}{\leavevmode\tagform@}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\df@tag}
+% \begin{macro}{\make@df@tag}
+% \begin{macro}{\make@df@tag@@}
+% \begin{macro}{\make@df@tag@@@}
+% Sometimes it is necessary for a \cn{tag} command to store a tag
+% in a safe place and to process it later, e.g., for a tag in a row
+% of an alignment where the tag can only be typeset when the
+% \cn{\\} at the end of the row was seen. Such a tag is stored in
+% the macro \cs{df@tag} (for `deferred tag'). For this purpose we
+% provide the \cs{make@df@tag} macro. It is built very similar to
+% the \cs{maketag@@} macro above.
+% \begin{macrocode}
+\let\df@tag\@empty
+\def\make@df@tag{\@ifstar\make@df@tag@@\make@df@tag@@@}
+% \end{macrocode}
+% \cs{make@df@tag} sets \cs{@currentlabel} and defines
+% \cs{df@tag} appropriately.
+%
+% To simplify the task of tracking \cs{tag} and \cs{label}
+% commands inside math display environments, we defer \cs{label}
+% commands until the tag is typeset, similar to the way that
+% \cs{tag}s themselves are deferred. This allows arbitrary
+% placement of \cs{label} and \cs{tag} commands and also means we
+% only increment the \cs{equation} counter when we really need to,
+% thus avoiding the \cs{setb@ck} nonsense that used to be required.
+%
+% \begin{macrocode}
+\def\make@df@tag@@#1{%
+ \gdef\df@tag{\maketag@@@{#1}\def\@currentlabel{#1}}}
+% \end{macrocode}
+% Autogenerated number:
+% \begin{macrocode}
+\def\make@df@tag@@@#1{\gdef\df@tag{\tagform@{#1}%
+ \toks@\@xp{\p@equation{#1}}\edef\@currentlabel{\the\toks@}}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\ltx@label}
+% \begin{macro}{\label@in@display}
+% \begin{macro}{\df@label}
+% Next, we store the default definition of \cs{label} in
+% \cs{ltx@label} and then define a new version of \cs{label} for use
+% in math display environments. \cs{label@in@display} merely issues a
+% warning message if there is already a pending label (which will be
+% discarded) and then stores the label in \cs{df@label}.
+% \begin{macrocode}
+\let\ltx@label\label
+%
+\def\label@in@display{%
+ \ifx\df@label\@empty\else
+ \@amsmath@err{Multiple \string\label's:
+ label '\df@label' will be lost}\@eha
+ \fi
+ \gdef\df@label
+}
+% \end{macrocode}
+% In case there is an enumerate inside a minipage inside an equation,
+% we need to reset \cn{label} to its normal value:
+% \begin{macrocode}
+\toks@\@xp{\@arrayparboxrestore \let\label\ltx@label}%
+\edef\@arrayboxrestore{\the\toks@}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\df@label\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\make@display@tag}
+% Now we define a macro to process \cs{tag} and \cs{label} commands
+% in various display environments. If the |@eqnsw| switch is set,
+% then we should supply an equation number; otherwise, if the
+% |@tag| switch is set, we should use the tag stored in
+% \cs{df@tag}. Finally, we process any pending \cs{label}s.
+%
+% TODO: Arguably, \cs{make@display@tag} should issue a warning
+% message if there is a \cs{label} but neither a tag nor an
+% equation number. Also, it would probably be worthwhile to
+% explore whether \cs{iftag@} could be done away with and replaced
+% by checks to see if \cs{df@tag} is empty or not.
+% \begin{macrocode}
+\def\make@display@tag{%
+ \if@eqnsw \incr@eqnum \print@eqnum
+ \else \iftag@ \df@tag \global\let\df@tag\@empty \fi
+ \fi
+% \end{macrocode}
+% Need to check the \cs{ifmeasuring@} flag otherwise the \cs{write}
+% node from \cn{label} might be discarded in a temp box and clearing
+% \cs{df@label} will keep it from being reiterated on the real
+% typesetting pass.
+% \begin{macrocode}
+ \ifmeasuring@
+ \else
+ \ifx\df@label\@empty
+ \else
+ \@xp\ltx@label\@xp{\df@label}%
+ \global\let\df@label\@empty
+ \fi
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% Now we define the special versions of \cn{tag} used within the
+% \env{align} environments.
+%
+% \begin{macro}{\tag@in@align}
+% The \cn{tag} command may only appear once in a row of
+% an alignment. Therefore we first check the switch |tag@|
+% that is set to false at the begin of every row.
+% If this switch is true a \cn{tag} was already given in this
+% row and we define \cs{next@} to expand to a call to
+% \cs{invalid@tag}.
+% \begin{macrocode}
+\def\tag@in@align{%
+ \relax
+ \iftag@
+ \DN@{\invalid@tag{Multiple \string\tag}}%
+ \else
+% \end{macrocode}
+% Otherwise we set the |tag@| switch. But there is more to
+% be done: we must also prevent the automatic generation of a
+% tag. Therefore we also reset the |@eqnsw|.
+% \begin{macrocode}
+ \global\tag@true
+% \end{macrocode}
+% Changed to \cs{nonumber}, since that seems to be all that's
+% required.---dmj, 1994/12/21
+% \begin{macrocode}
+ \nonumber
+% \end{macrocode}
+% Within a row of an \env{align} environment the \cn{tag}
+% command must not typeset the tag immediately since its
+% position can be determined only later.
+% Therefore we use the \cs{make@df@tag} macro defined
+% earlier.
+% Finally we call \cs{next@} to process the argument
+% that follows.
+% \begin{macrocode}
+ \let\next@\make@df@tag
+ \fi
+ \next@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\raisetag}
+% Usage: \cn{raisetag} \meta{dimen}
+%
+% This will modify the vertical placement of the tag of the current
+% equation by \meta{dimen}. Note that according to the current uses
+% of \cs{raise@tag} in e.g., \cs{place@tag@gather}, no adjustment
+% occurs if the tag falls in its normal position; i.e., \cn{raisetag}
+% has no effect unless the tag has already been shifted off-line.
+%
+% \begin{macrocode}
+\newcommand{\raisetag}[1]{\skip@#1\relax
+ \xdef\raise@tag{\vskip\iftagsleft@\else-\fi\the\skip@\relax}%
+}
+% \end{macrocode}
+% \cn{raise@tag} will be reemptied at the beginning of each equation,
+% which might occur at a |\begin{xxx}| or \cn{\\}.
+% \begin{macrocode}
+\let\raise@tag\@empty
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\notag}
+% For consistency we provide \cn{notag}, equivalent to
+% \cn{nonumber}. The alternative would have been to rename
+% \cn{tag} as \cn{number} to go along with \cn{nonumber},
+% but of course \cs{number} is a \tex/ primitive that should not
+% be redefined.
+% \begin{macrocode}
+\newcommand{\notag}{\nonumber}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\nonumber}
+% Need to add some additional code to \cn{nonumber} to deal with some
+% complications related to nested environments.
+% \begin{macrocode}
+\renewcommand{\nonumber}{%
+ \if@eqnsw
+ \ifx\incr@eqnum\@empty \addtocounter{equation}\m@ne \fi
+ \fi
+ \let\print@eqnum\@empty \let\incr@eqnum\@empty
+ \global\@eqnswfalse
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\print@eqnum{\tagform@\theequation}
+\def\incr@eqnum{\refstepcounter{equation}\let\incr@eqnum\@empty}
+% \end{macrocode}
+% \end{macro}
+%
+% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% \section{Multiline equation environments}
+%
+% \subsection{Remarks}
+%
+% In late 1994 David M. Jones did a thorough overhaul of these
+% environments so that the number placement and a few other aspects
+% are substantially improved over the original versions that were
+% ported essentially unchanged from \fn{amstex.tex} in 1989. Most of
+% the commentary in this section is DMJ's, and comments of any
+% significance that I added are marked by my initials and date
+% [mjd, 1995/01/11].
+%
+% \subsection{Preliminaries}
+%
+% \begin{macro}{\ifinalign@}
+% \begin{macro}{\ifingather@}
+% We define two switches that are set to true in certain
+% alignments: |inalign@| and |ingather@| inside of
+% the \env{align} and \env{gather} environments.
+% These switches are needed to control certain actions that
+% depend on the surrounding conditions, more specifically:
+% on the setting already done by the surrounding environments.
+% \begin{macrocode}
+\newif\ifinalign@
+\newif\ifingather@
+% \end{macrocode}
+% \begin{histnote}
+% Removed the \cs{ifinany@} test [mjd,1999/06/28] since it was mainly
+% used for the purpose now handled by \cs{spread@equation}.
+% \changes{v1.2g}{1999/06/28}{Removed ifinany@}
+% \end{histnote}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@arrayparboxrestore}
+% Here we must reset a few additional parameters.
+% \begin{macrocode}
+\@xp\def\@xp\@arrayparboxrestore\@xp{\@arrayparboxrestore
+ \ingather@false\inalign@false \default@tag
+ \let\spread@equation\@spread@equation
+ \let\reset@equation\@empty
+ \def\print@eqnum{\tagform@\theequation}%
+ \def\incr@eqnum{\refstepcounter{equation}\let\incr@eqnum\@empty}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\iftag@}
+% The switch |tag@| is set to false at the beginning of every
+% row and set to true by a \cn{tag} command.
+% This allows us to check whether there is more than one tag on
+% a row.
+% \begin{macrocode}
+\newif\iftag@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ifst@rred}
+% The switch |st@rred| is set to true by all starred
+% environments
+% and set to false by the unstarred versions.
+% \begin{macrocode}
+\newif\ifst@rred
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ifmeasuring@}
+% All display environments get typeset twice---once during a
+% ``measuring'' phase and then again during a ``production'' phase;
+% \cs{ifmeasuring@} will be used to determine which case we're in,
+% so we can take appropriate action.
+%
+% \begin{macrocode}
+\newif\ifmeasuring@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ifshifttag@}
+% \cs{ifshifttag@} is used by \env{gather} to communicate between
+% \cs{calc@shift@gather} and \cs{place@tag@gather} whether an
+% equation tag should be shifted to a separate line. It's also
+% used by \env{multline}.
+% \begin{macrocode}
+\newif\ifshifttag@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\row@}
+% \begin{macrocode}
+\newcount\row@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\column@}
+% The counter \cs{column@} is used by the alignment macros to
+% keep track of the current column.
+%
+% \begin{macrocode}
+\newcount\column@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\column@plus}
+% \cs{\column@plus} is a useful abbreviation.
+% \begin{macrocode}
+\def\column@plus{%
+ \global\advance\column@\@ne
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\maxfields@}
+% \begin{macrocode}
+\newcount\maxfields@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\add@amp}
+% \begin{macro}{\add@amps}
+% \begin{macrocode}
+\def\add@amp#1{\if m#1&\@xp\add@amp\fi}
+\def\add@amps#1{%
+ \begingroup
+ \count@#1\advance\count@-\column@
+ \edef\@tempa{\endgroup
+ \@xp\add@amp\romannumeral\number\count@ 000q}%
+ \@tempa
+}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\andhelp@}
+% The help text stored in \cs{andhelp@} is used for errors
+% generated by too many \qc{\&} characters in a row.
+% \begin{macrocode}
+\newhelp\andhelp@
+{An extra & here is so disastrous that you should probably exit^^J
+and fix things up.}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\eqnshift@}
+% \cs{eqnshift@} is used by \env{align} and \env{gather} as the
+% indentation of the lines of the environment from the left margin.
+% \begin{macrocode}
+\newdimen\eqnshift@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\alignsep@}
+% \begin{macrocode}
+\newdimen\alignsep@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tagshift@}
+% \begin{macrocode}
+\newdimen\tagshift@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mintagsep}
+% \cs{mintagsep} is the minimum allowable separation between an
+% equation and its tag. We set it to half a quad in
+% \cs{textfont}2, which is \tex/'s built-in value.
+% \begin{macrocode}
+\newcommand{\mintagsep}{.5\fontdimen6\textfont\tw@}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\minalignsep}
+% This should probably be a skip register [mjd,1999/06/18]
+% \begin{macrocode}
+\newcommand{\minalignsep}{10pt}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tagwidth@}
+% \begin{macrocode}
+\newdimen\tagwidth@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\totwidth@}
+% \begin{macrocode}
+\newdimen\totwidth@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lineht@}
+% The dimen register \cs{lineht@} is used to keep track of the
+% height (or depth, if tags are on the right) of a row in an
+% alignment.
+% \begin{macrocode}
+\newdimen\lineht@
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\tag@width}
+% \begin{macro}{\savetaglength@}
+% \begin{macro}{\shift@tag}
+% \begin{macro}{\tag@shifts}
+% \begin{macrocode}
+\def\tag@width#1{%
+ \ifcase\@xp#1\tag@lengths\fi
+}
+
+\def\savetaglength@{%
+ \begingroup
+ \let\or\relax
+ \xdef\tag@lengths{\tag@lengths\or \the\wdz@}%
+ \endgroup
+}
+
+\def\shift@tag#1{%
+ \ifcase\@xp#1\tag@shifts\fi\relax
+}
+
+\let\tag@shifts\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\saveshift@}
+% \begin{macrocode}
+\def\saveshift@#1{%
+ \begingroup
+ \let\or\relax
+ \xdef\tag@shifts{\or#1\tag@shifts}%
+ \endgroup
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\spread@equation}
+% This does the line-spacing adjustment that is normally wanted for
+% displayed equations. We also call \cs{reset@strutbox@} here because
+% otherwise a preceding font size change might leave \cs{strutbox@}
+% with wrong contents. This is a less-than-ideal solution but
+% probably good enough for now, until the situation can be
+% overhauled.
+% \begin{macrocode}
+\def\spread@equation{\reset@strutbox@
+ \openup\jot \let\spread@equation\@empty}
+\let\@spread@equation\spread@equation
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\displ@y}
+% \begin{macro}{\displ@y@}
+% \begin{macro}{\@display@init}
+% \cs{displ@y} is from \fn{plain.tex}, with
+% \cs{interdisplaylinepenalty} changed to \cs{@eqpen}. Also we
+% transplanted most of its internal organs to \cs{@display@init} to
+% support \cs{displ@y@} and other possibilities. Don't try to make
+% sense of these naming conventions! They are a narrowly calculated
+% mishmash of Knuth/Spivak/Lamport/Mittelbach precedents. The reason
+% for not cleaning them up and forcing all names to a consistent
+% scheme is that then in principle we'd have to do it everywhere else
+% too. And we programmers are paranoid about the side effects of name
+% changes.
+% \begin{macrocode}
+\def\displ@y{\@display@init{}}
+\def\@display@init#1{%
+ \global\dt@ptrue \spread@equation
+ \everycr{%
+ \noalign{%
+ #1%
+ \ifdt@p
+ \global\dt@pfalse
+ \vskip-\lineskiplimit
+ \vskip\normallineskiplimit
+ \else
+ \penalty\@eqpen \global\dspbrk@lvl\m@ne
+ \fi
+ }%
+ }%
+}
+% \end{macrocode}
+% \cs{displ@y@} is nearly the same; it additionally sets the |tag@|
+% switch and the \cs{column@} and \cs{dspbrk@lvl} counters to their
+% default values. The argument is normally a bit of code to empty out
+% \cs{raise@tag}, but in \env{multline} we don't want that to happen
+% in \cs{everycr}.
+% \begin{macrocode}
+\def\displ@y@{\@display@init{%
+ \global\column@\z@ \global\dspbrk@lvl\m@ne
+ \global\tag@false \global\let\raise@tag\@empty
+}}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\black@}
+% \changes{v2.17a}{2017/09/02}{add fixed width box so overfull warning generated in centred environments in lists}
+% This macro is made to produce an overfull box message and
+% possibly (depending on the value of \cs{overfullrule})
+% a rule in the margin if the total width of an alignment
+% is larger than the value of \cs{displaywidth}.
+% \begin{macrocode}
+\def\black@#1{%
+ \noalign{%
+ \ifdim#1>\displaywidth
+ \dimen@\prevdepth
+ \nointerlineskip
+ \vskip-\ht\strutbox@
+ \vskip-\dp\strutbox@
+ \vbox{\noindent\hbox to\displaywidth{\hbox to#1{\strut@\hfill}}}%
+ \prevdepth\dimen@
+ \fi
+ }%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\savecounters@}
+% \begin{macro}{\restorecounters@}
+% These are used during the measuring phase of the various display
+% math environments to save and restore the values of all \latex/
+% counters. We make these local to a group, so nested environments
+% works.
+%
+% Changed \cn{stepcounter} to |\csname c@...\endcsname| to avoid
+% overhead of ifundefined test [mjd, 1995/01/20].
+% \begin{macrocode}
+\def\savecounters@{%
+ \begingroup
+ \def\@elt##1{%
+ \global\csname c@##1\endcsname\the\csname c@##1\endcsname}%
+ \xdef\@gtempa{%
+ \cl@@ckpt
+ \let\@nx\restorecounters@\@nx\@empty
+ }%
+ \endgroup
+ \let\restorecounters@\@gtempa
+}
+%
+\let\restorecounters@\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\savealignstate@}
+% \begin{macro}{\restorealignstate@}
+% These are used to save the values of various parameters that are
+% shared by \env{align} and \env{gather} when the former is used
+% inside the latter.
+% \begin{macrocode}
+\def\savealignstate@{%
+ \begingroup
+ \let\or\relax
+ \xdef\@gtempa{%
+ \global\totwidth@\the\totwidth@
+ \global\row@\the\row@
+ \gdef\@nx\tag@lengths{\tag@lengths}%
+ \let\@nx\restorealignstate@\@nx\@empty
+ }%
+ \endgroup
+ \let\restorealignstate@\@gtempa
+}
+
+\let\restorealignstate@\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\savecolumn@}
+% \begin{macro}{\restorecolumn@}
+%
+% \begin{macrocode}
+\def\savecolumn@{%
+ \edef\restorecolumn@{%
+ \global\column@\number\column@
+ \let\@nx\restorecolumn@\@nx\@empty
+ }%
+}
+\let\restorecolumn@\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Scanning the environment's body}
+%
+% Several of the math alignment macros must scan their body twice:
+% once to determine how wide the columns are and then to actually
+% typeset them. This means that we must collect all text in this body
+% before calling the environment macros.
+%
+% \begin{macro}{\@envbody}
+% We start by defining a token register to contain the body.
+% \begin{macrocode}
+\newtoks\@envbody
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\addto@envbody}
+% Then we define a macro to add something (i.e.\ its argument) to the
+% token register \cs{@envbody}.
+% \begin{macrocode}
+\def\addto@envbody#1{\global\@envbody\@xp{\the\@envbody#1}}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\collect@body}
+% The macro \cs{collect@body} starts the scan for the |\end{...}|
+% command of the current environment. It takes a macro name as
+% argument. This macro is supposed to take the whole body of the
+% environment as its argument. For example, |\begin{align}| would
+% call |\collect@body\@align| if |@align#1{...}| is the macro that
+% sets the alignment with body \arg{1}.
+%
+% \begin{macrocode}
+\def\collect@body#1{%
+ \@envbody{\@xp#1\@xp{\the\@envbody}}%
+ \edef\process@envbody{\the\@envbody\@nx\end{\@currenvir}}%
+ \@envbody\@emptytoks \def\begin@stack{b}%
+% \end{macrocode}
+%
+% If we simply called \cs{collect@@body} directly,
+% the error message for a \cn{par} token (usually from a blank line)
+% would be
+% \begin{verbatim}
+% ! Paragraph ended before \collect@@body was complete.
+% \end{verbatim}
+% But we use a little finesse to get a more intelligible error
+% message:
+% \begin{verbatim}
+% ! Paragraph ended before \multline* was complete.
+% \end{verbatim}
+% In order to avoid using up csnames unnecessarily we use the actual
+% environment name as the name of the temporary function that is
+% \cs{let} to \cs{collect@@body}; but then in order to preserve the
+% theoretical possibility of nesting for environments that use
+% \cs{collect@body} (not currently required by any \pkg{amsmath}
+% environment [mjd,1999/06/23]), we do the \cs{let} inside a group.
+% \begin{macrocode}
+ \begingroup
+ \@xp\let\csname\@currenvir\endcsname\collect@@body
+% \end{macrocode}
+% This small twist eliminates the need for \cs{expandafter}'s in
+% \cs{collect@@body}.
+% \begin{macrocode}
+ \edef\process@envbody{\@xp\@nx\csname\@currenvir\endcsname}%
+ \process@envbody
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\push@begins}
+% When adding a piece of the current environment's contents to
+% \cs{@envbody}, we scan it to check for additional \cn{begin}
+% tokens, and add a `b' to the stack for any that we find.
+% \begin{macrocode}
+\def\push@begins#1\begin#2{%
+ \ifx\end#2\else b\@xp\push@begins\fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\collect@@body}
+% \cs{collect@@body} takes two arguments: the first will consist of
+% all text up to the next \cn{end} command, the second will be the
+% \cn{end} command's argument. If there are any extra \cn{begin}
+% commands in the body text, a marker is pushed onto a stack by the
+% \cs{push@begins} function. Empty state for this stack means that we
+% have reached the \cn{end} that matches our original \cn{begin}.
+% Otherwise we need to include the \cn{end} and its argument in the
+% material that we are adding to our environment body accumulator.
+%
+% \begin{histnote}
+% In a former implementation, the error messages resulting from a
+% typo in the environment name were unsatisfactory, because it was
+% matching of the environment name that was used to determine the end
+% of our environment body, instead of counting begin-end pairs.
+% Thanks to Lars Hellstr\"{o}m for a suggestion that led to this
+% improvement. [mjd,1999/06/23]
+% \end{histnote}
+% \begin{macrocode}
+\def\collect@@body#1\end#2{%
+ \edef\begin@stack{\push@begins#1\begin\end \@xp\@gobble\begin@stack}%
+ \ifx\@empty\begin@stack
+ \endgroup
+ \@checkend{#2}%
+ \addto@envbody{#1}%
+ \else
+ \addto@envbody{#1\end{#2}}%
+ \fi
+ \process@envbody % A little tricky! Note the grouping
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Simple aligning environments}
+%
+% \begin{macro}{\math@cr@@@aligned}
+% From tabskip we get an extra space of minalignsep after every
+% second column; but when this falls at the right edge of the whole
+% aligned structure, we need to cancel that space.
+% \begin{macrocode}
+\def\math@cr@@@aligned{%
+ \ifodd\column@ \let\next@\@empty
+ \else \def\next@{&\kern-\alignsep@}%
+ \fi
+ \next@ \cr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\start@aligned}
+% The \env{aligned} and \env{alignedat} environments are identical
+% except that the latter takes a mandatory argument to specify the
+% number of align structures, while the former allows any number of
+% align structures automatically (the use of \env{alignedat} is
+% deprecated). So, they will be defined in terms of
+% \cs{start@aligned}, which will take two arguments. The first
+% argument specifies the placement of the environments; it is
+% either |c|, |t|, or |b|. The second is the number of align
+% structures; a value of~$-1$ means that an arbitrary number are
+% allowed.
+% \begin{macrocode}
+\newcommand{\start@aligned}[2]{%
+ \RIfM@\else
+ \nonmatherr@{\begin{\@currenvir}}%
+ \fi
+ \savecolumn@ % Assumption: called inside a group
+% \end{macrocode}
+% The \cs{null} here is to keep the \cs{,} glue from causing the
+% invocation of the clause in \tex/'s built-in tag placement
+% algorithm that can cause an equation to be shifted all the way over
+% to the margin.
+% \begin{macrocode}
+ \alignedspace@left
+ \if #1t\vtop \else \if#1b \vbox \else \vcenter \fi \fi \bgroup
+ \maxfields@#2\relax
+ \ifnum\maxfields@>\m@ne
+ \multiply\maxfields@\tw@
+% \end{macrocode}
+% Introduced new \cs{math@cr@@@} so we can provide standard error
+% message for too many \qc{\&}'s in \env{alignedat}.
+% \begin{macrocode}
+ \let\math@cr@@@\math@cr@@@alignedat
+ \alignsep@\z@skip
+ \else
+ \let\math@cr@@@\math@cr@@@aligned
+ \alignsep@\minalignsep
+ \fi
+% \end{macrocode}
+% Reset the meaning of \cn{\\}.
+% \begin{macrocode}
+ \Let@ \chardef\dspbrk@context\@ne
+% \end{macrocode}
+% Restore the default definition of \cn{tag} (error message), in
+% case \env{aligned} is used inside, e.g., a \env{gather}
+% environment that accepts \cn{tag}.
+% \begin{macrocode}
+ \default@tag
+ \spread@equation % no-op if already called
+% \end{macrocode}
+% Finally we start the alignment itself. For \env{aligned} we add
+% \cs{minalignsep} after every second column to mimic the
+% behavior of \env{align}. For \env{alignedat} the user has to
+% specify interalign space explicitly.
+% \begin{macrocode}
+ \global\column@\z@
+ \ialign\bgroup
+ &\column@plus
+ \hfil
+ \strut@
+ $\m@th\displaystyle{##}$%
+ \tabskip\z@skip
+ &\column@plus
+ $\m@th\displaystyle{{}##}$%
+ \hfil
+ \tabskip\alignsep@
+ \crcr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@@@alignedat}
+% \cs{math@cr@@@alignedat} checks to make sure the user hasn't put in
+% too many \qc{\&}s in \env{alignedat}. Since \env{alignedat}
+% doesn't use \cs{displ@y@}, we also reset \cs{column@} here. Note
+% than in \env{aligned}, \cs{column@} will increase without bound,
+% since it never gets reset, but this is harmless.
+% \begin{macrocode}
+\def\math@cr@@@alignedat{%
+ \ifnum\column@>\maxfields@
+ \begingroup
+ \measuring@false
+ \@amsmath@err{Extra & on this line}%
+ {\the\andhelp@}% "An extra & here is disastrous"
+ \endgroup
+ \fi
+ \global\column@\z@
+ \cr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\alignsafe@testopt}
+% Testing for an optional argument can be really, really tricky in
+% certain complicated contexts. This we discovered by getting some
+% bug reports for uses of \env{aligned}. So here is a safer
+% form of \latex/'s \cs{@testopt} function.
+% \begin{macrocode}
+\def\alignsafe@testopt#1#2{%
+ \relax\iffalse{\fi\ifnum`}=0\fi
+ \@ifnextchar[%
+ {\let\@let@token\relax \ifnum`{=\z@\fi\iffalse}\fi#1}%
+ {\let\@let@token\relax \ifnum`{=\z@\fi\iffalse}\fi#1[#2]}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{environment}{aligned}
+% The \env{aligned} environment takes an optional argument that
+% indicates its vertical position in relation to surrounding
+% material: |t|, |c|, or |b| for top, center, or bottom.
+% \begin{macrocode}
+\newenvironment{aligned}{%
+ \let\@testopt\alignsafe@testopt
+ \aligned@a
+}{%
+ \crcr\egroup
+ \restorecolumn@
+ \egroup
+}
+\newcommand{\aligned@a}[1][c]{\start@aligned{#1}\m@ne}
+% \end{macrocode}
+% \end{environment}
+%
+% \begin{environment}{alignedat}
+% To get a top or bottom positioned \env{alignedat} structure, you
+% would write something like
+% \begin{verbatim}
+% \begin{alignedat}[t]{3}
+% \end{verbatim}
+%
+% \begin{macrocode}
+\newenvironment{alignedat}{%
+ \let\@testopt\alignsafe@testopt
+ \alignedat@a
+}{%
+ \endaligned
+}
+\newcommand{\alignedat@a}[1][c]{\start@aligned{#1}}
+% \end{macrocode}
+% \end{environment}
+%
+% \begin{environment}{gathered}
+% The \env{gathered} environment is for several lines that are
+% centered independently.
+% \begin{macrocode}
+\newenvironment{gathered}[1][c]{%
+ \RIfM@\else
+ \nonmatherr@{\begin{gathered}}%
+ \fi
+ \alignedspace@left
+ \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi \bgroup
+ \Let@ \chardef\dspbrk@context\@ne \restore@math@cr
+ \spread@equation
+ \ialign\bgroup
+ \hfil\strut@$\m@th\displaystyle##$\hfil
+ \crcr
+}{%
+ \endaligned
+}
+% \end{macrocode}
+% \end{environment}
+%
+%
+% \subsection{The \env{gather} environment}
+%
+% \begin{macro}{\start@gather}
+% \begin{macrocode}
+\def\start@gather#1{%
+ \RIfM@
+ \nomath@env
+ \DN@{\@namedef{end\@currenvir}{}\@gobble}%
+ \else
+ $$%
+ #1%
+ \ifst@rred \else \global\@eqnswtrue \fi
+ \let\next@\gather@
+ \fi
+ \collect@body\next@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{environment}{gather}
+% \begin{environment}{gather*}
+% \begin{macrocode}
+\newenvironment{gather}{%
+ \start@gather\st@rredfalse
+}{%
+ \math@cr \black@\totwidth@ \egroup
+ $$\ignorespacesafterend
+}
+
+\newenvironment{gather*}{%
+ \start@gather\st@rredtrue
+}{%
+ \endgather
+}
+% \end{macrocode}
+% \end{environment}
+% \end{environment}
+%
+% \begin{macro}{\gather@}
+% \begin{macrocode}
+\def\gather@#1{%
+ \ingather@true \let\split\insplit@
+ \let\tag\tag@in@align \let\label\label@in@display
+ \chardef\dspbrk@context\z@
+ \intertext@ \displ@y@ \Let@
+ \let\math@cr@@@\math@cr@@@gather
+ \gmeasure@{#1}%
+ \global\shifttag@false
+ \tabskip\z@skip
+ \global\row@\@ne
+ \halign to\displaywidth\bgroup
+ \strut@
+ \setboxz@h{$\m@th\displaystyle{##}$}%
+ \calc@shift@gather
+ \set@gather@field
+ \tabskip\@centering
+ &\setboxz@h{\strut@{##}}%
+ \place@tag@gather
+ \tabskip \iftagsleft@ \gdisplaywidth@ \else \z@skip \span\fi
+ \crcr
+ #1%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\gmeasure@}
+% \begin{macrocode}
+\def\gmeasure@#1{%
+ \begingroup
+ \measuring@true
+ \totwidth@\z@
+ \global\let\tag@lengths\@empty
+ \savecounters@
+ \setbox\@ne\vbox{%
+ \everycr{\noalign{\global\tag@false
+ \global\let\raise@tag\@empty \global\column@\z@}}%
+ \let\label\@gobble
+ \halign{%
+ \setboxz@h{$\m@th\displaystyle{##}$}%
+ \ifdim\wdz@>\totwidth@
+ \global\totwidth@\wdz@
+ \fi
+ &\setboxz@h{\strut@{##}}%
+ \savetaglength@
+ \crcr
+ #1%
+ \math@cr@@@
+ }%
+ }%
+ \restorecounters@
+ \if@fleqn
+ \global\advance\totwidth@\@mathmargin
+ \fi
+ \iftagsleft@
+ \ifdim\totwidth@>\displaywidth
+ \global\let\gdisplaywidth@\totwidth@
+ \else
+ \global\let\gdisplaywidth@\displaywidth
+ \fi
+ \fi
+ \endgroup
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@@@gather}
+% Modified \cs{math@cr@@@gather} so that it always puts in the
+% final field, which needs to be done under the new method for
+% determining tag placement. This is probably more efficient
+% anyway.
+%
+% \begin{macrocode}
+\def\math@cr@@@gather{%
+ \ifst@rred\nonumber\fi
+ &\relax
+ \make@display@tag
+ \ifst@rred\else\global\@eqnswtrue\fi
+% \end{macrocode}
+% We advance \cs{row@} here, rather than at the beginning of the
+% preamble, because otherwise the \env{split} environment will
+% cause \cs{row@} to be advanced twice instead of once.
+% \begin{macrocode}
+ \global\advance\row@\@ne
+ \cr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\calc@shift@gather}
+% \cs{calc@shift@gather} has must make two decisions: (1) whether the
+% equation tag for the current line should be put on a separate
+% line and (2) what the distance between the equation and the
+% equation tag should be. We implement \tex/'s built-in
+% tag-placement as well as possible, with one improvement: the
+% minimum separation between tag and equation is now a
+% user-settable parameter.
+%
+% [1995/01/17] Added a check to make sure that the width of the tag
+% on the current line is $>0$ before testing to see if tagwidth +
+% linewidth + mintagsep $>$ displaywidth. Since an imbedded align
+% shows up as line with width \cn{displaywidth}, and even lines
+% without a tag get processed as if an empty tag were present, the
+% result was that the empty tag assigned to the line containing the
+% align was being shifted downwards, creating extra space after the
+% align.
+% \begin{macrocode}
+\def\calc@shift@gather{%
+ \dimen@\mintagsep\relax
+ \tagwidth@\tag@width\row@\relax
+% \end{macrocode}
+% If we're in \opt{fleqn} mode, there is no flexibility about
+% placement of the equation, so all we can do is see if there's
+% room for the tag in the given margin.
+% \begin{macrocode}
+ \if@fleqn
+ \global\eqnshift@\@mathmargin
+ \ifdim\tagwidth@>\z@
+ \advance\dimen@\tagwidth@
+ \iftagsleft@
+ \ifdim\dimen@>\@mathmargin
+ \global\shifttag@true
+ \fi
+ \else
+ \advance\dimen@\@mathmargin
+ \advance\dimen@\wdz@
+ \ifdim\dimen@>\displaywidth
+ \global\shifttag@true
+ \fi
+ \fi
+ \fi
+ \else
+ \global\eqnshift@\displaywidth
+ \global\advance\eqnshift@-\wdz@
+ \ifdim\tagwidth@>\z@
+ \multiply\dimen@\tw@
+ \advance\dimen@\wdz@
+ \advance\dimen@\tagwidth@
+ \ifdim\dimen@>\displaywidth
+ \global\shifttag@true
+ \else
+ \ifdim\eqnshift@<4\tagwidth@
+ \global\advance\eqnshift@-\tagwidth@
+ \fi
+ \fi
+ \fi
+ \global\divide\eqnshift@\tw@
+ \iftagsleft@
+ \global\eqnshift@-\eqnshift@
+ \global\advance\eqnshift@\displaywidth
+ \global\advance\eqnshift@-\wdz@
+ \fi
+ \ifdim\eqnshift@<\z@
+ \global\eqnshift@\z@
+ \fi
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\place@tag@gather}
+% \begin{macro}{\set@gather@field}
+% \begin{macrocode}
+\def\place@tag@gather{%
+ \iftagsleft@
+ \kern-\gdisplaywidth@
+ \ifshifttag@
+ \rlap{\vbox{%
+ \normalbaselines
+ \boxz@
+ \vbox to\lineht@{}%
+ \raise@tag
+ }}%
+ \global\shifttag@false
+ \else
+ \rlap{\boxz@}%
+ \fi
+ \else
+ \ifdim\totwidth@>\displaywidth
+ \dimen@\totwidth@
+ \advance\dimen@-\displaywidth
+ \kern-\dimen@
+ \fi
+ \ifshifttag@
+ \llap{\vtop{%
+ \raise@tag
+ \normalbaselines
+ \setbox\@ne\null
+ \dp\@ne\lineht@
+ \box\@ne
+ \boxz@
+ }}%
+ \global\shifttag@false
+ \else
+ \llap{\boxz@}%
+ \fi
+ \fi
+}
+%
+\def\set@gather@field{%
+ \iftagsleft@
+ \global\lineht@\ht\z@
+ \else
+ \global\lineht@\dp\z@
+ \fi
+ \kern\eqnshift@
+ \boxz@
+ \hfil
+}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%
+% \subsection{The \env{align} family of environments}
+%
+% The \env{align}, \env{flalign}, \env{alignat}, \env{xalignat},
+% and \env{xxalignat} environments are virtually
+% identical, and thus will share much code. We'll refer to the
+% environments generically as ``\env{align}'' and will
+% distinguish between them explicitly
+% only when necessary.
+%
+% \begin{macro}{\ifxxat@}
+% \begin{macro}{\ifcheckat@}
+% \begin{macro}{\xatlevel@}
+% The \cs{xatlevel@} macro will be used, informally speaking, to
+% distinguish between the \env{alignat} and \env{xalignat}, and
+% \env{xxalignat} environments.
+%
+% \begin{macrocode}
+\newif\ifxxat@
+
+\newif\ifcheckat@
+
+\let\xatlevel@\@empty
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\start@align}
+% \cs{start@align} will be called by all of the \env{align}-like
+% environments. The first argument will be the \cs{xatlevel@},
+% i.e., 0, 1, or~2; the second argument will be either
+% \cs{st@rredtrue} or \cs{st@rredfalse}. The third argument will
+% be the number of aligned
+% structures in the environment (either as supplied by the user, or
+% $-1$ to indicate that checking shouldn't be done). After
+% performing the appropriate error detection and initialization,
+% \cs{start@align} calls \cs{align@}.
+%
+% Note that the \cs{equation} counter is no longer stepped at the
+% beginning of these environments.
+%
+% TODO: Implement \cs{shoveleft} and \cs{shoveright} for
+% \env{align}.
+% \begin{macrocode}
+\def\start@align#1#2#3{%
+ \let\xatlevel@#1% always \z@, \@ne, or \tw@
+ \maxfields@#3\relax
+ \ifnum\maxfields@>\m@ne
+ \checkat@true
+ \ifnum\xatlevel@=\tw@
+ \xxat@true
+ \fi
+ \multiply\maxfields@\tw@
+ \else
+ \checkat@false
+ \fi
+ \ifingather@
+ \iffalse{\fi\ifnum0=`}\fi
+ \DN@{\vcenter\bgroup\savealignstate@\align@#2}%
+ \else
+ \ifmmode
+ \if@display
+ \DN@{\align@recover}%
+ \else
+ \nomath@env
+ \DN@{\@namedef{end\@currenvir}{}\@gobble}%
+ \fi
+ \else
+ $$%
+ \let\split\insplit@
+ \DN@{\align@#2}%
+ \fi
+ \fi
+ \collect@body\next@
+}
+% \end{macrocode}
+%
+% With version 1.2 of \pkg{amsmath}, it was possible to use
+% \env{align*} and relatives in certain wrong contexts without
+% getting an error, e.g.
+% \begin{verbatim}
+% \begin{equation*}
+% \begin{align*}
+% ...
+% \end{align*}
+% \end{equation*}
+% \end{verbatim}
+%
+% For backward compatibility we therefore give only a warning for
+% this condition instead of a full error, and try to recover using
+% the \env{aligned} environment. The alignment of the material may be
+% adversely affected but it will at least remain readable.
+% \begin{macrocode}
+\def\align@recover#1#2#3{%
+ \endgroup
+ \@amsmath@err{%
+Erroneous nesting of equation structures;\MessageBreak
+trying to recover with `aligned'%
+ }\@ehc
+ \begin{aligned}\relax#1\end{aligned}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{environment}{align}
+% \begin{environment}{align*}
+% \begin{environment}{flalign}
+% \begin{environment}{flalign*}
+% \begin{environment}{alignat}
+% \begin{environment}{alignat*}
+% \begin{environment}{xalignat}
+% \begin{environment}{xalignat*}
+% \begin{environment}{xxalignat}
+% The definitions of the various \env{align} environments are quite
+% straight-forward.
+%
+% \begin{macrocode}
+\newenvironment{alignat}{%
+ \start@align\z@\st@rredfalse
+}{%
+ \endalign
+}
+\newenvironment{alignat*}{%
+ \start@align\z@\st@rredtrue
+}{%
+ \endalign
+}
+\newenvironment{xalignat}{%
+ \start@align\@ne\st@rredfalse
+}{%
+ \endalign
+}
+\newenvironment{xalignat*}{%
+ \start@align\@ne\st@rredtrue
+}{%
+ \endalign
+}
+\newenvironment{xxalignat}{%
+ \start@align\tw@\st@rredtrue
+}{%
+ \endalign
+}
+\newenvironment{align}{%
+ \start@align\@ne\st@rredfalse\m@ne
+}{%
+ \math@cr \black@\totwidth@
+ \egroup
+ \ifingather@
+ \restorealignstate@
+ \egroup
+ \nonumber
+ \ifnum0=`{\fi\iffalse}\fi
+ \else
+ $$%
+ \fi
+ \ignorespacesafterend
+}
+\newenvironment{align*}{%
+ \start@align\@ne\st@rredtrue\m@ne
+}{%
+ \endalign
+}
+\newenvironment{flalign}{%
+ \start@align\tw@\st@rredfalse\m@ne
+}{%
+ \endalign
+}
+\newenvironment{flalign*}{%
+ \start@align\tw@\st@rredtrue\m@ne
+}{%
+ \endalign
+}
+% \end{macrocode}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+% \end{environment}
+%
+%
+% \begin{macro}{\align@}
+% TODO: Some of these sets of initializations show up in multiple
+% places. It might be worth making an abbreviation for them.
+%
+% \begin{macrocode}
+\def\align@#1#2{%
+ \inalign@true \intertext@ \Let@ \chardef\dspbrk@context\z@
+ \ifingather@\else\displ@y@\fi
+ \let\math@cr@@@\math@cr@@@align
+ \ifxxat@\else \let\tag\tag@in@align \fi
+ \let\label\label@in@display
+ #1% set st@r
+ \ifst@rred\else \global\@eqnswtrue \fi
+ \measure@{#2}%
+ \global\row@\z@
+ \tabskip\eqnshift@
+ \halign\bgroup
+ \span\align@preamble\crcr
+ #2%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@@@align}
+% \begin{macrocode}
+\def\math@cr@@@align{%
+ \ifst@rred\nonumber\fi
+ \if@eqnsw \global\tag@true \fi
+ \global\advance\row@\@ne
+ \add@amps\maxfields@
+ \omit
+ \kern-\alignsep@
+ \iftag@
+ \setboxz@h{\@lign\strut@{\make@display@tag}}%
+ \place@tag
+ \fi
+ \ifst@rred\else\global\@eqnswtrue\fi
+ \global\lineht@\z@
+ \cr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\math@cr@@@align@measure}
+% \begin{macrocode}
+\def\math@cr@@@align@measure{%
+ &\omit
+ \global\advance\row@\@ne
+ \ifst@rred\nonumber\fi
+ \if@eqnsw \global\tag@true \fi
+ \ifnum\column@>\maxfields@
+ \ifcheckat@
+ \begingroup
+ \measuring@false
+ \@amsmath@err{Extra & on this line}%
+ {\the\andhelp@}% "An extra & here is disastrous"
+ \endgroup
+ \else
+ \global\maxfields@\column@
+ \fi
+ \fi
+ \setboxz@h{\@lign\strut@{%
+ \if@eqnsw
+ \stepcounter{equation}%
+ \tagform@\theequation
+ \else
+ \iftag@\df@tag\fi
+ \fi
+ }}%
+ \savetaglength@
+ \ifst@rred\else\global\@eqnswtrue\fi
+ \cr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\field@lengths}
+% \begin{macro}{\savefieldlength@}
+% \begin{macro}{\fieldlengths@}
+% \begin{macrocode}
+\let\field@lengths\@empty
+
+\def\savefieldlength@{%
+ \begingroup
+ \let\or\relax
+ \xdef\field@lengths{%
+ \field@lengths
+ \ifnum\column@=0
+ \or
+ \else
+ ,%
+ \fi
+ \the\wdz@
+ }%
+ \endgroup
+}
+
+\def\fieldlengths@#1{%
+ \ifcase\@xp#1\field@lengths\fi
+}
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\maxcolumn@widths}
+% \cs{maxcolumn@widths} will be used to hold the widths of the
+% fields of the \env{alignat} environment. The widths will be
+% separated by the token \cn{or}, making it easy to extract a given
+% width using \cn{ifcase}.
+% \begin{macrocode}
+\let\maxcolumn@widths\@empty
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\maxcol@width}
+% \cs{maxcol@width} $n$ = maximum width of $n$th column of the current
+% \env{alignat} (i.e., the $n$th field of \cs{maxcolumn@widths}.)
+% It expands to a \<dimen>, so it can be used as the right-hand
+% side of a \<variable assignment> or \<arithmetic> statement.
+% It's argument can be any \<number>, \<integer variable> or macro
+% that expands to one of these. [Check to make sure this is true.]
+%
+% This is subtler than it looks.
+% \begin{macrocode}
+\def\maxcol@width#1{%
+ \ifcase\@xp#1\maxcolumn@widths\fi\relax
+}
+% \end{macrocode}
+% \end{macro}
+%
+% Now comes the real fun. A typical \env{align} environments looks
+% something like this, where the vertical bars mark the edges of
+% the fields of the underlying \cs{halign}:
+% \[
+% \makeatletter\tabskip\@centering\offinterlineskip
+% \halign to\displaywidth{%^^A
+% &$\strut$\vrule\hfil$\m@th\displaystyle{\@lign#}$\vrule
+% \tabskip1pt&\vrule$\m@th\displaystyle{\@lign#}$\hfil\vrule
+% \tabskip\@centering\cr
+% \omit\small\hfil 1\hfil &\omit\small\hfil 2 &\omit\small\hfil
+% 3\hfil &\omit\small\hfil 4\hfil & \omit\small\hfil 5\hfil
+% &\omit\small\hfil 6\hfil\cr
+% \noalign{\vskip8pt\relax}
+% V_i + q_i v_j & =v_i , & X_i & = x_i - q_i x_j,
+% & U_i & = u_i,\qquad
+% \hbox{for $i\ne j$;} %&\omit\hfill \llap{(3)}
+% \cr
+% V_j & = v_j, & X_j & = x_j,
+% & U_j & = u_j + \sum_{i\ne j} q_i u_i. %&\omit\hfill \llap{(4)}
+% \cr}
+% \]
+% Note that each align structure consists of two fields, with no
+% space between them (a small space has been added here to
+% highlight the boundaries). Furthermore, the text inside the
+% odd-numbered fields is flushright, while the text inside the
+% even-numbered fields is flushleft. The equation tags (shown on
+% the right here) can be on either the right or the left. If there
+% is not room (in a sense to be defined shortly) for the tag on the
+% same line as the equation, the tag will be shifted to a separate
+% line.
+%
+% Each environment also has a certain number of ``flexible
+% spaces,'' meaning spaces whose width we are allowed to adjust to
+% take up the amount of ``free space'' in the line, meaning the
+% space not taken up by the equation tag and the fields of the
+% underlying \cs{halign}.
+%
+% The flexible spaces come in two flavors: interalign spaces and
+% margin spaces. If there are $n$ align structures ($n=3$ in the
+% illustration above), there are $n-1$ interalign spaces, unless we
+% are in an \env{alignat} environment, in which case there are no
+% flexible interalign spaces.
+%
+% The number of margin spaces is a little more complicated:
+% Normally, there are two, but if we're in \opt{fleqn} mode, there
+% is only one. Furthermore, if we're in an \env{xxalignat} or
+% \env{flalign} environment (corresponding to $\cs{xatlevel@} = 2$,
+% then there are no flexible margin spaces.
+%
+% Calculating the interalign and margin spaces is done in two
+% stages.
+%
+% First, the total amount of free space is divided uniformly among
+% all the flexible spaces, without regard for the lengths of the tags
+% on the various lines. For the non-\opt{fleqn} case, this
+% corresponds to centering the align structures between the margins.
+% Note that in \opt{fleqn} mode, the right margin is still allowed to
+% be larger than \cs{@mathmargin}. This introduces an element of
+% asymmetry into the appearance of the environment, but it has the
+% advantage of leaving more space for equation tags in the right
+% margin. If the right margin were constrained to be equal to the
+% left margin in this case, tags would need to be shifted to a
+% separate line more often than would be desirable.
+%
+% Ordinarily, all flexible spaces will be given the same width.
+% However, this is not invariably true, since the interalign spaces
+% are constrained to be at least \cs{minalignsep} wide, while---in
+% the absence of equation tags, at least---the margin spaces are
+% allowed to shrink to zero. As we shall see in a minute, if there
+% are tags in the environment, then the margins are also bounded
+% below by \cs{mintagsep}.
+%
+% Next, we examine each line of the environment that has a tag to
+% see if there is a gap of at least \cs{mintagsep} between the
+% equation and its tag. If there isn't, we attempt to center the
+% equation between the tag and the opposite margin, leaving a gap
+% of at least \cs{mintagsep} on either side, in order to preserve
+% some symmetry, i.e., we want the equation to \emph{look} like
+% it's centered between the margin and the tag, so we don't want
+% the margin space to be less than the gap between the tag and the
+% equation. (Arguably, it would be better to allow the margin
+% space to shrink to zero in this case in order to avoid shifting
+% the tag to a separate line at any cost, but that would require
+% all of our calculations to be a little more complicated and hence
+% a little slower.) Finally, if no values of the interalign spaces
+% and the margins (with the constraints outlined above) will
+% produce an acceptable distance between the equation and its tag,
+% then the tag will be shifted to a separate line.
+%
+% \begin{macro}{\measure@}
+% \cs{measure@} collects the various bits of information that we'll
+% need to perform the calculations outlined above, namely, the
+% number of align structures in the environment, the natural
+% lengths of the fields on each row, the maximum widths of each
+% column, and the widths of the equation tags on each line. It
+% also calculates the number of flexible interalign and margin
+% spaces and computes the initial values of the parameters
+% \cs{eqnshift@} and \cs{alignsep@}, which correspond to the widths
+% of the margins and the interalign spaces, respectively.
+% \begin{macrocode}
+\def\measure@#1{%
+ \begingroup
+ \measuring@true
+ \global\eqnshift@\z@
+ \global\alignsep@\z@
+ \global\let\tag@lengths\@empty
+ \global\let\field@lengths\@empty
+ \savecounters@
+ \global\setbox0\vbox{%
+ \let\math@cr@@@\math@cr@@@align@measure
+ \everycr{\noalign{\global\tag@false
+ \global\let\raise@tag\@empty \global\column@\z@}}%
+ \let\label\@gobble
+ \global\row@\z@
+ \tabskip\z@
+ \halign{\span\align@preamble\crcr
+ #1%
+ \math@cr@@@
+ \global\column@\z@
+ \add@amps\maxfields@\cr
+ }%
+ }%
+ \restorecounters@
+% \end{macrocode}
+% It's convenient to have \cs{maxfields@} rounded up to the nearest
+% even number, so that \cs{maxfields@} is precisely twice the
+% number of align structures.
+% \begin{macrocode}
+ \ifodd\maxfields@
+ \global\advance\maxfields@\@ne
+ \fi
+% \end{macrocode}
+% It doesn't make sense to have a single align structure in either
+% \env{flalign} or \env{xxalignat}. So, we check for that case now
+% and, if necessary, switch to an \env{align} or \env{alignat}.
+% Arguably, we should issue a warning message, but why bother?
+% \begin{macrocode}
+ \ifnum\xatlevel@=\tw@
+ \ifnum\maxfields@<\thr@@
+ \let\xatlevel@\z@
+ \fi
+ \fi
+% \end{macrocode}
+% |\box0| now contains the lines of the \cs{halign}. After the
+% following maneuver, |\box1| will contain the last line of the
+% \cs{halign}, which is what we're interested in. (Incidentally,
+% the penalty we're removing is the \cs{@eqpen} inserted by
+% \cs{math@cr}. Normally, this is \cs{interdisplaylinepenalty},
+% unless the user has overridden that with a \cs{displaybreak}
+% command.)
+% \begin{macrocode}
+ \setbox\z@\vbox{%
+ \unvbox\z@ \unpenalty \global\setbox\@ne\lastbox
+ }%
+% \end{macrocode}
+% |\box1| begins with \cs{tabskip} glue and contains alternating
+% \cs{hbox}es (the fields whose widths we're trying to get) and
+% \cs{tabskip} glue [need better diagram]:
+% \begin{verbatim}
+% \hbox{\tabskip\hbox\tabskip...\hbox\tabskip}\end{verbatim}
+% In fact, all the \cs{tabskip} glue will be 0pt, because all the
+% \cs{tabskip}s in an \env{alignat} environment have a natural
+% width of 0pt, and the \cs{halign} has been set in its natural
+% width.
+%
+% One nice result of this is that we can read \cs{totwidth@} off
+% immediately, since it is just the width of |\box1|, plus
+% \cs{@mathmargin} if we're in \opt{fleqn} mode. (Actually, we
+% also have to take \cs{minalignsep} into account, but we'll do
+% that later):
+% \begin{macrocode}
+ \global\totwidth@\wd\@ne
+ \if@fleqn \global\advance\totwidth@\@mathmargin \fi
+% \end{macrocode}
+% Now we initialize \cs{align@lengths} and start peeling the boxes
+% off, one by one, and adding their widths to \cs{align@lengths}.
+% We stop when we run out of boxes, i.e., when \cs{lastbox} returns
+% a void box. We're going to build a list using \cs{or} as a
+% delimiter, so we want to disable it temporarily.
+% \begin{macrocode}
+ \global\let\maxcolumn@widths\@empty
+ \begingroup
+ \let\or\relax
+ \loop
+ \global\setbox\@ne\hbox{%
+ \unhbox\@ne \unskip \global\setbox\thr@@\lastbox
+ }%
+ \ifhbox\thr@@
+ \xdef\maxcolumn@widths{ \or \the\wd\thr@@ \maxcolumn@widths}%
+ \repeat
+ \endgroup
+% \end{macrocode}
+% Now we calculate the number of flexible spaces and the initial
+% values of \cs{eqnshift@} and \cs{alignsep@}.
+% We start by calculating $\cs{displaywidth}-\cs{totwidth@}$,
+% which gives us the total amount of ``free space'' in a row.
+% \begin{macrocode}
+ \dimen@\displaywidth
+ \advance\dimen@-\totwidth@
+% \end{macrocode}
+% Next we calculate the number of columns of flexible spaces in the
+% display, which depends on whether we're in \opt{fleqn} mode and
+% in which particular environment we are in.
+%
+% We use \cs{@tempcnta} to store the total number of flexible spaces
+% in the align and \cs{@tempcntb} for the number of interalign
+% spaces.
+% \begin{macrocode}
+ \ifcase\xatlevel@
+% \end{macrocode}
+% In \env{alignat}, the interalign spaces are under user control,
+% not ours. So, we set \cs{alignsep@} and \cs{minalignsep} both
+% equal to 0pt. Later, when calculating a new value for
+% \cs{alignsep@}, we will only save the new value if it is less
+% than the current value of \cs{alignsep@} (i.e., \cs{alignsep@}
+% will never increase). Since the values we calculate will never
+% be negative, this will ensure that \cs{alignsep@} remains zero in
+% \env{alignat}.
+% \begin{macrocode}
+ \global\alignsep@\z@
+ \let\minalignsep\z@
+ \@tempcntb\z@
+% \end{macrocode}
+% In \opt{fleqn} mode, the left margin---and hence the right margin
+% in this case---is fixed. Otherwise, we divide the free space
+% equally between the two margins.
+% \begin{macrocode}
+ \if@fleqn
+ \@tempcnta\@ne
+ \global\eqnshift@\@mathmargin
+ \else
+ \@tempcnta\tw@
+ \global\eqnshift@\dimen@
+ \global\divide\eqnshift@\@tempcnta
+ \fi
+ \or
+% \end{macrocode}
+% In an \env{align} or \env{xalignat} environment with $n$ aligned
+% structures, there are $n-1$ interalign spaces and either 1 or~2
+% flexible margins, depending on whether we're in \opt{fleqn} mode
+% or not.
+% \begin{macrocode}
+ \@tempcntb\maxfields@
+ \divide\@tempcntb\tw@
+ \@tempcnta\@tempcntb
+ \advance\@tempcntb\m@ne
+% \end{macrocode}
+% If we are in \opt{fleqn} mode, we fix the left margin and divide
+% the free space equally among the interalign spaces and the right
+% margin.
+% \begin{macrocode}
+ \if@fleqn
+ \global\eqnshift@\@mathmargin
+ \global\alignsep@\dimen@
+ \global\divide\alignsep@\@tempcnta
+ \else
+% \end{macrocode}
+% Otherwise, we divide the free space equally among the interalign
+% spaces and both margins.
+% \begin{macrocode}
+ \global\advance\@tempcnta\@ne
+ \global\eqnshift@\dimen@
+ \global\divide\eqnshift@\@tempcnta
+ \global\alignsep@\eqnshift@
+ \fi
+ \or
+% \end{macrocode}
+% Finally, if we're in an \env{flalign} or \env{xxalignat}
+% environment, there are no flexible margins and $n-1$ flexible
+% interalign spaces.
+% \begin{macrocode}
+ \@tempcntb\maxfields@
+ \divide\@tempcntb\tw@
+ \global\advance\@tempcntb\m@ne
+ \global\@tempcnta\@tempcntb
+ \global\eqnshift@\z@
+ \global\alignsep@\dimen@
+% \end{macrocode}
+% If we're in \opt{fleqn} mode, we need to add back the
+% \cs{@mathmargin} that was removed when \cs{dimen@} was originally
+% calculated above.
+% \begin{macrocode}
+ \if@fleqn
+ \global\advance\alignsep@\@mathmargin\relax
+ \fi
+ \global\divide\alignsep@\@tempcntb
+ \fi
+% \end{macrocode}
+% Now we make sure \cs{alignsep@} isn't too small.
+% \begin{macrocode}
+ \ifdim\alignsep@<\minalignsep\relax
+ \global\alignsep@\minalignsep\relax
+ \ifdim\eqnshift@>\z@
+ \if@fleqn\else
+ \global\eqnshift@\displaywidth
+ \global\advance\eqnshift@-\totwidth@
+ \global\advance\eqnshift@-\@tempcntb\alignsep@
+ \global\divide\eqnshift@\tw@
+ \fi
+ \fi
+ \fi
+ \ifdim\eqnshift@<\z@
+ \global\eqnshift@\z@
+ \fi
+ \calc@shift@align
+% \end{macrocode}
+% Next, we calculate the value of \cs{tagshift@}. This is the glue
+% that will be inserted in front of the equation tag to make sure
+% it lines up flush against the appropriate margin.
+% \begin{macrocode}
+ \global\tagshift@\totwidth@
+ \global\advance\tagshift@\@tempcntb\alignsep@
+ \if@fleqn
+ \ifnum\xatlevel@=\tw@
+ \global\advance\tagshift@-\@mathmargin\relax
+ \fi
+ \else
+ \global\advance\tagshift@\eqnshift@
+ \fi
+ \iftagsleft@ \else
+ \global\advance\tagshift@-\displaywidth
+ \fi
+% \end{macrocode}
+% Finally, we increase \cs{totwidth@} by an appropriate multiple of
+% \cs{minalignsep}. If the result is greater than
+% \cs{displaywidth}, it means that at least one line in the
+% \env{align} is overfull and we will issue an appropriate warning
+% message (via \cs{bl@ck}) at the end of the environment.
+% \begin{macrocode}
+ \dimen@\minalignsep\relax
+ \global\advance\totwidth@\@tempcntb\dimen@
+ \ifdim\totwidth@>\displaywidth
+ \global\let\displaywidth@\totwidth@
+ \else
+ \global\let\displaywidth@\displaywidth
+ \fi
+ \endgroup
+}
+% \end{macrocode}
+% \end{macro}
+%
+% The code for calculating the appropriate placement of equation
+% tags in the \env{align} environments is quite complicated and
+% varies wildly depending on the settings of the |tagsleft@| and
+% |@fleqn| switches. To minimize memory and hash space usage, we
+% only define the variant appropriate for the current setting of
+% those switches.
+%
+% It would be worthwhile to examine this code more closely someday
+% and see if it could be optimized any.
+%
+% \paragraph{Tag placement when \cs{tagsleft@true},
+% \cs{@fleqntrue}.}
+%
+% We begin with the version of \cs{calc@shift@align} appropriate
+% for flush-left equations with tags on the left.
+%
+% \begin{macro}{\calc@shift@align}
+% This is the simplest case. Since the left margin is fixed, in
+% general the only thing to do is check whether there is room for
+% the tag in the left margin. The only exception is that if
+% $\cs{eqnshift@} = 0\,\mathrm{pt}$---meaning that we're in a
+% \env{flalign} environment and this is the first line with a tag
+% that we've encountered---then we set $\cs{eqnshift@} =
+% \cs{@mathmargin}$ and recalculate \cs{alignsep@}. This is done
+% by \cs{x@calc@shift@lf}.
+% \begin{macrocode}
+\iftagsleft@\if@fleqn
+ \def\calc@shift@align{%
+ \global\let\tag@shifts\@empty
+ \begingroup
+% \end{macrocode}
+% \cs{@tempdima} is initialized to $\cs{@mathmargin} -
+% \cs{mintagsep}$, which yields the maximum size of a tag that will
+% not be shifted to another line.
+% \begin{macrocode}
+ \@tempdima\@mathmargin\relax
+ \advance\@tempdima-\mintagsep\relax
+% \end{macrocode}
+% Now we examine each row in turn. If the width of the tag on the
+% line is non-positive---meaning either that there is no tag or
+% else that the user has forced it to have zero width---we mark the
+% tag to remain unshifted. Otherwise, we call \cs{x@calc@shift@lf}
+% to determine whether any adjustments need to be made to
+% \cs{eqnshift@} and \cs{alignsep@}. Note the difference in
+% treatment of zero-width tags between this code and \tex/'s
+% built-in algorithm: here, a width of zero prohibits the tag from
+% being shifted, while in \tex/'s built-in algorithm, a width of
+% zero forces the tag to be shifted.
+% \begin{macrocode}
+ \loop
+ \ifnum\row@>0
+ \ifdim\tag@width\row@>\z@
+ \x@calc@shift@lf
+ \else
+ \saveshift@0%
+ \fi
+ \advance\row@\m@ne
+ \repeat
+ \endgroup
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\x@calc@shift@lf}
+% As mentioned above, \cs{x@calc@shift@lf} first checks to see if
+% the current left margin is set to 0 and, if so, resets it to
+% \cs{@mathmargin} and recalculates \cs{alignsep@}. Next, it
+% checks whether the length of the current tag exceeds the
+% previously calculated limit and, if so, marks the tag to be
+% shifted to a separate line.
+% \begin{macrocode}
+ \def\x@calc@shift@lf{%
+ \ifdim\eqnshift@=\z@
+ \global\eqnshift@\@mathmargin\relax
+ \alignsep@\displaywidth
+ \advance\alignsep@-\totwidth@
+ \global\divide\alignsep@\@tempcntb
+ \ifdim\alignsep@<\minalignsep\relax
+ \global\alignsep@\minalignsep\relax
+ \fi
+ \fi
+ \ifdim\tag@width\row@>\@tempdima
+ \saveshift@1%
+ \else
+ \saveshift@0%
+ \fi
+ }
+\fi\fi
+% \end{macrocode}
+% \end{macro}
+%
+% \paragraph{Tag placement when \cs{tagsleft@false},
+% \cs{@fleqntrue}.}
+%
+% Next we consider the case when equations are flush-left, but tags
+% are on the right. This case is somewhat more complicated than
+% the previous one, since we can adjust the right margin by varying
+% the inter-align separatin. Thus, when a tag is found to be too
+% close to its equation, we first attempt to decrease
+% \cs{alignsep@} enough to move the equation off to an acceptable
+% distance. Only if that would require a value of \cs{alignsep@}
+% less than \cs{minalignsep} do we move the tag to a separate line.
+%
+% \begin{macro}{\calc@shift@align}
+% This version of \cs{calc@shift@align} differs from the previous
+% version only in calling \cs{x@calc@shift@rf} rather than
+% \cs{x@calc@shift@lf}.
+% \begin{macrocode}
+\iftagsleft@\else\if@fleqn
+ \def\calc@shift@align{%
+ \global\let\tag@shifts\@empty
+ \begingroup
+ \loop
+ \ifnum\row@>0
+ \ifdim\tag@width\row@>\z@
+ \x@calc@shift@rf
+ \else
+ \saveshift@0%
+ \fi
+ \advance\row@\m@ne
+ \repeat
+ \endgroup
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\x@calc@shift@rf}
+% To start, we need to know two quantities: the number of align
+% structures in the current row and the ``effective length'' of the
+% row, defined as the distance from the left margin to the
+% right edge of the text assuming that \cs{eqnshift@} and
+% \cs{alignsep@} are both~0. To get the number of align
+% structures, we first count the number of columns by counting the
+% number of entries in the \cs{fieldlengths@} for the current row.
+% The effective length is calcuated by \cs{x@rcalc@width} and put
+% in the temporary register \cs{@tempdimc}, using \cs{@tempdimb} as
+% an auxiliary variable.
+% \begin{macrocode}
+ \def\x@calc@shift@rf{%
+ \column@\z@
+ \@tempdimb\z@
+ \@tempdimc\z@
+ \edef\@tempb{\fieldlengths@\row@}%
+ \@for\@tempa:=\@tempb\do{%
+ \advance\column@\@ne
+ \x@rcalc@width
+ }%
+ \begingroup
+% \end{macrocode}
+% If there are $n$ columns in the current row, then there are
+% $\lfloor (n+1)/2 \rfloor$ align structures and $\lfloor (n-1)/2
+% \rfloor$ interalign spaces.
+% \begin{macrocode}
+ \advance\column@\m@ne
+ \divide\column@\tw@
+% \end{macrocode}
+% If this is smaller than the maximum number of interalign spaces
+% in the environment, then we need to reduce \cs{@tempcnta} (the
+% total number of flexible spaces in the current line) by
+% $\cs{@tempcntb} - \cs{column@}$ and reset \cs{@tempcntb} to
+% \cs{column@}.
+% \begin{macrocode}
+ \ifnum\@tempcntb>\column@
+ \advance\@tempcnta-\@tempcntb
+ \advance\@tempcnta\column@
+ \@tempcntb\column@
+ \fi
+% \end{macrocode}
+% Next, we add the width of the tag and the (fixed) left margin to
+% the effective length calculated above. This can be used to
+% calculate how much ``free space'' there is in the current line
+% and thus how much leeway we have to increase the amount of space
+% between the tag and the equation.
+% \begin{macrocode}
+ \tagwidth@\tag@width\row@\relax
+ \@tempdima\eqnshift@
+ \advance\@tempdima\@tempdimc\relax
+ \advance\@tempdima\tagwidth@
+% \end{macrocode}
+% The first thing to check is whether the tag should be shifted to
+% a separate line. To do this, we add the minimum interalign
+% separation and the \cs{mintagsep} to the value of \cs{@tempdima}
+% just calculated. This yields the minimum acceptable length of
+% the current line. If that is greater than \cs{displaywidth}, we
+% mark the tag to be calculated. Otherwise, we mark the tag to be
+% kept on the same line and then check to see if the \cs{alignsep@}
+% needs to be reduced to make room for the tag.
+% \begin{macrocode}
+ \dimen@\minalignsep\relax
+ \multiply\dimen@\@tempcntb
+ \advance\dimen@\mintagsep\relax
+ \advance\dimen@\@tempdima
+ \ifdim\dimen@>\displaywidth
+ \saveshift@1%
+ \else
+ \saveshift@0%
+% \end{macrocode}
+% Now we perform essentially the same calculation, but using the
+% current value of \cs{alignsep@} instead of \cs{minalignsep}.
+% This gives the current length of the line. If this is greater
+% than \cs{displaywidth}, we recalculate \cs{alignsep@} to make
+% room for the tag.
+% \begin{macrocode}
+ \dimen@\alignsep@\relax
+ \multiply\dimen@\@tempcntb
+ \advance\dimen@\@tempdima
+ \advance\dimen@\tagwidth@
+ \ifdim\dimen@>\displaywidth
+ \dimen@\displaywidth
+ \advance\dimen@-\@tempdima
+ \ifnum\xatlevel@=\tw@
+ \advance\dimen@-\mintagsep\relax
+ \fi
+ \divide\dimen@\@tempcnta
+ \ifdim\dimen@<\minalignsep\relax
+ \global\alignsep@\minalignsep\relax
+ \else
+ \global\alignsep@\dimen@
+ \fi
+ \fi
+ \fi
+ \endgroup
+ }
+\fi\fi
+% \end{macrocode}
+% \end{macro}
+%
+% \paragraph{Tag placement when \cs{tagsleft@false},
+% \cs{@fleqnfalse}.}
+%
+% This is similar to the previous case, except for the added
+% complication that both \cs{alignsep@} and \cs{eqnshift@} can
+% vary, which makes the computations correspondingly more
+% complicated.
+%
+% \begin{macro}{\calc@shift@align}
+% \begin{macrocode}
+\iftagsleft@\else\if@fleqn\else
+ \def\calc@shift@align{%
+ \global\let\tag@shifts\@empty
+ \begingroup
+ \loop
+ \ifnum\row@>0
+ \ifdim\tag@width\row@>\z@
+ \x@calc@shift@rc
+ \else
+ \saveshift@0%
+ \fi
+ \advance\row@\m@ne
+ \repeat
+ \endgroup
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\x@calc@shift@rc}
+% \begin{macrocode}
+ \def\x@calc@shift@rc{%
+ \column@\z@
+ \@tempdimb\z@
+ \@tempdimc\z@
+ \edef\@tempb{\fieldlengths@\row@}%
+ \@for\@tempa:=\@tempb\do{%
+ \advance\column@\@ne
+ \x@rcalc@width
+ }%
+ \begingroup
+ \advance\column@\m@ne
+ \divide\column@\tw@
+ \ifnum\@tempcntb>\column@
+ \advance\@tempcnta-\@tempcntb
+ \advance\@tempcnta\column@
+ \@tempcntb\column@
+ \fi
+ \tagwidth@\tag@width\row@\relax
+ \@tempdima\@tempdimc
+ \advance\@tempdima\tagwidth@
+ \dimen@\minalignsep\relax
+ \multiply\dimen@\@tempcntb
+ \advance\dimen@\mintagsep\relax
+ \ifnum\xatlevel@=\tw@ \else
+ \advance\dimen@\mintagsep\relax
+ \fi
+ \advance\dimen@\@tempdima
+ \ifdim\dimen@>\displaywidth
+ \saveshift@1%
+ \else
+ \saveshift@0%
+ \dimen@\eqnshift@
+ \advance\dimen@\@tempdima
+ \advance\dimen@\@tempcntb\alignsep@
+ \advance\dimen@\tagwidth@
+ \ifdim\dimen@>\displaywidth
+ \dimen@\displaywidth
+ \advance\dimen@-\@tempdima
+ \ifnum\xatlevel@=\tw@
+ \advance\dimen@-\mintagsep\relax
+ \fi
+ \divide\dimen@\@tempcnta
+ \ifdim\dimen@<\minalignsep\relax
+ \global\alignsep@\minalignsep\relax
+ \eqnshift@\displaywidth
+ \advance\eqnshift@-\@tempdima
+ \advance\eqnshift@-\@tempcntb\alignsep@
+ \global\divide\eqnshift@\tw@
+ \else
+ \ifdim\dimen@<\eqnshift@
+ \ifdim\dimen@<\z@
+ \global\eqnshift@\z@
+ \else
+ \global\eqnshift@\dimen@
+ \fi
+ \fi
+ \ifdim\dimen@<\alignsep@
+ \global\alignsep@\dimen@
+ \fi
+ \fi
+ \fi
+ \fi
+ \endgroup
+ }
+\fi\fi
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\x@rcalc@width}
+% \begin{macrocode}
+\iftagsleft@\else
+ \def\x@rcalc@width{%
+ \ifdim\@tempa > \z@
+ \advance\@tempdimc\@tempdimb
+ \ifodd\column@
+ \advance\@tempdimc\maxcol@width\column@
+ \@tempdimb\z@
+ \else
+ \advance\@tempdimc\@tempa\relax
+ \@tempdimb\maxcol@width\column@
+ \advance\@tempdimb-\@tempa\relax
+ \fi
+ \else
+ \advance\@tempdimb\maxcol@width\column@\relax
+ \fi
+ }
+\fi
+% \end{macrocode}
+% \end{macro}
+%
+% \paragraph{Tag placement when \cs{tagsleft@true},
+% \cs{@fleqnfalse}.}
+%
+% \begin{macro}{\calc@shift@align}
+% \begin{macrocode}
+\iftagsleft@\if@fleqn\else
+ \def\calc@shift@align{%
+ \global\let\tag@shifts\@empty
+ \begingroup
+ \loop
+ \ifnum\row@>\z@
+ \ifdim\tag@width\row@>\z@
+ \x@calc@shift@lc
+ \else
+ \saveshift@0%
+ \fi
+ \advance\row@\m@ne
+ \repeat
+ \endgroup
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\x@calc@shift@lc}
+% \begin{macrocode}
+ \def\x@calc@shift@lc{%
+ \column@\z@
+% \end{macrocode}
+% \cs{@tempdima} will (eventually) be set to the effective width of
+% the current row, defined as the distance from the leftmost point
+% of the current line to the end of the last field of the
+% \cs{halign}, ignoring any intervening \cs{tabskip}s, plus the
+% width of the current tag. That is, it will be the width of the
+% first non-empty field plus the sum of the maximum widths of all
+% following fields, plus the tag width.
+%
+% \cs{@tempdimb} will be the ``indentation'' of leftmost end of
+% text, ignoring the \cs{tabskip} glue, i.e., it will be the sum of
+% the maximum widths of any fields to the left of the first
+% non-empty field, plus whatever empty space there is at the
+% beginning of the first non-empty field.
+% \begin{macrocode}
+ \@tempdima\z@ % ``width of equation''
+ \@tempdimb\z@ % ``indent of equation''
+ \edef\@tempb{\fieldlengths@\row@}%
+ \@for\@tempa:=\@tempb\do{%
+ \advance\column@\@ne
+ \x@lcalc@width
+ }%
+ \begingroup
+ \tagwidth@\tag@width\row@\relax
+% \end{macrocode}
+% \cs{@tempdima} is now easy to calculate, since it is just
+% $\cs{totwidth@} - \cs{@tempdimb} + \cs{tagwidth@}$.
+% \begin{macrocode}
+ \@tempdima\totwidth@
+ \advance\@tempdima-\@tempdimb
+ \advance\@tempdima\tagwidth@
+% \end{macrocode}
+% Next, we check to see whether there is room for both the equation
+% and the tag on the same line, by calculating the minimum
+% acceptable length of the current row and comparing that to
+% \cs{displaywidth}. Note that here we use \cs{@tempcntb}, i.e.,
+% the number of interalign spaces after the first non-empty align
+% structure.
+% \begin{macrocode}
+ \dimen@\minalignsep\relax
+ \multiply\dimen@\@tempcntb
+ \advance\dimen@\mintagsep\relax
+ \ifnum\xatlevel@=\tw@ \else
+ \advance\dimen@\mintagsep\relax
+ \fi
+ \advance\dimen@\@tempdima
+% \end{macrocode}
+% If the minimum acceptable width of the current line is greater
+% than \cs{displaywidth}, we mark the current tag to be shifted to
+% a separate line.
+% \begin{macrocode}
+ \ifdim\dimen@>\displaywidth
+ \saveshift@1%
+ \else
+% \end{macrocode}
+% Otherwise, the tag can stay on the same line as the equation, but
+% we need to check whether it is too close to the equation. So, we
+% calculate the distance between the left margin and the left side
+% of the equation, using the current values of \cs{eqnshift@} and
+% \cs{alignsep@}. Note that we use \cs{count@} here, not
+% \cs{@tempcntb}, as above.
+% \begin{macrocode}
+ \saveshift@0%
+ \dimen@\alignsep@
+ \multiply\dimen@\count@
+ \advance\dimen@\eqnshift@
+ \advance\dimen@\@tempdimb
+% \end{macrocode}
+% If the left margin is less than twice the tag width, we calculate
+% new values of \cs{eqnshift@} and \cs{alignsep@} to move the
+% equation further away from the tag. In particular, we center the
+% current line between its tag and the right margin. Note that
+% although we later will need to transform \cs{dimen@} into a value
+% suitable for use as \cs{eqnshift@}, for the time being it is more
+% useful to think of it as the space separating the tag from the
+% equation.
+% \begin{macrocode}
+ \ifdim\dimen@<2\tagwidth@
+ \dimen@\displaywidth
+ \advance\dimen@-\@tempdima
+ \ifnum\xatlevel@=\tw@
+ \advance\dimen@-\mintagsep\relax
+ \fi
+% \end{macrocode}
+% In certain circumstances we will get a divide-by-zero error here
+% unless we guard against it. Use of \cs{@tempcnta} is complicated,
+% sometimes it is assigned globally, sometimes locally. Need to sort
+% it out one of these days [mjd,2000/06/02].
+% \begin{macrocode}
+ \ifnum\@tempcnta>\z@
+ \divide\dimen@\@tempcnta
+ \else \dimen@\z@
+ \fi
+% \end{macrocode}
+% As usual, we check to make sure we don't set \cs{alignsep@}
+% smaller than \cs{minalignsep} and, in any case, that we don't
+% replace \cs{alignsep@} by a larger value.
+% \begin{macrocode}
+ \ifdim\dimen@<\minalignsep\relax
+ \global\alignsep@\minalignsep\relax
+ \dimen@\displaywidth
+ \advance\dimen@-\@tempdima
+ \advance\dimen@-\@tempcntb\alignsep@
+ \global\divide\dimen@\tw@
+ \else
+ \ifdim\dimen@<\alignsep@
+ \global\alignsep@\dimen@
+ \fi
+ \fi
+% \end{macrocode}
+% Next, we calculate an appropriate value of \cs{eqnshift@},
+% assuming that \cs{dimen@} is the desired separation between the
+% tag and equation of the current line. This means that we first
+% need to adjust \cs{dimen@} if we're in an \env{flalign}
+% environment.
+% \begin{macrocode}
+ \ifnum\xatlevel@=\tw@
+ \dimen@\mintagsep\relax
+ \fi
+% \end{macrocode}
+% Now we calculate the value of \cs{eqnshift@} needed to produce a
+% separation of \cs{dimen@} between the equation tag and the
+% beginning of the equation. To do this, we need the following
+% equation to hold:
+% \[
+% \cs{eqnshift@} + n\cs{alignsep@} + \cs{@tempdimb}
+% = \cs{tagwidth@} + \cs{dimen@}
+% \]
+% where $n = \cs{count@}$ is the number of interalign spaces before
+% the first non-empty field of the current line.
+% \begin{macrocode}
+ \advance\dimen@\tagwidth@
+ \advance\dimen@-\@tempdimb
+ \advance\dimen@-\count@\alignsep@
+% \end{macrocode}
+% The value of \cs{eqnshift@} just calculated is the minimum
+% acceptable value; thus, we save it only if it is larger than the
+% current value.
+% \begin{macrocode}
+ \ifdim\dimen@>\eqnshift@
+ \global\eqnshift@\dimen@
+ \fi
+ \fi
+ \fi
+ \endgroup
+ }
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\x@lcalc@width}
+% This macro calculates the ``indentation'' of the current row, as
+% defined above under the description of \cs{x@calc@shift@lc}.
+% This macro is called for each field of the current line, with
+% \cs{@tempa} set to the width of the current field. Ideally, the
+% loop enclosing \cs{x@lcalc@width} would terminate as soon as
+% \cs{@tempa} is non-zero, but that would be a bit tricky to
+% arrange. Instead, we use \cs{@tempdima} as a flag to signal when
+% we've encountered the first non-empty field.
+%
+% \begin{macrocode}
+ \def\x@lcalc@width{%
+ \ifdim\@tempdima = \z@
+% \end{macrocode}
+% If the current field is empty (i.e., $\cs{@tempa} =
+% \mathrm{0\,pt}$, then we increment \cs{@tempdimb} by the width of
+% the current field). Otherwise, we set $\cs{@tempdima} =
+% \mathrm{1\,pt}$ as a signal value and increment \cs{@tempdimb} by
+% the width of whatever empty space there might be at the left of
+% the current field.
+% \begin{macrocode}
+ \ifdim\@tempa > \z@
+ \@tempdima\p@
+ \ifodd\column@
+ \advance\@tempdimb \maxcol@width\column@
+ \advance\@tempdimb-\@tempa
+ \fi
+% \end{macrocode}
+% In addition, we need to adjust the values of \cs{@tempcnta} and
+% \cs{@tempcntb} to account for any empty align structures that
+% might occur at the beginning of the current line. More
+% specifically, we first set \cs{count@} equal to the number of
+% interalign spaces preceding the current field (namely, $\lfloor
+% (\cs{\column@}-1)/2 \rfloor$), and then subtract \cs{count@} from
+% both \cs{@tempcnta} and \cs{@tempcntb}. The rationale is that
+% for the purposes of adjusting the spacing between the tag and the
+% equation, the only flexible interalign spaces are those after
+% the first non-empty align structure, so we need to treat those
+% different from the ones before the first non-empty align
+% structure.
+% \begin{macrocode}
+ \count@\column@
+ \advance\count@\m@ne
+ \divide\count@\tw@
+ \advance\@tempcnta-\count@
+ \advance\@tempcntb-\count@
+ \else
+ \advance\@tempdimb \maxcol@width\column@\relax
+ \fi
+ \fi
+ }
+\fi\fi
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\place@tag}
+% \cs{place@tag} takes care of the placment of tags in the
+% \env{align} environments.
+% \begin{macrocode}
+\def\place@tag{%
+ \iftagsleft@
+ \kern-\tagshift@
+ \if1\shift@tag\row@\relax
+ \rlap{\vbox{%
+ \normalbaselines
+ \boxz@
+ \vbox to\lineht@{}%
+ \raise@tag
+ }}%
+ \else
+ \rlap{\boxz@}%
+ \fi
+ \kern\displaywidth@
+ \else
+ \kern-\tagshift@
+ \if1\shift@tag\row@\relax
+% \end{macrocode}
+% Added depth to correct vertical spacing of shifted
+% equation tags.---dmj, 1994/12/29
+% \begin{macrocode}
+ \llap{\vtop{%
+ \raise@tag
+ \normalbaselines
+ \setbox\@ne\null
+ \dp\@ne\lineht@
+ \box\@ne
+ \boxz@
+ }}%
+ \else
+ \llap{\boxz@}%
+ \fi
+ \fi
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\align@preamble}
+% \begin{macrocode}
+\def\align@preamble{%
+ &\hfil
+ \strut@
+ \setboxz@h{\@lign$\m@th\displaystyle{##}$}%
+ \ifmeasuring@\savefieldlength@\fi
+ \set@field
+ \tabskip\z@skip
+ &\setboxz@h{\@lign$\m@th\displaystyle{{}##}$}%
+ \ifmeasuring@\savefieldlength@\fi
+ \set@field
+ \hfil
+ \tabskip\alignsep@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\set@field}
+% \cs{set@field} increments the column counter, tracks the value of
+% \cs{lineht@} and finally inserts the box containing the contents
+% of the current field.
+% \begin{macrocode}
+\def\set@field{%
+ \column@plus
+ \iftagsleft@
+ \ifdim\ht\z@>\lineht@
+ \global\lineht@\ht\z@
+ \fi
+ \else
+ \ifdim\dp\z@>\lineht@
+ \global\lineht@\dp\z@
+ \fi
+ \fi
+ \boxz@
+}
+% \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection {The \env{split} environment}
+%
+% \begin{macro}{\split@err}
+% A special error function for \env{split} to conserve main mem (at a
+% cost of string pool/hash size.
+% \begin{macrocode}
+\edef\split@err#1{%
+ \@nx\@amsmath@err{%
+ \string\begin{split} won't work here%
+ }{%
+ \@xp\@nx\csname
+ Did you forget a preceding \string\begin{equation}?^^J%
+ If not, perhaps the `aligned' environment is what
+ you want.\endcsname}%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{environment}{split}
+% If the \env{split} environment occurs inside \env{align} or
+% \env{gather}, it can make use of the enclosing halign; if it is
+% called inside a simple equation, we add an implicit `gather'
+% container.
+%
+% \begin{macrocode}
+\newenvironment{split}{%
+ \if@display
+ \ifinner
+ \@xp\@xp\@xp\split@aligned
+ \else
+ \ifst@rred \else \global\@eqnswtrue \fi
+ \fi
+ \else \let\endsplit\@empty \@xp\collect@body\@xp\split@err
+ \fi
+ \collect@body\gather@split
+}{%
+ \crcr
+ \egroup
+ \egroup
+ \iftagsleft@ \@xp\lendsplit@ \else \@xp\rendsplit@ \fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\split@tag\relax % init
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\gather@split#1#2#3{%
+ \@xp\endgroup \reset@equation % math@cr will handle equation numbering
+ \iftag@
+ \toks@\@xp{\df@tag}%
+ \edef\split@tag{%
+ \gdef\@nx\df@tag{\the\toks@}%
+ \global\@nx\tag@true \@nx\nonumber
+ }%
+ \else \let\split@tag\@empty
+ \fi
+ \spread@equation
+% \end{macrocode}
+% The extra vcenter wrapper here is not really a good thing but
+% without it there are compatibility problems with old documents that
+% throw in some extra material between \verb'\begin{equation}' and
+% \verb'\begin{split}' (for example, \verb'\hspace{-1pc}' or
+% \verb'\left\{'). [mjd,1999/09/20]
+% \begin{macrocode}
+ \vcenter\bgroup
+ \gather@{\split@tag \begin{split}#1\end{split}}%
+ \def\endmathdisplay@a{%
+ \math@cr \black@ \totwidth@ \egroup
+ \egroup
+ }%
+}
+% \end{macrocode}
+%
+% \end{environment}
+%
+% \begin{macro}{\insplit@}
+% \begin{macrocode}
+\def\insplit@{%
+ \global\setbox\z@\vbox\bgroup
+ \Let@ \chardef\dspbrk@context\@ne \restore@math@cr
+ \default@tag % disallow use of \tag here
+ \ialign\bgroup
+ \hfil
+ \strut@
+ $\m@th\displaystyle{##}$%
+ &$\m@th\displaystyle{{}##}$%
+ \hfill % Why not \hfil?---dmj, 1994/12/28
+ \crcr
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\rendsplit@}
+% Moved the box maneuvers inside the \cs{ifinalign@}, since that is
+% the only place they are needed.---dmj, 1994/12/28
+%
+% TODO: Explore interaction of tag-placement algorithm with
+% \env{split}. Is there any way for \env{split} to pass the
+% relevant information out to the enclosing \env{gather} or
+% \env{align}?
+% \begin{macrocode}
+\def\rendsplit@{%
+ \ifinalign@
+% \end{macrocode}
+% Changed |\box9| into a \cs{vtop} here for better spacing.
+% \begin{macrocode}
+ \global\setbox9 \vtop{%
+ \unvcopy\z@
+ \global\setbox8 \lastbox
+ \unskip
+ }%
+ \setbox\@ne\hbox{%
+ \unhcopy8
+ \unskip
+ \global\setbox\tw@\lastbox
+ \unskip
+ \global\setbox\thr@@\lastbox
+ }%
+ \ifctagsplit@
+ \gdef\split@{%
+ \hbox to\wd\thr@@{}%
+ &\vcenter{\vbox{\moveleft\wd\thr@@\boxz@}}%
+ }%
+ \else
+ \global\setbox7 \hbox{\unhbox\tw@\unskip}%
+% \end{macrocode}
+% Added \cs{add@amps} to make sure we put the last line of the
+% \env{split} into the proper column of an \env{align} environment
+% with multiple align structures.---dmj, 1994/12/28
+%
+% Special care has to be taken in this case because the \env{split}
+% turns into two lines of the \env{align} instead of just one. So,
+% we have to make sure that the first line produced by the
+% \env{split} doesn't upset our bookkeeping, hence we call
+% \cs{savetaglength@} to insert 0\,pt as the tag for this
+% pseudo-line, and we advance the \cs{row@} counter and reset
+% \cs{lineht@} afterwards. It would be nice if we could just
+% replace the \cs{crcr} by \cs{math@cr@@@}, but that would cause
+% problems with the tag processing.
+% \begin{macrocode}
+ \gdef\split@{%
+ \global\@tempcnta\column@
+ &\setboxz@h{}%
+ \savetaglength@
+ \global\advance\row@\@ne
+ \vbox{\moveleft\wd\thr@@\box9}%
+ \crcr
+ \noalign{\global\lineht@\z@}%
+ \add@amps\@tempcnta
+ \box\thr@@
+ &\box7
+ }%
+ \fi
+ \else
+ \ifctagsplit@
+ \gdef\split@{\vcenter{\boxz@}}%
+ \else
+% \end{macrocode}
+% Changed to just \cs{boxz@}, otherwise last line gets centered
+% rather than aligned properly with respect to the rest of the
+% lines. But this means that we can't see inside of the last line
+% to decide whether the tag needs to be moved. Will have to think
+% about this.---dmj, 1994/12/28
+% \begin{macrocode}
+ \gdef\split@{%
+ \boxz@
+% \box9
+% \crcr
+% \hbox{\box\thr@@\box7}%
+ }%
+ \fi
+ \fi
+ \aftergroup\split@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lendsplit@}
+% \begin{macrocode}
+\def\lendsplit@{%
+ \global\setbox9\vtop{\unvcopy\z@}%
+ \ifinalign@
+% \end{macrocode}
+% Moved following two boxes inside the \cs{ifinalign@}, since they
+% are only used in that case. In fact, if we just kept track of
+% the width of the first column, we could dispense with this
+% entirely. Surely that would be more efficient than all these box
+% copies.---dmj, 1994/12/28
+% \begin{macrocode}
+ \setbox\@ne\vbox{%
+ \unvcopy\z@
+ \global\setbox8\lastbox
+ }%
+ \setbox\@ne\hbox{%
+ \unhcopy8%
+ \unskip
+ \setbox\tw@\lastbox
+ \unskip
+ \global\setbox\thr@@\lastbox
+ }%
+ \ifctagsplit@
+ \gdef\split@{%
+ \hbox to\wd\thr@@{}%
+ &\vcenter{\vbox{\moveleft\wd\thr@@\box9}}%
+ }%
+ \else
+ \gdef\split@{%
+ \hbox to\wd\thr@@{}%
+ &\vbox{\moveleft\wd\thr@@\box9}%
+ }%
+ \fi
+ \else
+ \ifctagsplit@
+ \gdef\split@{\vcenter{\box9}}%
+ \else
+ \gdef\split@{\box9}%
+ \fi
+ \fi
+ \aftergroup\split@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% With \pkg{amsmath} 1.2 it was possible to put things like
+% \verb'\left\{' between \verb'\begin{equation}' and
+% \verb'\begin{split}' without getting any error message. For
+% backward compatibility we try to avoid a fatal error in this case
+% and instead attempt recovery with \env{aligned}.
+% \begin{macrocode}
+\def\split@aligned#1#2{%
+ \iffalse{\fi\ifnum0=`}\fi
+ \collect@body\split@al@a}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\split@al@a#1#2#3{%
+ \split@warning
+ \endgroup
+% \end{macrocode}
+% If the \opt{fleqn} and \opt{tbtags} options are both in effect then
+% we will need to add an optional argument on the \env{aligned}
+% environment.
+% \begin{macrocode}
+ \toks@{\begin{aligned}}%
+ \if@fleqn \split@al@tagcheck \fi
+% \end{macrocode}
+% The \cs{relax} here is to prevent \cs{@let@token} from being left
+% equal to an ampersand if that happens to be the first thing in the body.
+% \begin{macrocode}
+ \the\toks@\relax#1\end{aligned}%
+ \ifnum0=`{\fi\iffalse}\fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\split@al@tagcheck{%
+ \ifctagsplit@
+ \else
+ \iftagsleft@ \toks@\@xp{\the\toks@ [t]}%
+ \else \toks@\@xp{\the\toks@ [b]}%
+ \fi
+ \fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\split@warning{%
+ \PackageWarning{amsmath}{%
+Cannot use `split' here;\MessageBreak trying to recover with `aligned'}%
+}
+% \end{macrocode}
+%
+% \subsection{The \env{multline} environment}
+%
+% In the original \amstex/, \cn{multlinegap} is a macro with an
+% argument that resets an internal dimension (one with an \qc{\@}
+% character in its name). Here, to save control sequence names, we
+% define \cn{multlinegap} to be the dimension itself and the
+% documentation instructs users to use \cn{setlength} if they
+% need to change it.
+% \begin{macro}{\multlinegap}
+% \begin{macro}{\multlinetaggap}
+% Changed \cs{multlinegap} and \cs{multlinetaggap} to skip
+% registers. Also changed name to \cs{multlinetaggap} from
+% \cs{multlinetaggap@}.
+% \begin{macrocode}
+\newskip\multlinegap
+\multlinegap10pt
+\newskip\multlinetaggap
+\multlinetaggap10pt
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\start@multline}
+% \begin{macrocode}
+\def\start@multline#1{%
+ \RIfM@
+ \nomath@env
+ \DN@{\@namedef{end\@currenvir}{}\@gobble}%
+ \else
+ $$%
+ #1%
+ \ifst@rred
+ \nonumber
+ \else
+ \global\@eqnswtrue
+ \fi
+ \let\next@\multline@
+ \fi
+ \collect@body\next@
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{environment}{multline}
+% \begin{environment}{multline*}
+% \begin{macrocode}
+\newenvironment{multline}{%
+ \start@multline\st@rredfalse
+}{%
+ \iftagsleft@ \@xp\lendmultline@ \else \@xp\rendmultline@ \fi
+ \ignorespacesafterend
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newenvironment{multline*}{\start@multline\st@rredtrue}{\endmultline}
+% \end{macrocode}
+% \end{environment}
+% \end{environment}
+%
+% \begin{macro}{\multline@}
+% \begin{macrocode}
+\def\multline@#1{%
+ \Let@
+% \end{macrocode}
+%
+% For multline neither \cs{displ@y} no \cs{displ@y@} is quite right;
+% we want to advance the row number and (I suppose?) the
+% display-pagebreak level, but we only want to do tag-related stuff
+% once before the first line, not repeat it for every line. (Recall
+% that the arg of \cs{@display@init} goes into \cs{everycr}.)
+% \begin{macrocode}
+ \@display@init{\global\advance\row@\@ne \global\dspbrk@lvl\m@ne}%
+ \chardef\dspbrk@context\z@
+ \restore@math@cr
+% \end{macrocode}
+% The \env{multline} environment is somewhat unusual, in that
+% \cs{tag} and \cs{label} are enabled only during the measuring
+% phase and disabled during the production phase.
+% Here we disable \cs{tag} and \cs{label}; \cs{mmeasure@} will
+% re-enable them temporarily.
+% \begin{macrocode}
+ \let\tag\tag@in@align
+ \global\tag@false \global\let\raise@tag\@empty
+ \mmeasure@{#1}%
+ \let\tag\gobble@tag \let\label\@gobble
+ \tabskip \if@fleqn \@mathmargin \else \z@skip \fi
+ \totwidth@\displaywidth
+ \if@fleqn
+ \advance\totwidth@-\@mathmargin
+ \fi
+ \halign\bgroup
+ \hbox to\totwidth@{%
+% \end{macrocode}
+% In order to get the spacing of the last line right in fleqn
+% mode, we need to play a little game here. Normally the
+% stretchability of the \cs{hskip} here will be suppressed by the
+% \cs{hfil} at the end of the template, except inside the last line,
+% when that \cs{hfil} will be removed by the \cs{hfilneg} in
+% \cs{lendmultline@}.
+% \begin{macrocode}
+ \if@fleqn
+ \hskip \@centering \relax
+ \else
+ \hfil
+ \fi
+ \strut@
+ $\m@th\displaystyle{}##\endmultline@math
+ \hfil
+ }%
+ \crcr
+% \end{macrocode}
+% In \opt{fleqn} mode, it's the \cs{tabskip} of \cs{@mathmargin}
+% that needs to be removed in the first line, not the \cs{hfil} at
+% the beginning of the template.
+% \begin{macrocode}
+ \if@fleqn
+ \hskip-\@mathmargin
+ \def\multline@indent{\hskip\@mathmargin}% put it back
+ \else
+ \hfilneg
+ \def\multline@indent{\hskip\multlinegap}%
+ \fi
+ \iftagsleft@
+ \iftag@
+ \begingroup
+ \ifshifttag@
+ \rlap{\vbox{%
+ \normalbaselines
+ \hbox{%
+ \strut@
+ \make@display@tag
+ }%
+ \vbox to\lineht@{}%
+ \raise@tag
+ }}%
+% \end{macrocode}
+% If the equation tag doesn't fit on the same line with the first
+% line of the display, we'll indent the first line by
+% \cn{multlinegap}. This is a change from \pkg{amstex}, where the
+% first line would have been flush against the left margin in this
+% case. A corresponding change will be made in \cs{rendmultline@}.
+% \begin{macrocode}
+ \multline@indent
+ \else
+ \setbox\z@\hbox{\make@display@tag}%
+ \dimen@\@mathmargin \advance\dimen@-\wd\z@
+ \ifdim\dimen@<\multlinetaggap
+ \dimen@\multlinetaggap
+ \fi
+ \box\z@ \hskip\dimen@\relax
+ \fi
+ \endgroup
+ \else
+ \multline@indent
+ \fi
+ \else
+ \multline@indent
+ \fi
+ #1%
+}
+% \end{macrocode}
+%
+% An extra level of indirection for the closing \verb'$' in multline
+% allows us to avoid getting an extra thinmuskip from a final
+% mathpunct in the equation contents, when equation numbers are on
+% the right. If we did not use this workaround, the sequence of
+% elements for a final comma would be, e.g.,
+% \begin{verbatim}
+% ... ,<hskip><box containing equation number>
+% \end{verbatim}
+% which is equivalent to a sequence \verb'<mathpunct><mathord>' as
+% far as the automatic math spacing is concerned.
+% \begin{macrocode}
+\def\endmultline@math{$}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\lendmultline@}
+% Bug fix: changed \cs{crcr} to \cs{math@cr} so that \cs{@eqpen}
+% gets reset properly if \cs{displaybreak} is used on the
+% penultimate line of an \env{align}.
+% \begin{macrocode}
+\def\lendmultline@{%
+ \hfilneg
+ \hskip\multlinegap
+ \math@cr
+ \egroup
+ $$%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\rendmultline@}
+% \begin{macrocode}
+\def\rendmultline@{%
+ \iftag@
+ $\let\endmultline@math\relax
+ \ifshifttag@
+ \hskip\multlinegap
+% \end{macrocode}
+% Added depth to correct vertical spacing of shifted equation
+% tags.---dmj, 1994/12/29
+% \begin{macrocode}
+ \llap{\vtop{%
+ \raise@tag
+ \normalbaselines
+ \setbox\@ne\null
+ \dp\@ne\lineht@
+ \box\@ne
+ \hbox{\strut@\make@display@tag}%
+ }}%
+ \else
+ \hskip\multlinetaggap
+ \make@display@tag
+ \fi
+ \else
+ \hskip\multlinegap
+ \fi
+ \hfilneg
+% \end{macrocode}
+% Use \cs{math@cr} rather than just \cs{crcr} so that \cs{@eqpen}
+% gets reset properly if \cs{displaybreak} is used.
+% \begin{macrocode}
+ \math@cr
+ \egroup$$%
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mmeasure@}
+% \begin{macrocode}
+\def\mmeasure@#1{%
+ \begingroup
+ \measuring@true
+% \end{macrocode}
+% We use \cs{begin/endgroup} rather than |{}| in this definition of
+% \cn{label} because the latter would create an extra (wasteful of
+% main mem) null box in the current math list. [mjd, 1995/01/17]
+% \begin{macrocode}
+ \def\label##1{%
+ \begingroup\measuring@false\label@in@display{##1}\endgroup}%
+ \def\math@cr@@@{\cr}%
+ \let\shoveleft\@iden \let\shoveright\@iden
+ \savecounters@
+ \global\row@\z@
+ \setbox\@ne\vbox{%
+ \global\let\df@tag\@empty
+ \halign{%
+ \setboxz@h{\@lign$\m@th\displaystyle{}##$}%
+ \iftagsleft@
+ \ifnum\row@=\@ne
+ \global\totwidth@\wdz@
+ \global\lineht@\ht\z@
+ \fi
+ \else
+ \global\totwidth@\wdz@
+ \global\lineht@\dp\z@
+ \fi
+ \crcr
+ #1%
+ \crcr
+ }%
+ }%
+ \ifx\df@tag\@empty\else\global\tag@true\fi
+ \if@eqnsw\global\tag@true\fi
+ \iftag@
+ \setboxz@h{%
+ \if@eqnsw
+ \stepcounter{equation}%
+ \tagform@\theequation
+ \else
+ \df@tag
+ \fi
+ }%
+ \global\tagwidth@\wdz@
+ \dimen@\totwidth@
+ \advance\dimen@\tagwidth@
+ \advance\dimen@\multlinetaggap
+ \iftagsleft@\else
+ \if@fleqn
+ \advance\dimen@\@mathmargin
+ \fi
+ \fi
+ \ifdim\dimen@>\displaywidth
+ \global\shifttag@true
+ \else
+ \global\shifttag@false
+ \fi
+ \fi
+ \restorecounters@
+ \endgroup
+}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\shoveleft}
+% \begin{macro}{\shoveright}
+% \cs{shoveleft} and \cs{shoveright} need to do slightly different
+% things depending on whether tags are on the left or the right and
+% whether we're in \opt{fleqn} mode. For compactness of code, we
+% make the appropriate decisions at ``compile'' time rather than at
+% load time.
+%
+% TODO: Investigate making \cs{shoveright} behave ``properly''(?) if
+% used on the first line of a \env{multline} and make \cs{shoveleft}
+% behave properly if used on the last line of a \env{multline}. But
+% in his \fn{amstex.doc} Spivak indicates those commands should never
+% be used on a first or last line. Perhaps better to leave the
+% question open unless/until real-life examples turn up.
+% \begin{macrocode}
+\iftagsleft@
+ \def\shoveright#1{%
+ #1%
+ \hfilneg
+ \hskip\multlinegap
+ }
+\else
+ \def\shoveright#1{%
+ #1%
+ \hfilneg
+ \iftag@
+ \ifshifttag@
+ \hskip\multlinegap
+ \else
+ \hskip\tagwidth@
+ \hskip\multlinetaggap
+ \fi
+ \else
+ \hskip\multlinegap
+ \fi
+ }
+\fi
+
+\if@fleqn
+ \def\shoveleft#1{#1}%
+\else
+ \iftagsleft@
+ \def\shoveleft#1{%
+ \setboxz@h{$\m@th\displaystyle{}#1$}%
+ \setbox\@ne\hbox{$\m@th\displaystyle#1$}%
+ \hfilneg
+ \iftag@
+ \ifshifttag@
+ \hskip\multlinegap
+ \else
+ \hskip\tagwidth@
+ \hskip\multlinetaggap
+ \fi
+ \else
+ \hskip\multlinegap
+ \fi
+ \hskip.5\wd\@ne
+ \hskip-.5\wdz@
+ #1%
+ }
+ \else
+ \def\shoveleft#1{%
+ \setboxz@h{$\m@th\displaystyle{}#1$}%
+ \setbox\@ne\hbox{$\m@th\displaystyle#1$}%
+ \hfilneg
+ \hskip\multlinegap
+ \hskip.5\wd\@ne
+ \hskip-.5\wdz@
+ #1%
+ }
+ \fi
+\fi
+% \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{The \env{equation} environment}
+%
+% Rewritten from the ground up for version 2.0 to fix no-shrink and
+% no-shortskips bugs [mjd,2000/01/06].
+%
+% Standard \latex/ provides three environments for one-line equations:
+% \cn{[}\cn{]}, \env{equation}, and \env{displaymath}. We add
+% \env{equation*} as a synonym for \env{displaymath}.
+% \begin{macrocode}
+\@saveprimitive\leqno\@@leqno
+\@saveprimitive\eqno\@@eqno
+\def\eqno{\@@eqno\let\eqno\relax\let\leqno\relax}
+\def\leqno{\@@leqno\let\leqno\relax\let\eqno\relax}
+%
+\let\veqno=\@@eqno
+\iftagsleft@ \let\veqno=\@@leqno \fi
+% \end{macrocode}
+%
+% Support for the \pkg{showkeys} package: provide no-op definitions
+% for a couple of SK functions, if they are not already defined. Then
+% we can just call them directly in our code without any extra fuss.
+% If the \pkg{showkeys} package is loaded later, our trivial
+% definitions will get overridden and everything works fine.
+% \begin{macrocode}
+\@ifundefined{SK@@label}{%
+ \let\SK@@label\relax \let\SK@equationtrue\relax
+}{}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\reset@equation\@empty
+% \end{macrocode}
+%
+% Cf \cs{tag@in@align}. This is a bit of a mess though. Could use
+% some work. [mjd,1999/12/21]
+% \begin{macrocode}
+\let\alt@tag\@empty
+\def\tag@in@display#1#{\relax\tag@in@display@a{#1}}
+\def\tag@in@display@a#1#2{%
+ \iftag@
+ \invalid@tag{Multiple \string\tag}\relax
+ \else
+ \global\tag@true \nonumber \reset@equation \st@rredtrue
+ \if *\string#1%
+ \gdef\alt@tag{\def\SK@tagform@{#2\@gobble}%
+ \ifx\SK@@label\relax \let\tagform@\SK@tagform@ \fi
+ }%
+ \make@df@tag@@{#2}%
+ \else
+ \make@df@tag@@@{#2}%
+ \fi
+ \fi
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\restore@hfuzz\@empty
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\mathdisplay#1{%
+ \ifmmode \@badmath
+ \else
+ $$\def\@currenvir{#1}%
+% \end{macrocode}
+% Allow use of \cn{displaybreak}.
+% \begin{macrocode}
+ \let\dspbrk@context\z@
+% \end{macrocode}
+% Although in some cases simpler label handling would seem to be
+% sufficient, always using \cs{label@in@display} makes it easier to
+% support the \pkg{showkeys} package.
+% \begin{macrocode}
+ \let\tag\tag@in@display \let\label\label@in@display \SK@equationtrue
+ \global\let\df@label\@empty \global\let\df@tag\@empty
+ \global\tag@false
+ \let\mathdisplay@push\mathdisplay@@push
+ \let\mathdisplay@pop\mathdisplay@@pop
+ \if@fleqn
+% \end{macrocode}
+% Turn off overfull box messages temporarily\mdash otherwise there
+% would be unwanted extra ones emitted during our measuring
+% operations.
+% \begin{macrocode}
+ \edef\restore@hfuzz{\hfuzz\the\hfuzz\relax}%
+ \hfuzz\maxdimen
+% \end{macrocode}
+% Initially set the equation body in a box of displaywidth. Then if
+% the box is not overfull, as we find by checking \cs{badness}, we
+% have acquired useful information for the subsequent processing.
+% \begin{macrocode}
+ \setbox\z@\hbox to\displaywidth\bgroup
+ \let\split@warning\relax \restore@hfuzz
+ \everymath\@emptytoks \m@th $\displaystyle
+ \fi
+ \fi
+}
+% \end{macrocode}
+%
+% Arg 1 is not currently used. I thought it might come in handy for
+% error messages.
+% \begin{macrocode}
+\def\endmathdisplay#1{%
+ \ifmmode \else \@badmath \fi
+ \endmathdisplay@a
+ $$%
+% \end{macrocode}
+% I guess the following code means this structure is non-reentrant.
+% But there is plenty of scope for tricky bugs here; suppressing them
+% by brute force at least makes it possible to get things working
+% correctly for normal use. [mjd,2000/01/06]
+% \begin{macrocode}
+ \global\let\df@label\@empty \global\let\df@tag\@empty
+ \global\tag@false \global\let\alt@tag\@empty
+ \global\@eqnswfalse
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\def\endmathdisplay@a{%
+ \if@eqnsw \gdef\df@tag{\tagform@\theequation}\fi
+ \if@fleqn \@xp\endmathdisplay@fleqn
+ \else \ifx\df@tag\@empty \else \veqno \alt@tag \df@tag \fi
+ \ifx\df@label\@empty \else \@xp\ltx@label\@xp{\df@label}\fi
+ \fi
+ \ifnum\dspbrk@lvl>\m@ne
+ \postdisplaypenalty -\@getpen\dspbrk@lvl
+ \global\dspbrk@lvl\m@ne
+ \fi
+}
+% \end{macrocode}
+%
+% A boolean variable: Was that last box overfull or not? A value of 0
+% means yes, it was overfull.
+% \begin{macrocode}
+\let\too@wide\@ne
+% \end{macrocode}
+%
+% Special handling is needed for flush-left equations. We need to
+% measure the equation body (found in box 0 after we close it with
+% the \cs{egroup}). Then after a fairly normal test to see if it fits
+% within the available space, we need to consider overlapping into
+% the displayindent area if displayindent is nonzero (as in an
+% indented list). If there is an equation number we may have to shift
+% it by hand to a separate line when there is not enough room;
+% we can no longer take advantage of the automatic shifting provided
+% by the \cn{leqno}, \cn{eqno} primitives.
+%
+% We initially add \cs{@mathmargin} glue at the end of box 0 to get
+% an accurate overfull test. If \cs{@mathmargin} contains any shrink
+% then we cannot reliably tell whether the box will be overfull or
+% not simply by doing hand calculations from the actual width of the
+% equation body. We have to actually set the box and find out what
+% happens.
+%
+% On the other hand if we put the \cs{@mathmargin} glue at the
+% beginning of the box it's awkward to remove it afterwards. So we
+% first put it in at the end and later we will move it to the
+% beginning as needed.
+%
+% \begin{macrocode}
+\def\endmathdisplay@fleqn{%
+ $\hfil\hskip\@mathmargin\egroup
+% \end{macrocode}
+% We need to save the information about whether box 0 was overfull in
+% a variable, otherwise it will disappear in the next setbox
+% operation. And we couldn't set the equation number box earlier than
+% now, because the body of the equation might have contained a
+% \cs{tag} command (well, it could have been done, but this way
+% we can reuse the tag-handling code from elsewhere).
+% \begin{macrocode}
+ \ifnum\badness<\inf@bad \let\too@wide\@ne \else \let\too@wide\z@ \fi
+ \ifx\@empty\df@tag
+ \else
+ \setbox4\hbox{\df@tag
+ \ifx\df@label\@empty \else \@xp\ltx@label\@xp{\df@label}\fi
+ }%
+ \fi
+ \csname emdf@%
+ \ifx\df@tag\@empty U\else \iftagsleft@ L\else R\fi\fi
+ \endcsname
+}
+% \end{macrocode}
+%
+% For an unnumbered flush-left equation we hope first that the
+% the contents fit within displaywidth. If not we need to fall back
+% on a more complicated reboxing operation.
+% \begin{macrocode}
+\def\emdf@U{%
+ \restore@hfuzz
+ \ifodd\too@wide % not too wide: just need to swap the glue around
+ \hbox to\displaywidth{\hskip\@mathmargin\unhbox\z@\unskip}%
+ \else % M+B > displaywidth
+ \emdf@Ua
+ \fi
+}
+% \end{macrocode}
+%
+% Some notation: $M$ \cs{@mathmargin}, $B$ the width of the equation
+% body, $I$ \cs{displayindent}, $D$ \cs{displaywidth}, $N$ the width
+% of the equation number (aka the tag), $S$ \cs{mintagsep}, $C$
+% \cs{columnwidth}. If $M+B > \mbox{displaywidth}$, and if we assume
+% $M$ contains shrink, then the only solution left is to encroach
+% into the displayindent space.
+% \begin{macrocode}
+\def\emdf@Ua{%
+ \hbox to\columnwidth{%
+ \ifdim\displayindent>\z@
+ \hskip\displayindent minus\displayindent
+ \fi
+ \hskip\@mathmargin \unhbox\z@ \unskip
+ }%
+ \displayindent\z@ \displaywidth\columnwidth
+}
+% \end{macrocode}
+%
+% Find out first if the tag fits in ideal position. If so we can just
+% plunk down box 2. Otherwise we need to do something more complicated.
+% \begin{macrocode}
+\def\emdf@R{%
+ \setbox\tw@\hbox to\displaywidth{%
+ \hskip\@mathmargin \unhcopy\z@\unskip\hfil\hskip\mintagsep\copy4
+ }%
+ \restore@hfuzz
+ \ifnum\badness<\inf@bad \box\tw@ \else \emdf@Ra \fi
+}
+% \end{macrocode}
+%
+% We shift the equation number to line 2 if it does not fit within
+% \cs{displaywidth}. Note that we do not first attempt to let the
+% equation body shift leftward into the \cs{displayindent} space. If
+% that is desired it will have to be done by hand by adding negative
+% space at the beginning of the equation body. I don't expect this to
+% arise very often in practice since most of the time
+% \cs{displayindent} is zero anyway.
+% \begin{macrocode}
+\def\emdf@Ra{%
+ \skip@\displayindent minus\displayindent
+ \displayindent\z@ \displaywidth\columnwidth
+ \spread@equation \everycr{}\tabskip\z@skip
+ \halign{\hbox to\displaywidth{##}\cr
+ \relax
+ \ifdim\skip@>\z@ \hskip\skip@ \fi
+ \hskip\@mathmargin\unhbox\z@\unskip\hfil\cr
+ \noalign{\raise@tag}%
+ \hfil\box4 \cr}%
+}
+% \end{macrocode}
+%
+% Find out first if the tag fits in ideal position. If so we can just
+% plunk down box 2. Otherwise we need to do something more
+% complicated.
+% \begin{macrocode}
+\def\emdf@L{%
+% \end{macrocode}
+% Calculate the difference between $M$ and $N+S$. If the latter is
+% greater, we don't want to add any extra glue between the number and
+% the equation body. Otherwise the amount that we want to add is
+% \verb'x minus x' where $x=M-(N+S)$. I.e., the distribution of
+% spaces across the line is $N,S,x minus x,B,hfil$.
+% \begin{macrocode}
+ \@tempdima\@mathmargin
+ \advance\@tempdima-\wd4 \advance\@tempdima-\mintagsep
+ \skip@\@tempdima minus\@tempdima
+ \setbox\tw@\hbox to\displaywidth{%
+ \copy4\hskip\mintagsep
+ \ifdim\skip@>\z@ \hskip\skip@\fi
+ \unhcopy\z@\unskip
+ }%
+ \restore@hfuzz
+ \ifnum\badness<\inf@bad \box\tw@ \else \emdf@La \fi
+}
+% \end{macrocode}
+%
+% If the equation body and equation number will not fit on the same
+% line, we put the number on line 1 and the body on line 2, with the
+% body positioned as for an unnumbered equation.
+% \begin{macrocode}
+\def\emdf@La{%
+ \spread@equation \everycr{}\tabskip\z@skip
+ \halign{\hbox to\displaywidth{##}\cr
+ \box4 \hfil \cr
+ \noalign{\raise@tag}%
+ \hskip\@mathmargin\unhbox\z@\unskip\hfil\cr}%
+}
+% \end{macrocode}
+%
+% If someone has \verb'\[ \]' nested inside a minipage environment
+% nested inside a numbered equation, the mathdisplay variables that
+% are global will get out of whack unless we take extra care. So we
+% make a stack and push all the variables before entering mathdisplay
+% and pop them afterwards. But we can save a little work by not doing
+% this at the top level, only at inner levels.
+% \begin{macrocode}
+\newtoks\mathdisplay@stack
+\let\mathdisplay@push\@empty
+\def\mathdisplay@@push{%
+ \begingroup
+ \toks@\@xp{\df@label}\@temptokena\@xp{\df@tag}%
+ \toks8\@xp{\alt@tag}%
+ \edef\@tempa{%
+ \global\if@eqnsw\@nx\@eqnswtrue\else\@nx\@eqnswfalse\fi
+ \global\iftag@\@nx\tag@false\else\@nx\tag@true\fi
+ \gdef\@nx\df@label{\the\toks@}\gdef\@nx\df@tag{\the\@temptokena}%
+ \gdef\@nx\alt@tag{\the\toks8}%
+ \global\mathdisplay@stack{\the\mathdisplay@stack}%
+ }%
+ \global\mathdisplay@stack\@xp{\@tempa}
+ \endgroup
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\let\mathdisplay@pop\@empty
+\def\mathdisplay@@pop{\the\mathdisplay@stack}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\renewenvironment{equation}{%
+ \incr@eqnum
+ \mathdisplay@push
+ \st@rredfalse \global\@eqnswtrue
+ \mathdisplay{equation}%
+}{%
+ \endmathdisplay{equation}%
+ \mathdisplay@pop
+ \ignorespacesafterend
+}
+% \end{macrocode}
+%
+% \begin{macrocode}
+\newenvironment{equation*}{%
+ \mathdisplay@push
+ \st@rredtrue \global\@eqnswfalse
+ \mathdisplay{equation*}%
+}{%
+ \endmathdisplay{equation*}%
+ \mathdisplay@pop
+ \ignorespacesafterend
+}
+% \end{macrocode}
+%
+% Note: \latex/ defines the \env{displaymath} environment in
+% terms of \cn{[} and \cn{]}.
+% \begin{macrocode}
+\DeclareRobustCommand{\[}{\begin{equation*}}
+\DeclareRobustCommand{\]}{\end{equation*}}
+% \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}
+%
+% \section{Credits}
+%
+% Much of the code for the \pkg{amsmath} package had its orgin in
+% \fn{amstex.tex}, written by Michael Spivak. The initial work of
+% porting \fn{amstex.tex} to \fn{amstex.sty} was done in 1988--1989
+% by Frank Mittelbach and Rainer Sch\"opf. In 1994 David M. Jones
+% added the support for the \opt{fleqn} option and did extensive
+% improvements to the \env{align[at]} family of environments and to
+% the equation number handling in general. Michael Downes at the AMS
+% served as coordinator for the efforts of Mittelbach, Sch\"opf, and
+% Jones, and has contributed various bug fixes and additional
+% refinements over time.
+%
+% Versions 1.0 and 1.1 of the package carried the name \pkg{amstex}
+% instead of \pkg{amsmath}, to indicate its origins; the name was
+% changed in 1994 to make it user-oriented rather than
+% history-oriented.
+%
+\endinput