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diff --git a/Master/texmf-dist/source/latex/amslatex/amsmath.dtx b/Master/texmf-dist/source/latex/amslatex/amsmath.dtx new file mode 100644 index 00000000000..9810bc283f0 --- /dev/null +++ b/Master/texmf-dist/source/latex/amslatex/amsmath.dtx @@ -0,0 +1,5829 @@ +%%% ==================================================================== +%%% @LaTeX-file{ +%%% filename = "amsmath.dtx", +%%% version = "2.13", +%%% date = "2000/07/18", +%%% time = "08:16:41 EDT", +%%% author = "American Mathematical Society", +%%% copyright = "Copyright 1995, 2000 American Mathematical Society, +%%% all rights reserved. Copying of this file is +%%% authorized only if either: +%%% (1) you make absolutely no changes to your copy, +%%% including name; OR +%%% (2) if you do make changes, you first rename it +%%% to some other name.", +%%% address = "American Mathematical Society, +%%% Technical Support, +%%% Publications Technical Group, +%%% P. O. Box 6248, +%%% Providence, RI 02940, +%%% USA", +%%% telephone = "401-455-4080 or (in the USA and Canada) +%%% 800-321-4AMS (321-4267)", +%%% FAX = "401-331-3842", +%%% checksum = "38084 5829 21569 202795", +%%% email = "tech-support@ams.org (Internet)", +%%% codetable = "ISO/ASCII", +%%% keywords = "latex, amslatex, math, amsmath", +%%% supported = "yes", +%%% abstract = "This is a \LaTeX{} package that provides a variety of +%%% extra mathematical features, largely derived from +%%% AMS-\TeX{}.", +%%% docstring = "The checksum field above contains a CRC-16 checksum +%%% as the first value, followed by the equivalent of +%%% the standard UNIX wc (word count) utility output of +%%% lines, words, and characters. This is produced by +%%% Robert Solovay's checksum utility.", +%%% } +%%% ==================================================================== +% +%\iffalse +%<*driver> +\documentclass{amsdtx} +\raggedbottom +\begin{document} +\title{The \pkg{amsmath} package} +\author{Frank Mittelbach\and Rainer Sch\"opf\and Michael Downes\and + David M. Jones} +\date{Version \fileversion, \filedate} +\providecommand{\histnote}{} +\renewenvironment{histnote}{% + \trivlist\item[\hspace{\labelsep}\bfseries Historical Note:]% +}{% + \endtrivlist +} +\hDocInput{amsmath.dtx} +\end{document} +%</driver> +%\fi +% +% \maketitle +% +% \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 +\ProvidesPackage{amsmath}[2000/07/18 v2.13 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. +% +% \begin{macrocode} +\DeclareOption{?}{} +% \end{macrocode} +% +% \begin{macrocode} +\ExecuteOptions{nointlimits,sumlimits,namelimits,centertags} +% \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 http://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}{\@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|). +% \begin{macrocode} +\def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks + \m@th$#2#3$}} +% \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} +% +% 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}. +% \begin{macrocode} +\DeclareRobustCommand{\tmspace}[3]{% + \ifmmode\mskip#1#2\else\kern#1#3\fi\relax} +\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} +% +% \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} +% 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} +% +% \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} +% +% 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 +} +\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} +% 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). +% \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} +% \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. +% +% \begin{macrocode} +\begingroup +\edef\@tempa{\string\mathchar"} +\def\@tempb#1"#2\@nil{#1"} +\edef\@tempc{\expandafter\@tempb\meaning\coprod "\@nil} +\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} +% +% 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} +% +% \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} +% +% \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} +% +% 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} +% +% \begin{macrocode} +\newcommand{\implies}{\DOTSB\;\Longrightarrow\;} +\newcommand{\impliedby}{\DOTSB\;\Longleftarrow\;} +% \end{macrocode} +% +% \begin{macrocode} +\def\And{\DOTSB\;\mathchar"3026 \;} +% \end{macrocode} +% +% 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} +% +% \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} +% +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% \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}}} +\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@}}} +\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} +% 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 +} +\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@@} +\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@\gdef\thedots@{\dotsb@}% + \else\xdef\meaning@{\meaning\@let@token..........}% + \xdef\meaning@@{\meaning@}% + \@xp\math@\meaning@\math@ + \ifgtest@ + \@xp\mathch@\meaning@\mathch@ + \ifgtest@\@xp\getmathch@\meaning@\getmathch@\fi + \else\@xp\macro@\meaning@@\macro@ + \ifgtest@ + \@xp\not@\meaning@\not@\ifgtest@\gdef\thedots@{\dotsb@}% + \else\@xp\DOTS@\meaning@\DOTS@ + \ifgtest@ + \ifcase\number\DOTSCASE@\gdef\thedots@{\dotsb@}% + \or\gdef\thedots@{\dotsi}\else\fi + \else\@xp\math@\meaning@\math@ + \ifgtest@\@xp\mathbin@\meaning@\mathbin@ + \ifgtest@\gdef\thedots@{\dotsb@}% + \else\@xp\mathrel@\meaning@\mathrel@ + \ifgtest@\gdef\thedots@{\dotsb@}% + \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi + \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} +\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} +% +% The \cn{cdots} command. +% \begin{macrocode} +\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@} +\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} +% 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} +% +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% \section{Integral signs} +% +% 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} +% +% 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}}} +% +\newcommand{\iint}{\DOTSI\protect\MultiIntegral{2}} +\newcommand{\iiint}{\DOTSI\protect\MultiIntegral{3}} +\newcommand{\iiiint}{\DOTSI\protect\MultiIntegral{4}} +\newcommand{\idotsint}{\DOTSI\protect\MultiIntegral{0}} +% \end{macrocode} +% +% 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} +% +% \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. +% \begin{macrocode} +\def\resetMathstrut@{% + \setbox\z@\hbox{% + \mathchardef\@tempa\mathcode`\(\relax + \def\@tempb##1"##2##3{\the\textfont"##3\char"}% + \expandafter\@tempb\meaning\@tempa \relax + }% +% \end{macrocode} +% These height and depth assignments are implicitly global. +% \begin{macrocode} + \ht\Mathstrutbox@\ht\z@ \dp\Mathstrutbox@\dp\z@ +} +\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. +% \begin{macrocode} +\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@}} +% \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} +% +% Triple and quadruple dot accents. +% \begin{macrocode} +\newcommand{\dddot}[1]{% + {\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@ + \hbox{\normalfont ...}\vss}}}} +\newcommand{\ddddot}[1]{% + {\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@ + \hbox{\normalfont....}\vss}}}} +% \end{macrocode} +% +% 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} +% +% 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. +% \begin{macrocode} +\def\@tempa#1{\@xp\@tempb\meaning#1\@nil#1} +\def\@tempb#1>#2#3 #4\@nil#5{% + \@xp\ifx\csname#3\endcsname\mathaccent + \@tempc#4?"7777\@nil#5% + \else + \PackageWarningNoLine{amsmath}{% + Unable to redefine math accent \string#5}% + \fi +} +\def\@tempc#1"#2#3#4#5#6\@nil#7{% + \chardef\@tempd="#3\relax\set@mathaccent\@tempd{#7}{#2}{#4#5}} +\@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} +% +% 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. +% \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.} +% +% 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} +% +% 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} +% +% \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} +% +% \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} +% +% \begin{macro}{\smash} +% We add to the \cn{smash} command an optional argument +% denoting the part of the formula to be smashed. +% \begin{macrocode} +\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 +} +% \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{macrocode} +\def\relbar{\mathrel{\mathpalette\mathsm@sh\std@minus}} +\def\Relbar{\mathrel\std@equal} +% \end{macrocode} +% +% \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}}} +\renewcommand{\overrightarrow}{% + \mathpalette{\overarrow@\rightarrowfill@}} +\renewcommand{\overleftarrow}{% + \mathpalette{\overarrow@\leftarrowfill@}} +\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}}} +\newcommand{\underrightarrow}{% + \mathpalette{\underarrow@\rightarrowfill@}} +\newcommand{\underleftarrow}{% + \mathpalette{\underarrow@\leftarrowfill@}} +\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 \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{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} +% +% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% \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. +% +% 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} +% +% 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} +% +% \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. +% \begin{macrocode} + \ifdim\linewidth=\columnwidth + \else \parshape\@ne \@totalleftmargin \linewidth + \fi + \noindent##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@} +% 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#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} + \null\,% + \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@@@aligned} +% \cs{math@cr@@@aligned} 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 + \null\,% + \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. +% +% \changes{v1.2b}{1995/02/15}{Added kern -alignsep@ to math@cr@@@align} +% \changes{v1.2b}{1995/02/15}{Modified one piece of measure@} +% \changes{v1.2b}{1995/02/15}{Cleaned out some obsolete commentary} +% \changes{v1.2b}{1995/02/15}{Changed kern tagshift@ to kern -tagshift@ +% in the reqno case of place@tag} +% +% \changes{v1.2c}{1996/11/01}{Changed `over etc from error to warning} +% +% \changes{v1.2d}{1997/03/20}{% +% Removed dependency on mixed-case fd file names} +% +% \CheckSum{6699} +% \Finale |