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ltmath.dtx
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ltmath.dtx
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% \iffalse meta-comment
%
% Copyright (C) 1993-2022
% The LaTeX Project and any individual authors listed elsewhere
% in this file.
%
% This file is part of the LaTeX base system.
% -------------------------------------------
%
% It may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3c
% of this license or (at your option) any later version.
% The latest version of this license is in
% https://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of LaTeX
% version 2008 or later.
%
% This file has the LPPL maintenance status "maintained".
%
% The list of all files belonging to the LaTeX base distribution is
% given in the file `manifest.txt'. See also `legal.txt' for additional
% information.
%
% The list of derived (unpacked) files belonging to the distribution
% and covered by LPPL is defined by the unpacking scripts (with
% extension .ins) which are part of the distribution.
%
% \fi
% \iffalse
%%% From File: ltmath.dtx
%
%<leqno>\ProvidesFile{leqno.clo}
%<fleqn>\ProvidesFile{fleqn.clo}
%<leqno,fleqn> [2016/12/29 v1.2b Standard LaTeX option
%<leqno> (left equation numbers)]
%<fleqn> (flush left equations)]
%
%<*driver>
% \fi
\ProvidesFile{ltmath.dtx}
[2022/05/08 v1.2l LaTeX Kernel (Math Setup)]
% \iffalse
%</driver>
%
%<*driver>
\documentclass{ltxdoc}
\GetFileInfo{ltmath.dtx}
\title{\filename}
\date{\filedate}
\author{%
Johannes Braams\and
David Carlisle\and
Alan Jeffrey\and
Leslie Lamport\and
Frank Mittelbach\and
Chris Rowley\and
Rainer Sch\"opf}
\begin{document}
\MaintainedByLaTeXTeam{latex}
\maketitle
\DocInput{\filename}
\end{document}
%</driver>
% \fi
%
%
% \changes{v1.1b}{1996/07/26}{Removed \cs{global} before
% \cs{@ignoretrue} in various places.}
% \changes{v1.1c}{1998/08/17}{(RmS) Minor documentation fixes.}
% \changes{v1.1g}{2005/11/10}{(MH) Minor documentation fixes.}
%
% \section{Math setup}
%
% This file contains a lot of the original plain \TeX{} code, as well
% as the \LaTeX{} environments for math. It still needs sorting out.
%
% \MaybeStop{}
%
% \begin{macrocode}
%<*2ekernel>
\message{math definitions,}
% \end{macrocode}
%
%
%
% \subsection{Math commands based on plain \TeX}
%
% \subsubsection{The log-like functions}
%
% \changes{1.0m}{1994/10/29}{ASAJ: Added \cs{DeclareMathOperator}.}
% \changes{v1.0o}{1994/11/17}
% {\cs{@tempa} to \cs{reserved@a}}
% \changes{1.0q}{1994/11/30}{ASAJ: \cs{DeclareMathOperator} moved to
% AMS\LaTeX.}
% \changes{v1.0r}{1995/05/07}{Use \cs{hb@xt@}}
% \changes{v1.0r}{1995/05/21}{Update some plain macros}
% \changes{v1.0t}{1995/06/28}{minor doc edits}
% \changes{v1.2c}{2019/08/27}{Make various commands robust}
%
% \begin{macro}{\log}
% The standard operators:
% \begin{macrocode}
\DeclareRobustCommand\log{\mathop{\operator@font log}\nolimits}
\DeclareRobustCommand\lg{\mathop{\operator@font lg}\nolimits}
\DeclareRobustCommand\ln{\mathop{\operator@font ln}\nolimits}
\DeclareRobustCommand\lim{\mathop{\operator@font lim}}
\DeclareRobustCommand\limsup{\mathop{\operator@font lim\,sup}}
\DeclareRobustCommand\liminf{\mathop{\operator@font lim\,inf}}
\DeclareRobustCommand\sin{\mathop{\operator@font sin}\nolimits}
\DeclareRobustCommand\arcsin{\mathop{\operator@font arcsin}\nolimits}
\DeclareRobustCommand\sinh{\mathop{\operator@font sinh}\nolimits}
\DeclareRobustCommand\cos{\mathop{\operator@font cos}\nolimits}
\DeclareRobustCommand\arccos{\mathop{\operator@font arccos}\nolimits}
\DeclareRobustCommand\cosh{\mathop{\operator@font cosh}\nolimits}
\DeclareRobustCommand\tan{\mathop{\operator@font tan}\nolimits}
\DeclareRobustCommand\arctan{\mathop{\operator@font arctan}\nolimits}
\DeclareRobustCommand\tanh{\mathop{\operator@font tanh}\nolimits}
\DeclareRobustCommand\cot{\mathop{\operator@font cot}\nolimits}
\DeclareRobustCommand\coth{\mathop{\operator@font coth}\nolimits}
\DeclareRobustCommand\sec{\mathop{\operator@font sec}\nolimits}
\DeclareRobustCommand\csc{\mathop{\operator@font csc}\nolimits}
\DeclareRobustCommand\max{\mathop{\operator@font max}}
\DeclareRobustCommand\min{\mathop{\operator@font min}}
\DeclareRobustCommand\sup{\mathop{\operator@font sup}}
\DeclareRobustCommand\inf{\mathop{\operator@font inf}}
\DeclareRobustCommand\arg{\mathop{\operator@font arg}\nolimits}
\DeclareRobustCommand\ker{\mathop{\operator@font ker}\nolimits}
\DeclareRobustCommand\dim{\mathop{\operator@font dim}\nolimits}
\DeclareRobustCommand\hom{\mathop{\operator@font hom}\nolimits}
\DeclareRobustCommand\det{\mathop{\operator@font det}}
\DeclareRobustCommand\exp{\mathop{\operator@font exp}\nolimits}
\DeclareRobustCommand\Pr{\mathop{\operator@font Pr}}
\DeclareRobustCommand\gcd{\mathop{\operator@font gcd}}
\DeclareRobustCommand\deg{\mathop{\operator@font deg}\nolimits}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\bmod}
% And some operators have to be done by hand:
% \begin{macrocode}
\DeclareRobustCommand\bmod{%
\nonscript\mskip-\medmuskip\mkern5mu%
\mathbin{\operator@font mod}\penalty900\mkern5mu%
\nonscript\mskip-\medmuskip}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\pmod}
% \begin{macrocode}
\DeclareRobustCommand\pmod[1]{%
\allowbreak\mkern18mu({\operator@font mod}\,\,#1)}
% \end{macrocode}
% \end{macro}
%
% \subsubsection{Biggggg}
%
% \begin{macro}{\big}
% Variants on |\big| and friends for use with delimiters:
% \begin{macrocode}
\DeclareRobustCommand\bigl{\mathopen\big}
\DeclareRobustCommand\bigm{\mathrel\big}
\DeclareRobustCommand\bigr{\mathclose\big}
\DeclareRobustCommand\Bigl{\mathopen\Big}
\DeclareRobustCommand\Bigm{\mathrel\Big}
\DeclareRobustCommand\Bigr{\mathclose\Big}
\DeclareRobustCommand\biggl{\mathopen\bigg}
\DeclareRobustCommand\biggm{\mathrel\bigg}
\DeclareRobustCommand\biggr{\mathclose\bigg}
\DeclareRobustCommand\Biggl{\mathopen\Bigg}
\DeclareRobustCommand\Biggm{\mathrel\Bigg}
\DeclareRobustCommand\Biggr{\mathclose\Bigg}
% \end{macrocode}
% \end{macro}
%
% \subsubsection{The UNSORTED Rest}
%
% The other math commands are lifted from plain \TeX.
%
% \begin{macro}{\jot}
% \begin{macrocode}
\newdimen\jot
\jot=3pt
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\interdisplaylinepenalty}
% \begin{macrocode}
\newcount\interdisplaylinepenalty
\interdisplaylinepenalty=100
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\choose}
% \begin{macrocode}
\def\choose{\atopwithdelims()}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\brack}
% \begin{macrocode}
\def\brack{\atopwithdelims[]}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\brace}
% \begin{macrocode}
\def\brace{\atopwithdelims\{\}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\mathpalette}
% \begin{macrocode}
\def\mathpalette#1#2{%
\mathchoice
{#1\displaystyle{#2}}%
{#1\textstyle{#2}}%
{#1\scriptstyle{#2}}%
{#1\scriptscriptstyle{#2}}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\root}
% \changes{v1.1d}{1997/01/08}
% {(DPC) Remove spurious space tokens from
% plain \TeX\ definition /2359}
% \begin{macro}{\rootbox}
% \begin{macro}{\r@@t}
% \changes{v1.0r}{1995/05/21}{Use \cs{sqrtsign} instead of
% \cs{sqrt}}
% \begin{macrocode}
\newbox\rootbox
% \end{macrocode}
%
% \begin{macrocode}
\def\root#1\of{%
\setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#1}$}%
\mathpalette\r@@t}
% \end{macrocode}
%
% \begin{macrocode}
\def\r@@t#1#2{%
\setbox\z@\hbox{$\m@th#1\sqrtsign{#2}$}%
\dimen@\ht\z@ \advance\dimen@-\dp\z@
\mkern5mu\raise.6\dimen@\copy\rootbox
\mkern-10mu\box\z@}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\phantom}
% \changes{v1.0p}{1994/11/18}
% {(DPC) use \cs{expandafter} instead of \cs{next}}
% \changes{v1.0p}{1994/11/18}
% {(DPC) colour support}
% \begin{macro}{\hphantom}
% \begin{macro}{\vphantom}
% \begin{macrocode}
\newif\ifv@
\newif\ifh@
% \end{macrocode}
%
%
%
%
% \begin{macrocode}
%</2ekernel>
%<*2ekernel|latexrelease>
%<latexrelease>\IncludeInRelease{2019/10/01}%
%<latexrelease> {\vphantom}{Make commands robust}%
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\vphantom{\v@true\h@false\ph@nt}
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\hphantom{\v@false\h@true\ph@nt}
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\phantom{\v@true\h@true\ph@nt}
% \end{macrocode}
%
% \begin{macro}{\mathstrut}
% \begin{macrocode}
\DeclareRobustCommand\mathstrut{\vphantom(}
% \end{macrocode}
% \end{macro}
%
% \begin{macrocode}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
%<latexrelease>\IncludeInRelease{0000/00/00}%
%<latexrelease> {\vphantom}{Make commands robust}%
%<latexrelease>
%<latexrelease>\kernel@make@fragile\vphantom
%<latexrelease>\kernel@make@fragile\hphantom
%<latexrelease>\kernel@make@fragile\phantom
%<latexrelease>\kernel@make@fragile\mathstrut
%<latexrelease>
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
%
% \begin{macrocode}
\def\ph@nt{%
\ifmmode
\expandafter\mathpalette\expandafter\mathph@nt
\else
\expandafter\makeph@nt
\fi}
% \end{macrocode}
%
% \begin{macrocode}
\def\makeph@nt#1{%
\setbox\z@\hbox{\color@begingroup#1\color@endgroup}\finph@nt}
% \end{macrocode}
%
% \begin{macrocode}
\def\mathph@nt#1#2{%
\setbox\z@\hbox{$\m@th#1{#2}$}\finph@nt}
% \end{macrocode}
%
% \begin{macrocode}
%</2ekernel>
%<*2ekernel|latexrelease>
%<latexrelease>\IncludeInRelease{2018/12/01}%
%<latexrelease> {\finph@nt}{Start LR-mode}%
\def\finph@nt{%
\setbox\tw@\null
\ifv@ \ht\tw@\ht\z@ \dp\tw@\dp\z@\fi
\ifh@ \wd\tw@\wd\z@\fi
% \end{macrocode}
% \changes{v1.2b}{2018/09/24}{Start LR-mode if necessary (git/49)}
% \begin{macrocode}
\leavevmode@ifvmode\box\tw@}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
%<latexrelease>\IncludeInRelease{0000/00/00}%
%<latexrelease> {\finph@nt}{Start LR-mode}%
%<latexrelease>\def\finph@nt{%
%<latexrelease> \setbox\tw@\null
%<latexrelease> \ifv@ \ht\tw@\ht\z@ \dp\tw@\dp\z@\fi
%<latexrelease> \ifh@ \wd\tw@\wd\z@\fi \box\tw@}
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%
% \begin{macro}{\smash}
% \changes{v1.0p}{1994/11/18}
% {(DPC) use \cs{expandafter} instead of \cs{next}}
% \changes{v1.0p}{1994/11/18}
% {(DPC) colour support}
% \begin{macrocode}
\DeclareRobustCommand\smash{%
\relax % \relax, in case this comes first in \halign
\ifmmode
\expandafter\mathpalette\expandafter\mathsm@sh
\else
\expandafter\makesm@sh
\fi}
% \end{macrocode}
%
% \begin{macrocode}
\def\makesm@sh#1{%
\setbox\z@\hbox{\color@begingroup#1\color@endgroup}\finsm@sh}
\def\mathsm@sh#1#2{%
\setbox\z@\hbox{$\m@th#1{#2}$}\finsm@sh}
% \end{macrocode}
% \changes{v1.2b}{2018/09/24}{Start LR-mode if necessary (git/49)}
% \begin{macrocode}
%</2ekernel>
%<*2ekernel|latexrelease>
%<latexrelease>\IncludeInRelease{2018/12/01}%
%<latexrelease> {\finsm@sh}{Start LR-mode}%
\def\finsm@sh{\ht\z@\z@ \dp\z@\z@ \leavevmode@ifvmode\box\z@}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
%<latexrelease>\IncludeInRelease{0000/00/00}%
%<latexrelease> {\finsm@sh}{Start LR-mode}%
%<latexrelease>\def\finsm@sh{\ht\z@\z@ \dp\z@\z@ \box\z@}
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\buildrel}
% \begin{macrocode}
\def\buildrel#1\over#2{\mathrel{\mathop{\kern\z@#2}\limits^{#1}}}
% \end{macrocode}
% \end{macro}
%
%
% \begin{macrocode}
%</2ekernel>
%<*2ekernel|latexrelease>
%<latexrelease>\IncludeInRelease{2019/10/01}%
%<latexrelease> {\cases}{Make commands robust}%
% \end{macrocode}
%
% \begin{macro}{\cases}
% \changes{LaTeX2.09}{1991/08/14}
% {(RmS) inserted extra braces around entry for NFSS}
% \changes{v1.2g}{2020/07/27}{Don't make the command \cs{long} (gh/354)}
% \begin{macrocode}
\DeclareRobustCommand*\cases[1]{\left\{\,\vcenter{\normalbaselines\m@th
\ialign{$##\hfil$&\quad{##}\hfil\crcr#1\crcr}}\right.}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\matrix}
% \changes{v1.2g}{2020/07/27}{Don't make the command \cs{long} (gh/354)}
% \begin{macrocode}
\DeclareRobustCommand*\matrix[1]{\null\,\vcenter{\normalbaselines\m@th
\ialign{\hfil$##$\hfil&&\quad\hfil$##$\hfil\crcr
\mathstrut\crcr\noalign{\kern-\baselineskip}
#1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\pmatrix}
% \changes{v1.2g}{2020/07/27}{Don't make the command \cs{long} (gh/354)}
% \begin{macrocode}
\DeclareRobustCommand*\pmatrix[1]{\left(\matrix{#1}\right)}
% \end{macrocode}
% \end{macro}
%
% \begin{macrocode}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
%<latexrelease>\IncludeInRelease{0000/00/00}%
%<latexrelease> {\cases}{Make commands robust}%
%<latexrelease>
%<latexrelease>\kernel@make@fragile\cases
%<latexrelease>\kernel@make@fragile\matrix
%<latexrelease>\kernel@make@fragile\pmatrix
%<latexrelease>
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
%
%
% \begin{macro}{\bordermatrix}
% \changes{LaTeX2e}{1994/01/25}{Removed \cs{p@renwd}.}
% \begin{macrocode}
\def\bordermatrix#1{\begingroup \m@th
\@tempdima 8.75\p@
\setbox\z@\vbox{%
\def\cr{\crcr\noalign{\kern2\p@\global\let\cr\endline}}%
\ialign{$##$\hfil\kern2\p@\kern\@tempdima&\thinspace\hfil$##$\hfil
&&\quad\hfil$##$\hfil\crcr
\omit\strut\hfil\crcr\noalign{\kern-\baselineskip}%
#1\crcr\omit\strut\cr}}%
\setbox\tw@\vbox{\unvcopy\z@\global\setbox\@ne\lastbox}%
\setbox\tw@\hbox{\unhbox\@ne\unskip\global\setbox\@ne\lastbox}%
\setbox\tw@\hbox{$\kern\wd\@ne\kern-\@tempdima\left(\kern-\wd\@ne
\global\setbox\@ne\vbox{\box\@ne\kern2\p@}%
\vcenter{\kern-\ht\@ne\unvbox\z@\kern-\baselineskip}\,\right)$}%
\null\;\vbox{\kern\ht\@ne\box\tw@}\endgroup}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\openup}
% \changes{v1.2k}{2022/04/08}{Make \cs{protected} (gh/123)}
% \begin{macrocode}
\protected\def\openup{\afterassignment\@penup\dimen@}
% \end{macrocode}
%
% \begin{macrocode}
\def\@penup{\advance\lineskip\dimen@
\advance\baselineskip\dimen@
\advance\lineskiplimit\dimen@}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\displaylines}
% \begin{macrocode}
\newif\ifdt@p
% \end{macrocode}
%
% \begin{macrocode}
\def\displ@y{\global\dt@ptrue\openup\jot\m@th
\everycr{\noalign{\ifdt@p \global\dt@pfalse \ifdim\prevdepth>-1000\p@
\vskip-\lineskiplimit \vskip\normallineskiplimit \fi
\else \penalty\interdisplaylinepenalty \fi}}}
% \end{macrocode}
%
% \begin{macrocode}
\def\@lign{\tabskip\z@skip\everycr{}} % restore inside \displ@y
% \end{macrocode}
%
% \begin{macrocode}
\def\displaylines#1{\displ@y \tabskip\z@skip
\halign{\hb@xt@\displaywidth{$\@lign\hfil\displaystyle##\hfil$}\crcr
#1\crcr}}
% \end{macrocode}
% \end{macro}
%
% \changes{v1.0r}{1995/05/21}{Remove \cs{mathhexbox} from this file}
%
% \begin{macro}{\sp}
% \begin{macro}{\sb}
% \begin{macrocode}
\let\sp=^
\let\sb=_
% \end{macrocode}
% \end{macro}
% \end{macro}
%
%
% \begin{macro}{\tmspace}
% \begin{macro}{\,}
% \begin{macro}{\thinspace}
% \begin{macro}{\!}
% \begin{macro}{\negthinspace}
% \begin{macro}{\:}
% \begin{macro}{\medspace}
% \begin{macro}{\negmedspace}
% \begin{macro}{\;}
% \begin{macro}{\thickspace}
% \begin{macro}{\negthickspace}
%
% Originally \LaTeX{} only provided a small set of spacing commands
% for use in text and math, some of the commands like \cs{;} were
% only supported in math mode. \texttt{amsmath} normalized and
% provided all of them in text and math. This code has now been
% moved to the kernel so that it is generally available.
%
%
% \begin{macrocode}
%</2ekernel>
%<*2ekernel|latexrelease>
%<latexrelease>\IncludeInRelease{2020/10/01}%
%<latexrelease> {\tmspace}{amsmath spacing commands}%
% \end{macrocode}
% \cs{tmspace} is really meant to be an internal command so it
% doesn't necessarily has to be robust but it was robust in
% \texttt{amsmath} so we leave it like that.
% \changes{v1.2e}{2020/03/07}{Add \texttt{amsmath} math/text spacing
% commands to the kernel (gh/303)}
% \begin{macrocode}
\DeclareRobustCommand\tmspace[3]{%
\ifmmode\mskip#1#2\else\leavevmode@ifvmode\kern#1#3\fi\relax}
% \end{macrocode}
% In \texttt{amsmath} the text kern is \texttt{.1667em}. For
% compatibility reasons we keep the longer one.
% \begin{macrocode}
\DeclareRobustCommand\,{\tmspace+\thinmuskip{.16667em}}
\let\thinspace\,
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\!{\tmspace-\thinmuskip{.16667em}}
\let\negthinspace\!
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\:{\tmspace+\medmuskip{.2222em}}
\let\medspace\:
% \end{macrocode}
% \LaTeX{} has a second name for this in its manual:
% \begin{macrocode}
\let\>=\:
\DeclareRobustCommand\negmedspace{\tmspace-\medmuskip{.2222em}}
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\;{\tmspace+\thickmuskip{.2777em}}
\let\thickspace\;
\DeclareRobustCommand\negthickspace{\tmspace-\thickmuskip{.2777em}}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
% \end{macrocode}
%
% \begin{macrocode}
%<latexrelease>\IncludeInRelease{0000/00/00}%
%<latexrelease> {\tmspace}{amsmath spacing commands}%
%<latexrelease>
%<latexrelease>\let\tmspace\@undefined
%<latexrelease>\DeclareRobustCommand{\,}{%
%<latexrelease> \relax\ifmmode\mskip\thinmuskip\else\thinspace\fi}
%<latexrelease>\DeclareRobustCommand\thinspace{\leavevmode@ifvmode\kern .16667em }
%<latexrelease>\DeclareRobustCommand\negthinspace{\leavevmode@ifvmode\kern-.16667em }
%<latexrelease>\def\>{\mskip\medmuskip}
%<latexrelease>\let\:=\>
%<latexrelease>\def\;{\mskip\thickmuskip}
%<latexrelease>\def\!{\mskip-\thinmuskip}
%<latexrelease>
% \end{macrocode}
% \changes{v1.2h}{2020/11/09}{\cs{negmedspace} and \cs{negthickspace}
% have been only in amsmath, so we need to undefine for rollback (gh/423)}
% \begin{macrocode}
%<latexrelease>\let\negmedspace\@undefined
%<latexrelease>\let\negthickspace\@undefined
%<latexrelease>
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
%
%
%
% \begin{macro}{\*}
% \begin{macrocode}
\DeclareRobustCommand\*{\discretionary{\thinspace\the\textfont2\char2}{}{}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\:}
% Nickname for the medium space since |\>| is not available inside
% \texttt{tabbing}.
% \begin{macrocode}
%\let\:=\>
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\active@math@prime}
% \changes{v1.1e}{1999/10/09}{Macro added, see PR 3104.}
% This is the definition of the active math prime.
% \begin{macrocode}
\def\active@math@prime{^\bgroup\prim@s}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\prime@s}
% \changes{v1.0p}{1994/11/18}
% {(DPC) use \cs{@let@token} instead of \cs{next}
% and \cs{expandafter} instead of \cs{nxt}}
% \changes{v1.1e}{1999/10/09}{Introduce \cs{active@math@prime}.}
% \begin{macrocode}
{\catcode`\'=\active \global\let'\active@math@prime}
% \end{macrocode}
%
% \begin{macrocode}
\def\prim@s{%
\prime\futurelet\@let@token\pr@m@s}
% \end{macrocode}
%
% \begin{macrocode}
\def\pr@m@s{%
\ifx'\@let@token
\expandafter\pr@@@s
\else
\ifx^\@let@token
\expandafter\expandafter\expandafter\pr@@@t
\else
\egroup
\fi
\fi}
% \end{macrocode}
%
% \begin{macrocode}
\def\pr@@@s#1{\prim@s}
% \end{macrocode}
%
% \begin{macrocode}
\def\pr@@@t#1#2{#2\egroup}
% \end{macrocode}
% \end{macro}
%
% \changes{v1.0i}{1994/05/17}{Replaced \cs{let} by \cs{gdef}, for
% indirect definition.}
% \begin{macrocode}
{\catcode`\_=\active \gdef_{\_}} % _ in math is
% either subscript or \_
% \end{macrocode}
%
%
% \changes{v1.0m}{1994/10/29}{ASAJ: Removed \cs{dag}, \cs{ddag}.}
% \changes{v1.0m}{1994/10/29}{ASAJ: Renamed \cs{S} and \cs{P} to
% \cs{mathsection} and \cs{mathparagraph} and made them
% \cs{mathchardef}s.}
% \changes{v1.0m}{1994/10/29}{ASAJ: Added \cs{mathellipsis},
% \cs{mathdollar} and \cs{mathsterling}.}
% \changes{v1.0n}{1994/10/30}{ASAJ: Moved the new commands to ltoutenc.}
%
% \subsection{Math Environments}
%
% \changes{1.0m}{1994/10/29}{ASAJ: Tidied up documentation.}
%
% \begin{macro}{\(}
% \begin{macro}{\)}
% Produces |$...$| with checks that |\(| isn't used in math mode, and
% that |\)| is only used in math mode begun with |\(|.
% \changes{v1.1h}{2015/01/08}{Make Robust (latexrelease)}
% \begin{macrocode}
%</2ekernel>
%<latexrelease>\IncludeInRelease{2015/01/01}{\(}{Make \( robust}%
%<*2ekernel|latexrelease>
\DeclareRobustCommand\({%
\relax\ifmmode\@badmath\else$\fi}%
\DeclareRobustCommand\){%
\relax\ifmmode\ifinner$\else\@badmath\fi\else \@badmath\fi}%
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
%<latexrelease>\IncludeInRelease{0000/00/00}{\(}{Make \( robust}%
%<latexrelease>\def\({%
%<latexrelease> \relax\ifmmode\@badmath\else$\fi}%
%<latexrelease>\expandafter\let\csname\string( \endcsname\@undefined
%<latexrelease>\def\){%
%<latexrelease> \relax\ifmmode\ifinner$\else\@badmath\fi\else \@badmath\fi}%
%<latexrelease>\expandafter\let\csname\string) \endcsname\@undefined
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\[}
% \changes{v1.1g}{2005/11/10}
% {(MH) Fixed potential problem in \cs{[} (pr/3399).}
% \begin{macro}{\]}
% Produces |$$...$$| with checks that |\[| isn't used in math mode,
% and that |\]| is only used in display math mode (though there is no
% real test that this display math started with |\[| and not with |$$|).
% \changes{v1.1h}{2015/01/08}{Make Robust (latexrelease)}
% \begin{macrocode}
%</2ekernel>
%<latexrelease>\IncludeInRelease{2015/01/01}{\[}{Make \[ robust}%
%<*2ekernel|latexrelease>
\DeclareRobustCommand\[{%
\relax\ifmmode
\@badmath
\else
\ifvmode
\nointerlineskip
\makebox[.6\linewidth]{}%
\fi
$$%%$$ BRACE MATCH HACK
\fi
}%
% \end{macrocode}
%
% \begin{macrocode}
\DeclareRobustCommand\]{%
\relax\ifmmode
\ifinner
\@badmath
\else
$$%%$$ BRACE MATCH HACK
\fi
\else
\@badmath
\fi
\ignorespaces
}%
% \end{macrocode}
%
% \begin{macrocode}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
%<latexrelease>\IncludeInRelease{0000/00/00}{\[}{Make \[ robust}%
%<latexrelease>\def\[{%
%<latexrelease> \relax\ifmmode
%<latexrelease> \@badmath
%<latexrelease> \else
%<latexrelease> \ifvmode
%<latexrelease> \nointerlineskip
%<latexrelease> \makebox[.6\linewidth]{}%
%<latexrelease> \fi
%<latexrelease> $$%%$$ BRACE MATCH HACK
%<latexrelease> \fi
%<latexrelease>}%
%<latexrelease>\expandafter\let\csname\string[ \endcsname\@undefined
% \end{macrocode}
%
% \begin{macrocode}
%<latexrelease>\def\]{%
%<latexrelease> \relax\ifmmode
%<latexrelease> \ifinner
%<latexrelease> \@badmath
%<latexrelease> \else
%<latexrelease> $$%%$$ BRACE MATCH HACK
%<latexrelease> \fi
%<latexrelease> \else
%<latexrelease> \@badmath
%<latexrelease> \fi
%<latexrelease> \ignorespaces
%<latexrelease>}%
%<latexrelease>\expandafter\let\csname\string] \endcsname\@undefined
%<latexrelease>\EndIncludeInRelease
%<*2ekernel>
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{environment}{math}
% \begin{environment}{displaymath}
% Disguises for |\(...\)| and |\[...\]|.
% \begin{macrocode}
\let\math=\(
\let\endmath=\)
% \end{macrocode}
%
% \begin{macrocode}
\def\displaymath{\[}
\def\enddisplaymath{\]\@ignoretrue}
% \end{macrocode}
% \end{environment}
% \end{environment}
%
%
% \begin{environment}{equation}
% \changes{LaTeX2.09}{1992/01/10}{RmS: put \cs{hbox} around \cs{@eqnnum}
% to typeset the equation number in text mode
% (as in the eqnarray env.)}
% \begin{macro}{\c@equation}
% Numbered equations, using the counter |\c@equation|.
% \emph{Note}: The document style must define |\theequation| etc., and
% do the appropriate |\@addtoreset|. It should also redefine |\@eqnnum|
% if another format for the equation number is desired other than the
% standard (...), or to move the equation numbers to the flushleft.
% (See comment on the |\def| of |\@eqnnum|.)
% \begin{macrocode}
\@definecounter{equation}
\def\equation{$$\refstepcounter{equation}}
\def\endequation{\eqno \hbox{\@eqnnum}$$\@ignoretrue}
% \end{macrocode}
% \end{macro}
% \end{environment}
%
% \begin{macro}{\@eqnnum}
% \changes{LaTeX2.09}{1991/09/29}{RmS: \cs{reset@font} added.}
% \changes{v1.0l}{1994/10/23}{Added \cs{normalcolor} since \cs{eqno}
% introduces a subgroup of the displayed math group}
%
% Produces the equation number for equation and
% eqnarray environments. The following definition is for
% flushright numbers; for flushleft numbers, see leqno.clo.
% The equation number is set in black roman type even
% if an eqnarray environment appears in an italic environment.
% \changes{v1.0s}{1995/05/26}{Removed \cs{rmfamily} (PR 1578),
% replaced \cs{reset@font} with \cs{normalfont}}
% \begin{macrocode}
\def\@eqnnum{{\normalfont \normalcolor (\theequation)}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\stackrel}
% A disguise for plain \TeX's buildrel.
% \begin{macrocode}
\DeclareRobustCommand\stackrel[2]{\mathrel{\mathop{#2}\limits^{#1}}}
% \end{macrocode}
% \end{macro}
%
% \changes{v0.9g}{1993/12/11}{Added a group around the first argument
% of \cs{frac} to prevent
% changes (for example font changes) from modifying the contents of
% the second argument.}
%
% \begin{macro}{\frac}
% A disguise for plain \TeX's |\over|.
% \begin{macrocode}
\DeclareRobustCommand\frac[2]{{\begingroup#1\endgroup\over#2}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sqrt}
% \changes{v1.0y}{1995/10/16}{(DPC) Make robust /1808}
% \begin{macro}{\@sqrt}
% Add an optional argument to plain's |\sqrt| to give the $n$th root
% of an expression $\sqrt[n]{e}$.
% \changes{v1.0r}{1995/05/21}{Use \cs{sqrtsign}}
% \begin{macrocode}
\DeclareRobustCommand\sqrt{\@ifnextchar[\@sqrt\sqrtsign}
\def\@sqrt[#1]{\root #1\of}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \changes{LaTeX2.09}{1985/11/04}{produce warning message if line
% extends into margin. Doesn't warn about formula
% overprinting equation number.}
% \changes{LaTeX2.09}{1993/11/02}{RmS:
% Corrected description of \cs{@eqnsel}, moved \cs{@eqnsel}
% accordingly and removed extra \cs{tabskip} assignment.}
% \changes{LaTeX2e}{1993/11/03}{RmS: Initialized \cs{everycr} to empty}
% \changes{v0.9i}{1993/12/16}
% {use \cs{refstepcounter} instead of shortcut}
% \changes{v0.9o}{1994/01/13}{correcting 0.9i}
%
% \begin{environment}{eqnarray}
% \begin{macro}{\@eqcnt}
% \begin{macro}{\@eqpen}
% \begin{macro}{\if@eqnsw}
% \begin{macro}{\@eqnsel}
% Here's the eqnarray environment:
% Default is for left-hand side of equations to be flushright.
% To make them flushleft, |\let\@eqnsel = \hfil|.
% \begin{macrocode}
\newcount\@eqcnt
\newcount\@eqpen
\newif\if@eqnsw\@eqnswtrue
\newskip\@centering
\@centering = 0pt plus 1000pt
% \end{macrocode}
% To get a proper \cs{@currentlabel} we have to redefine it for the
% whole display. Note that we can't use \cs{refstepcounter} as this
% results in |\@currentlabel| getting restored at the wrong and
% thus always writing the first label to the \texttt{.aux} file.
% \changes{v1.2j}{2021/10/14}
% {Explicitly set \cs{@currentcounter} (gh/687)}
% \begin{macrocode}
\def\eqnarray{%
\stepcounter{equation}%
\def\@currentlabel{\p@equation\theequation}%
\def\@currentcounter{equation}%
\global\@eqnswtrue
\m@th
\global\@eqcnt\z@
\tabskip\@centering
\let\\\@eqncr
$$\everycr{}\halign to\displaywidth\bgroup
\hskip\@centering$\displaystyle\tabskip\z@skip{##}$\@eqnsel
&\global\@eqcnt\@ne\hskip \tw@\arraycolsep \hfil${##}$\hfil
&\global\@eqcnt\tw@ \hskip \tw@\arraycolsep
$\displaystyle{##}$\hfil\tabskip\@centering
&\global\@eqcnt\thr@@ \hb@xt@\z@\bgroup\hss##\egroup
\tabskip\z@skip
\cr
}
% \end{macrocode}
%
% \begin{macrocode}
\def\endeqnarray{%
\@@eqncr
\egroup
\global\advance\c@equation\m@ne
$$\@ignoretrue
}
% \end{macrocode}
%
% \begin{macrocode}
\let\@eqnsel=\relax
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{macro}
% \end{environment}
%
% \begin{macro}{\nonumber}
% Switches off equation numbering.
% \begin{macrocode}
\def\nonumber{\global\@eqnswfalse}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@eqncr}
% \changes{v1.2i}{2021/04/20}{Use \cs{protected} for \cs{\bslash} variant (gh/548)}
% \begin{macro}{\@xeqncr}
% \begin{macro}{\@yeqncr}
% \changes{v1.0y}{1995/10/16}{(DPC) Use \cs{@testopt} /1911}
% \begin{macrocode}
\protected\def\@eqncr{%
{\ifnum0=`}\fi
\@ifstar{%
\global\@eqpen\@M\@yeqncr
}{%
\global\@eqpen\interdisplaylinepenalty \@yeqncr
}%
}
% \end{macrocode}
%
% \begin{macrocode}
\def\@yeqncr{\@testopt\@xeqncr\z@skip}
% \end{macrocode}
%
% \changes{v1.2f}{2020/04/21}{Support calc syntax (gh/152)}
% \begin{macrocode}
%</2ekernel>
%<*2ekernel|latexrelease>
%<latexrelease>\IncludeInRelease{2020/10/01}%
%<latexrelease> {\@xeqncr}{eqnarray support calc syntax}%
\def\@xeqncr[#1]{%
\ifnum0=`{\fi}%
\@@eqncr
\noalign{\penalty\@eqpen\vskip\jot\@vspace@calcify{#1}}%
}
%</2ekernel|latexrelease>
%<latexrelease>\EndIncludeInRelease
% \end{macrocode}