% \iffalse meta-comment
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% more than one year old, see bugs.txt.
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% IMPORTANT COPYRIGHT NOTICE:
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% is distributed together with all the files listed in manifest.txt.
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% \fi
% \iffalse
%%% From File: ltmath.dtx
%
%<leqno>\ProvidesFile{leqno.clo}
%<fleqn>\ProvidesFile{fleqn.clo}
%<leqno,fleqn> [1996/07/26 v1.1b Standard LaTeX option
%<leqno> (left equation numbers)]
%<fleqn> (flush left equations)]
%
%<*driver>
% \fi
\ProvidesFile{ltmath.dtx}
[1997/01/08 v1.1d 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}
\maketitle
\DocInput{\filename}
\end{document}
%</driver>
% \fi
%
% \CheckSum{1097}
%
% \changes{v1.1b}{1996/07/26}{removed \cs{global} before
% \cs{@ignoretrue} in various places}
%
% \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.
%
% \StopEventually{}
%
% \begin{macrocode}
%<*2ekernel>
\message{math definitions,}
% \end{macrocode}
%
%
%% \CharacterTable
%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%% Digits \0\1\2\3\4\5\6\7\8\9
%% Exclamation \! Double quote \" Hash (number) \#
%% Dollar \$ Percent \% Ampersand \&
%% Acute accent \' Left paren \( Right paren \)
%% Asterisk \* Plus \+ Comma \,
%% Minus \- Point \. Solidus \/
%% Colon \: Semicolon \; Less than \<
%% Equals \= Greater than \> Question mark \?
%% Commercial at \@ Left bracket \[ Backslash \\
%% Right bracket \] Circumflex \^ Underscore \_
%% Grave accent \` Left brace \{ Vertical bar \|
%% Right brace \} Tilde \~}
%%
%
% \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}
%
% \begin{macro}{\log}
% The standard operators:
% \begin{macrocode}
\def\log{\mathop{\operator@font log}\nolimits}
\def\lg{\mathop{\operator@font lg}\nolimits}
\def\ln{\mathop{\operator@font ln}\nolimits}
\def\lim{\mathop{\operator@font lim}}
\def\limsup{\mathop{\operator@font lim\,sup}}
\def\liminf{\mathop{\operator@font lim\,inf}}
\def\sin{\mathop{\operator@font sin}\nolimits}
\def\arcsin{\mathop{\operator@font arcsin}\nolimits}
\def\sinh{\mathop{\operator@font sinh}\nolimits}
\def\cos{\mathop{\operator@font cos}\nolimits}
\def\arccos{\mathop{\operator@font arccos}\nolimits}
\def\cosh{\mathop{\operator@font cosh}\nolimits}
\def\tan{\mathop{\operator@font tan}\nolimits}
\def\arctan{\mathop{\operator@font arctan}\nolimits}
\def\tanh{\mathop{\operator@font tanh}\nolimits}
\def\cot{\mathop{\operator@font cot}\nolimits}
\def\coth{\mathop{\operator@font coth}\nolimits}
\def\sec{\mathop{\operator@font sec}\nolimits}
\def\csc{\mathop{\operator@font csc}\nolimits}
\def\max{\mathop{\operator@font max}}
\def\min{\mathop{\operator@font min}}
\def\sup{\mathop{\operator@font sup}}
\def\inf{\mathop{\operator@font inf}}
\def\arg{\mathop{\operator@font arg}\nolimits}
\def\ker{\mathop{\operator@font ker}\nolimits}
\def\dim{\mathop{\operator@font dim}\nolimits}
\def\hom{\mathop{\operator@font hom}\nolimits}
\def\det{\mathop{\operator@font det}}
\def\exp{\mathop{\operator@font exp}\nolimits}
\def\Pr{\mathop{\operator@font Pr}}
\def\gcd{\mathop{\operator@font gcd}}
\def\deg{\mathop{\operator@font deg}\nolimits}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\bmod}
% And some operators have to be done by hand:
% \begin{macrocode}
\def\bmod{%
\nonscript\mskip-\medmuskip\mkern5mu%
\mathbin{\operator@font mod}\penalty900\mkern5mu%
\nonscript\mskip-\medmuskip}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\pmod}
% \begin{macrocode}
\def\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}
\def\bigl{\mathopen\big}
\def\bigm{\mathrel\big}
\def\bigr{\mathclose\big}
\def\Bigl{\mathopen\Big}
\def\Bigm{\mathrel\Big}
\def\Bigr{\mathclose\Big}
\def\biggl{\mathopen\bigg}
\def\biggm{\mathrel\bigg}
\def\biggr{\mathclose\bigg}
\def\Biggl{\mathopen\Bigg}
\def\Biggm{\mathrel\Bigg}
\def\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}{\atopwithdelims}
% \begin{macrocode}
\def\brack{\atopwithdelims[]}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\brace}
% \begin{macrocode}
\def\brace{\atopwithdelims\{\}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\mathpalette}
% \changes{v1.0r}{1995/05/21}{Use \cs{sqrtsign} instead of
% \cs{sqrt}}
% \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}
% \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}
\def\vphantom{\v@true\h@false\ph@nt}
% \end{macrocode}
%
% \begin{macrocode}
\def\hphantom{\v@false\h@true\ph@nt}
% \end{macrocode}
%
% \begin{macrocode}
\def\phantom{\v@true\h@true\ph@nt}
% \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}
\def\finph@nt{%
\setbox\tw@\null
\ifv@ \ht\tw@\ht\z@ \dp\tw@\dp\z@\fi
\ifh@ \wd\tw@\wd\z@\fi \box\tw@}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\mathstrut}
% \begin{macrocode}
\def\mathstrut{\vphantom(}
% \end{macrocode}
% \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}
\def\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}
\def\finsm@sh{\ht\z@\z@ \dp\z@\z@ \box\z@}
% \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{macro}{\cases}
% \changes{LaTeX2.09}{1991/08/14}
% {(RmS) inserted extra braces around entry for NFSS}
% \begin{macrocode}
\def\cases#1{\left\{\,\vcenter{\normalbaselines\m@th
\ialign{$##\hfil$&\quad{##}\hfil\crcr#1\crcr}}\right.}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\matrix}
% \begin{macrocode}
\def\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}
% \begin{macrocode}
\def\pmatrix#1{\left(\matrix{#1}\right)}
% \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\bordermatrix}
% \changes{LaTeX2e}{1994/01/25}{Removed \cmd{\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}
% \begin{macrocode}
\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}{\>}
% \begin{macro}{\;}
% \begin{macro}{\!}
% \begin{macrocode}
%\def\,{\mskip\thinmuskip} % already defined in ltspace
\def\>{\mskip\medmuskip}
\def\;{\mskip\thickmuskip}
\def\!{\mskip-\thinmuskip}
% \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\*}
% \begin{macrocode}
\def\*{\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}{\prime@s}
% \changes{v1.0p}{1994/11/18}
% {(DPC) use \cs{@let@token} instead of \cs{next}
% and \cs{expandafter} instead of \cs{nxt}}
% \begin{macrocode}
{\catcode`\'=\active \gdef'{^\bgroup\prim@s}}
% \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 |\(|.
% \begin{macrocode}
\def\({\relax\ifmmode\@badmath\else$\fi}
\def\){\relax\ifmmode\ifinner$\else\@badmath\fi\else \@badmath\fi}
% \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\[}
% \begin{macro}{\]}
% Produces |$$...$$| with checks that |\[| isn't used in math mode,
% and that |\]| is only used in math mode begun with |\]|.
% \begin{macrocode}
\def\[{%
\relax\ifmmode
\@badmath
\else
\ifvmode
\nointerlineskip
\makebox[.6\linewidth]%
\fi
$$%%$$ BRACE MATCH HACK
\fi
}
% \end{macrocode}
%
% \begin{macrocode}
\def\]{%
\relax\ifmmode
\ifinner
\@badmath
\else
$$%%$$ BRACE MATCH HACK
\fi
\else
\@badmath
\fi
\ignorespaces
}
% \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}
\def\stackrel#1#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}
\def\frac#1#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.
% \begin{macrocode}
\def\eqnarray{%
\stepcounter{equation}%
\def\@currentlabel{\p@equation\theequation}%
\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}
% \begin{macro}{\@xeqncr}
% \begin{macro}{\@yeqncr}
% \changes{v1.0y}{1995/10/16}{(DPC) Use \cs{@testopt} /1911}
% \begin{macrocode}
\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}
%
% \begin{macrocode}
\def\@xeqncr[#1]{%
\ifnum0=`{\fi}%
\@@eqncr
\noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}%
}
% \end{macrocode}
%
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@@eqncr}
% \changes{v0.9i}{1993/12/16}{use `refstepcounter instead of shortcut}
% \changes{v0.9o}{1994/01/13}{correcting 0.9i}
%
% \begin{macrocode}
\def\@@eqncr{\let\reserved@a\relax
\ifcase\@eqcnt \def\reserved@a{& & &}\or \def\reserved@a{& &}%
\or \def\reserved@a{&}\else
\let\reserved@a\@empty
\@latex@error{Too many columns in eqnarray environment}\@ehc\fi
\reserved@a \if@eqnsw\@eqnnum\stepcounter{equation}\fi
\global\@eqnswtrue\global\@eqcnt\z@\cr}
% \end{macrocode}
% \end{macro}
%
% \begin{environment}{eqnarray*}
% \begin{macro}{\@seqncr}
% Here's the eqnarray* environment:
% \begin{macrocode}
\let\@seqncr=\@eqncr
% \end{macrocode}
%
% \begin{macrocode}
\@namedef{eqnarray*}{\def\@eqncr{\nonumber\@seqncr}\eqnarray}
% \end{macrocode}
%
% \begin{macrocode}
\@namedef{endeqnarray*}{\nonumber\endeqnarray}
% \end{macrocode}
% \end{macro}
% \end{environment}
%
% \begin{macro}{\lefteqn}
% |\lefteqn{FORMULA}| typesets |FORMULA| in display math style
% flushleft in a box of width zero.
% \changes{v1.0r}{1995/05/21}{Use \cs{rlap}}
% \begin{macrocode}
\def\lefteqn#1{\rlap{$\displaystyle #1$}}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\ensuremath}
% In math mode, |\ensuremath{text}| is equivalent to text; in LR or
% paragraph mode, it is equivalent to |$|text|$|.
% |\relax| is not needed
% in front of the |\ifmmode| as |\protect| will be |\let| to |\relax|.
% This version (due to Donald Arseneau) avoids duplicating its
% argument in the `then' and `else' part of the |\ifmath| which is
% necessary in nested `tabular' like environments. See amslatex/2104.
% \changes{v1.0k}{1994/05/16}
% {Use \cs{DeclareRobustCommand} and add extra braces in math mode}
% \changes{v1.0l}{1994/10/23}{Remove extra braces: but see p 168 of
% Leslie's book}
% \changes{v1.1a}{1996/03/25}{Reimplement for amslatex/2104}
% \begin{macrocode}
\DeclareRobustCommand{\ensuremath}{%
\ifmmode
\expandafter\@firstofone
\else
\expandafter\@ensuredmath
\fi}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@ensuredmath}
% \changes{v1.1a}{1996/03/25}{Macro added for amslatex/2104}
% \changes{v1.1c}{1996/11/09}{Made long, as it was before. /2104}
% The |\relax| stops |\ensuremath{}| starting display math.
% \begin{macrocode}
\long\def\@ensuredmath#1{$\relax#1$}
% \end{macrocode}
% \end{macro}
%
% \begin{macrocode}
%</2ekernel>
% \end{macrocode}
%
%
%
% \subsection{External options to the standard document classes}
%
% \changes{v1.0u}{1995/08/09}
% {Added code for class options leqno and fleqn}
%
% \subsubsection{Left equation numbering}
%
% \begin{macro}{\@eqnnum}
% To put the equation number on the left side of an equation we
% have to use a little trick. The number is shifted |\displaywidth|
% to the left inside a box of (approximately) zero width. This
% fails when the quation is too wide, the equation number than may
% overprint the equation itself.
% \changes{v1.2y classes}{1995/01/12}{Added \cs{normalcolor}}
% \changes{v1.3c classes}{1995/05/25}
% {replace \cs{reset@font}\cs{rmfamily} with \cs{normalfont}
% (PR 1578)}
% \begin{macrocode}
%<*leqno>
\renewcommand\@eqnnum{\hb@[email protected]\p@{}%
\rlap{\normalfont\normalcolor
\hskip -\displaywidth(\theequation)}}
%</leqno>
% \end{macrocode}
% \end{macro}
%
% \subsubsection{Flush left equations}
%
% To get the displayed math environments to print the contents
% flush left (with an indentation) we have to redefine all of
% \LaTeXe's displayed math environments.
%
% \begin{macro}{\mathindent}
% The amount of indentation of the equations is stored in a register.
% \begin{macrocode}
%<*fleqn>
\newdimen\mathindent
% \end{macrocode}
% The setting of |\mathindent| has to be deferred until the class
% file has been processed, because |\leftmargini| is still 0pt
% wide at the moment \texttt{fleqn.clo} is read in.
% \changes{v1.0n classes}
% {1994/01/19}{Deferred setting of \cs{mathindent}}
% \changes{v1.2t classes}
% {1994/06/22}{Set \cs{mathindent} at the end of the
% class instead of at begin document}
% \begin{macrocode}
\AtEndOfClass{\mathindent\leftmargini}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\[}
% Begin display math;
% \begin{macrocode}
\renewcommand\[{\relax
\ifmmode\@badmath
\else
\begin{trivlist}%
\@beginparpenalty\predisplaypenalty
\@endparpenalty\postdisplaypenalty
\item[]\leavevmode
\hb@xt@\linewidth\bgroup $\m@th\displaystyle %$
\hskip\mathindent\bgroup
\fi}
% \end{macrocode}
% \end{macro}
%
% \begin{macro}{\]}
% end display math;
% \begin{macrocode}
\renewcommand\]{\relax
\ifmmode
\egroup $\hfil% $
\egroup
\end{trivlist}%
\else \@badmath
\fi}
% \end{macrocode}
% \end{macro}
%
% \begin{environment}{equation}
% The \textsf{equation} environment
% \begin{macrocode}
\renewenvironment{equation}%
{\@beginparpenalty\predisplaypenalty
\@endparpenalty\postdisplaypenalty
\refstepcounter{equation}%
\trivlist \item[]\leavevmode
\hb@xt@\linewidth\bgroup $\m@th% $
\displaystyle
\hskip\mathindent}%
{$\hfil % $
\displaywidth\linewidth\hbox{\@eqnnum}%
\egroup
\endtrivlist}
% \end{macrocode}
% \end{environment}
%
% \begin{environment}{eqnarray}
% The \textsf{eqnarray} environment
% \begin{macrocode}
\renewenvironment{eqnarray}{%
\stepcounter{equation}%
\def\@currentlabel{\p@equation\theequation}%
\global\@eqnswtrue\m@th
\global\@eqcnt\z@
\tabskip\mathindent
\let\\=\@eqncr
\setlength\abovedisplayskip{\topsep}%
\ifvmode
\addtolength\abovedisplayskip{\partopsep}%
\fi
% \end{macrocode}
% When the documentclass uses a non-zero |\parskip| setting the
% |\topsep| might have a negative value to compensate for
% that. Therefore we add |\parskip| to |\abovedisplayskip|.
% \changes{v1.2v classes}{1994/11/10}{Added value of \cs{parskip} to
% \cs{abovedisplayskip} to compensate for negative \cs{topsep}}
% \begin{macrocode}
\addtolength\abovedisplayskip{\parskip}%
\setlength\belowdisplayskip{\abovedisplayskip}%
\setlength\belowdisplayshortskip{\abovedisplayskip}%
\setlength\abovedisplayshortskip{\abovedisplayskip}%
$$\everycr{}\halign to\linewidth% $$
\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}%
{\@@eqncr
\egroup
\global\advance\c@equation\m@ne$$% $$
\@ignoretrue
}
%</fleqn>
% \end{macrocode}
% \end{environment}
%
%
%
% \Finale
%
|
