%%
%% This is file `amsmath.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% amsmath.dtx
%%% ====================================================================
%%% @LaTeX-file{
%%% filename = "amsmath.dtx",
%%% version = "1.2c",
%%% date = "1996/11/01",
%%% time = "12:34:08 EST",
%%% author = "American Mathematical Society",
%%% copyright = "Copyright (C) 1996 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,
%%% Electronic Products and Services,
%%% 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 = "64909 4970 18142 173891",
%%% email = "[email protected] (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "latex, amslatex, ams-latex, math, amsmath",
%%% supported = "yes",
%%% abstract = "This is part of the AMS-\LaTeX{} distribution. It
%%% 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.",
%%% }
%%% ====================================================================
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1994/12/01]% LaTeX date must December 1994 or later
\ProvidesPackage{amsmath}[1996/11/01 v1.2c AMS math features]
\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}}
\newif\ifctagsplit@
\newif\iftagsleft@
\DeclareOption{leqno}{\tagsleft@true}
\DeclareOption{reqno}{\tagsleft@false}
\DeclareOption{centertags}{\ctagsplit@true}
\DeclareOption{tbtags}{\ctagsplit@false}
\DeclareOption{cmex10}{%
\ifnum\cmex@opt=\@ne \def\cmex@opt{0}%
\else \def\cmex@opt{10}\fi
}
\@ifundefined{cmex@opt}{\def\cmex@opt{7}}{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newif\if@fleqn
\newskip\@mathmargin
\@mathmargin\@centering
\DeclareOption{fleqn}{%
\@fleqntrue
\@mathmargin = -1sp
\AtBeginDocument{%
\ifdim\@mathmargin= -1sp
\@mathmargin\leftmargini
\fi
}%
}
\ExecuteOptions{nointlimits,sumlimits,namelimits,centertags}
\ProcessOptions\relax
\ifnum\cmex@opt=7 \relax
\catcode`\ =9
\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
\catcode`\ =10
\else
\ifnum\cmex@opt=\z@ % need to override cmex7 fontdef from amsfonts
\input{OMXcmex.fd}%
\expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
\def\cmex@opt{10}%
\fi
\fi
\RequirePackage{amstext}
\RequirePackage{amsbsy}
\RequirePackage{amsopn}
\def\@amsmath@err{\PackageError{amsmath}}
\def\AmS{{\protect\AmSfont
A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
\def\AmSfont{%
\usefont{OMS}{cmsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}
\def\pr@m@s{%
\ifx\@let@token'\DN@##1{\prim@s}\else\let\next@\egroup\fi\next@}
\def\prim@s{\prime\futurelet\@let@token\pr@m@s}
\let\@prime=\prime
\renewcommand{\prime}{{\kern\z@\@prime}}
\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}}
\newcommand{\mspace}[1]{\mskip#1\relax}
\begingroup\catcode`\"=12
\def\@tempa#1{\expandafter\@tempb\meaning#1\relax\relax\relax\relax"0000\@nil#1}
\def\@tempb#1"#2#3#4#5#6\@nil#7{%
\ifnum"#2=7 \count@"1#3#4#5\relax
\ifnum\count@<"1000 \else \global\mathchardef#7="0#3#4#5\relax \fi
\fi}
\@tempa\Gamma \@tempa\Delta \@tempa\Theta \@tempa\Lambda \@tempa\Xi
\@tempa\Pi \@tempa\Sigma \@tempa\Upsilon \@tempa\Phi \@tempa\Psi
\@tempa\Omega
\@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}
}{}
\endgroup
\begingroup \catcode`\"=12
\gdef\@@sqrt#1{\radical"270370 {#1}}
\endgroup
\@saveprimitive\overline\@@overline
\def\overline#1{\@@overline{#1}}
\def\boxed#1{\fbox{\m@th$\displaystyle#1$}}
\def\implies{\DOTSB\;\Longrightarrow\;}
\def\impliedby{\DOTSB\;\Longleftarrow\;}
\begingroup \catcode`\"=12 % in case activated by a preceding package
\gdef\And{\DOTSB\;\mathchar"3026 \;}
\@tempcnta=\@xp\@gobble\vert \advance\@tempcnta "4000000
\xdef\lvert{\delimiter\number\@tempcnta\space }
\advance\@tempcnta "1000000
\xdef\rvert{\delimiter\number\@tempcnta\space }
\@tempcnta=\@xp\@gobble\Vert \advance\@tempcnta "4000000
\xdef\lVert{\delimiter\number\@tempcnta\space }
\advance\@tempcnta "1000000
\xdef\rVert{\delimiter\number\@tempcnta\space }
\endgroup % restore "
\@saveprimitive\over\@@over
\@saveprimitive\atop\@@atop
\@saveprimitive\above\@@above
\@saveprimitive\overwithdelims\@@overwithdelims
\@saveprimitive\atopwithdelims\@@atopwithdelims
\@saveprimitive\abovewithdelims\@@abovewithdelims
\DeclareRobustCommand{\primfrac}[1]{%
\PackageWarning{amsmath}{%
Foreign command \@backslashchar#1; %
\protect\frac\space or \protect\genfrac\space should be used instead%
}
\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}}
\DeclareRobustCommand{\frac}[2]{{\begingroup#1\endgroup\@@over#2}}
\newcommand{\dfrac}{\genfrac{}{}{}0}
\newcommand{\tfrac}{\genfrac{}{}{}1}
\DeclareRobustCommand{\binom}{\genfrac()\z@{}}
\newcommand{\dbinom}{\genfrac(){0pt}0}
\newcommand{\tbinom}{\genfrac(){0pt}1}
\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}}
\def\@genfrac#1#2#3#4#5{{#1{\begingroup#4\endgroup#2#3\relax#5}}}
\def\@mathstyle#1{%
\ifx\@empty#1\@empty\relax
\else\ifcase#1\displaystyle % case 0
\or\textstyle\or\scriptstyle\else\scriptscriptstyle\fi\fi}
\def\colon{\nobreak\mskip2mu\mathpunct{}\nonscript
\mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
\begingroup \catcode`\"=12
\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
\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@
}
\def\leftroot{\@amsmath@err{\Invalid@@\leftroot}\@eha}
\def\uproot{\@amsmath@err{\Invalid@@\uproot}\@eha}
\newcount\uproot@
\newcount\leftroot@
\def\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}
\def\r@@t#1#2{\setboxz@h{$\m@th#1\@@sqrt{#2}$}%
\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@}
\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}
\@ifundefined{@ldots}{\def\@ldots{\mathellipsis}}{}
\DeclareRobustCommand{\dots}{\relax
\csname\ifmmode m\else t\fi dots@\endcsname}
\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@}
\def\boldsymboldots@#1{\bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
\boldsymbol#1\bold@false}
\def\@cdots{\mathinner{\cdotp\cdotp\cdotp}}
\def\dotsi{\!\@cdots}
\let\dotsb@\@cdots
\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@}
\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@}
\DeclareRobustCommand{\ldots}{\relax
\ifmmode \DN@{\extrap@\@ldots}%
\else \let\next@\tdots@\fi
\FN@\next@}
\DeclareRobustCommand{\cdots}{\DN@{\extrap@\@cdots}\FN@\next@}
\let\dotso\ldots
\let\dotsb\cdots
\let\dotsm\dotsb
\DeclareRobustCommand{\dotsc}{%
\DN@{\ifx\@let@token;\@ldots\,%
\else \ifx\@let@token.\@ldots\,%
\else \extra@\@ldots \ifgtest@\,\fi
\fi\fi}%
\FN@\next@}
\def\longrightarrow{\DOTSB\relbar\joinrel\rightarrow}
\def\Longrightarrow{\DOTSB\Relbar\joinrel\Rightarrow}
\def\longleftarrow{\DOTSB\leftarrow\joinrel\relbar}
\def\Longleftarrow{\DOTSB\Leftarrow\joinrel\Relbar}
\def\longleftrightarrow{\DOTSB\leftarrow\joinrel\rightarrow}
\def\Longleftrightarrow{\DOTSB\Leftarrow\joinrel\Rightarrow}
\def\mapsto{\DOTSB\mapstochar\rightarrow}
\def\longmapsto{\DOTSB\mapstochar\longrightarrow}
\def\hookrightarrow{\DOTSB\lhook\joinrel\rightarrow}
\def\hookleftarrow{\DOTSB\leftarrow\joinrel\rhook}
\def\iff{\DOTSB\;\Longleftrightarrow\;}
\def\doteq{\DOTSB\mathrel{\mathop{\kern\z@ =}\limits^{\textstyle.}}}
\newif\if@display
\everydisplay\@xp{\the\everydisplay \@displaytrue}
\def\int{\DOTSI\intop\ilimits@}
\def\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}}}
\def\iint{\DOTSI\protect\ints@\tw@}
\def\iiint{\DOTSI\protect\ints@\thr@@}
\def\iiiint{\DOTSI\protect\ints@{4}}
\def\idotsint{\DOTSI\protect\ints@\z@}
\def\ints@#1{%
\mkern-7mu\mathchoice{\mkern-2mu}{}{}{}%
\mathop{\mkern7mu\mathchoice{\mkern2mu}{}{}{}%
\intop\ifnum#1=\z@\intdots@
\else\intkern@\fi
\ifnum#1>\tw@\intop\intkern@\fi
\ifnum#1>\thr@@\intop\intkern@\fi
\intop
}\ilimits@
}
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@=\hbox{}
\def\Mathstrut@{\copy\Mathstrutbox@}
\begingroup \catcode`\"=12
\gdef\resetMathstrut@{%
\setbox\z@\hbox{%
\mathchardef\@tempa\mathcode`\(\relax
\def\@tempb##1"##2##3{\the\textfont"##3\char"}%
\expandafter\@tempb\meaning\@tempa \relax
}%
\ht\Mathstrutbox@\ht\z@ \dp\Mathstrutbox@\dp\z@
}
\endgroup
\addto@hook\every@math@size{\resetMathstrut@}
\newbox\strutbox@
\def\strut@{\copy\strutbox@}
\addto@hook\every@math@size{%
\global\setbox\strutbox@\hbox{\lower.5\normallineskiplimit
\vbox{\kern-\normallineskiplimit\copy\strutbox}}}
\def\big{\bBigg@\@ne}
\def\Big{\bBigg@{1.5}}
\def\bigg{\bBigg@\tw@}
\def\Bigg{\bBigg@{2.5}}
\def\bBigg@#1#2{%
{\@mathmeasure\z@{\nulldelimiterspace\z@}%
{\left#2\vcenter to#1\big@size{}\right.}%
\box\z@}}
\addto@hook\every@math@size{%
\global\big@size 1.2\ht\Mathstrutbox@
\global\advance\big@size 1.2\dp\Mathstrutbox@ }
\newdimen\big@size
\def\accentclass@{7}
\def\noaccents@{\def\accentclass@{0}}
\DeclareFontEncoding{OML}{}{\noaccents@}
\DeclareFontEncoding{OMS}{}{\noaccents@}
\begingroup \catcode`\"=12
\def\@tempa#1#2\@nil{\def\@tempc{#1}}\def\@tempb{\mathaccent}
\expandafter\@tempa\hat \relax\relax\@nil
\ifx\@tempb\@tempc
\def\@tempa#1\@nil{#1}%
\def\@tempb#1{\afterassignment\@tempa\mathchardef\@tempc=}%
\def\@tempe#1"{}
\def\do#1"#2{}
\def\@tempd#1#2{\expandafter\@tempb#1\@nil
\ifnum\@tempc<"1000
\edef\@tempc{"\@nx\accentclass@
\ifnum\@tempc<"100 0\fi
\@xp\@tempe\meaning\@tempc\space}%
\else
\edef\@tempc{"\@nx\@nx\@nx\accentclass@
\@xp\do\meaning\@tempc\space}%
\fi
\xdef#1{\mathaccent\@tempc}%
\toks@{%
\relax\ifmmode \else\DN@##1##2{\nonmatherr@{#2}}\@xp\next@\fi
\mathaccent@}%
\xdef#2{\the\toks@{\@tempc}}%
}
\@tempd\hat\Hat \@tempd\check\Check \@tempd\tilde\Tilde
\@tempd\acute\Acute \@tempd\grave\Grave \@tempd\dot\Dot
\@tempd\ddot\Ddot \@tempd\breve\Breve \@tempd\bar\Bar
\fi
\endgroup
\newcount\skewcharcount@
\newcount\familycount@
\def\theskewchar@{\familycount@\@ne
\global\skewcharcount@\the\skewchar\textfont\@ne
\ifnum\mathgroup>\m@ne\ifnum\mathgroup<16
\global\familycount@\the\mathgroup\relax
\global\skewcharcount@\the\skewchar\textfont\the\mathgroup\relax\fi\fi
\ifnum\skewcharcount@>\m@ne
\ifnum\skewcharcount@<128
\multiply\familycount@256
\global\advance\skewcharcount@\familycount@
\global\advance\skewcharcount@28672
\mathchar\skewcharcount@\else
\global\skewcharcount@\m@ne\fi\else
\global\skewcharcount@\m@ne\fi}
\newcount\pointcount@
\def\getpoints@#1.#2\getpoints@{\pointcount@#1 }
\newdimen\accentdimen@
\newcount\accentmu@
\def\dimentomu@{\multiply\accentdimen@ 100
\@xp\getpoints@\the\accentdimen@\getpoints@
\multiply\pointcount@18
\divide\pointcount@\@m
\global\accentmu@\pointcount@}
\def\mathaccent@#1#2{\ifnum\mathgroup=\m@ne\xdef\thefam@{1}\else
\xdef\thefam@{\the\mathgroup}\fi
\accentdimen@\z@
\setboxz@h{\unbracefonts@$\m@th\mathgroup\thefam@\relax#2$}%
\ifdim\accentdimen@=\z@\DN@{\mathaccent#1{#2}}%
\setbox\@ne\hbox{\unbracefonts@
$\m@th\mathgroup\thefam@\relax#2\theskewchar@$}
\setbox\tw@\hbox{$\m@th\ifnum\skewcharcount@=\m@ne\else
\mathchar\skewcharcount@\fi$}%
\global\accentdimen@\wd\@ne\global\advance\accentdimen@-\wdz@
\global\advance\accentdimen@-\wd\tw@
\global\multiply\accentdimen@\tw@
\dimentomu@\global\advance\accentmu@\@ne
\else\DN@{{\mathaccent#1{#2\mkern\accentmu@ mu}%
\mkern-\accentmu@ mu}{}}\fi
\next@}
\def\unbracefonts@{\let\math@bgroup\@empty\let\math@egroup\@empty}
\def\nonmatherr@#1{\@amsmath@err{\protect
#1 allowed only in math mode}\@ehd}
\begingroup \catcode`\"=12
\def\@tempa#1#2{\gdef#1{\RIfM@\DN@{\mathaccent@{"\accentclass@#2 }}%
\else\DN@{\nonmatherr@{#1}}\fi\next@}}
\@tempa\Hat{05E}\@tempa\Check{014}\@tempa\Tilde{07E}\@tempa\Acute{013}
\@tempa\Grave{012}\@tempa\Dot{05F}\@tempa\Ddot{07F}\@tempa\Breve{015}
\@tempa\Bar{016}
\gdef\Vec{\RIfM@\DN@{\mathaccent@{"017E }}\else
\DN@{\nonmatherr@\Vec}\fi\next@}
\endgroup
\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalfont ...}\vss}}}}
\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalfont....}\vss}}}}
\def\bmod{\mskip-\medmuskip\mkern5mu\mathbin
{\operator@font mod}\penalty900
\mkern5mu\mskip-\medmuskip}
\def\pod#1{\allowbreak\if@display\mkern18mu\else\mkern8mu\fi(#1)}
\def\pmod#1{\pod{{\operator@font mod}\mkern6mu#1}}
\def\mod#1{\allowbreak\if@display\mkern18mu
\else\mkern12mu\fi{\operator@font mod}\,\,#1}
\newcommand{\cfrac}[3][c]{{\displaystyle\frac{%
\strut\ifx r#1\hfill\fi#2\ifx l#1\hfill\fi}{#3}}%
\kern-\nulldelimiterspace}
\def\overset#1#2{\binrel@{#2}%
\binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
\def\underset#1#2{\binrel@{#2}%
\binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
\def\sideset#1#2#3{%
\@mathmeasure\z@\displaystyle{#3}%
\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}%
}
\renewcommand{\smash}[2][tb]{%
\def\smash@{#1}%
\ifmmode\@xp\mathpalette\@xp\mathsm@sh\else
\@xp\makesm@sh\fi{#2}}
\def\finsm@sh{\def\mb@t{\ht\z@\z@}\def\mb@b{\dp\z@\z@}%
\def\mb@tb{\mb@t\mb@b}%
{\csname mb@\smash@\endcsname}%
\leavevmode\boxz@}
\def\rightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
$#1\copy\z@\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
\mkern-6mu\mathord\rightarrow$}
\def\leftarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
$#1\mathord\leftarrow\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
\mkern-6mu\box\z@$}
\def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
$#1\mathord\leftarrow\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
\mkern-6mu\mathord\rightarrow$}
\def\overarrow@#1#2#3{\vbox{\ialign{##\crcr#1#2\crcr
\noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#2#3\hfil$\crcr}}}
\def\overrightarrow{\mathpalette{\overarrow@\rightarrowfill@}}
\def\overleftarrow{\mathpalette{\overarrow@\leftarrowfill@}}
\def\overleftrightarrow{\mathpalette{\overarrow@\leftrightarrowfill@}}
\def\underarrow@#1#2#3{%
\vtop{\ialign{##\crcr$\m@th\hfil#2#3\hfil$\crcr
\noalign{\nointerlineskip\kern-.5\ex@}#1#2\crcr}}}
\def\underrightarrow{\mathpalette{\underarrow@\rightarrowfill@}}
\def\underleftarrow{\mathpalette{\underarrow@\leftarrowfill@}}
\def\underleftrightarrow{\mathpalette{\underarrow@\leftrightarrowfill@}}
\newcommand{\xrightarrow}[2][]{%
\mathrel{\mathop{%
\setbox\z@\vbox{\m@th
\hbox{$\scriptstyle\;{#1}\;\;$}%
\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%
}%
\hbox to\ifdim\wd\z@>\minaw@\wd\z@\else\minaw@\fi{%
\rightarrowfill@\displaystyle}}%
\limits^{#2}\@ifnotempty{#1}{_{#1}}}%
}
\newcommand{\xleftarrow}[2][]{%
\mathrel{\mathop{%
\setbox\z@\vbox{\m@th
\hbox{$\scriptstyle\;\;{#1}\;$}%
\hbox{$\m@th\scriptstyle\;\;{#2}\;\;$}%
}%
\hbox to\ifdim\wd\z@>\minaw@\wd\z@\else\minaw@\fi{%
\leftarrowfill@\displaystyle}}%
\limits^{#2}\@ifnotempty{#1}{_{#1}}}%
}
\@ifundefined{minaw@}{\newdimen\minaw@\minaw@11pt}{}
\newcommand{\Sb}{\PackageError{amsmath}%
{Environment `Sb' is obsolete; use `substack' instead}%
{The \protect\\protect\ used to separate lines in a `Sb' environment can
cause problems if `Sb' is embedded in some aligning environments.}}
\newcommand{\Sp}{\PackageError{amsmath}%
{Environment `Sp' is obsolete; use `substack' instead}%
{The \protect\\protect\ used to separate lines in a `Sp' environment can
cause problems if `Sp' is embedded in some aligning environments.}}
\newenvironment{subarray}[1]{%
\vcenter\bgroup
\Let@ \restore@math@cr \default@tag
\baselineskip\fontdimen10 \scriptfont\tw@
\advance\baselineskip\fontdimen12 \scriptfont\tw@
\lineskip\thr@@\fontdimen8 \scriptfont\thr@@
\lineskiplimit\lineskip
\ialign\bgroup\ifx c#1\hfil\fi
$\m@th\scriptstyle##$\hfil\crcr
}{%
\crcr\egroup\egroup
}
\newcommand{\substack}[1]{\subarray{c}#1\endsubarray}
\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\,%
}
\newcount\c@MaxMatrixCols \c@MaxMatrixCols=10
\renewenvironment{matrix}{%
\hskip -\arraycolsep\array{*\c@MaxMatrixCols c}%
}{%
\endarray \hskip -\arraycolsep
}
\renewenvironment{pmatrix}{\left(\matrix}{\endmatrix\right)}
\newenvironment{bmatrix}{\left[\matrix}{\endmatrix\right]}
\newenvironment{Bmatrix}{\left\lbrace\matrix}{\endmatrix\right\rbrace}
\newenvironment{vmatrix}{\left\lvert\matrix}{\endmatrix\right\rvert}
\newenvironment{Vmatrix}{\left\lVert\matrix}{\endmatrix\right\rVert}
\let\hdots\@ldots
\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\[email protected]\mkern-#1\dotsspace@
\xleaders\hbox{$\m@th\mkern#1\dotsspace@.\mkern#1\dotsspace@$}%
\hfill
\mkern-#1\dotsspace@}%
}
\renewenvironment{cases}{%
\left\{\def\arraystretch{1.2}%
\array{@{}l@{\quad}l@{}}%
}{%
\endarray\right.%
}
\newcounter{parentequation}% Counter for ``parent equation''.
\newenvironment{subequations}{%
\refstepcounter{equation}%
\begingroup % conservative approach
\let\protect\@nx
\edef\@tempa{\def\@nx\theparentequation{\theequation}}%
\@xp\endgroup\@tempa
\setcounter{parentequation}{\value{equation}}%
\setcounter{equation}{0}%
\def\theequation{\theparentequation\alph{equation}}%
\ignorespaces
}{%
\setcounter{equation}{\value{parentequation}}%
\global\@ignoretrue
}
\def\numberwithin#1#2{\@ifundefined{c@#1}{\@nocounterr{#1}}{%
\@ifundefined{c@#2}{\@nocnterr{#2}}{%
\@addtoreset{#1}{#2}%
\toks@\@xp\@xp\@xp{\csname the#1\endcsname}%
\@xp\xdef\csname the#1\endcsname
{\@xp\@nx\csname the#2\endcsname
.\the\toks@}}}}
\def\eqref#1{\textup{\tagform@{\ref{#1}}}}
\newcount\dspbrk@lvl
\dspbrk@lvl=-1
\interdisplaylinepenalty\@M
\def\allowdisplaybreaks{%
\new@ifnextchar[\allowdspbrks@{\allowdspbrks@[4]}}
\def\allowdspbrks@[#1]{%
\interdisplaylinepenalty\getdsp@pen{#1}}
\def\getdsp@pen#1{%
\ifcase #1\relax \@M
\or 9999
\or 6999
\or 2999
\or \z@\fi}
\def\displaybreak{\@amsmath@err{\Invalid@@\displaybreak}\@eha}
\def\displaybreak@{%
\def\displaybreak{\new@ifnextchar[\dspbrk@{\dspbrk@[4]}}}
\def\dspbrk@[#1]{\global\dspbrk@lvl #1\relax}
\def\math@cr{{\ifnum0=`}\fi
\@ifstar{\global\@eqpen\@M\math@cr@}%
{\global\@eqpen
\ifnum\dspbrk@lvl <\z@ \interdisplaylinepenalty
\else -\@getpen\dspbrk@lvl \fi
\math@cr@}}
\def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
\def\math@cr@@[#1]{\ifnum0=`{\fi}\math@cr@@@
\noalign{\vskip#1\relax}}
\def\Let@{\let\\\math@cr}
\def\restore@math@cr{\def\math@cr@@@{\cr}}
\restore@math@cr
\def\intertext{\@amsmath@err{\Invalid@@\intertext}\@eha}
\def\intertext@{%
\def\intertext##1{%
\ifvmode\else\\\@empty\fi
\noalign{%
\penalty\postdisplaypenalty\vskip\belowdisplayskip
\vbox{\normalbaselines
\ifdim\linewidth=\columnwidth
\else \parshape\@ne \@totalleftmargin \linewidth
\fi
\noindent##1\par}%
\penalty\predisplaypenalty\vskip\abovedisplayskip%
}%
}}
\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.}
\def\gobble@tag{\@ifstar\@gobble\@gobble}
\def\invalid@tag#1{\@amsmath@err{#1}{\the\tag@help}\gobble@tag}
\def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
\def\default@tag{\let\tag\dft@tag}
\default@tag
\def\maketag@@{\@ifstar\maketag@@@\tagform@}
\def\maketag@@@#1{\hbox{\m@th\normalfont#1}}
\def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip\@@italiccorr)}}
\iftagsleft@
\def\@eqnnum{\hbox to1sp{}\rlap{\normalfont\normalcolor
\hskip -\displaywidth\tagform@\theequation}}
\else
\def\@eqnnum{{\normalfont\normalcolor \tagform@\theequation}}
\fi
\def\thetag{\leavevmode\tagform@}
\def\make@df@tag{\@ifstar\make@df@tag@@\make@df@tag@@@}
\def\make@df@tag@@#1{%
\gdef\df@tag{\maketag@@@{#1}\def\@currentlabel{#1}}}
\def\make@df@tag@@@#1{\gdef\df@tag{\tagform@{#1}%
\toks@\@xp{\p@equation{#1}}\edef\@currentlabel{\the\toks@}}}
\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
}
\let\df@label\@empty
\def\make@display@tag{%
\if@eqnsw
\refstepcounter{equation}%
\tagform@\theequation
\else
\iftag@
\df@tag
\global\let\df@tag\@empty
\fi
\fi
\ifx\df@label\@empty\else
\ltx@label{\df@label}%
\global\let\df@label\@empty
\fi
}
\def\tag@in@align{%
\relax
\iftag@
\DN@{\invalid@tag{Multiple \string\tag}}%
\else
\global\tag@true
\nonumber
\let\next@\make@df@tag
\fi
\next@
}
\def\raisetag#1{\skip@#1\relax
\xdef\raise@tag{\vskip\iftagsleft@\else-\fi\the\skip@\relax}%
}
\let\raise@tag\@empty
\def\notag{\nonumber}
\newif\ifinany@
\newif\ifinalign@
\newif\ifingather@
\newif\iftag@
\newif\ifst@rred
\newif\ifmeasuring@
\newif\ifshifttag@
\newcount\row@
\newcount\column@
\def\column@plus{%
\global\advance\column@\@ne
}
\newcount\maxfields@
\def\add@amps#1{%
\begingroup
\count@#1
\DN@{}%
\loop
\ifnum\count@>\column@
\edef\next@{&\next@}%
\advance\count@\m@ne
\repeat
\@xp\endgroup
\next@
}
\newhelp\andhelp@
{An extra & here is so disastrous that you should probably exit^^J
and fix things up.}
\newdimen\eqnshift@
\newdimen\alignsep@
\newdimen\tagshift@
\def\mintagsep{.5\fontdimen6\textfont2}
\def\minalignsep{10pt}
\newdimen\tagwidth@
\newdimen\totwidth@
\newdimen\lineht@
\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
\def\saveshift@#1{%
\begingroup
\let\or\relax
\xdef\tag@shifts{\or#1\tag@shifts}%
\endgroup
}
\def\displ@y{\@display@init{}}
\def\@display@init#1{%
\global\dt@ptrue
\openup\jot\m@th
\everycr{%
\noalign{%
#1%
\ifdt@p
\global\dt@pfalse
\vskip-\lineskiplimit
\vskip\normallineskiplimit
\else
\penalty\@eqpen
\fi
}%
}%
}
\def\displ@y@{\@display@init{%
\global\column@\z@ \global\dspbrk@lvl\m@ne
\global\tag@false \global\let\raise@tag\@empty
}}
\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
}%
}
\def\savecounters@{%
\begingroup
\def\@elt##1{%
\global\csname c@##1\endcsname\the\csname c@##1\endcsname}%
\xdef\@tempa{%
\cl@@ckpt
\let\@nx\restorecounters@\@nx\@empty
}%
\endgroup
\let\restorecounters@\@tempa
}
\let\restorecounters@\@empty
\def\savealignstate@{%
\begingroup
\let\or\relax
\xdef\@tempa{%
\global\totwidth@\the\totwidth@
\global\row@\the\row@
\gdef\@nx\tag@lengths{\tag@lengths}%
\let\@nx\restorealignstate@\@nx\@empty
}%
\endgroup
\let\restorealignstate@\@tempa
}
\let\restorealignstate@\@empty
\newtoks\@envbody
\def\addto@envbody#1{\@envbody\@xp{\the\@envbody#1}}
\def\collect@body#1{%
\@envbody{}%
\def\process@envbody{%
\@xp#1\@xp{\the\@envbody}%
}%
\@xp\let\csname\@currenvir\endcsname\collect@@body
\csname\@currenvir\endcsname
}
\def\collect@@body#1\end#2{%
\def\@tempa{#2}%
\ifx\@tempa\@currenvir
\addto@envbody{#1}%
\@xp\edef\csname\@currenvir\endcsname{%
\@nx\process@envbody\@nx\end{\@tempa}%
}%
\else
\addto@envbody{#1\end{#2}}%
\fi
\csname\@currenvir\endcsname
}
\newcommand{\start@aligned}[2]{%
\RIfM@\else
\nonmatherr@{\begin{\@currenvir}}%
\fi
\null\,%
\if #1t\vtop \else \if#1b \vbox \else \vcenter \fi \fi \bgroup
\maxfields@#2\relax
\ifnum\maxfields@>\m@ne
\multiply\maxfields@\tw@
\let\math@cr@@@\math@cr@@@alignedat
\else
\restore@math@cr
\fi
\Let@
\default@tag
\ifinany@\else\openup\jot\fi
\column@\z@
\ialign\bgroup
&\column@plus
\hfil
\strut@
$\m@th\displaystyle{##}$%
&\column@plus
$\m@th\displaystyle{{}##}$%
\hfil
\crcr
}
\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
\column@\z@
\cr
}
\newenvironment{aligned}[1][c]{%
\start@aligned{#1}\m@ne
}{%
\crcr\egroup\egroup
}
\newcommand{\alignedat}[2][c]{%
\start@aligned{#1}%
}
\let\endalignedat\endaligned
\newcommand{\gathered}[1][c]{%
\RIfM@\else
\nonmatherr@{\begin{gathered}}%
\fi
\null\,%
\if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi \bgroup
\Let@
\restore@math@cr
\ifinany@\else\openup\jot\fi
\ialign\bgroup
\hfil\strut@$\m@th\displaystyle##$\hfil
\crcr
}
\let\endgathered\endaligned
\def\start@gather#1{%
\RIfM@
\nomath@env
\DN@{\@namedef{end\@currenvir}{}\@gobble}%
\else
$$%
#1%
\ifst@rred\else
\global\@eqnswtrue
\fi
\let\next@\gather@
\fi
\collect@body\next@
}
\def\gather{\start@gather\st@rredfalse}
\@namedef{gather*}{\start@gather\st@rredtrue}
\def\gather@#1{%
\ingather@true
\inany@true
\let\tag\tag@in@align
\let\label\label@in@display
\displaybreak@
\intertext@
\displ@y@
\Let@
\let\math@cr@@@\math@cr@@@gather
\gmeasure@{#1}%
\global\shifttag@false
\tabskip\z@skip
\global\row@\@ne
\halign to\displaywidth\bgroup
\strut@
\setboxz@h{$\m@th\displaystyle{##}$}%
\calc@shift@gather
\set@gather@field
\tabskip\@centering
&\setboxz@h{\strut@{##}}%
\place@tag@gather
\tabskip \iftagsleft@ \gdisplaywidth@ \else \z@skip \span\fi
\crcr
#1%
}
\def\endgather{%
\math@cr
\black@\totwidth@
\egroup
$$%
\global\@ignoretrue
}
\@xp\let\csname endgather*\endcsname\endgather
\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
}
\def\math@cr@@@gather{%
\ifst@rred\nonumber\fi
&\relax
\make@display@tag
\ifst@rred\else\global\@eqnswtrue\fi
\global\advance\row@\@ne
\cr
}
\def\calc@shift@gather{%
\dimen@\mintagsep\relax
\tagwidth@\tag@width\row@\relax
\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
}
\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
}
\newif\ifxxat@
\newif\ifcheckat@
\let\xatlevel@\@empty
\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@
{\ifnum0=`}\fi
\DN@{\vcenter\bgroup\savealignstate@\align@#2}%
\else
\ifmmode
\nomath@env
\DN@{\@namedef{end\@currenvir}{}\@gobble}%
\else
$$%
\DN@{\align@#2}%
\fi
\fi
\collect@body\next@
}
\def\alignat{\start@align\z@\st@rredfalse}
\@namedef{alignat*}{\start@align\z@\st@rredtrue}
\def\xalignat{\start@align\@ne\st@rredfalse}
\@namedef{xalignat*}{\start@align\@ne\st@rredtrue}
\def\xxalignat{\start@align\tw@\st@rredtrue}
\def\align{\start@align\@ne\st@rredfalse\m@ne}
\@namedef{align*}{\start@align\@ne\st@rredtrue\m@ne}
\def\flalign{\start@align\tw@\st@rredfalse\m@ne}
\@namedef{flalign*}{\start@align\tw@\st@rredtrue\m@ne}
\def\align@#1#2{%
\inany@true
\inalign@true
\displaybreak@
\intertext@
\ifingather@\else\displ@y@\fi
\Let@
\let\math@cr@@@\math@cr@@@align
\ifxxat@\else
\let\tag\tag@in@align
\fi
\let\label\label@in@display
#1% set st@r
\ifst@rred\else
\global\@eqnswtrue
\fi
\measure@{#2}%
\global\row@\z@
\tabskip\eqnshift@
\halign\bgroup
\span\align@preamble\crcr
#2%
}
\def\endalign{%
\math@cr
\black@\totwidth@
\egroup
\ifingather@
\restorealignstate@
\egroup
\nonumber
\ifnum0=`{\fi}%
\else
$$%
\fi
\global\@ignoretrue
}
\@xp\let\csname endalign*\endcsname\endalign
\let\endxalignat\endalign
\@xp\let\csname endxalignat*\endcsname\endalign
\let\endxxalignat\endalign
\let\endalignat\endalign
\@xp\let\csname endalignat*\endcsname\endalign
\let\endflalign\endalign
\@xp\let\csname endflalign*\endcsname\endalign
\def\math@cr@@@align{%
\kern-\alignsep@
\ifst@rred\nonumber\fi
\if@eqnsw \global\tag@true \fi
\global\advance\row@\@ne
\iftag@
\add@amps\maxfields@
\omit
\setboxz@h{\@lign\strut@{\make@display@tag}}%
\place@tag
\fi
\ifst@rred\else\global\@eqnswtrue\fi
\global\lineht@\z@
\cr
}
\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
}
\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
}
\let\maxcolumn@widths\@empty
\def\maxcol@width#1{%
\ifcase\@xp#1\maxcolumn@widths\fi\relax
}
\def\measure@#1{%
\begingroup
\measuring@true
\eqnshift@\z@
\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@@@
\column@\z@
\add@amps\maxfields@\cr
}%
}%
\restorecounters@
\ifodd\maxfields@
\global\advance\maxfields@\@ne
\fi
\ifnum\xatlevel@=\tw@
\ifnum\maxfields@<\thr@@
\let\xatlevel@\z@
\fi
\fi
\setbox0\vbox{%
\unvbox0
\unpenalty
\global\setbox1\lastbox
}%
\global\totwidth@\wd1
\if@fleqn
\global\advance\totwidth@\@mathmargin
\fi
\global\let\maxcolumn@widths\@empty
\begingroup
\let\or\relax
\loop
\setbox1\hbox{%
\unhbox1
\unskip
\global\setbox0\lastbox
}%
\ifhbox0
\xdef\maxcolumn@widths{ \or \the\wd0 \maxcolumn@widths}%
\repeat
\endgroup
\dimen@\displaywidth
\advance\dimen@-\totwidth@
\ifcase\xatlevel@
\global\alignsep@\z@
\let\minalignsep\z@
\@tempcntb\z@
\if@fleqn
\@tempcnta\@ne
\global\eqnshift@\@mathmargin
\else
\@tempcnta\tw@
\global\eqnshift@\dimen@
\global\divide\eqnshift@\@tempcnta
\fi
\or
\@tempcntb\maxfields@
\divide\@tempcntb\tw@
\@tempcnta\@tempcntb
\advance\@tempcntb\m@ne
\if@fleqn
\global\eqnshift@\@mathmargin
\alignsep@\dimen@
\global\divide\alignsep@\@tempcnta
\else
\global\advance\@tempcnta\@ne
\global\eqnshift@\dimen@
\global\divide\eqnshift@\@tempcnta
\global\alignsep@\eqnshift@
\fi
\or
\@tempcntb\maxfields@
\divide\@tempcntb\tw@
\global\advance\@tempcntb\m@ne
\global\@tempcnta\@tempcntb
\global\eqnshift@\z@
\global\alignsep@\dimen@
\if@fleqn
\advance\alignsep@\@mathmargin\relax
\fi
\global\divide\alignsep@\@tempcntb
\fi
\ifdim\alignsep@<\minalignsep\relax
\global\alignsep@\minalignsep\relax
\ifdim\eqnshift@>\z@
\if@fleqn\else
\eqnshift@\displaywidth
\advance\eqnshift@-\totwidth@
\advance\eqnshift@-\@tempcntb\alignsep@
\global\divide\eqnshift@\tw@
\fi
\fi
\fi
\ifdim\eqnshift@<\z@
\global\eqnshift@\z@
\fi
\calc@shift@align
\tagshift@\totwidth@
\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
\dimen@\minalignsep\relax
\advance\totwidth@\@tempcntb\dimen@
\ifdim\totwidth@>\displaywidth
\global\let\displaywidth@\totwidth@
\else
\global\let\displaywidth@\displaywidth
\fi
\endgroup
}
\iftagsleft@\if@fleqn
\def\calc@shift@align{%
\global\let\tag@shifts\@empty
\begingroup
\@tempdima\@mathmargin\relax
\advance\@tempdima-\mintagsep\relax
\loop
\ifnum\row@>0
\ifdim\tag@width\row@>\z@
\x@calc@shift@lf
\else
\saveshift@0%
\fi
\advance\row@\m@ne
\repeat
\endgroup
}
\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
\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
}
\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
\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\eqnshift@
\advance\@tempdima\@tempdimc\relax
\advance\@tempdima\tagwidth@
\dimen@\minalignsep\relax
\multiply\dimen@\@tempcntb
\advance\dimen@\mintagsep\relax
\advance\dimen@\@tempdima
\ifdim\dimen@>\displaywidth
\saveshift@1%
\else
\saveshift@0%
\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
\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
}
\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
\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
\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
}
\def\x@calc@shift@lc{%
\column@\z@
\@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
\@tempdima\totwidth@
\advance\@tempdima-\@tempdimb
\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@\alignsep@
\multiply\dimen@\count@
\advance\dimen@\eqnshift@
\advance\dimen@\@tempdimb
\ifdim\dimen@<2\tagwidth@
\dimen@\displaywidth
\advance\dimen@-\@tempdima
\ifnum\xatlevel@=\tw@
\advance\dimen@-\mintagsep\relax
\fi
\divide\dimen@\@tempcnta
\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
\ifnum\xatlevel@=\tw@
\dimen@\mintagsep\relax
\fi
\advance\dimen@\tagwidth@
\advance\dimen@-\@tempdimb
\advance\dimen@-\count@\alignsep@
\ifdim\dimen@>\eqnshift@
\global\eqnshift@\dimen@
\fi
\fi
\fi
\endgroup
}
\def\x@lcalc@width{%
\ifdim\@tempdima = \z@
\ifdim\@tempa > \z@
\@tempdima\p@
\ifodd\column@
\advance\@tempdimb \maxcol@width\column@
\advance\@tempdimb-\@tempa
\fi
\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
\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
\llap{\vtop{%
\raise@tag
\normalbaselines
\setbox\@ne\null
\dp\@ne\lineht@
\box\@ne
\boxz@
}}%
\else
\llap{\boxz@}%
\fi
\fi
}
\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@
}
\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@
}
\def\split{%
\ifinany@
\@xp\insplit@
\else
\@xp\split@err
\fi
}
\edef\split@err{%
\@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}%
}
\def\insplit@{%
\global\setbox\z@\vbox\bgroup
\Let@
\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
}
\def\endsplit{%
\crcr
\egroup
\egroup
\iftagsleft@
\@xp\lendsplit@
\else
\@xp\rendsplit@
\fi
}
\def\rendsplit@{%
\ifinalign@
\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}%
\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
\gdef\split@{%
\boxz@
}%
\fi
\fi
\aftergroup\split@
}
\def\lendsplit@{%
\global\setbox9\vtop{\unvcopy\z@}%
\ifinalign@
\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@
}
\newskip\multlinegap
\multlinegap10pt
\newskip\multlinetaggap
\multlinetaggap10pt
\def\start@multline#1{%
\RIfM@
\nomath@env
\DN@{\@namedef{end\@currenvir}{}\@gobble}%
\else
$$%
#1%
\ifst@rred
\nonumber
\else
\global\@eqnswtrue
\fi
\let\next@\multline@
\fi
\collect@body\next@
}
\def\multline{\start@multline\st@rredfalse}
\@namedef{multline*}{\start@multline\st@rredtrue}
\def\multline@#1{%
\inany@true
\Let@
\@display@init{\global\advance\row@\@ne \global\dspbrk@lvl\m@ne}%
\displaybreak@
\restore@math@cr
\let\tag\tag@in@align
\global\tag@false \global\let\raise@tag\@empty
\mmeasure@{#1}%
\let\tag\gobble@tag \let\label\@gobble
\tabskip \if@fleqn \@mathmargin \else \z@skip \fi
\totwidth@\displaywidth
\if@fleqn
\advance\totwidth@-\@mathmargin
\fi
\halign\bgroup
\hbox to\totwidth@{%
\if@fleqn
\hskip \@centering \relax
\else
\hfil
\fi
\strut@
$\m@th\displaystyle{}##$%
\hfil
}%
\crcr
\if@fleqn
\hskip-\@mathmargin
\else
\hfilneg
\fi
\iftagsleft@
\iftag@
\begingroup
\ifshifttag@
\rlap{\vbox{%
\normalbaselines
\hbox{%
\strut@
\make@display@tag
}%
\vbox to\lineht@{}%
\raise@tag
}}%
\hskip\multlinegap
\else
\make@display@tag
\hskip\multlinetaggap
\fi
\endgroup
\else
\hskip\multlinegap
\fi
\else
\hskip\multlinegap
\fi
#1%
}
\def\endmultline{%
\iftagsleft@
\@xp\lendmultline@
\else
\@xp\rendmultline@
\fi
\global\@ignoretrue
}
\@xp\let\csname endmultline*\endcsname=\endmultline
\def\lendmultline@{%
\hfilneg
\hskip\multlinegap
\math@cr
\egroup
$$%
}
\def\rendmultline@{%
\iftag@
\begingroup
\ifshifttag@
\hskip\multlinegap
\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
\endgroup
\else
\hskip\multlinegap
\fi
\hfilneg
\math@cr
\egroup$$%
}
\def\mmeasure@#1{%
\begingroup
\measuring@true
\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
}
\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
\def\[{%
\RIfM@
\@badmath
\else
\DN@{%
$$%
\ingather@true
\inany@true
\def\\{\@amsmath@err{\Invalid@@\\}\@eha}%
\tabskip\@mathmargin
\halign to\displaywidth\bgroup
\if@fleqn\else\hfil\fi
\setboxz@h{$\m@th\displaystyle{####}$}%
\global\totwidth@\wdz@
\boxz@
\hfil
\tabskip\@centering
\cr
}%
\@xp\next@
\fi
}
\def\]{%
\RIfM@
\DN@{%
\crcr
\black@\totwidth@
\egroup
$$%
}%
\@xp\next@
\else
\@badmath
\fi
}
\@xp\def\@xp\@arrayparboxrestore\@xp{\@arrayparboxrestore
\inany@false\ingather@false\inalign@false \default@tag}
\def\equation{\gather\def\\{\@amsmath@err{\Invalid@@\\}\@eha}}
\def\endequation{\endgather}
\newenvironment{equation*}{%
\equation
}{%
\nonumber\endequation
}
\endinput
%%
%% End of file `amsmath.sty'.
|
