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amsmath-2018-12-01.sty
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amsmath-2018-12-01.sty
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%%
%% This is file `amsmath.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% amsmath.dtx
%%
%% Copyright (C) 1995, 1999, 2000, 2013 American Mathematical Society.
%% Copyright (C) 2016-2021 LaTeX Project and American Mathematical Society.
%%
%% This work may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%% The latest version of this license is in
%% https://www.latex-project.org/lppl.txt
%% and version 1.3c or later is part of all distributions of LaTeX
%% version 2005/12/01 or later.
%%
%% This work has the LPPL maintenance status `maintained'.
%%
%% The Current Maintainer of this work is the LaTeX Project.
%%
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1994/12/01]% LaTeX date must be December 1994 or later
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\@temp
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\catcode`\^=7 \catcode`\_=8
\DeclareOption{intlimits}{\let\ilimits@\displaylimits}
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\DeclareOption{namelimits}{\PassOptionsToPackage{namelimits}{amsopn}}
\DeclareOption{nonamelimits}{%
\PassOptionsToPackage{nonamelimits}{amsopn}}
\newif\ifctagsplit@
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\DeclareOption{leqno}{\tagsleft@true}
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\DeclareOption{centertags}{\ctagsplit@true}
\DeclareOption{tbtags}{\ctagsplit@false}
\DeclareOption{cmex10}{%
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\else \def\cmex@opt{10}\fi
}
\@ifundefined{cmex@opt}{\def\cmex@opt{7}}{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newif\if@fleqn
\newskip\@mathmargin
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}%
}
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}
\DeclareOption{?}{}
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\@ifpackagewith{amsmath}{?}{%
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Documentation for the amsmath package is found in amsldoc.dvi^^J%
(or .pdf or .tex).^^J%
^^J%
See also https://www.ams.org/tex/amslatex.html.^^J%
^^J%
Note: Using the first edition of The LaTeX Companion (1994) without^^J%
errata as a guide for amsmath use is not recommended.^^J%
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\fi
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Foreign command \@backslashchar#1;\MessageBreak
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\begingroup
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\edef\@tempc{\expandafter\@tempb\meaning\coprod "\@nil}
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\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@}
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\gdef\biguplus{\DOTSB\biguplus@\slimits@}
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\gdef\bigcap{\DOTSB\bigcap@\slimits@}
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\gdef\bigcup{\DOTSB\bigcup@\slimits@}
\global\let\prod@\prod
\gdef\prod{\DOTSB\prod@\slimits@}
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\gdef\bigodot{\DOTSB\bigodot@\slimits@}
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\fi
\endgroup
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\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}
\@ifundefined{sqrtsign}{\let\sqrtsign\@@sqrt}{}
\def\r@@t#1#2{\setboxz@h{$\m@th#1\sqrtsign{#2}$}%
\dimen@\ht\z@\advance\dimen@-\dp\z@
\setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
\advance\dimen@ by1.667\wd\@ne
\mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
\mkern-10mu\mkern\leftroot@ mu\boxz@}
\@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}
}{}
\@saveprimitive\overline\@@overline
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\newcommand{\boxed}[1]{\fbox{\m@th$\displaystyle#1$}}
\newcommand{\implies}{\DOTSB\;\Longrightarrow\;}
\newcommand{\impliedby}{\DOTSB\;\Longleftarrow\;}
\def\And{\DOTSB\;\mathchar"3026 \;}
\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@
}
\renewcommand{\colon}{\nobreak\mskip2mu\mathpunct{}\nonscript
\mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
\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
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{\uccode`(=`U \uccode`)=`m
\uppercase{\gdef\Umathch@#1#2#3#4"#5"#6\Umathch@{\gtest@false
\ifx(#2\ifx)#3\gtest@true
\ifcase"#5 \or\or\gdef\thedots@{\dotsb@}\or\gdef\thedots@{\dotsb@}\fi
\fi\fi
}}}
\ifx\Umathcharnumdef\@undefined
\gdef\thecharacter@#1\thecharacter@{}
\else
{\uccode`(=`t \uccode`)=`c
\uppercase{\gdef\thecharacter@#1#2#3#4#5\thecharacter@{%
\ifx(#1\ifx)#4%
\@xp\getmathcode@\meaning@\getmathcode@
\fi\fi
}}}
\def\getmathcode@#1 #2 #3#4\getmathcode@{%
\Umathcharnumdef\@tempa\Umathcodenum`#3\relax
\edef\meaning@{\meaning\@tempa}%
\@xp\Umathch@\meaning@\Umathch@
}
\fi
\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@}}}
{\uccode`9=`\l %
\uppercase{\gdef\striplong@#1#2#3\relax{%
\ifx9#2 \@xp\@xp\@xp\zap@to@space\fi}}}
\def\zap@to@space#1 {}
\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{\ldots}{%
\ifmmode \mathellipsis \else \textellipsis \fi
}
\DeclareRobustCommand{\dots}{%
\ifmmode \@xp\mdots@\else \@xp\textellipsis \fi
}
\def\tdots@{\leavevmode\unskip\relaxnext@
\DN@{$\m@th\@ldots\,
\ifx\@let@token,\,$\else\ifx\@let@token.\,$\else
\ifx\@let@token;\,$\else\ifx\@let@token:\,$\else
\ifx\@let@token?\,$\else\ifx\@let@token!\,$\else
$ \fi\fi\fi\fi\fi\fi}%
\ \FN@\next@}
\def\mdots@{\FN@\mdots@@}
\def\mdots@@{\gdef\thedots@{\dotso@}%
\ifx\@let@token\boldsymbol
\gdef\thedots@\boldsymbol{\boldsymboldots@}%
\else
\ifx,\@let@token \gdef\thedots@{\dotsc}%
\else
\ifx\not\@let@token
\gdef\thedots@{\dotsb@}%
\else
\keybin@
\ifgtest@ % if \keybin@ test
\gdef\thedots@{\dotsb@}%
\else
\xdef\meaning@{\meaning\@let@token. .........}%
\xdef\meaning@@{\@xp\striplong@\meaning@\relax\meaning@}%
\@xp\math@\meaning@\math@
\ifgtest@ % if \mathxxx test
\@xp\mathch@\meaning@\mathch@
\ifgtest@ % if \mathchar
\@xp\getmathch@\meaning@\getmathch@
\fi % end if \mathchar
\else % \not \mathxxx
\@xp\Umathch@\meaning@"0"\Umathch@
\ifgtest@ % if \Umathchar
\else % else not \Umathcar
\@xp\macro@\meaning@@\macro@
\ifgtest@ % if macro test
\@xp\not@\meaning@\not@
\ifgtest@ % if macro starts \not test
\gdef\thedots@{\dotsb@}%
\else% else not \not
\@xp\DOTS@\meaning@\DOTS@
\ifgtest@ % \if DOTS
\ifcase\number\DOTSCASE@ %ifcase dots
\gdef\thedots@{\dotsb@}%
\or\gdef\thedots@{\dotsi}\else
\fi % endifcase dots
\else % not macro starts \DOTS
\@xp\math@\meaning@\math@
\ifgtest@ % \if macro starts \mathxxxx
\@xp\mathbin@\meaning@\mathbin@
\ifgtest@ % if macro starts \mathbin
\gdef\thedots@{\dotsb@}%
\else % not macro starting \mathbin
\@xp\mathrel@\meaning@\mathrel@
\ifgtest@ % if macro starts \mathrel
\gdef\thedots@{\dotsb@}%
\fi % endif macro starts \mathrel (no else)
\fi % endif macro starts \mathbin
\fi % endif macro starts with \mathxxx (no else)
\fi % endif macro starts \DOTS else
\fi % end macro starting \not \ifgtest@ test (no else)
\else
\@xp\thecharacter@\meaning@\thecharacter@
\fi % end macro \ifgtest@ test (no else)
\fi % end if \Umathchar test
\fi % end \math@ \ifgtest@
\fi % end \keybin@ \ifgtest@ test (no else)
\fi % end if \not (no else)
\fi % end if comma (no else)
\fi % end if boldsymbol (no else)
\thedots@}
\def\boldsymboldots@#1{%
\bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
\boldsymbol#1\bold@false}
\ams@def\@cdots{\mathinner{\cdotp\cdotp\cdotp}}
\newcommand{\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@}
\ams@DeclareRobustCommand{\cdots}{\DN@{\extrap@\@cdots}\FN@\next@}
\let\dotsb\cdots
\let\dotsm\cdots
\DeclareRobustCommand{\dotso}{\relax
\ifmmode \DN@{\extrap@\@ldots}%
\else \let\next@\tdots@\fi
\FN@\next@}
\DeclareRobustCommand{\dotsc}{%
\DN@{\ifx\@let@token;\@ldots\,%
\else \ifx\@let@token.\@ldots\,%
\else \extra@\@ldots \ifgtest@\,\fi
\fi\fi}%
\FN@\next@}
\renewcommand{\longrightarrow}{%
\DOTSB\protect\relbar\protect\joinrel\rightarrow}
\renewcommand{\Longrightarrow}{%
\DOTSB\protect\Relbar\protect\joinrel\Rightarrow}
\renewcommand{\longleftarrow}{%
\DOTSB\leftarrow\protect\joinrel\protect\relbar}
\renewcommand{\Longleftarrow}{%
\DOTSB\Leftarrow\protect\joinrel\protect\Relbar}
\renewcommand{\longleftrightarrow}{\DOTSB\leftarrow\joinrel\rightarrow}
\renewcommand{\Longleftrightarrow}{\DOTSB\Leftarrow\joinrel\Rightarrow}
\renewcommand{\mapsto}{\DOTSB\mapstochar\rightarrow}
\renewcommand{\longmapsto}{\DOTSB\mapstochar\longrightarrow}
\renewcommand{\hookrightarrow}{\DOTSB\lhook\joinrel\rightarrow}
\renewcommand{\hookleftarrow}{\DOTSB\leftarrow\joinrel\rhook}
\renewcommand{\iff}{\DOTSB\;\Longleftrightarrow\;}
\renewcommand{\doteq}{%
\DOTSB\mathrel{\mathop{\kern0pt =}\limits^{\textstyle.}}}
\newif\if@display
\everydisplay\@xp{\the\everydisplay \@displaytrue}
\renewcommand{\int}{\DOTSI\intop\ilimits@}
\renewcommand{\oint}{\DOTSI\ointop\ilimits@}
\def\intkern@{\mkern-6mu\mathchoice{\mkern-3mu}{}{}{}}
\def\intdots@{\mathchoice{\@cdots}%
{{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}%
{{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}%
{{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
\ams@newcommand{\iint}{\DOTSI\protect\MultiIntegral{2}}
\ams@newcommand{\iiint}{\DOTSI\protect\MultiIntegral{3}}
\ams@newcommand{\iiiint}{\DOTSI\protect\MultiIntegral{4}}
\newcommand{\idotsint}{\DOTSI\protect\MultiIntegral{0}}
\newcommand{\MultiIntegral}[1]{%
\edef\ints@c{\noexpand\intop
\ifnum#1=\z@\noexpand\intdots@\else\noexpand\intkern@\fi
\ifnum#1>\tw@\noexpand\intop\noexpand\intkern@\fi
\ifnum#1>\thr@@\noexpand\intop\noexpand\intkern@\fi
\noexpand\intop
\noexpand\ilimits@
}%
\futurelet\@let@token\ints@a
}
\def\ints@a{%
\ifx\limits\@let@token \ints@b
\else \ifx\displaylimits\@let@token \ints@b
\else\ifx\ilimits@\displaylimits \ints@b
\fi\fi\fi
\ints@c
}
\def\ints@b{%
\mkern-7mu\mathchoice{\mkern-2mu}{}{}{}%
\mathop\bgroup
\mkern7mu\mathchoice{\mkern2mu}{}{}{}%
\let\ilimits@\egroup
}%
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@=\hbox{}
\def\Mathstrut@{\copy\Mathstrutbox@}
\ifx\Umathcharnumdef\@undefined
\def\resetMathstrut@{%
\begingroup
\setbox\z@\hbox{%
\mathchardef\@tempa\mathcode`\(\relax
\def\@tempb##1"##2##3{\the\textfont"##3\char"}%
\expandafter\@tempb\meaning\@tempa \relax
}%
\edef\@tempa{%
\ht\Mathstrutbox@\the\ht\z@\relax
\dp\Mathstrutbox@\the\dp\z@\relax}%
\expandafter\endgroup\@tempa
}
\else
\def\resetMathstrut@{%
\begingroup
\Umathcharnumdef\@tempa\Umathcodenum`\(\relax
\def\@tempb##1"##2"##3"##4\relax{%
\endgroup
\ht\Mathstrutbox@=\fontcharht\textfont"##3 "##4\relax
\dp\Mathstrutbox@=\fontchardp\textfont"##3 "##4\relax}%
\expandafter\@tempb\meaning\@tempa \relax
}
\fi
\addto@hook\every@math@size{\resetMathstrut@}
\newbox\strutbox@
\def\strut@{\copy\strutbox@}
\def\reset@strutbox@{%
\global\setbox\strutbox@\hbox{%
\lower.5\normallineskiplimit
\vbox{\kern-\normallineskiplimit\copy\strutbox}}}
\addto@hook\every@math@size{\reset@strutbox@}
\AtBeginDocument{\reset@strutbox@}
\renewcommand{\big}{\bBigg@\@ne}
\renewcommand{\Big}{\bBigg@{1.5}}
\renewcommand{\bigg}{\bBigg@\tw@}
\renewcommand{\Bigg}{\bBigg@{2.5}}
\ifx\leavevmode@ifvmode\@undefined
\def\bBigg@#1#2{%
{\@mathmeasure\z@{\nulldelimiterspace\z@}%
{\left#2\vcenter to#1\big@size{}\right.}%
\box\z@}}
\else
\def\bBigg@#1#2{\leavevmode@ifvmode
{\@mathmeasure\z@{\nulldelimiterspace\z@}%
{\left#2\vcenter to#1\big@size{}\right.}%
\box\z@}}
\fi
\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@}
\ams@newcommand{\dddot}[1]{%
{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalfont ...}\vss}}}}
\ams@newcommand{\ddddot}[1]{%
{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalfont....}\vss}}}}
\def\set@mathaccent#1#2#3#4{%
\xdef#2{\@nx\protect\@nx\mathaccentV
{\@xp\@gobble\string#2}\hexnumber@#1#4}%
}
\def\@tempa#1{\@xp\@tempb\meaning#1\@nil#1}
\def\@tempb#1>#2#3 #4\@nil#5{%
\@xp\ifx\csname#3\endcsname\mathaccent
\@tempc#4?"7777\@nil#5%
\else
\@xp\ifx\csname#3\endcsname\Umathaccent
\@tempd#4\@nil#5%
\else
\PackageWarningNoLine{amsmath}{%
Unable to redefine math accent \string#5}%
\fi\fi}
\def\@tempc#1"#2#3#4#5#6\@nil#7{%
\chardef\@tempd="#3\relax\set@mathaccent\@tempd{#7}{#2}{#4#5}}
\def\@tempd#1\@nil#2{%
\PackageWarningNoLine{amsmath}{%
Unable to redefine \string\Umathaccent\space\string#2}%
}
\@tempa{\hat}
\@tempa{\check}
\@tempa{\tilde}
\@tempa{\acute}
\@tempa{\grave}
\@tempa{\dot}
\@tempa{\ddot}
\@tempa{\breve}
\@tempa{\bar}
\@tempa{\vec}
\@ifundefined{mathring}{%
\DeclareMathAccent{\mathring}{\mathalpha}{operators}{"17}
}{%
\@tempa{\mathring}
}
%%\@tempa\widetilde
%%\@tempa\widehat
\newcommand{\acc@check}{}
\newcommand{\acc@error}{}
\def\acc@check{\@ifnextchar\@empty\relax\acc@error}
\def\acc@error{%
\@amsmath@err{%
Improper argument for math accent:\MessageBreak
Extra braces must be added to prevent wrong output%
}\@ehc
}
\newcount\macc@depth
\long\def\@gobblethree#1#2#3{}
\def\mathaccentV#1#2#3#4#5{%
\ifmmode
\gdef\macc@tmp{\macc@depth\@ne}%
\setbox\z@\hbox{%
\let\mathaccentV\macc@test
\let\use@mathgroup\@gobbletwo \let\select@group\@gobblethree
\frozen@everymath{}$#5$%
}%
\macc@tmp
\ifnum\macc@depth=\@ne
\global\let\macc@nucleus\@empty
\mathaccent"\accentclass@
\else
\@xp\macc@nested
\fi
#2#3#4{#5}%
\macc@nucleus
\else
\@xp\nonmatherr@\csname#1\endcsname
\fi
}
\def\macc@test#1#2#3#4{\xdef\macc@tmp{\macc@tmp\advance\macc@depth\@ne}}
\def\macc@group{-1}
\def\macc@nested#1#2#3#4{%
\begingroup
\let\math@bgroup\@empty \let\math@egroup\macc@set@skewchar
\mathsurround\z@ \frozen@everymath{\mathgroup\macc@group\relax}%
\macc@set@skewchar\relax
\let\mathaccentV\macc@nested@a
\macc@nested@a\relax#1#2#3{#4}%
\endgroup
}
\let\macc@palette\mathpalette
\def\macc@nested@a#1#2#3#4#5{%
\ifnum\macc@group=\mathgroup
\else \macc@set@skewchar\relax \edef\macc@group{\the\mathgroup}%
\fi
\mathchardef\macc@code "\accentclass@ #2#3#4\relax
\macc@palette\macc@a{#5}%
}
\def\macc@set@skewchar#1{%
\begingroup
\ifnum\mathgroup=\m@ne \let\@tempa\@ne
\else
\ifnum\skewchar\textfont\mathgroup=\m@ne \let\@tempa\@ne
\else \let\@tempa\mathgroup
\fi
\fi
\count@=\skewchar\textfont\@tempa
\advance\count@"7100
\edef\@tempa{\endgroup
\mathchardef\noexpand\macc@skewchar=\number\count@\relax}%
\@tempa
#1%
}
\def\macc@a#1#2{%
\begingroup
\let\macc@style#1\relax
\def\macc@palette##1{##1\macc@style}%
\advance\macc@depth\m@ne
\ifnum\macc@depth=\z@
\gdef\macc@nucleus{#2}%
\setbox\z@\hbox{$#1#2\@empty{}\macc@skewchar$}%
\setbox\tw@\hbox{$#1#2\@empty\macc@skewchar$}%
\dimen@\tw@\wd\tw@ \advance\dimen@-\tw@\wd\z@
\xdef\macc@kerna{\the\dimen@\relax}%
\setbox4\hbox{$#1#2\acc@check\@empty$}%
\global\setbox\@ne\hbox to\wd4{}%
\ht\@ne\ht4 \dp\@ne\dp4
\xdef\macc@kernb{\the\wd4\relax}%
\mathaccent\macc@code{\box\@ne\kern\macc@kerna}%
\else
\mathaccent\macc@code{\let\macc@adjust\@empty #1#2\@empty}%
\macc@adjust
\fi
\endgroup
}
\def\macc@adjust{%
\dimen@\macc@kerna\advance\dimen@\macc@kernb
\kern-\dimen@
}
\def\Hat{\hat}
\def\Check{\check}
\def\Tilde{\tilde}
\def\Acute{\acute}
\def\Grave{\grave}
\def\Dot{\dot}
\def\Ddot{\ddot}
\def\Breve{\breve}
\def\Bar{\bar}
\def\Vec{\vec}
\def\nonmatherr@#1{\@amsmath@err{\protect
#1 allowed only in math mode}\@ehd}
\renewcommand{\bmod}{\nonscript\mskip-\medmuskip\mkern5mu\mathbin
{\operator@font mod}\penalty900
\mkern5mu\nonscript\mskip-\medmuskip}
\newcommand{\pod}[1]{\allowbreak
\if@display\mkern18mu\else\mkern8mu\fi(#1)}
\renewcommand{\pmod}[1]{\pod{{\operator@font mod}\mkern6mu#1}}
\newcommand{\mod}[1]{\allowbreak\if@display\mkern18mu
\else\mkern12mu\fi{\operator@font mod}\,\,#1}
\newcommand{\cfrac}[3][c]{{\displaystyle\frac{%
\strut\ifx r#1\hfill\fi#2\ifx l#1\hfill\fi}{#3}}%
\kern-\nulldelimiterspace}
\newcommand{\overset}[2]{\binrel@{#2}%
\binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
\newcommand{\underset}[2]{\binrel@{#2}%
\binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
\newcommand{\sideset}[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}%
}
\ifx\leavevmode@ifvmode\@undefined
\renewcommand{\smash}[1][tb]{%
\def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
\edef\finsm@sh{\csname mb@#1\endcsname\z@\z@\box\z@}%
\ifmmode \@xp\mathpalette\@xp\mathsm@sh
\else \@xp\makesm@sh
\fi
}
\else
\renewcommand{\smash}[1][tb]{%
\def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
\edef\finsm@sh{\csname mb@#1\endcsname\z@\z@ \leavevmode@ifvmode\box\z@}%
\ifmmode \@xp\mathpalette\@xp\mathsm@sh
\else \@xp\makesm@sh
\fi
}
\fi
\mathchardef\std@minus\mathcode`\-\relax
\mathchardef\std@equal\mathcode`\=\relax
\AtBeginDocument{%
\mathchardef\std@minus\mathcode`\-\relax
\mathchardef\std@equal\mathcode`\=\relax
}
\ams@def\relbar{\mathrel{\mathpalette\mathsm@sh\std@minus}}
\ams@def\Relbar{\mathrel\std@equal}
\def\arrowfill@#1#2#3#4{%
$\m@th\thickmuskip0mu\medmuskip\thickmuskip\thinmuskip\thickmuskip
\relax#4#1\mkern-7mu%
\cleaders\hbox{$#4\mkern-2mu#2\mkern-2mu$}\hfill
\mkern-7mu#3$%
}
\def\leftarrowfill@{\arrowfill@\leftarrow\relbar\relbar}
\def\rightarrowfill@{\arrowfill@\relbar\relbar\rightarrow}
\def\leftrightarrowfill@{\arrowfill@\leftarrow\relbar\rightarrow}
\def\Leftarrowfill@{\arrowfill@\Leftarrow\Relbar\Relbar}
\def\Rightarrowfill@{\arrowfill@\Relbar\Relbar\Rightarrow}
\def\Leftrightarrowfill@{\arrowfill@\Leftarrow\Relbar\Rightarrow}
\def\overarrow@#1#2#3{\vbox{\ialign{##\crcr#1#2\crcr
\noalign{\nointerlineskip}$\m@th\hfil#2#3\hfil$\crcr}}}
\ams@renewcommand{\overrightarrow}{%
\mathpalette{\overarrow@\rightarrowfill@}}
\ams@renewcommand{\overleftarrow}{%
\mathpalette{\overarrow@\leftarrowfill@}}
\ams@newcommand{\overleftrightarrow}{%
\mathpalette{\overarrow@\leftrightarrowfill@}}
\def\underarrow@#1#2#3{%
\vtop{\ialign{##\crcr$\m@th\hfil#2#3\hfil$\crcr
\noalign{\nointerlineskip\kern1.3\ex@}#1#2\crcr}}}
\ams@newcommand{\underrightarrow}{%
\mathpalette{\underarrow@\rightarrowfill@}}
\ams@newcommand{\underleftarrow}{%
\mathpalette{\underarrow@\leftarrowfill@}}
\ams@newcommand{\underleftrightarrow}{%
\mathpalette{\underarrow@\leftrightarrowfill@}}
\def\ext@arrow#1#2#3#4#5#6#7{%
\mathrel{\mathop{%
\setbox\z@\hbox{#5\displaystyle}%
\setbox\tw@\vbox{\m@th
\hbox{$\scriptstyle\mkern#3mu{#6}\mkern#4mu$}%
\hbox{$\scriptstyle\mkern#3mu{#7}\mkern#4mu$}%
\copy\z@
}%
\hbox to\wd\tw@{\unhbox\z@}}%
\limits
\@ifnotempty{#7}{^{\if0#1\else\mkern#1mu\fi
#7\if0#2\else\mkern#2mu\fi}}%
\@ifnotempty{#6}{_{\if0#1\else\mkern#1mu\fi
#6\if0#2\else\mkern#2mu\fi}}}%
}
\newcommand{\xrightarrow}[2][]{\ext@arrow 0359\rightarrowfill@{#1}{#2}}
\newcommand{\xleftarrow}[2][]{\ext@arrow 3095\leftarrowfill@{#1}{#2}}
\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\,%
}
\renewenvironment{matrix}{%
\matrix@check\matrix\env@matrix
}{%
\endarray \hskip -\arraycolsep
}
\def\env@matrix{\hskip -\arraycolsep