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amsmath.sty
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amsmath.sty
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%%
%% This is file `amsmath.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% amsmath.dtx
%%
%%% ====================================================================
%%% @LaTeX-file{
%%% filename = "amsmath.dtx",
%%% version = "2.13",
%%% date = "2000/07/18",
%%% time = "08:16:41 EDT",
%%% author = "American Mathematical Society",
%%% copyright = "Copyright 1995, 2000 American Mathematical Society,
%%% all rights reserved. Copying of this file is
%%% authorized only if either:
%%% (1) you make absolutely no changes to your copy,
%%% including name; OR
%%% (2) if you do make changes, you first rename it
%%% to some other name.",
%%% address = "American Mathematical Society,
%%% Technical Support,
%%% Publications Technical Group,
%%% P. O. Box 6248,
%%% Providence, RI 02940,
%%% USA",
%%% telephone = "401-455-4080 or (in the USA and Canada)
%%% 800-321-4AMS (321-4267)",
%%% FAX = "401-331-3842",
%%% checksum = "38084 5829 21569 202795",
%%% email = "tech-support@ams.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "latex, amslatex, math, amsmath",
%%% supported = "yes",
%%% abstract = "This is a \LaTeX{} package that provides a variety of
%%% extra mathematical features, largely derived from
%%% AMS-\TeX{}.",
%%% docstring = "The checksum field above contains a CRC-16 checksum
%%% as the first value, followed by the equivalent of
%%% the standard UNIX wc (word count) utility output of
%%% lines, words, and characters. This is produced by
%%% Robert Solovay's checksum utility.",
%%% }
%%% ====================================================================
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1994/12/01]% LaTeX date must be December 1994 or later
\ProvidesPackage{amsmath}[2000/07/18 v2.13 AMS math features]
\edef\@temp{\catcode 96=\number\catcode 96 }
\catcode\string `\`=12
\def\do#1{\catcode\number`#1=\number\catcode`#1}
\edef\@temp{%
\noexpand\AtEndOfPackage{%
\@temp
\do\"\do\'\do\(\do\)\do\*\do\+\do\,\do\-\do\.%
\do\/\do\<\do\=\do\>\do\[\do\]\do\^\do\_\relax
}%
}
\@temp
\def\do#1{\catcode\number`#1=12 }
\do\"\do\'\do\(\do\)\do\*\do\+\do\,\do\-\do\.
\do\/\do\<\do\=\do\>\do\[\do\]
\catcode`\^=7 \catcode`\_=8
\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
\let\mathindent=\@mathmargin
\AtBeginDocument{%
\ifdim\@mathmargin= -1sp
\@mathmargin\leftmargini minus\leftmargini
\fi
}%
}
\DeclareOption{?}{}
\ExecuteOptions{nointlimits,sumlimits,namelimits,centertags}
\ProcessOptions\par
\@ifpackagewith{amsmath}{?}{%
\typeout{^^J%
Documentation for the amsmath package is found in amsldoc.dvi^^J%
(or .pdf or .tex).^^J%
^^J%
See also http://www.ams.org/tex/amslatex.html.^^J%
^^J%
Note: Using the first edition of The LaTeX Companion (1994) without^^J%
errata as a guide for amsmath use is not recommended.^^J%
}%
}{%
\typeout{%
For additional information on amsmath, use the \lq ?\rq\space option.%
}%
}
\ifnum\cmex@opt=7 \relax
\DeclareFontShape{OMX}{cmex}{m}{n}{%
<-8>cmex7<8>cmex8<9>cmex9%
<10><10.95><12><14.4><17.28><20.74><24.88>cmex10%
}{}%
\expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
\else
\ifnum\cmex@opt=\z@ % need to override cmex7 fontdef from amsfonts
\begingroup
\fontencoding{OMX}\fontfamily{cmex}%
\expandafter\let\csname OMX+cmex\endcsname\relax
\try@load@fontshape
\endgroup
\expandafter\let\csname OMX/cmex/m/n/10\endcsname\relax
\def\cmex@opt{10}%
\fi
\fi
\RequirePackage{amstext}[1995/01/25]
\RequirePackage{amsbsy}[1995/01/20]
\RequirePackage{amsopn}[1995/01/20]
\def\@amsmath@err{\PackageError{amsmath}}
\providecommand{\AmS}{{\protect\AmSfont
A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
\newcommand{\AmSfont}{%
\usefont{OMS}{cmsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}
\def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
\m@th$#2#3$}}
\@ifundefined{inf@bad}{%
\newcount\inf@bad \inf@bad=1000000 \relax
}{}
\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}
\def\@tempa#1#2\@nil{%
\ifx\delimiter#1\@tempcnta#2\relax\else\@tempcnta\z@\fi
}
\@xp\@tempa\vert\@empty\@nil
\ifnum\@tempcnta>\z@
\advance\@tempcnta "4000000
\xdef\lvert{\delimiter\number\@tempcnta\space }
\advance\@tempcnta "1000000
\xdef\rvert{\delimiter\number\@tempcnta\space }
\else
\ifx\@@undefined\lvert
% Fall back to cmex encoding since we don't know what else to do.
\DeclareMathDelimiter{\lvert}
{\mathopen}{symbols}{"6A}{largesymbols}{"0C}
\DeclareMathDelimiter{\rvert}
{\mathclose}{symbols}{"6A}{largesymbols}{"0C}
\fi
\fi
\@xp\@tempa\Vert\@empty\@nil
\ifnum\@tempcnta>\z@
\advance\@tempcnta "4000000
\xdef\lVert{\delimiter\number\@tempcnta\space }
\advance\@tempcnta "1000000
\xdef\rVert{\delimiter\number\@tempcnta\space }
\else
\ifx\@@undefined\lVert
\DeclareMathDelimiter{\lVert}
{\mathopen}{symbols}{"6B}{largesymbols}{"0D}
\DeclareMathDelimiter{\rVert}
{\mathclose}{symbols}{"6B}{largesymbols}{"0D}
\fi
\fi
\@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;\MessageBreak
\protect\frac\space or \protect\genfrac\space should be used instead%
\MessageBreak
}
\global\@xp\let\csname#1\@xp\endcsname\csname @@#1\endcsname
\csname#1\endcsname
}
\renewcommand{\over}{\primfrac{over}}
\renewcommand{\atop}{\primfrac{atop}}
\renewcommand{\above}{\primfrac{above}}
\renewcommand{\overwithdelims}{\primfrac{overwithdelims}}
\renewcommand{\atopwithdelims}{\primfrac{atopwithdelims}}
\renewcommand{\abovewithdelims}{\primfrac{abovewithdelims}}
\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}
\begingroup
\edef\@tempa{\string\mathchar"}
\def\@tempb#1"#2\@nil{#1"}
\edef\@tempc{\expandafter\@tempb\meaning\coprod "\@nil}
\ifx\@tempa\@tempc
\global\let\coprod@\coprod
\gdef\coprod{\DOTSB\coprod@\slimits@}
\global\let\bigvee@\bigvee
\gdef\bigvee{\DOTSB\bigvee@\slimits@}
\global\let\bigwedge@\bigwedge
\gdef\bigwedge{\DOTSB\bigwedge@\slimits@}
\global\let\biguplus@\biguplus
\gdef\biguplus{\DOTSB\biguplus@\slimits@}
\global\let\bigcap@\bigcap
\gdef\bigcap{\DOTSB\bigcap@\slimits@}
\global\let\bigcup@\bigcup
\gdef\bigcup{\DOTSB\bigcup@\slimits@}
\global\let\prod@\prod
\gdef\prod{\DOTSB\prod@\slimits@}
\global\let\sum@\sum
\gdef\sum{\DOTSB\sum@\slimits@}
\global\let\bigotimes@\bigotimes
\gdef\bigotimes{\DOTSB\bigotimes@\slimits@}
\global\let\bigoplus@\bigoplus
\gdef\bigoplus{\DOTSB\bigoplus@\slimits@}
\global\let\bigodot@\bigodot
\gdef\bigodot{\DOTSB\bigodot@\slimits@}
\global\let\bigsqcup@\bigsqcup
\gdef\bigsqcup{\DOTSB\bigsqcup@\slimits@}
\fi
\endgroup
\newcommand{\leftroot}{\@amsmath@err{\Invalid@@\leftroot}\@eha}
\newcommand{\uproot}{\@amsmath@err{\Invalid@@\uproot}\@eha}
\newcount\uproot@
\newcount\leftroot@
\renewcommand{\root}{\relaxnext@
\DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
\ifx\@let@token\leftroot\let\next@\nextiii@\else
\let\next@\plainroot@\fi\fi\next@}%
\def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
\def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
\DN@.{\FN@\nextv@}\fi\next@.}%
\def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
\let\next@\plainroot@\fi\next@}%
\def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
\def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
\def\nextvii@{\ifx\@let@token\@sptoken
\DN@. {\FN@\nextviii@}\else
\DN@.{\FN@\nextviii@}\fi\next@.}%
\def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
\let\next@\plainroot@\fi\next@}%
\def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
\bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
\def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
$\m@th\scriptscriptstyle{#1}$}%
\mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
{\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
\@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
\DeclareRobustCommand{\overline}[1]{\@@overline{#1}}
\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
\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{\ldots}{%
\ifmmode \mathellipsis \else \textellipsis \fi
}
\DeclareRobustCommand{\dots}{%
\ifmmode \@xp\mdots@\else \@xp\textellipsis \fi
}
\def\tdots@{\leavevmode\unskip\relaxnext@
\DN@{$\m@th\@ldots\,
\ifx\@let@token,\,$\else\ifx\@let@token.\,$\else
\ifx\@let@token;\,$\else\ifx\@let@token:\,$\else
\ifx\@let@token?\,$\else\ifx\@let@token!\,$\else
$ \fi\fi\fi\fi\fi\fi}%
\ \FN@\next@}
\def\mdots@{\FN@\mdots@@}
\def\mdots@@{\gdef\thedots@{\dotso@}%
\ifx\@let@token\boldsymbol \gdef\thedots@\boldsymbol{\boldsymboldots@}%
\else\ifx,\@let@token \gdef\thedots@{\dotsc}%
\else\ifx\not\@let@token \gdef\thedots@{\dotsb@}%
\else\keybin@
\ifgtest@\gdef\thedots@{\dotsb@}%
\else\xdef\meaning@{\meaning\@let@token..........}%
\xdef\meaning@@{\meaning@}%
\@xp\math@\meaning@\math@
\ifgtest@
\@xp\mathch@\meaning@\mathch@
\ifgtest@\@xp\getmathch@\meaning@\getmathch@\fi
\else\@xp\macro@\meaning@@\macro@
\ifgtest@
\@xp\not@\meaning@\not@\ifgtest@\gdef\thedots@{\dotsb@}%
\else\@xp\DOTS@\meaning@\DOTS@
\ifgtest@
\ifcase\number\DOTSCASE@\gdef\thedots@{\dotsb@}%
\or\gdef\thedots@{\dotsi}\else\fi
\else\@xp\math@\meaning@\math@
\ifgtest@\@xp\mathbin@\meaning@\mathbin@
\ifgtest@\gdef\thedots@{\dotsb@}%
\else\@xp\mathrel@\meaning@\mathrel@
\ifgtest@\gdef\thedots@{\dotsb@}%
\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
\thedots@}
\def\boldsymboldots@#1{%
\bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
\boldsymbol#1\bold@false}
\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@}
\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}}}
\newcommand{\iint}{\DOTSI\protect\MultiIntegral{2}}
\newcommand{\iiint}{\DOTSI\protect\MultiIntegral{3}}
\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@}
\def\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@
}
\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}}
\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@}
\newcommand{\dddot}[1]{%
{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalfont ...}\vss}}}}
\newcommand{\ddddot}[1]{%
{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalfont....}\vss}}}}
\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
\PackageWarningNoLine{amsmath}{%
Unable to redefine math accent \string#5}%
\fi
}
\def\@tempc#1"#2#3#4#5#6\@nil#7{%
\chardef\@tempd="#3\relax\set@mathaccent\@tempd{#7}{#2}{#4#5}}
\@tempa{\hat}
\@tempa{\check}
\@tempa{\tilde}
\@tempa{\acute}
\@tempa{\grave}
\@tempa{\dot}
\@tempa{\ddot}
\@tempa{\breve}
\@tempa{\bar}
\@tempa{\vec}
\@ifundefined{mathring}{%
\DeclareMathAccent{\mathring}{\mathalpha}{operators}{"17}
}{%
\@tempa{\mathring}
}
%%\@tempa\widetilde
%%\@tempa\widehat
\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}%
}
\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
}
\mathchardef\std@minus\mathcode`\-\relax
\mathchardef\std@equal\mathcode`\=\relax
\AtBeginDocument{%
\mathchardef\std@minus\mathcode`\-\relax
\mathchardef\std@equal\mathcode`\=\relax
}
\def\relbar{\mathrel{\mathpalette\mathsm@sh\std@minus}}
\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}}}
\renewcommand{\overrightarrow}{%
\mathpalette{\overarrow@\rightarrowfill@}}
\renewcommand{\overleftarrow}{%
\mathpalette{\overarrow@\leftarrowfill@}}
\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}}}
\newcommand{\underrightarrow}{%
\mathpalette{\underarrow@\rightarrowfill@}}
\newcommand{\underleftarrow}{%
\mathpalette{\underarrow@\leftarrowfill@}}
\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
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\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
\let\@ifnextchar\new@ifnextchar
\array{*\c@MaxMatrixCols c}}
\newcount\c@MaxMatrixCols \c@MaxMatrixCols=10
\def\matrix@check#1{%
\@xp\ifx\csname\@currenvir\endcsname#1%
\else\matrix@error#1%
\@xp\@gobble
\fi
}
\def\matrix@error#1{%
\@amsmath@err{%
Old form `\string#1' should be \string\begin{\@xp\@gobble\string#1}%
}{%
`\string#1{...}' is old Plain-TeX syntax whose use is
ill-advised in LaTeX.%
}%
}
\renewenvironment{pmatrix}{%
\left(%
\matrix@check\pmatrix\env@matrix
}{
\endmatrix\right)%
}
\newenvironment{bmatrix}{\left[\env@matrix}{\endmatrix\right]}
\newenvironment{Bmatrix}{%
\left\lbrace\env@matrix
}{%
\endmatrix\right\rbrace
}
\newenvironment{vmatrix}{\left\lvert\env@matrix}{\endmatrix\right\rvert}
\newenvironment{Vmatrix}{\left\lVert\env@matrix}{\endmatrix\right\rVert}
\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\dotsspace@1.5mu\mkern-#1\dotsspace@
\xleaders\hbox{$\m@th\mkern#1\dotsspace@.\mkern#1\dotsspace@$}%
\hfill
\mkern-#1\dotsspace@}%
}
\renewenvironment{cases}{%
\matrix@check\cases\env@cases
}{%
\endarray\right.%
}
\def\env@cases{%
\let\@ifnextchar\new@ifnextchar
\left\lbrace
\def\arraystretch{1.2}%
\array{@{}l@{\quad}l@{}}%
}
\newcounter{parentequation}% Counter for ``parent equation''.
\@ifundefined{ignorespacesafterend}{%
\def\ignorespacesafterend{\global\@ignoretrue}%
}{}
\newenvironment{subequations}{%
\refstepcounter{equation}%
\protected@edef\theparentequation{\theequation}%
\setcounter{parentequation}{\value{equation}}%
\setcounter{equation}{0}%
\def\theequation{\theparentequation\alph{equation}}%
\ignorespaces
}{%
\setcounter{equation}{\value{parentequation}}%
\ignorespacesafterend
}
\newcommand{\numberwithin}[3][\arabic]{%
\@ifundefined{c@#2}{\@nocounterr{#2}}{%
\@ifundefined{c@#3}{\@nocnterr{#3}}{%
\@addtoreset{#2}{#3}%
\@xp\xdef\csname the#2\endcsname{%
\@xp\@nx\csname the#3\endcsname .\@nx#1{#2}}}}%
}
\newcommand{\eqref}[1]{\textup{\tagform@{\ref{#1}}}}
\newcount\dspbrk@lvl
\dspbrk@lvl=-1
\interdisplaylinepenalty\@M
\newcommand{\allowdisplaybreaks}[1][4]{%
\interdisplaylinepenalty\getdsp@pen{#1}\relax
}
\def\getdsp@pen#1{%
\ifcase #1\@M \or 9999 \or 6999 \or 2999 \or \z@\fi
}
\newcommand{\displaybreak}{\new@ifnextchar[\dspbrk@{\dspbrk@[4]}}
\chardef\dspbrk@context=\sixt@@n
\def\dspbrk@[#1]{%
\ifmeasuring@
\else
\ifcase\dspbrk@context % case 0 --- OK
\global\dspbrk@lvl #1\relax
\or % case 1 --- inside a box
\nogood@displaybreak
\else % other cases --- outside of a display
\@amsmath@err{\Invalid@@\displaybreak}\@eha
\fi
\fi
}
\def\nogood@displaybreak{%
\@amsmath@err{\protect
\displaybreak\space cannot be applied here}%
{One of the enclosing environments creates an
unbreakable box\MessageBreak
(e.g., split, aligned, gathered, ...).}%
}
\def\math@cr{\relax\iffalse{\fi\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 \iffalse}\fi\math@cr@@@
\noalign{\vskip#1\relax}}
\def\Let@{\let\\\math@cr}
\def\restore@math@cr{\def\math@cr@@@{\cr}}
\restore@math@cr
\newcommand{\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
\newcommand{\thetag}{\leavevmode\tagform@}
\let\df@tag\@empty
\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
}
\toks@\@xp{\@arrayparboxrestore \let\label\ltx@label}%
\edef\@arrayboxrestore{\the\toks@}
\let\df@label\@empty
\def\make@display@tag{%
\if@eqnsw \incr@eqnum \print@eqnum
\else \iftag@ \df@tag \global\let\df@tag\@empty \fi
\fi
\ifmeasuring@
\else
\ifx\df@label\@empty
\else
\@xp\ltx@label\@xp{\df@label}%