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-rw-r--r--Master/texmf-dist/tex/latex/amslatex/amstex.sty2043
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diff --git a/Master/texmf-dist/tex/latex/amslatex/amstex.sty b/Master/texmf-dist/tex/latex/amslatex/amstex.sty
deleted file mode 100644
index f67435c5829..00000000000
--- a/Master/texmf-dist/tex/latex/amslatex/amstex.sty
+++ /dev/null
@@ -1,2043 +0,0 @@
-%%% ====================================================================
-%%% @LaTeX-file{
-%%% filename = "amstex.sty",
-%%% version = "1.2f",
-%%% date = "1999/11/15",
-%%% time = "14:07:07 EST",
-%%% checksum = "05218 2043 3020 71018",
-%%% author = "American Mathematical Society",
-%%% copyright = "Copyright 1995, 1999 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",
-%%% email = "tech-support@math.ams.org (Internet)",
-%%% keywords = "latex, amslatex, ams-latex, math, amstex, ams-tex",
-%%% supported = "yes",
-%%% abstract = "This package provides a variety of extra
-%%% mathematical features, largely derived from
-%%% AMS-\TeX{}. It was superseded in 1995 by the
-%%% amsmath package.",
-%%% 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.",
-%%% }
-%%% ====================================================================
-% This file was generated from version 1.2beta of amstex.dtx and then
-% underwent additional hand-editing.
-\if@compatibility \else \catcode`\%=9 \fi
-%\PackageError{amstex}{%
-%Package `amstex' is obsolete, substituting `amsmath'}{You
-%should use \string\usepackage{amsmath} instead. If
-%that does not give satisfactory results, rename your previous copy
-%of amstex.sty to amstex12beta.sty and call it with
-%\string\usepackage{amstex12beta}.}
-%\catcode`\%=14 \relax \input{amsmath.sty}\endinput
-%
-\ProvidesPackage{amstex}[1999/11/15 v1.2f AMS extra math features]
-\let\@amsfonts=T
-\DeclareOption{noamsfonts}{\let\@amsfonts=F}
-\DeclareOption{psamsfonts}{\let\@amsfonts=P}
-\DeclareOption{intlimits}{\let\ilimits@\displaylimits}
-\DeclareOption{nointlimits}{\let\ilimits@\nolimits}
-\DeclareOption{sumlimits}{\let\slimits@\displaylimits}
-\DeclareOption{nosumlimits}{\let\slimits@\nolimits}
-\DeclareOption{namelimits}{\let\nlimits@\displaylimits}
-\DeclareOption{nonamelimits}{\let\nlimits@\nolimits}
-\newif\ifctagsplit@
-\newif\iftagsleft@
-\DeclareOption{leqno}{\tagsleft@true}
-\DeclareOption{reqno}{\tagsleft@false}
-\DeclareOption{centertags}{\ctagsplit@true}
-\DeclareOption{tbtags}{\ctagsplit@false}
-\newif\if@fleqn
-\newskip\@mathmargin
-\@mathmargin\@centering
-\DeclareOption{fleqn}{%
- \@fleqntrue
- \@mathmargin\m@ne sp
- \AtBeginDocument{%
- \ifdim\@mathmargin=\m@ne sp
- \@mathmargin\leftmargini
- \fi
- }%
-}
-\DeclareOption{righttag}{\tagsleft@false}
-\DeclareOption{ctagsplt}{\ctagsplit@true}
-\DeclareOption{intlim}{\let\ilimits@\displaylimits}
-\DeclareOption{nosumlim}{\let\slimits@\nolimits}
-\DeclareOption{nonamelm}{\let\nlimits@\nolimits}
-\ExecuteOptions{nointlimits,sumlimits,namelimits,centertags}
-\ProcessOptions
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% In this section \RequirePackage statements were replaced with the
-%% contents of the referenced files.
-%%% filename = "amsgen.dtx",
-%%% version = "1.2beta",
-%%% date = "1994/12/13",
-\providecommand{\@saveprimitive}[2]{\begingroup\escapechar`\\\relax
- \edef\@tempa{\string#1}\edef\@tempb{\meaning#1}%
- \ifx\@tempa\@tempb \global\let#2#1%
- \else
- \edef\@tempb{\meaning#2}%
- \ifx\@tempa\@tempb
- \else
- \@latex@error{Unable to properly define \string#2; primitive
- \noexpand#1no longer primitive}\@eha
- \fi
- \fi
- \endgroup}
-\let\@xp=\expandafter
-\let\@nx=\noexpand
-\newtoks\@emptytoks
-\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
-\def\@ifempty#1{\@xifempty#1@@..\@nil}
-\long\def\@xifempty#1#2@#3#4#5\@nil{%
- \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
-\long\def\@ifnotempty#1{\@ifempty{#1}{}}
-\def\FN@{\futurelet\@let@token}
-\def\DN@{\def\next@}
-\def\RIfM@{\relax\ifmmode}
-\def\setboxz@h{\setbox\z@\hbox}
-\def\wdz@{\wd\z@}
-\def\boxz@{\box\z@}
-\def\relaxnext@{\let\@let@token\relax}
-\def\new@ifnextchar#1#2#3{%
- \let\@tempe #1\def\@tempa{#2}\def\@tempb{#3}\futurelet
- \@tempc\new@ifnch}
-\def\new@ifnch{\ifx\@tempc \@tempe \let\@tempd\@tempa
- \else\let\@tempd\@tempb\fi\@tempd}
-\def\new@ifstar#1#2{\new@ifnextchar *{\def\@tempa*{#1}\@tempa}{#2}}
-\@ifundefined{every@math@size}{%
-\let\every@math@size=\every@size
-\def\glb@settings{%
- \expandafter\ifx\csname S@\f@size\endcsname\relax
- \calculate@math@sizes
- \fi
- \csname S@\f@size\endcsname
- \ifmath@fonts
- \begingroup
- \escapechar\m@ne
- \csname mv@\math@version \endcsname
- \globaldefs\@ne
- \let \glb@currsize \f@size
- \math@fonts
- \endgroup
- \the\every@math@size
- \else
- \fi
-}
-\def\set@fontsize#1#2#3{%
- \@defaultunits\@tempdimb#2pt\relax\@nnil
- \edef\f@size{\strip@pt\@tempdimb}%
- \@defaultunits\@tempskipa#3pt\relax\@nnil
- \edef\f@baselineskip{\the\@tempskipa}%
- \edef\f@linespread{#1}%
- \let\baselinestretch\f@linespread
- \def\size@update{%
- \baselineskip\f@baselineskip\relax
- \baselineskip\f@linespread\baselineskip
- \normalbaselineskip\baselineskip
- \setbox\strutbox\hbox{%
- \vrule\@height.7\baselineskip
- \@depth.3\baselineskip
- \@width\z@}%
-%%% \the\every@size
- \let\size@update\relax}%
- }
-}{}% end \@ifundefined test
-\newdimen\ex@
-\addto@hook\every@math@size{\compute@ex@}
-\def\compute@ex@{%
- \begingroup
- \dimen@-\f@size\p@
- \ifdim\dimen@<-20\p@
- \global\ex@ 1.5\p@
- \else
- \advance\dimen@10\p@ \multiply\dimen@\tw@
- \edef\@tempa{\ifdim\dimen@>\z@ -\fi}%
- \dimen@ \ifdim\dimen@<\z@ -\fi \dimen@
- \advance\dimen@-\@m sp % fudge factor
- \vfuzz\p@
- \def\do{\ifdim\dimen@>\z@
- \vfuzz=.97\vfuzz
- \advance\dimen@ -\p@
- \@xp\do \fi}%
- \do
- \dimen@\p@ \advance\dimen@-\vfuzz
- \global\ex@\p@
- \global\advance\ex@ \@tempa\dimen@
- \fi
- \endgroup
-}
-\def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}
-\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
- \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
-\def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
- \m@th$#2#3$}}
-\def\nomath@env{\PackageError{amstex}{%
- \string\begin{\@currenvir} allowed only in paragraph mode%
-}\@ehb% "You've lost some text"
-}
-\def\Invalid@@{Invalid use of \string}
-\def\nonmatherr@#1{\PackageError{amsfonts}%
- {\noexpand#1allowed only in math mode}\@ehd}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%% filename = "amstext.dtx",
-%%% version = "1.2beta",
-%%% date = "1994/12/13",
-\DeclareRobustCommand{\text}{%
- \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
-\let\nfss@text\text
-\def\text@#1{\mathchoice
- {\textdef@\displaystyle\f@size{#1}}%
- {\textdef@\textstyle\tf@size{\firstchoice@false #1}}%
- {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
- {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
- \check@mathfonts
-}
-\def\textdef@#1#2#3{\hbox{{%
- \everymath{#1}%
- \let\f@size#2\selectfont
- #3}}}
-\newif\iffirstchoice@
-\firstchoice@true
-\def\stepcounter#1{%
- \iffirstchoice@
- \global\expandafter\advance\csname c@#1\endcsname \@ne
- \begingroup
- \let\@elt\@stpelt
- \csname cl@#1\endcsname
- \endgroup
- \fi}
-\toks@{\iffirstchoice@\else\@xp\@gobblefour\fi\protect}
-\edef\GenericInfo{\the\toks@
- \@xp\@nx\csname GenericInfo \endcsname}
-\edef\GenericWarning{\the\toks@
- \@xp\@nx\csname GenericWarning \endcsname}
-\toks@{\iffirstchoice@\else
- \@xp\@xp\@xp\@gobblefour
- \@xp\@gobbletwo\fi\protect}
-\edef\GenericError{\the\toks@
- \@xp\@nx\csname GenericError \endcsname}
-\def\label#1{\@bsphack\iffirstchoice@\if@filesw {\let\thepage\relax
- \def\protect{\noexpand\noexpand\noexpand}%
-\xdef\@gtempa{\write\@auxout{\string
- \newlabel{#1}{{\@currentlabel}{\thepage}}}}}\@gtempa
- \if@nobreak \ifvmode\nobreak\fi\fi\fi\fi\@esphack}
-\begingroup \catcode`\"=12
-\gdef\mathhexbox#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
-\endgroup
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%% filename = "amsfonts.dtx",
-%%% version = "1.2beta",
-%%% date = "1994/12/13",
-\newbox\Mathstrutbox@
-\setbox\Mathstrutbox@=\hbox{}
-\def\Mathstrut@{\copy\Mathstrutbox@}
-\addto@hook\every@math@size{\setbox\z@\hbox{\normalfont(}%
- \ht\Mathstrutbox@\ht\z@ \dp\Mathstrutbox@\dp\z@}
-\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{%
- {%
- \hbox{$\left#2\vcenter to#1\big@size{}\right.%
- \n@space
- $}}}
-\addto@hook\every@math@size{%
- \global\big@size 1.2\ht\Mathstrutbox@
- \global\advance\big@size 1.2\dp\Mathstrutbox@ }
-\newdimen\big@size
-%% msam, msbm, eufm fonts dealt with at end of file
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%% filename = "amsbsy.dtx",
-%%% version = "1.2beta",
-%%% date = "1994/10/27",
-\DeclareRobustCommand{\boldsymbol}[1]{%
- \begingroup
- \let\@nomath\@gobble \mathversion{bold}%
- \math@atom{#1}{%
- \mathchoice%
- {\hbox{$\m@th\displaystyle#1$}}%
- {\hbox{$\m@th\textstyle#1$}}%
- {\hbox{$\m@th\scriptstyle#1$}}%
- {\hbox{$\m@th\scriptscriptstyle#1$}}}%
- \endgroup}
-\def\math@atom#1#2{%
- \binrel@{#1}\binrel@@{#2}}
-\DeclareRobustCommand{\pmb}{%
- \ifmmode\else \expandafter\pmb@@\fi\mathpalette\pmb@}
-\def\pmb@@#1#2#3{\leavevmode\setboxz@h{#3}%
- \dimen@-\wdz@
- \kern-.5\ex@\copy\z@
- \kern\dimen@\kern.25\ex@\raise.4\ex@\copy\z@
- \kern\dimen@\kern.25\ex@\box\z@
-}
-\newdimen\pmbraise@
-\def\pmb@#1#2{\setbox8\hbox{$\m@th#1{#2}$}%
- \setboxz@h{$\m@th#1\mkern.5mu$}\pmbraise@\wdz@
- \binrel@{#2}%
- \dimen@-\wd8 %
- \binrel@@{%
- \mkern-.8mu\copy8 %
- \kern\dimen@\mkern.4mu\raise\pmbraise@\copy8 %
- \kern\dimen@\mkern.4mu\box8 }%
-}
-\def\binrel@#1{\begingroup
- \setboxz@h{\thinmuskip0mu
- \medmuskip\m@ne mu\thickmuskip\@ne mu
- \setbox\tw@\hbox{$#1\m@th$}\kern-\wd\tw@
- ${}#1{}\m@th$}%
- \edef\@tempa{\endgroup\let\noexpand\binrel@@
- \ifdim\wdz@<\z@ \mathbin
- \else\ifdim\wdz@>\z@ \mathrel
- \else \relax\fi\fi}%
- \@tempa
-}
-\let\binrel@@\relax
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\def\AmSTeX{\protect\AmS-\protect\TeX{}}
-\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\prim@s{\prime\futurelet\@let@token\pr@m@s}
-\def\pr@m@s{%
- \ifx\@let@token'\DN@##1{\prim@s}\else\let\next@\egroup\fi\next@}
-\let\@prime=\prime
-\renewcommand{\prime}{{\kern\z@\@prime}}
-\DeclareRobustCommand{\mspace}[3]{%
- \ifmmode\mskip#1#2\else\kern#1#3\fi\relax}
-\renewcommand{\,}{\mspace+\thinmuskip{.1667em}}
-\let\thinspace\,
-\renewcommand{\!}{\mspace-\thinmuskip{.1667em}}
-\let\negthinspace\!
-\renewcommand{\:}{\mspace+\medmuskip{.2222em}}
-\let\medspace\:
-\newcommand{\negmedspace}{\mspace-\medmuskip{.2222em}}
-\renewcommand{\;}{\mspace+\thickmuskip{.2777em}}
-\let\thickspace\;
-\newcommand{\negthickspace}{\mspace-\thickmuskip{.2777em}}
-\def\implies{\DOTSB\;\Longrightarrow\;}
-\def\impliedby{\DOTSB\;\Longleftarrow\;}
-\begingroup \catcode`\"=12 % in case activated by a preceding package
-\gdef\And{\DOTSB\;\mathchar"3026 \;}
-\gdef\lvert{\delimiter"426A30C }
-\gdef\rvert{\delimiter"526A30C }
-\gdef\lVert{\delimiter"426B30D }
-\gdef\rVert{\delimiter"526B30D }
-\endgroup % restore "
-\DeclareRobustCommand{\frac}{\new@ifnextchar[{\frfrac{}}{\frfrac{}[]}}
-\def\frfrac#1[#2]#3#4{\def\next@{#2}%
- \ifx\next@\@empty \def\next@{#1{#3\over#4}}%
- \else \def\next@{{#1{#3\above#2\relax#4}}}%
- \fi
- \next@}
-\def\dfrac{\protect\frfrac\displaystyle[]}
-\def\tfrac{\protect\frfrac\textstyle[]}
-\DeclareRobustCommand{\binom}{\frbinom{}}
-\def\frbinom#1#2#3{{#1{#2\atopwithdelims()#3}}}
-\def\dbinom{\protect\frbinom\displaystyle}
-\def\tbinom{\protect\frbinom\textstyle}
-\def\colon{\nobreak\mskip2mu\mathpunct{}\nonscript
- \mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
-\begingroup \catcode`\"=12
-\DeclareMathSymbol{\coprod@}{\mathop}{largesymbols}{"60}
-\gdef\coprod{\DOTSB\coprod@\slimits@}
-\DeclareMathSymbol{\bigvee@}{\mathop}{largesymbols}{"57}
-\gdef\bigvee{\DOTSB\bigvee@\slimits@}
-\DeclareMathSymbol{\bigwedge@}{\mathop}{largesymbols}{"56}
-\gdef\bigwedge{\DOTSB\bigwedge@\slimits@}
-\DeclareMathSymbol{\biguplus@}{\mathop}{largesymbols}{"55}
-\gdef\biguplus{\DOTSB\biguplus@\slimits@}
-\DeclareMathSymbol{\bigcap@}{\mathop}{largesymbols}{"54}
-\gdef\bigcap{\DOTSB\bigcap@\slimits@}
-\DeclareMathSymbol{\bigcup@}{\mathop}{largesymbols}{"53}
-\gdef\bigcup{\DOTSB\bigcup@\slimits@}
-\DeclareMathSymbol{\prod@}{\mathop}{largesymbols}{"51}
-\gdef\prod{\DOTSB\prod@\slimits@}
-\DeclareMathSymbol{\sum@}{\mathop}{largesymbols}{"50}
-\gdef\sum{\DOTSB\sum@\slimits@}
-\DeclareMathSymbol{\bigotimes@}{\mathop}{largesymbols}{"4E}
-\gdef\bigotimes{\DOTSB\bigotimes@\slimits@}
-\DeclareMathSymbol{\bigoplus@}{\mathop}{largesymbols}{"4C}
-\gdef\bigoplus{\DOTSB\bigoplus@\slimits@}
-\DeclareMathSymbol{\bigodot@}{\mathop}{largesymbols}{"4A}
-\gdef\bigodot{\DOTSB\bigodot@\slimits@}
-\DeclareMathSymbol{\bigsqcup@}{\mathop}{largesymbols}{"46}
-\gdef\bigsqcup{\DOTSB\bigsqcup@\slimits@}
-\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~{\nobreakspace}
-\DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newif\if@display
-\everydisplay\expandafter{\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@
-}
-\def\nolimits@{%
- \DN@{\nolimits\ifx\@let@token\limits\expandafter\@gobble\fi}%
- \FN@\next@}
-\begingroup \catcode`\"=12
-\gdef\newmcodes@{\mathcode`\'39\mathcode`\*42\mathcode`\."613A%
- \mathcode`\-45\mathcode`\/47\mathcode`\:"603A\relax}
-\endgroup
-\DeclareRobustCommand{\operatorname}{%
- \@ifstar{\qopname\newmcodes@ n}%
- {\qopname\newmcodes@{no}}}%
-\DeclareRobustCommand{\qopname}[3]{\mathop{#1\kern\z@\operator@font#3}%
- \csname #2limits@\endcsname}
-\def\arccos{\qopname\relax{no}{arccos}}
-\def\arcsin{\qopname\relax{no}{arcsin}}
-\def\arctan{\qopname\relax{no}{arctan}}
-\def\arg{\qopname\relax{no}{arg}}
-\def\cos{\qopname\relax{no}{cos}}
-\def\cosh{\qopname\relax{no}{cosh}}
-\def\cot{\qopname\relax{no}{cot}}
-\def\coth{\qopname\relax{no}{coth}}
-\def\csc{\qopname\relax{no}{csc}}
-\def\deg{\qopname\relax{no}{deg}}
-\def\det{\qopname\relax n{det}}
-\def\dim{\qopname\relax{no}{dim}}
-\def\exp{\qopname\relax{no}{exp}}
-\def\gcd{\qopname\relax n{gcd}}
-\def\hom{\qopname\relax{no}{hom}}
-\def\inf{\qopname\relax n{inf}}
-\def\injlim{\qopname\relax n{inj\,lim}}
-\def\ker{\qopname\relax{no}{ker}}
-\def\lg{\qopname\relax{no}{lg}}
-\def\lim{\qopname\relax n{lim}}
-\def\liminf{\qopname\relax n{lim\,inf}}
-\def\limsup{\qopname\relax n{lim\,sup}}
-\def\ln{\qopname\relax{no}{ln}}
-\def\log{\qopname\relax{no}{log}}
-\def\max{\qopname\relax n{max}}
-\def\min{\qopname\relax n{min}}
-\def\Pr{\qopname\relax n{Pr}}
-\def\projlim{\qopname\relax n{proj\,lim}}
-\def\sec{\qopname\relax{no}{sec}}
-\def\sin{\qopname\relax{no}{sin}}
-\def\sinh{\qopname\relax{no}{sinh}}
-\def\sup{\qopname\relax n{sup}}
-\def\tan{\qopname\relax{no}{tan}}
-\def\tanh{\qopname\relax{no}{tanh}}
-\def\operator@font{\mathgroup\symoperators}
-\def\operatornamewithlimits{\operatorname*}
-\def\varlim@#1#2{\mathop{\vtop{\ialign{##\crcr
- \hfil$#1\m@th\operator@font lim$\hfil\crcr
- \noalign{\nointerlineskip\kern\ex@}#2#1\crcr
- \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
-\def\varinjlim{\mathpalette\varlim@\rightarrowfill@}
-\def\varprojlim{\mathpalette\varlim@\leftarrowfill@}
-\def\varliminf{\mathpalette\varliminf@{}}
-\def\varliminf@#1{\mathop{\@@underline{\vrule\@depth.2\ex@\@width\z@
- \hbox{$#1\m@th\operator@font lim$}}}}
-\def\varlimsup{\mathpalette\varlimsup@{}}
-\def\varlimsup@#1{\mathop{\@@overline
- {\hbox{$#1\m@th\operator@font lim$}}}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\def\numberwithin#1#2{\@ifundefined{c@#1}{\@nocounterr{#1}}{%
- \@ifundefined{c@#2}{\@nocnterr{#2}}{%
- \@addtoreset{#1}{#2}%
- \toks@\expandafter\expandafter\expandafter{\csname the#1\endcsname}%
- \expandafter\xdef\csname the#1\endcsname
- {\expandafter\noexpand\csname the#2\endcsname
- .\the\toks@}}}}
-\def\eqref#1{\textup{\tagform@{\ref{#1}}}}
-\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\lcfrac{\cfrac[l]}
-\def\rcfrac{\cfrac[r]}
-\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{%
- \setbox\z@\hbox{$\displaystyle{\vphantom{#3}}#1{#3}\m@th$}%
- \setbox\tw@\hbox{$\displaystyle{#3}#2\m@th$}%
- \hskip\wd\z@\hskip-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wd\z@
- {\vphantom{#3}}#1{#3}#2}}
-\renewcommand{\smash}[2][tb]{%
- \def\smash@{#1}%
- \ifmmode\expandafter\mathpalette\expandafter\mathsm@sh\else
- \expandafter\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@}}
-\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@}%
- \expandafter\math@\meaning@\math@
- \ifgtest@
- \expandafter\mathch@\meaning@\mathch@
- \ifgtest@\expandafter\getmathch@\meaning@\getmathch@\fi
- \else\expandafter\macro@\meaning@@\macro@
- \ifgtest@
- \expandafter\not@\meaning@\not@\ifgtest@\gdef\thedots@{\dotsb@}%
- \else\expandafter\DOTS@\meaning@\DOTS@
- \ifgtest@
- \ifcase\number\DOTSCASE@\gdef\thedots@{\dotsb@}%
- \or\gdef\thedots@{\dotsi}\else\fi
- \else\expandafter\math@\meaning@\math@
- \ifgtest@\expandafter\mathbin@\meaning@\mathbin@
- \ifgtest@\gdef\thedots@{\dotsb@}%
- \else\expandafter\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..........}%
- \expandafter\macro@\meaning@\macro@\ifgtest@
- \expandafter\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\doteq{\DOTSB\buildrel\textstyle.\over=}
-\def\iff{\DOTSB\;\Longleftrightarrow\;}
-\begingroup \catcode`\"=12
-\mathchardef\@tempa="7000
-\ifx\@tempa\Gamma
- \DeclareMathSymbol{\Gamma}{\mathord}{operators}{"00}
- \DeclareMathSymbol{\Delta}{\mathord}{operators}{"01}
- \DeclareMathSymbol{\Theta}{\mathord}{operators}{"02}
- \DeclareMathSymbol{\Lambda}{\mathord}{operators}{"03}
- \DeclareMathSymbol{\Xi}{\mathord}{operators}{"04}
- \DeclareMathSymbol{\Pi}{\mathord}{operators}{"05}
- \DeclareMathSymbol{\Sigma}{\mathord}{operators}{"06}
- \DeclareMathSymbol{\Upsilon}{\mathord}{operators}{"07}
- \DeclareMathSymbol{\Phi}{\mathord}{operators}{"08}
- \DeclareMathSymbol{\Psi}{\mathord}{operators}{"09}
- \DeclareMathSymbol{\Omega}{\mathord}{operators}{"0A}
- \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}
-\fi
-\endgroup
-\def\accentclass@{7}
-\def\noaccents@{\def\accentclass@{0}}
-\DeclareFontEncoding{OML}{}{\noaccents@}
-\DeclareFontEncoding{OMS}{}{\noaccents@}
-\edef\@tempa#1#2{\def#1{\mathaccent\string"\noexpand\accentclass@#2 }}
-\@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}
-\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
- \expandafter\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}
-\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
-\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\setb@ck{\iffirstchoice@\global\advance\c@equation\m@ne\fi}
-\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{\PackageError{amstex}{\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
- \new@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{\PackageError{amstex}{\Invalid@@\intertext}\@eha}
-\def\intertext@{\def\intertext##1{\noalign{%
- \penalty\postdisplaypenalty\vskip\belowdisplayskip
- \vbox{\normalbaselines\noindent##1}%
- \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{\new@ifstar\@gobble\@gobble}
-\def\invalid@tag#1{\PackageError{amstex}{#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@@{\new@ifstar\maketag@@@\tagform@}
-\def\maketag@@@#1{\hbox{\m@th\normalfont#1}}
-\def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip)}}
-\def\thetag{\leavevmode\tagform@}
-\def\make@df@tag{\new@ifstar\make@df@tag@@\make@df@tag@@@}
-\def\make@df@tag@@#1{%
- \def\@currentlabel{#1}%
- \gdef\df@tag{\maketag@@@{#1}}}
-\def\make@df@tag@@@#1{\@seteqlabel{#1}\gdef\df@tag{\tagform@{#1}}}
-\def\@seteqlabel#1{\toks@\@xp{\p@equation{#1}}%
- \edef\@currentlabel{\the\toks@}}
-\def\notag{\nonumber}
-\iftagsleft@
-\def\@eqnnum{\hbox to1sp{}\rlap{\normalfont
- \hskip -\displaywidth\tagform@\theequation}}
-\fi
-
-\let\@adjusttag\@empty
-
-\def\adjusttag#1{\skip@#1\relax\gdef\@adjusttag{#1}}
-
-\def\@movetag{%
- \ifx\@adjusttag\@empty \else
- \vskip\@adjusttag\relax
- \global\let\@adjusttag\@empty
- \fi
-}
-\def\multilimits@{\bgroup
- \Let@
- \restore@math@cr
- \default@tag
- \baselineskip\fontdimen10 \scriptfont\tw@
- \advance\baselineskip\fontdimen12 \scriptfont\tw@
- \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
- \lineskiplimit\lineskip
- \vbox\bgroup\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil\crcr}
-\def\Sb{_\multilimits@}
-\def\Sp{^\multilimits@}
-\def\endSb{\crcr\egroup\egroup\egroup}
-\let\endSp=\endSb
-\def\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}
-\def\endsmallmatrix{\crcr\egroup\egroup\,}
-\newcount\c@MaxMatrixCols
-\c@MaxMatrixCols=10
-
-\def\matrix{\hskip -\arraycolsep\array{*\c@MaxMatrixCols c}}
-\def\endmatrix{\endarray \hskip -\arraycolsep}
-\@ifundefined{prepnext@tok}{%
- \def\@array[#1]#2{%
- \setbox\@arstrutbox\hbox{\vrule\@height\arraystretch\ht\strutbox
- \@depth\arraystretch\dp\strutbox \@width\z@}%
- \@mkpream{#2}\edef\@preamble{\ialign \noexpand\@halignto
- \bgroup \tabskip\z@ \@arstrut \@preamble \tabskip\z@ \cr}%
- \let\@startpbox\@@startpbox \let\@endpbox\@@endpbox
- \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
- \bgroup \let\par\@empty
- \let\@sharp##\let\protect\relax
- \lineskip\z@\baselineskip\z@\@preamble}%
-\begingroup \lccode`\~=`\@ \catcode`\~=\active % just to be sure!
-\lowercase{%
-\gdef\@xexpast#1*#2#3#4\@@{\begingroup
- \def~{@}\edef\reserved@a{#1}\@tempcnta#2\relax
- \ifnum\@tempcnta >\z@
- \@whilenum\@tempcnta >\z@\do
- {\edef\reserved@a{\reserved@a#3}\advance\@tempcnta \m@ne}%
- \let\reserved@b\@xexpast
- \else \let\reserved@b\@xexnoop\fi
- \expandafter\reserved@b \reserved@a #4\@@
- \expandafter\endgroup
- \expandafter\def\expandafter\reserved@a\expandafter{\reserved@a}%
- \let\@tempa\reserved@a
-}% End of \@xexpast
-}% End of \lowercase
-\endgroup
-}{}% End of \@ifundefined test.
-\def\pmatrix{\left(\matrix}
-\def\endpmatrix{\endmatrix\right)}
-\def\bmatrix{\left[\matrix}
-\def\endbmatrix{\endmatrix\right]}
-\def\vmatrix{\left|\matrix}
-\def\endvmatrix{\endmatrix\right|}
-\def\Vmatrix{\left\|\matrix}
-\def\endVmatrix{\endmatrix\right\|}
-\let\hdots\@ldots
-\def\hdotsfor#1{\if\noexpand#1[\expandafter\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@}%
- }
-\def\cases{\left\{\def\arraystretch{1.2}\hskip-\arraycolsep
- \array{l@{\quad}l}}
-\def\endcases{\endarray\hskip-\arraycolsep\right.}
-\newif\ifinany@
-\newif\ifinalign@
-\newif\ifingather@
-\newcount\and@
-\newif\iftag@
-\newhelp\andhelp@
-{An extra & here is so disastrous that you should probably exit^^J
-and fix things up.}
-\newif\ifst@rred
-\newtoks\@envbody
-\def\addto@envbody#1{\@envbody\expandafter{\the\@envbody#1}}
-\def\collect@body#1{%
- \@envbody{}%
- \def\process@envbody{%
- \expandafter#1\expandafter{\the\@envbody}}%
- \expandafter\let\csname\@currenvir\endcsname\collect@@body
- \csname\@currenvir\endcsname}
-\def\collect@@body#1\end#2{%
- \def\@tempa{#2}%
- \ifx\@tempa\@currenvir
- \addto@envbody{#1}%
- \expandafter\edef\csname\@currenvir\endcsname
- {\noexpand\process@envbody\noexpand\end{\@tempa}}%
- \else
- \addto@envbody{#1\end{#2}}%
- \fi
- \csname\@currenvir\endcsname}
-\newenvironment{aligned}{%
- \relax\ifmmode\else\nonmatherr@{\begin{aligned}}\fi
- \null\,\new@ifnextchar[{\aligned@}{\aligned@[c]}%
-}{%
- \crcr\egroup\egroup
-}
-\def\aligned@[#1]{%
- \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
- \bgroup
- \Let@\restore@math@cr
- \default@tag
- \ifinany@\else\openup\jot\fi
- \ialign\bgroup\hfil\strut@$\m@th\displaystyle{##}$&%
- $\m@th\displaystyle{{}##}$\hfil\crcr}
-\newtoks\hashtoks@
-\hashtoks@{#}
-\newcount\atcount@
-\def\doat@#1{\toks@{\hfil\strut@$\m@th
- \displaystyle{\the\hashtoks@}$&$\m@th\displaystyle
- {{}\the\hashtoks@}$\hfil}%
- \atcount@#1\relax\advance\atcount@\m@ne
- \loop\ifnum\atcount@>\z@\toks@\expandafter{\the\toks@&\hfil$\m@th
- \displaystyle{\the\hashtoks@}$&$\m@th
- \displaystyle{{}\the\hashtoks@}$\hfil}\advance
- \atcount@\m@ne\repeat
- \xdef\preamble@{\the\toks@}\xdef\preamble@@{\preamble@}}
-\newenvironment{alignedat}[2][c]{%
- \null\,%
- \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
- \bgroup\doat@{#2}\Let@ \restore@math@cr\default@tag
- \ifinany@\else\openup\jot\fi\ialign\bgroup\span\preamble@@\crcr
-}{%
- \endaligned
-}
-\newenvironment{gathered}[1][c]{%
- \relax\ifmmode\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
-}{%
- \endaligned
-}
-\def\tag@in@align{\relax
- \iftag@\DN@{\invalid@tag{Multiple \string\tag}}\else
- \global\tag@true
- \if@eqnsw\global\@eqnswfalse\fi
- \let\next@\make@df@tag\fi
- \next@}
-\def\math@cr@@@align{%
- \if@eqnsw\global\tag@true\fi
- \iftag@
- \ifcase\and@
- \DN@{&&}\else
- \DN@{&}\fi\else
- \let\next@\relax\fi
- \next@
- \relax
- \if@eqnsw\tagform@\theequation\stepcounter{equation}\else
- \iftag@\df@tag\fi\fi
- \global\@eqnswtrue\cr}
-\def\Tag@{\relax\iftag@\else\firstchoice@true
- \PackageError{amstex}{%
- Extra & on this line%
- }{\the\andhelp@% "An extra & here is disastrous"
-}\fi}
-\newdimen\lwidth@
-\newdimen\rwidth@
-\newdimen\maxlwidth@
-\newdimen\maxrwidth@
-\newdimen\totwidth@
-\def\measure@#1{\lwidth@\z@\rwidth@\z@\maxlwidth@\z@\maxrwidth@\z@
- \global\and@\z@
- \setbox\@ne\vbox{%
- \everycr{\noalign{\global\tag@false\global\and@\z@}}\Let@
- \let\tag\gobble@tag
- \let\notag\@empty \let\nonumber\@empty
- \firstchoice@false
- \halign{\setboxz@h{$\m@th\displaystyle{\@lign##}$}%
- \global\lwidth@\wdz@
- \ifdim\lwidth@>\maxlwidth@\global\maxlwidth@\lwidth@\fi
- \global\advance\and@\@ne
- &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
- \global\rwidth@\wdz@
- \ifdim\rwidth@>\maxrwidth@\global\maxrwidth@\rwidth@\fi
- \global\advance\and@\@ne
- &\Tag@\@gobble{##}\crcr#1\crcr}}%
- \totwidth@\maxlwidth@\advance\totwidth@\maxrwidth@}
-\def\displ@y{\global\dt@ptrue\openup\jot\m@th
- \everycr{\noalign{\ifdt@p \global\dt@pfalse
- \vskip-\lineskiplimit \vskip\normallineskiplimit
- \else \penalty\@eqpen \fi}}}
-\def\displ@y@{\global\dt@ptrue\openup\jot
- \everycr{\noalign{\global\tag@false
- \global\and@\z@
- \global\dspbrk@lvl\m@ne
- \ifdt@p\global\dt@pfalse
- \vskip-\lineskiplimit\vskip\normallineskiplimit\else
- \penalty\@eqpen\fi}}}
-\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\align{\ifingather@
- {\ifnum0=`}\fi
- \DN@{\@nameuse{align (in \string\gather)}}%
- \else \ifmmode\nomath@env
- \DN@{\let\endalign\relax\@gobble}\else
- $$\stepcounter{equation}%
- \st@rredfalse\let\next@\align@\fi\fi
- \collect@body\next@}
-\@namedef{align*}{\ifingather@
- {\ifnum0=`}\fi
- \DN@{\@nameuse{align* (in \string\gather)}}\else
- \ifmmode\nomath@env
- \DN@{\@namedef{endalign*}{}\@gobble}\else
- $$\st@rredtrue
- \let\next@\align@\fi\fi
- \collect@body\next@}
-\newdimen\lineht@
-\def\align@{\inalign@true\inany@true
- \displaybreak@\intertext@
- \let\math@cr@@@\math@cr@@@align
- \let\tag\tag@in@align
- \global\and@\z@\global\dspbrk@lvl\m@ne
- \iftagsleft@\DN@{\@nameuse{align }}\else
- \DN@{\@nameuse{align \space}}\fi\next@}
-\@namedef{align }#1{%
- \measure@{#1}%
- \global\and@\z@
- \global\dspbrk@lvl\m@ne
- \if@fleqn %%*F
- \advance\totwidth@\@mathmargin %%*F
- \fi %%*F
- \ifdim\totwidth@>\displaywidth
- \let\displaywidth@\totwidth@
- \else
- \let\displaywidth@\displaywidth
- \fi
- \ifingather@
- \everycr{%
- \noalign{%
- \global\and@\z@
- \global\dspbrk@lvl\m@ne
- }%
- }%
- \else
- \displ@y@
- \fi
- \Let@
- \ifst@rred\else\@seteqlabel\theequation\fi
- \tabskip\@mathmargin %%*F
- \dimen@\displaywidth %%*F
- \if@fleqn %%*F
- \ifingather@ %%*F
- \tabskip\z@skip %%*F
- \advance\dimen@-\@mathmargin %%*F
- \fi %%*F
- \fi %%*F
- \halign to\dimen@\bgroup %%*F
- \ifst@rred\nonumber\fi
- \hfil
- \strut@
- \setboxz@h{\global\tag@false$\m@th\displaystyle{\@lign##}$}%
- \global\lwidth@\wdz@
- \global\lineht@\ht\z@
- \boxz@
- \global\advance\and@\@ne
- \tabskip\z@skip
- &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
- \global\rwidth@\wdz@
- \ifdim\ht\z@>\lineht@
- \global\lineht@\ht\z@
- \fi
- \boxz@
- \hfil
- \global\advance\and@\@ne
- \tabskip\@centering
- &\kern-\displaywidth@
- \setboxz@h{\@lign\strut@{##}}%
- \if@fleqn %%*F
- \dimen@\@mathmargin %%*F
- \advance\dimen@\maxlwidth@ %%*F
- \advance\dimen@-\lwidth@ %%*F
- \else %%*F
- \dimen@\displaywidth
- \advance\dimen@-\totwidth@
- \divide\dimen@\tw@
- \advance\dimen@\maxlwidth@
- \advance\dimen@-\lwidth@
- \fi %%*F
- \ifdim\dimen@<\tw@\wdz@
- \rlap{\vbox{\normalbaselines\boxz@\vbox to\lineht@{}}}%
- \else
- \rlap{\boxz@}%
- \fi
- \tabskip\displaywidth@
- \crcr
- #1%
-}
-\@namedef{align \space}#1{%
- \measure@{#1}%
- \if@fleqn %%*F
- \advance\totwidth@\@mathmargin %%*F
- \fi %%*F
- \global\and@\z@
- \global\dspbrk@lvl\m@ne
- \ifingather@
- \everycr{\noalign{\global\and@\z@\global\dspbrk@lvl\m@ne}}%
- \else
- \displ@y@
- \fi
- \Let@
- \ifst@rred\else\@seteqlabel\theequation\fi
- \tabskip\@mathmargin %%*F
- \dimen@\displaywidth %%*F
- \if@fleqn %%*
- \ifingather@ %%*F
- \tabskip\z@skip %%*F
- \advance\dimen@-\@mathmargin %%*F
- \fi %%*F
- \fi %%*F
- \halign to\dimen@\bgroup %%*F
- \ifst@rred\nonumber\fi
- \hfil
- \strut@
- \setboxz@h{\global\tag@false$\m@th\displaystyle{\@lign##}$}%
- \global\lwidth@\wdz@\boxz@
- \global\advance\and@\@ne
- \tabskip\z@skip
- &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
- \global\rwidth@\wdz@
- \boxz@
- \hfill
- \global\advance\and@\@ne
- \tabskip\@centering
- &\setboxz@h{\@lign\strut@{##}}%
- \dimen@\displaywidth
- \advance\dimen@-\totwidth@
- \divide\dimen@\tw@
- \advance\dimen@\maxrwidth@
- \advance\dimen@-\rwidth@
- \ifdim\dimen@<\tw@\wdz@
- \llap{\vtop{\@movetag\normalbaselines\null\boxz@}}%%*T
- \else
- \llap{\boxz@}%
- \fi
- \tabskip\z@skip
- \crcr#1%
-}
-\def\endalign{\math@cr@@@align
- \black@\totwidth@
- \egroup$$\global\@ignoretrue\setb@ck}
-
-\@namedef{endalign*}{\math@cr@@@align\black@\totwidth@
- \egroup$$\global\@ignoretrue}
-\@namedef{align (in \string\gather)}{%
- \ifst@rred\stepcounter{equation}\fi
- \def\endalign{\@nameuse{endalign (in \string\gather)}\ifnum0=`{\fi}}%
- \vcenter\bgroup\st@rredfalse
- \collect@body\align@}
-\@namedef{endalign (in \string\gather)}{%
- \math@cr@@@align\black@\totwidth@
- \egroup\egroup
- \ifst@rred\setb@ck\fi% this ifst@rred is set by the enclosing gather
- \global\tag@false\global\@eqnswfalse}
-\@namedef{align* (in \string\gather)}{%
- \@namedef{endalign*}{\@nameuse{endalign* (in \string\gather)}%
- \ifnum0=`{\fi}}%
- \vcenter\bgroup\st@rredtrue
- \collect@body\align@}
-\@namedef{endalign* (in \string\gather)}{%
- \math@cr@@@align\black@\totwidth@\egroup\egroup
- \global\tag@false\global\@eqnswfalse}
-\newif\ifxat@
-\def\alignat#1{%
- \ifmmode\nomath@env\DN@{\let\endalignat\relax\@gobble}\else$$%
- \st@rredfalse\stepcounter{equation}\@seteqlabel\theequation
- \DN@{\@nameuse{alignat }#1}\fi
- \collect@body\next@}
-\@namedef{alignat*}#1{%
- \ifmmode\nomath@env\DN@{\@namedef{endalignat*}{}\@gobble}\else$$%
- \st@rredtrue
- \DN@{\@nameuse{alignat }#1}\fi
- \collect@body\next@}
-\newif\ifmeasuring@
-\newbox\savealignat@
-\def\math@cr@@@alignat{%
- \if@eqnsw\global\tag@true\fi
- \iftag@
- \multiply\count@\tw@
- \xdef\next@{}\loop\ifnum\count@>\and@\xdef\next@{&\next@}%
- \advance\count@\m@ne\repeat\else
- \let\next@\relax\fi
- \next@
- \relax
- \if@eqnsw\tagform@\theequation\stepcounter{equation}\else
- \iftag@\df@tag\fi\fi
- \global\@eqnswtrue\cr}%
-\@namedef{alignat }#1#2{%
- \inany@true
- \xat@false
- \let\tag\tag@in@align
- \def\math@cr@@@{\count@#1\relax \math@cr@@@alignat}%
- \displaybreak@
- \intertext@
- \displ@y@
- \ifst@rred
- \global\@eqnswfalse
- \else
- \global\@eqnswtrue
- \fi
- \measuring@true
- \setbox\savealignat@\hbox{%
- $\m@th\displaystyle\Let@
- \attag@{#1}%
- \vbox{\firstchoice@false\halign{\span\preamble@@\crcr#2\crcr}}$%
- }%
- \measuring@false
- \Let@
- \attag@{#1}%
- \tabskip\@mathmargin %%*F
- \halign to\displaywidth\bgroup
- \span\preamble@@\crcr
- #2%
-}
-\def\endalignat{\math@cr@@@\black@{\wd\savealignat@}%
- \egroup\setb@ck$$\global\@ignoretrue}
-\@namedef{endalignat*}{\math@cr@@@\black@{\wd\savealignat@}\egroup
- $$\global\@ignoretrue}
-\def\xalignat#1{%
- \ifmmode\nomath@env\DN@{\let\endxalignat\relax\@gobble}\else$$%
- \st@rredfalse\stepcounter{equation}\@seteqlabel\theequation
- \DN@{\@nameuse{xalignat }#1}\fi
- \collect@body\next@}
-\@namedef{xalignat*}#1{%
- \ifmmode\nomath@env\DN@{\@namedef{endxalignat*}{}\@gobble}\else$$%
- \st@rredtrue
- \DN@{\@nameuse{xalignat }#1}\fi
- \collect@body\next@}
-\let\endxalignat=\endalignat
-
-\expandafter\let\csname endxalignat*\expandafter
- \endcsname\csname endalignat*\endcsname
-\@namedef{xalignat }#1#2{%
- \inany@true
- \xat@true
- \let\tag\tag@in@align
- \def\math@cr@@@{\count@#1\relax\math@cr@@@alignat}%
- \displaybreak@
- \intertext@
- \displ@y@
- \measuring@true
- \setbox\savealignat@\hbox{%
- $\m@th\displaystyle\Let@
- \attag@{#1}%
- \vbox{%
- \firstchoice@false
- \halign{\span\preamble@@\crcr#2\crcr}%
- }%
- $%
- }%
- \measuring@false
- \Let@
- \attag@{#1}%
- \tabskip\@mathmargin %%*F
- \halign to\displaywidth\bgroup
- \span\preamble@@\crcr#2%
-}
-\def\attag@#1{%
- \let\TAG@\Tag@\let\Tag@0%
- \ifmeasuring@\def\llap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}%
- \def\rlap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}\else
- \let\llap@\llap\let\rlap@\rlap\fi
- \toks@{\hfil\strut@$\m@th\displaystyle{\@lign\the\hashtoks@}$%
- \tabskip\z@skip
- \global\advance\and@\@ne
- &$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil
- \ifxat@\tabskip\@centering\fi\global\advance\and@\@ne}%
- \iftagsleft@
- \@temptokena{\tabskip\@centering&\Tag@\kern-\displaywidth
- \rlap@{\@lign
- \the\hashtoks@
- }%
- \global\advance\and@\@ne\tabskip\displaywidth}\else
- \@temptokena{\tabskip\@centering&\Tag@\llap@{\@lign
- \the\hashtoks@
- }\global\advance\and@\@ne\tabskip\z@skip}\fi
- \atcount@#1\relax\advance\atcount@\m@ne
- \loop\ifnum\atcount@>\z@
- \toks@\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\@lign
- \the\hashtoks@}$\global\advance\and@\@ne
- \tabskip\z@skip
- &$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil\ifxat@
- \tabskip\@centering\fi\global\advance\and@\@ne}\advance\atcount@\m@ne
- \repeat
- \xdef\preamble@{\the\toks@\the\@temptokena}%
- \xdef\preamble@@{\ifst@rred\noexpand\nonumber\fi\preamble@}%
- \let\Tag@\TAG@}
-\def\xxalignat#1{%
- \ifmmode\nomath@env\DN@{\let\endxxalignat\relax\@gobble}\else$$%
- \DN@{\@nameuse{xxalignat }#1}\fi
- \collect@body\next@}
-\@namedef{xxalignat }#1#2{\inany@true
- \displaybreak@\intertext@
- \displ@y\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
- \xxattag@{#1}%
- \vbox{\firstchoice@false\halign{\span\preamble@@\crcr#2\crcr}}$}%
- \Let@\xxattag@{#1}\tabskip\z@skip\halign to\displaywidth\bgroup
- \span\preamble@@\crcr#2}
-\expandafter\let\expandafter\endxxalignat\csname endxalignat*\endcsname
-\def\xxattag@#1{\toks@{\tabskip\z@skip\hfil\strut@
- $\m@th\displaystyle{\the\hashtoks@}$&%
- $\m@th\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\@centering&}%
- \atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
- \toks@
- \expandafter
- {\the\toks@&\hfil$\m@th\displaystyle{\the\hashtoks@}$%
- \tabskip\z@skip&$\m@th\displaystyle{{}\the\hashtoks@}$\hfil
- \tabskip\@centering}\advance\atcount@\m@ne\repeat
- \xdef\preamble@{\the\toks@\tabskip\z@skip}\xdef\preamble@@{\preamble@}}
-\newdimen\gwidth@
-\newdimen\gmaxwidth@
-\def\gmeasure@#1{\gwidth@\z@\gmaxwidth@\z@\setbox\@ne\vbox{\Let@
- \firstchoice@false\let\tag\gobble@tag
- \halign{\setboxz@h{$\m@th\displaystyle{##}$}\global\gwidth@\wdz@
- \ifdim\gwidth@>\gmaxwidth@\global\gmaxwidth@\gwidth@\fi
- &\@gobble{##}\crcr#1\crcr}}}
-\def\math@cr@@@gather{%
- \if@eqnsw\global\tag@true\fi
- \iftag@
- \DN@{&\relax \if@eqnsw
- \tagform@\theequation \stepcounter{equation}%
- \else\iftag@\df@tag\fi\fi}%
- \else
- \expandafter\@gobble\fi
- \next@
- \global\@eqnswtrue\cr}
-\def\gather{%
- \ifmmode\nomath@env\DN@{\let\endgather\relax\@gobble}\else $$%
- \ingather@true\inany@true
- \stepcounter{equation}%
- \let\tag\tag@in@align\st@rredfalse
- \displaybreak@\intertext@
- \displ@y
- \Let@\@seteqlabel\theequation
- \let\math@cr@@@\math@cr@@@gather
- \iftagsleft@\DN@{\@nameuse{gather }}\else
- \DN@{\@nameuse{gather \space}}\fi\fi
- \collect@body\next@}
-\@namedef{gather*}{%
- \ifmmode\nomath@env\DN@{\@namedef{endgather*}{}\@gobble}\else $$%
- \ingather@true\inany@true
- \let\tag\tag@in@align\st@rredtrue
- \displaybreak@\intertext@
- \displ@y\Let@
- \let\math@cr@@@\math@cr@@@gather
- \iftagsleft@\DN@{\@nameuse{gather }}\else
- \DN@{\@nameuse{gather \space}}\fi\fi
- \collect@body\next@}
-\newdimen\glineht@
-\@namedef{gather \space}#1{%
- \gmeasure@{#1}%
- \if@fleqn %%*F
- \advance\gmaxwidth@\@mathmargin %%*F
- \fi %%*F
- \global\dt@ptrue
- \tabskip\@mathmargin %%*F
- \halign to\displaywidth\bgroup
- \ifst@rred\nonumber\else\global\@eqnswtrue\fi
- \if@fleqn\else\hfil\fi %%*F
- \strut@
- \setboxz@h{\global\tag@false$\m@th\displaystyle{##}$}%
- \global\gwidth@\wdz@\boxz@
- \hfil
- \tabskip\@centering %%*F
- &\setboxz@h{\strut@{##}}%
- \dimen@\displaywidth
- \advance\dimen@-\gwidth@
- \if@fleqn %%*F
- \advance\dimen@-\@mathmargin %%*F
- \else %%*F
- \divide\dimen@\tw@ %%*B
- \fi %%*F
- \ifdim\dimen@<\tw@\wdz@ %%*
- \llap{\vtop{\@movetag\normalbaselines\null\boxz@}}%%*T %%*
- \else
- \llap{\boxz@}% %%*
- \fi
- \tabskip\z@skip
- \crcr
- #1%
-}
-\def\endgather{\math@cr
- \black@\gmaxwidth@\egroup $$\setb@ck\global\@ignoretrue}
-
-\@namedef{endgather*}{\math@cr
- \black@\gmaxwidth@\egroup $$\global\@ignoretrue}
-\@namedef{gather }#1{%
- \gmeasure@{#1}%
- \global\dt@ptrue
- \if@fleqn %%*F
- \advance\gmaxwidth@\@mathmargin %%*F
- \fi %%*F
- \ifdim\gmaxwidth@>\displaywidth
- \let\gdisplaywidth@\gmaxwidth@
- \else
- \let\gdisplaywidth@\displaywidth
- \fi
- \tabskip\@mathmargin %%*F
- \halign to\displaywidth\bgroup
- \ifst@rred\nonumber\else\global\@eqnswtrue\fi
- \if@fleqn\else\hfil\fi %%*F
- \strut@
- \setboxz@h{\global\tag@false$\m@th\displaystyle{##}$}%
- \global\gwidth@\wdz@
- \global\glineht@\ht\z@
- \boxz@
- \hfil
- \tabskip\@centering %%*F
- &\kern-\gdisplaywidth@
- \setboxz@h{\strut@{##}}%
- \if@fleqn %%*F
- \dimen@\@mathmargin %%*F
- \else %%*F
- \dimen@\displaywidth
- \advance\dimen@-\gwidth@
- \divide\dimen@\tw@ %%*B
- \fi %%*F
- \ifdim\dimen@<\tw@\wdz@ %%*
- \rlap{\vbox{\normalbaselines\boxz@\vbox to\glineht@{}}}% %%*
- \else
- \rlap{\boxz@}% %%*
- \fi
- \tabskip\gdisplaywidth@
- \crcr
- #1%
-}
-\def\split{%
- \ifinany@\let\next@\insplit@\else
- \DN@{\PackageError{amstex}{\string\begin{split} is not allowed
- here. Try the `aligned' environment.}\@ehb}\fi
- \next@}
-\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\crcr}
-\def\endsplit{\crcr\egroup\egroup
- \iftagsleft@\expandafter\lendsplit@\else
- \expandafter\rendsplit@\fi}
-\def\rendsplit@{\global\setbox9 \vbox
- {\unvcopy\z@\global\setbox8 \lastbox\unskip}%
- \setbox\@ne\hbox{\unhcopy8 \unskip\global\setbox\tw@\lastbox
- \unskip\global\setbox\thr@@\lastbox}%
- \global\setbox7 \hbox{\unhbox\tw@\unskip}%
- \ifinalign@\ifctagsplit@
- \gdef\split@{\hbox to\wd\thr@@{}&
- \vcenter{\vbox{\moveleft\wd\thr@@\boxz@}}}%
- \else\gdef\split@{&\vbox{\moveleft\wd\thr@@\box9}\crcr
- \box\thr@@&\box7}\fi
- \else
- \ifctagsplit@\gdef\split@{\vcenter{\boxz@}}\else
- \gdef\split@{\box9\crcr\hbox{\box\thr@@\box7}}\fi
- \fi
- \aftergroup\split@}
-\def\lendsplit@{\global\setbox9\vtop{\unvcopy\z@}%
- \setbox\@ne\vbox{\unvcopy\z@\global\setbox8\lastbox}%
- \setbox\@ne\hbox{\unhcopy8\unskip\setbox\tw@\lastbox
- \unskip\global\setbox\thr@@\lastbox}%
- \ifinalign@\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@}
-\newdimen\multlinegap
-\multlinegap10pt
-\newdimen\multlinetaggap@
-\multlinetaggap@10pt
-\def\multline{%
- \ifmmode\nomath@env\DN@{\let\endmultline\relax\@gobble}%
- \else $$\DN@{\collect@body\multline@}\fi
- \st@rredfalse\@eqnswtrue \@seteqlabel\theequation
- \stepcounter{equation}\next@}
-\@namedef{multline*}{%
- \ifmmode\nomath@env\DN@{\@namedef{endmultline*}{}\@gobble}%
- \else $$\DN@{\collect@body\multline@}\fi
- \st@rredtrue\@eqnswfalse \let\@currentlabel\@empty
- \next@}
-\def\multline@{\inany@true\displaybreak@
- \global\tag@false
- \def\tag{\ifst@rred\else
- \global\advance\c@equation\m@ne\fi\tag@in@align}%
- \iftagsleft@
- \expandafter\lmultline@@\else
- \expandafter\rmultline@@\fi}
-\newdimen\mwidth@
-\def\rmmeasure@#1{%
- \def\shoveleft##1{##1}\def\shoveright##1{##1}%
- \setbox\@ne\vbox{\firstchoice@false\Let@\halign{\setboxz@h
- {$\m@th\@lign\displaystyle{}##$}\global\mwidth@\wdz@
- \crcr#1\crcr}}}
-\newdimen\mlineht@
-\newif\ifzerocr@
-\newif\ifonecr@
-\def\lmmeasure@#1{\global\zerocr@true\global\onecr@false
- \everycr{\noalign{\ifonecr@\global\onecr@false\fi
- \ifzerocr@\global\zerocr@false\global\onecr@true\fi}}%
- \def\shoveleft##1{##1}\def\shoveright##1{##1}%
- \setbox\@ne\vbox{\Let@\firstchoice@false\halign{\setboxz@h
- {$\m@th\@lign\displaystyle{}##$}\ifonecr@\global\mwidth@\wdz@
- \global\mlineht@\ht\z@\fi\crcr#1\crcr}}}
-\newbox\mtagbox@
-\newdimen\ltwidth@
-\newdimen\rtwidth@
-\def\lmultline@@#1{%
- \lmmeasure@{#1}%
- \setbox\mtagbox@\hbox{%
- \iftag@
- \df@tag
- \else
- \if@eqnsw
- \global\tag@true
- \tagform@\theequation
- \fi
- \fi
- }%
- \dimen@\mwidth@
- \advance\dimen@\wd\mtagbox@
- \advance\dimen@\multlinetaggap@
- \if@fleqn %%*F
- \advance\dimen@\@mathmargin %%*F
- \fi %%*F
- \ifdim\dimen@>\displaywidth
- \ltwidth@\z@
- \else
- \ltwidth@\wd\mtagbox@
- \fi
- \lmultline@@@#1
-}
-\def\lmultline@@@{%
- \displ@y
- \def\shoveright##1{##1\hfilneg\hskip\multlinegap}%
- \if@fleqn %%*F
- \def\shoveleft##1{##1}% %%*F
- \else %%*F
- \def\shoveleft##1{%
- \setboxz@h{$\m@th\displaystyle{}##1$}%
- \setbox\@ne\hbox{$\m@th\displaystyle##1$}%
- \hfilneg
- \iftag@
- \ifdim\ltwidth@>\z@
- \hskip\ltwidth@
- \hskip\multlinetaggap@
- \fi
- \else
- \hskip\multlinegap
- \fi
- \hskip.5\wd\@ne
- \hskip-.5\wdz@##1%
- }%
- \fi %%*F
- \if@fleqn %%*F
- \tabskip\@mathmargin %%*F
- \else %%*F
- \tabskip\z@skip %%*
- \fi %%*F
- \totwidth@\displaywidth %%*F
- \if@fleqn %%*F
- \advance\totwidth@-\@mathmargin %%*F
- \fi %%*F
- \halign\bgroup
- \Let@
- \let\tag\gobble@tag
- \hbox to\totwidth@{% %%*F
- \strut@$\m@th\displaystyle
- \if@fleqn %%*F
- \hskip 0pt plus 1000pt %%*F
- \else %%*F
- \hfil
- \fi %%*F
- {}##\hfil$%
- }%
- \crcr
- \if@fleqn %%*F
- \hskip-\@mathmargin %%*F
- \else %%*F
- \hfilneg
- \fi %%*F
- \iftag@
- \ifdim\ltwidth@>\z@
- \box\mtagbox@
- \hskip\multlinetaggap@
- \else
- \rlap{%
- \vbox{%
- \normalbaselines
- \hbox{\strut@\box\mtagbox@}%
- \vbox to\mlineht@{}%
- }%
- }%
- \hskip\multlinegap %%*
- \fi
- \else
- \hskip\multlinegap
- \fi
-}
-\def\rmultline@@#1{%
- \rmmeasure@{#1}%
- \setbox\mtagbox@\hbox{%
- \iftag@
- \df@tag
- \else
- \if@eqnsw
- \global\tag@true
- \tagform@\theequation
- \fi
- \fi
- }%
- \dimen@\mwidth@
- \advance\dimen@\wd\mtagbox@
- \advance\dimen@\multlinetaggap@
- \if@fleqn %%*F
- \advance\dimen@\@mathmargin %%*F
- \fi %%*F
- \ifdim\dimen@>\displaywidth
- \rtwidth@\z@
- \else
- \rtwidth@\wd\mtagbox@
- \fi
- \rmultline@@@#1
-}
-\def\rmultline@@@{%
- \displ@y
- \def\shoveright##1{%
- ##1%
- \hfilneg
- \iftag@
- \ifdim\rtwidth@>\z@
- \hskip\rtwidth@
- \hskip\multlinetaggap@
- \fi
- \else
- \hskip\multlinegap
- \fi
- }%
- \if@fleqn %%*F
- \def\shoveleft##1{##1}% %%*F
- \else %%*F
- \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 %%*F
- \if@fleqn %%*F
- \tabskip\@mathmargin %%*F
- \else %%*F
- \tabskip\z@skip %%*
- \fi %%*F
- \totwidth@\displaywidth %%*F
- \if@fleqn %%*F
- \advance\totwidth@-\@mathmargin %%*F
- \fi %%*F
- \halign\bgroup
- \Let@
- \let\tag\gobble@tag
- \hbox to\totwidth@{%
- \strut@$\m@th\displaystyle
- \if@fleqn %%*F
- \hskip 0pt plus 1000pt %%*F
- \else %%*F
- \hfil
- \fi %%*F
- {}##\hfil$%
- }%
- \crcr
- \if@fleqn %%*F
- \hskip-\@mathmargin %%*F
- \else %%*F
- \hfilneg
- \fi %%*F
- \hskip\multlinegap
-}
-\def\endmultline{\iftagsleft@\expandafter\lendmultline@\else
- \expandafter\rendmultline@\fi\global\@ignoretrue}
-\expandafter\let\csname endmultline*\endcsname=\endmultline
-\def\lendmultline@{\hfilneg\hskip\multlinegap\crcr\egroup$$}
-\def\rendmultline@{%
- \iftag@
- \ifdim\rtwidth@>\z@
- \hskip\multlinetaggap@
- \box\mtagbox@
- \else
- \hskip\multlinegap %%*
- \llap{%
- \vtop{%
- \@movetag %%*T
- \normalbaselines\null\hbox{\strut@\box\mtagbox@}%
- }%
- }%
- \fi
- \else
- \hskip\multlinegap
- \fi
- \hfilneg
- \crcr
- \egroup$$%
-}
-\expandafter\def
- \expandafter\@arrayparboxrestore
- \expandafter{\@arrayparboxrestore
- \inany@false\ingather@false\inalign@false
- \default@tag}
-\def\equation{\gather\def\\{\PackageError{amstex}{\Invalid@@\\}\@eha}}
-\def\endequation{\endgather}
-\newenvironment{equation*}{%
- \equation
-}{%
- \nonumber\endequation
-}
-\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\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}
-\begingroup \catcode`\@=\active
-\gdef @{\Iat}
-\endgroup
-\DeclareRobustCommand{\Iat}{\FN@\at@}
-\def\at@{\let\next@\at@@
- \ifcat\noexpand\@let@token a\else
- \ifcat\noexpand\@let@token0\else
- \ifcat\noexpand\@let@token\relax\else
- \let\@let@token@\at@@@\fi\fi\fi\next@}
-\def\at@@#1{\expandafter
- \@ifundefined{ @\string#1}%
- {\DN@{\at@@@#1}}%
- {\DN@{\csname\space @\string#1\endcsname}}%
- \next@}%
-\def\at@@@{\PackageError{amstex}{\Invalid@@ @}%
- {\the\athelp@}% "I'll assume you wanted @@"
- \char64\relax}
-\newhelp\athelp@
-{Only certain combinations beginning with @ make sense to me.^^J%
-I'll assume you wanted @@ for a printed @.}
-\atdef@ @{{\atchar}}% to define @@
-\chardef\atchar=64
-\def\makeatother{\catcode64=\active}
-\def\@tempa#1#2#3#4#5#6{%
- {#1}{#2}\ifnum0#6=0{13}\@xp\@gobblefour
- \else{#3}\fi\@tempa{#4}{#5}{#6}}%
-\xdef\@currnamestack{\@xp\@tempa\@currnamestack{}{}{0}}
-{\def\@makeother{\noexpand\@makeother\noexpand}
-\xdef\@sanitize{\@sanitize\@makeother\@}}
-{\def\do{\noexpand\do\noexpand}
-\xdef\dospecials{\dospecials\do\@}}
-\atdef@,{\ifmmode\mskip.1\thinmuskip\else \nonmatherr@{@,}\fi}
-\atdef@!{\RIfM@\mskip-.1\thinmuskip\else \nonmatherr@{@!}\fi}
-
-\@ifpackageloaded{amscd}{%
-}{%
-\atdef@>#1>#2>{%
- \global\bigaw@\minaw@
- \setboxz@h{$\m@th\scriptstyle\;{#1}\;\;$}%
- \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
- \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%
- \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
- \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill@\displaystyle}}%
- \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
-}% end of @>>>
-\atdef@<#1<#2<{%
- \global\bigaw@\minaw@
- \setboxz@h{$\m@th\scriptstyle\;\;{#1}\;$}%
- \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
- \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;\;{#2}\;$}%
- \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
- \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill@\displaystyle}}%
- \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
-}% end of @<<<
-}% end of @ifpackageloaded
-\@ifundefined{minaw@}{\newdimen\minaw@}{}
-\minaw@11.111pt
-\@ifundefined{bigaw@}{\newdimen\bigaw@}{}
-\atdef@-{\let\next-%%
- \DN@{\ifx\next-%%
- \def\next-{\setbox\z@\hbox{-}\unhbox\z@\FN@\next@}%%
- \expandafter\next \else\nobreak\fi}%%
- \next@-}%%
-\def\leftroot{\PackageError{amstex}{\Invalid@@\leftroot}\@eha}
-\def\uproot{\PackageError{amstex}{\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@}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Fragment from old amsfonts.sty to deal with msam, msbm, eufm fonts;
-%% omit if `noamsfonts' option was specified.
-\ifx F\@amsfonts \endinput \fi
-\DeclareSymbolFont{AMSa}{U}{msa}{m}{n}
-\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
-\ifx P\@amsfonts
- \DeclareFontFamily{U}{msa}{}%
- \DeclareFontShape{U}{msa}{m}{n}{<-6>msam5<6-8>msam7<8->msam10}{}%
- \DeclareFontFamily{U}{msb}{}%
- \DeclareFontShape{U}{msb}{m}{n}{<-6>msbm5<6-8>msbm7<8->msbm10}{}%
- \DeclareFontFamily{U}{euf}{}%
- \DeclareFontShape{U}{euf}{m}{n}{<-6>eufm5<6-8>eufm7<8->eufm10}{}%
- \DeclareFontShape{U}{euf}{b}{n}{<-6>eufb5<6-8>eufb7<8->eufb10}{}%
-\fi
-\@ifundefined{yen}{%
- \edef\yen{\noexpand\mathhexbox{\hexnumber@\symAMSa}55}
-}{}
-\@ifundefined{checkmark}{%
- \edef\checkmark{\noexpand\mathhexbox{\hexnumber@\symAMSa}58}
-}{}
-\@ifundefined{circledR}{%
- \edef\circledR{\noexpand\mathhexbox{\hexnumber@\symAMSa}72}
-}{}
-\@ifundefined{maltese}{%
- \edef\maltese{\noexpand\mathhexbox{\hexnumber@\symAMSa}7A}
-}{}
-\begingroup \catcode`\"=12
-\DeclareMathDelimiter\ulcorner{\mathopen} {AMSa}{"70}{AMSa}{"70}
-\DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{"71}{AMSa}{"71}
-\DeclareMathDelimiter\llcorner{\mathopen} {AMSa}{"78}{AMSa}{"78}
-\DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{"79}{AMSa}{"79}
-\xdef\widehat#1{\noexpand\@mathmeasure\z@\textstyle{#1}%
- \noexpand\ifdim\noexpand\wdz@>\tw@ em%
- \mathaccent"0\hexnumber@\symAMSb 5B{#1}%
- \noexpand\else\mathaccent"0362{#1}\noexpand\fi}
-\xdef\widetilde#1{\noexpand\@mathmeasure\z@\textstyle{#1}%
- \noexpand\ifdim\noexpand\wdz@>\tw@ em%
- \mathaccent"0\hexnumber@\symAMSb 5D{#1}%
- \noexpand\else\mathaccent"0365{#1}\noexpand\fi}
-\DeclareMathSymbol\dabar@{\mathord}{AMSa}{"39}
-\xdef\dashrightarrow{\mathrel{\dabar@\dabar@
- \mathchar"0\hexnumber@\symAMSa 4B}}%
-\xdef\dashleftarrow{\mathrel{\mathchar"0\hexnumber@\symAMSa 4C\dabar@
- \dabar@}}%
-\global\let\dasharrow\dashrightarrow
-\global\let\rightleftharpoons\undefined
-\DeclareMathSymbol\rightleftharpoons{\mathrel}{AMSa}{"0A}
-\global\let\angle\undefined
-\DeclareMathSymbol\angle {\mathord}{AMSa}{"5C}
-\global\let\hbar\undefined
-\DeclareMathSymbol\hbar {\mathord}{AMSb}{"7E}
-\global\let\sqsubset\undefined
-\DeclareMathSymbol\sqsubset {\mathrel}{AMSa}{"40}
-\global\let\sqsupset\undefined
-\DeclareMathSymbol\sqsupset {\mathrel}{AMSa}{"41}
-\global\let\mho\undefined
-\DeclareMathSymbol\mho {\mathord}{AMSb}{"66}
-\DeclareMathSymbol\square {\mathord}{AMSa}{"03}
-\DeclareMathSymbol\lozenge {\mathord}{AMSa}{"06}
-\DeclareMathSymbol\vartriangleright {\mathrel}{AMSa}{"42}
-\DeclareMathSymbol\vartriangleleft {\mathrel}{AMSa}{"43}
-\DeclareMathSymbol\trianglerighteq {\mathrel}{AMSa}{"44}
-\DeclareMathSymbol\trianglelefteq {\mathrel}{AMSa}{"45}
-\DeclareMathSymbol\rightsquigarrow {\mathrel}{AMSa}{"20}
-\def\@tempa{\not@base\lhd}
-\ifx\lhd\@tempa
- \global\let\lhd\vartriangleleft
- \global\let\unlhd\trianglelefteq
- \global\let\rhd\vartriangleright
- \global\let\unrhd\trianglerighteq
- \global\let\Box\square
- \global\let\Diamond\lozenge
- \global\let\leadsto\rightsquigarrow
-\xdef\Join{\mathrel{\mathchar"0\hexnumber@\symAMSb 6F\mkern-13.8mu%
- \mathchar"0\hexnumber@\symAMSb 6E}}
-\fi
-\endgroup
-\DeclareMathAlphabet\mathfrak{U}{euf}{m}{n}
-\SetMathAlphabet\mathfrak{bold}{U}{euf}{b}{n}
-\DeclareSymbolFontAlphabet{\mathbb}{AMSb}
-\DeclareFontEncodingDefaults{\relax}{\def\accentclass@{7}}
-\def\frak{\mathfrak}
-\def\Bbb{\mathbb}
-\def\bold{\mathbf}
-\begingroup \catcode`\"=12 \relax
-\gdef\newsymbol#1#2#3#4#5{%
- \@ifdefinable#1{%
- \edef\next@
- {\ifcase #2 \or
- \hexnumber@\symAMSa\or
- \hexnumber@\symAMSb\fi}%
- \ifx\next@\@empty
- \PackageError{amsfonts}{\Invalid@@\newsymbol}\@ehd%
- \else
- \global\mathchardef#1"#3\next@#4#5
- \fi}}
-\endgroup
-%% Some odds and ends
-\def\sphat{^{\mathchoice{}{}%
- {\,\,\smash[b]{\hbox{\lower4\ex@\hbox{$\m@th\widehat{\null}$}}}}%
- {\,\smash[b]{\hbox{\lower3\ex@\hbox{$\m@th\hat{\null}$}}}}}}
-\def\spcheck{^\vee}
-\def\sptilde{^\sim}
-\def\spdot{^{\hbox{\raise\ex@\hbox{\normalfont .}}}}
-\def\spddot{^{\hbox{\raise\ex@\hbox{\normalfont ..}}}}
-\def\spdddot{^{\hbox{\raise\ex@\hbox{\normalfont...}}}}
-\def\spbreve{^{\!\smash[b]{\hbox{\lower4\ex@\hbox{\u{}}}}}}
-\def\fracwithdelims#1#2{\new@ifnextchar[{\fracwithdelims@#1#2}%
- {\fracwithdelims@#1#2[\@empty]}}
-\def\fracwithdelims@#1#2[#3]#4#5{\relax
- \ifx\@empty#3{#4\overwithdelims#1#2#5}\else
- {#4\abovewithdelims#1#2#3\relax#5}\fi}
-\def\accentedsymbol#1#2{%
- \expandafter\newbox
- \csname\expandafter\@gobble\string#1@box\endcsname
- \expandafter\setbox
- \csname\expandafter\@gobble\string#1@box\endcsname
- \hbox{$\m@th#2$}%
- \newcommand{#1}{%
- \expandafter\copy
- \csname\expandafter\@gobble\string#1@box\endcsname{}}%
-}
-\def~{\nobreakspace}
-\DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
-%%
-%% End of file `amstex.sty'.