From 7c55de4fbb8a3fd98697b47aa5500a56a590f2c0 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Sun, 27 Aug 2006 18:26:03 +0000 Subject: amslatex package amsmath update from latex-tds (27aug06) git-svn-id: svn://tug.org/texlive/trunk@2050 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/tex/latex/amsmath/amstex.sty | 2043 ++++++++++++++++++++++++ 1 file changed, 2043 insertions(+) create mode 100644 Master/texmf-dist/tex/latex/amsmath/amstex.sty (limited to 'Master/texmf-dist/tex/latex/amsmath/amstex.sty') diff --git a/Master/texmf-dist/tex/latex/amsmath/amstex.sty b/Master/texmf-dist/tex/latex/amsmath/amstex.sty new file mode 100644 index 00000000000..f67435c5829 --- /dev/null +++ b/Master/texmf-dist/tex/latex/amsmath/amstex.sty @@ -0,0 +1,2043 @@ +%%% ==================================================================== +%%% @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 It was superseded in 1995 by the +%%% amsmath package.", +%%% docstring = "The checksum field above contains a CRC-16 checksum +%%% as the first value, followed by the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'. -- cgit v1.2.3