From 7c55de4fbb8a3fd98697b47aa5500a56a590f2c0 Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
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 It was superseded in 1995 by the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'.
-- 
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