<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% \def\filename{amsclass.dtx}
% \def\fileversion{2.20.6}
% \def\filedate{2020/05/29}
%
% \iffalse meta-comment
%
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% Copyright 1995, 1999, 2004, 2009-2020 American Mathematical Society.
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% This work may be distributed and/or modified under the
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% of this license or (at your option) any later version.
% The latest version of this license is in
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% This work has the LPPL maintenance status `maintained'.
% 
% The Current Maintainer of this work is the American Mathematical
% Society.
% 
% \fi
%
% \iffalse
%&lt;*driver&gt;
\documentclass{amsdtx}

\CodelineIndex

\begin{document}
\title{%
  The \cls{amsart}, \cls{amsproc}, and \cls{amsbook} document~classes}
\author{American Mathematical Society\\Michael Downes\\
  updated by Barbara Beeton}
\date{Version \fileversion, \filedate}
\DocInput{amsclass.dtx}
\end{document}
%&lt;/driver&gt;
% \fi
%
% \maketitle
%
% \MakeShortVerb\|
%
%  \section{Introduction}
%    This file (\fn{amsclass.dtx}) is the master file for three \latex/
%    document classes, \cls{amsart}, \cls{amsproc}, and \cls{amsbook},
%    which are intended for articles and books containing mathematical
%    research. They produce output that follows the style conventions of
%    American Mathematical Society publications. The theorem setup
%    features of these document classes are also available in a separate
%    package, \pkg{amsthm}.
%
% \StopEventually{}
%
%  \section{Implementation}
%
%    Three document class files and one package file (\fn{amsthm.sty})
%    are produced from this source. Most of the code of the \fn{amsthm}
%    package is used in all four derived files. Most of the remaining
%    code is used in all three document class files. Fine tuning is done
%    with additional docstrip guards.
%
%    The usual name, date, and version information. (Note: the reason
%    each \cs{ProvidesClass} command is placed on a line by itself, with
%    separate begin and end guards for docstripping, is to make
%    automatic update of file date and version slightly easier and more
%    robust.)
%
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1995/06/01]% LaTeX date must be June 1995 or later
%&lt;*amsart&gt;
\ProvidesClass{amsart}[2020/05/29 v2.20.6]
%&lt;/amsart&gt;
%&lt;*amsproc&gt;
\ProvidesClass{amsproc}[2020/05/29 v2.20.6]
%&lt;/amsproc&gt;
%&lt;*amsbook&gt;
\ProvidesClass{amsbook}[2020/05/29 v2.20.6]
%&lt;/amsbook&gt;
%    \end{macrocode}
%    For \pkg{amsthm} we need to guard against redundant loading via
%\begin{verbatim}
% \documentclass{amsart}
% \usepackage{amsthm}
%\end{verbatim}
%    because in that case the usual \cs{RequirePackage} mechanism for
%    avoiding redundant loading will not apply. We need to simulate the
%    loading of the \pkg{amsthm} package.
%    \begin{macrocode}
%&lt;*classes&gt;
\global\expandafter\let\csname ver@amsthm.sty\expandafter\endcsname
  \csname ver@\@currname.\@currext\endcsname
%&lt;/classes&gt;
%&lt;*amsthm&gt;
\ProvidesPackage{amsthm}[2020/05/29 v2.20.6]
%&lt;/amsthm&gt;
%    \end{macrocode}
%
%    The following code is shared by the classes and the \pkg{amsthm}
%    package. Cf.~\fn{amsgen.sty}.
%    \begin{macrocode}
\let\@xp=\expandafter
\let\@nx=\noexpand
\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
\long\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\setboxz@h{\setbox\z@\hbox}
\def\@addpunct#1{%
  \relax\ifhmode
    \ifnum\spacefactor&gt;\@m \else#1\fi
  \fi}
%    \end{macrocode}
%    \cn{nopunct} should have a value for \cn{spacefactor} that is
%    not used for \cn{frenchspacing}.
%    \begin{macrocode}
\def\nopunct{\spacefactor 1007 }
\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
  \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
%    \end{macrocode}
%
%    If this class is loaded by a parent document class, then we want
%    to use the name of the parent class. Otherwise the name of the
%    current class file.
%    \begin{macrocode}
%&lt;*classes&gt;
\def\@tempa#1#2\@nil{\edef\@classname{#1}}
\expandafter\@tempa\@currnamestack{}{}{}\@nil
\ifx\@classname\@empty \edef\@classname{\@currname}\fi
%    \end{macrocode}
%
%  \subsection{Support for conditional text}
%
%    [This needs to be documented in the users' guide, including the
%    idea of using \verb'\for{5ed}{\linebreak}' to mark edition-specific
%    line and page breaks. [mjd,1999/12/27]]
%
%    We would sometimes like to be able to mark fragments of text to be
%    conditionally discarded or typeset. For example in the title of a
%    section if we want to add a linebreak but prevent this linebreak
%    from also taking effect in the table of contents.
%
%    Certain kinds of switches need to be built into the low-level
%    structure of our document class in order to be useful. For example,
%    inside the toc we need to arrange for an \qq{in-toc?} test to yield
%    true.
%
%    \begin{macrocode}
\def\@True{00}
\def\@False{01}
\newcommand\newswitch[2][False]{%
  \expandafter\@ifdefinable\csname ?@#2\endcsname{%
    \global\expandafter\let\csname ?@#2\expandafter\endcsname
      \csname @#1\endcsname
  }%
}
\newcommand{\setFalse}[1]{%
  \expandafter\let\csname ?@#1\endcsname\@False
}
\newcommand{\setTrue}[1]{%
  \expandafter\let\csname ?@#1\endcsname\@True
}
%    \end{macrocode}
%    The empty switch is by default false; i.e., if you write
%\begin{verbatim}
% \for{}{...}
%\end{verbatim}
%    the material will be discarded.
%    \begin{macrocode}
\newswitch{}
%    \end{macrocode}
%
%    To get a line break in a section title but not in the table of
%    contents line for that section, use
%    \verb'\except{toc}{\linebreak}'. (Presumably you are already giving
%    a shortened running head version separately, if applicable.)
%    \begin{macrocode}
\DeclareRobustCommand{\except}[1]{%
  \if\csname ?@#1\endcsname \expandafter\@gobble
  \else \expandafter\@firstofone
  \fi
}
\DeclareRobustCommand{\for}[1]{%
  \if\csname ?@#1\endcsname \expandafter\@firstofone
  \else \expandafter\@gobble
  \fi
}
%    \end{macrocode}
%
%    The \cn{forany} command needs to run through a comma-separated list
%    of switch names and print its second argument if any of the
%    switches are true.
%    \begin{macrocode}
\DeclareRobustCommand{\forany}[1]{%
  \csname for@any@01\endcsname#1,?,\@nil
}
\@namedef{for@any@\@False}#1,{%
  \csname for@any@%
    \csname ?@\zap@space#1 \@empty\endcsname
  \endcsname
}
\@namedef{?@?}{x}
\@namedef{for@any@\@True}#1\@nil#2{#2}
\def\for@any@x{\@car\@gobble}
%    \end{macrocode}
%
%  \subsection{Options}
%  \subsubsection{Notes}
%    Options will be processed in the order they are declared;
%    cf.~\cs{ProcessOptions}.
%
%  \subsubsection{Paper size}
%
%    The option \opt{letterpaper} (default) sets the target paper width
%    and height to U.S. letter size, 8.5 in x 11 in. An option
%    \opt{a4paper} is also supported, but we don't include some of the
%    more unusual paper options (\opt{legalpaper}, \opt{a5paper},
%    \opt{executivepaper}) of the generic \cls{article} class. For A4
%    paper we not only change the paper size but also add 4pc to the
%    normal textheight of 50.5pc (the difference between 297mm and 11in
%    is 50pt).
%    \begin{macrocode}
\DeclareOption{a4paper}{\paperheight 297mm\paperwidth 210mm
  \textheight 54.5pc }
\DeclareOption{letterpaper}{\paperheight 11in\paperwidth 8.5in }
%    \end{macrocode}
%
%    The options \opt{landscape} and \opt{portrait} swap paper height
%    and width.
%    \begin{macrocode}
\DeclareOption{landscape}{\@tempdima\paperheight
  \paperheight\paperwidth \paperwidth\@tempdima}
\DeclareOption{portrait}{}
%    \end{macrocode}
%
%  \subsubsection{Two-sided or one-sided printing}
%
%    For two-sided printing we set the switch \cs{if@twoside} which
%    will cause the margins to be adjusted so that the type blocks of
%    back-to-back pages will line up. The \cs{if@mparswitch} makes margin
%    paragraphs print in the outside margin.
%    \begin{macrocode}
\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
\DeclareOption{twoside}{\@twosidetrue  \@mparswitchtrue}
%    \end{macrocode}
%
%  \subsubsection{Draft or final version}
%
%    The \opt{draft} option causes overfull lines to be marked with
%    a black slug in the right margin.
%    \begin{macrocode}
\DeclareOption{draft}{\overfullrule5\p@
  \ClassWarningNoLine{\@classname}{%
    When the draft option is used, the
      \protect\includegraphics\MessageBreak
    command will print blank placeholder boxes\MessageBreak
    for the graphics}%
}
\DeclareOption{final}{\overfullrule\z@ }
%    \end{macrocode}
%
%  \subsubsection{Posting date}
%
%    The date when an article is officially posted to the WWW is recorded
%    in a variable \cs{@dateposted} with the \cn{dateposted} command.
%
%    \begin{macrocode}
\def\dateposted#1{\def\@dateposted{#1}}%
\let\@dateposted\@empty
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsart&gt;
\def\@setdateposted{%
  \newline Article electronically published on \@dateposted}
%&lt;/amsart&gt;
%    \end{macrocode}
%
%  \subsubsection{Logos}
%
%    The following logo is used for regular journal articles. The one
%    for proceedings articles and the one for e-only journals are given
%    separately.
%    \begin{macrocode}
%&lt;*amsart&gt;
\def\article@logo{%
  \set@logo{%
    \publname
%    \end{macrocode}
%    Current volume might be empty when an article is first posted to
%    the WWW. In that case leave out the issue-specific info.
%    \begin{macrocode}
    \ifx\@empty\currentvolume
    \else \newline\volinfo, \pageinfo
    \fi
    \newline \@PII
    \ifx\@empty\@dateposted \else \@setdateposted\fi
  }%
}
\def\eonly@logo{%
  \set@logo{%
    \publname
    \newline\volinfo, \pageinfo
    \ifx\@empty\@dateposted \else \@setdateposted\fi
    \newline \@PII
  }%
}
%&lt;/amsart&gt;
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\@logofont{\fontsize{6}{7\p@}\selectfont}
\long\def\set@logo#1{%
  \vbox to\headheight{%
    \@parboxrestore \@logofont
    \noindent#1\par\vss
  }%
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsproc&gt;
\def\procart@logo{%
  \set@logo{\publname
    \ifx\@empty\volinfo \else\newline\volinfo\fi}%
}
%&lt;/amsproc&gt;
%    \end{macrocode}
%
%  \subsubsection{E-only journal}
%
%    Electronic-only journals (for \cls{amsart} only) have different
%    information in the series logo than paper-only or dual journals.
%    Only the volume number is reported (no issue or year), and the
%    posting date is added following the page numbers.  [bnb, 1996/10/31]
%
%    This option will be invoked only from publication-specific \fn{.cls}
%    files.
%    \begin{macrocode}
%&lt;*amsart&gt;
\DeclareOption{e-only}{%
  \def\volinfo{Volume \currentvolume}%
  \dateposted{Xxxx XX, XXXX}%
  \def\@setdateposted{\ (\@dateposted)}%
  \let\article@logo\eonly@logo
}
%&lt;/amsart&gt;
%    \end{macrocode}
%
%  \subsubsection{Title page}
%
%    The title and related information can optionally be printed on a
%    separate page.
%    \begin{macrocode}
\newif\if@titlepage
\DeclareOption{titlepage}{\@titlepagetrue}
\DeclareOption{notitlepage}{\@titlepagefalse}
%    \end{macrocode}
%
%  \subsubsection{Start on right- or left-hand page}
%
%    For some book series, it's permissible to start chapters on a
%    left-hand page.  Default to `openright', the usual AMS book style.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\newif\if@openright
\DeclareOption{openright}{\@openrighttrue}
\DeclareOption{openany}{\@openrightfalse}
\@openrighttrue
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%  \subsubsection{Two-column printing}
%
%    Two-column layout is handled through a predefined internal switch.
%    \begin{macrocode}
\DeclareOption{onecolumn}{\@twocolumnfalse}
\DeclareOption{twocolumn}{\@twocolumntrue}
%    \end{macrocode}
%
%  \subsubsection{The nomath option}
%
%    The \opt{nomath} option causes most of the extra math features to
%    be omitted.  Some utility functions will be defined below if this
%    option is specified.
%    \begin{macrocode}
\DeclareOption{nomath}{}
%    \end{macrocode}
%
%  \subsubsection{Some font options}
%
%    The \opt{noamsfonts} option means to avoid declaring math alphabets
%    or symbol fonts for the extra math fonts in the AMSFonts set. If
%    these fonts are declared, it means that the corresponding \fn{.tfm}
%    files are required even for documents that do not use any symbols
%    from those fonts. So we allow optionally to not declare them, for
%    convenience of users who don't have those fonts on their system and
%    don't want the hassle of getting them.
%    \begin{macrocode}
\DeclareOption{noamsfonts}{}
%    \end{macrocode}
%    The \opt{psamsfonts} option, passed on to the \pkg{amsfonts} package,
%    means that alternative \fn{.fd} files should be used that do not
%    refer to \fn{.tfm} files for sizes 6,8,9 (which are not present in
%    the PostScript (Type 1) AMS fonts set from Y\&amp;Y/Blue Sky Research).
%    This should also trigger the \opt{cmex10} option of \pkg{amsmath},
%    to avoid trying to load sizes 7--9 of \fn{cmex}.
%    \begin{macrocode}
\DeclareOption{psamsfonts}{%
  \PassOptionsToPackage{psamsfonts}{amsfonts}%
  \PassOptionsToPackage{cmex10}{amsmath}}
%    \end{macrocode}
%
%  \subsubsection{Equation numbering on the left or right}
%
%    The option \opt{leqno}---equation numbers on the left---is the
%    default in AMS styles. Therefore we provide also a \opt{reqno}
%    option.
%    \begin{macrocode}
\newif\iftagsleft@
\DeclareOption{leqno}{%
  \tagsleft@true \PassOptionsToPackage{leqno}{amsmath}}
\DeclareOption{reqno}{%
  \tagsleft@false \PassOptionsToPackage{reqno}{amsmath}}
%    \end{macrocode}
%
%  \subsubsection{Vertical centering of equation numbers}
%    For multiline equations the equation number is by default centered
%    vertically on the total height of the equation. To make the
%    equation number print on the first line (for left-hand
%    numbers) or the last line (right-hand numbers), there is a
%    \opt{tbtags} option `top/bottom tags'.
%    \begin{macrocode}
\newif\ifctagsplit@
\DeclareOption{centertags}{%
  \ctagsplit@true \PassOptionsToPackage{centertags}{amsmath}}
\DeclareOption{tbtags}{%
  \ctagsplit@false \PassOptionsToPackage{tbtags}{amsmath}}
%    \end{macrocode}
%
%  \subsubsection{Flush left displays}
%
%    The option \opt{fleqn} causes displayed equations to print
%    aligned on the left instead of centered, with an indentation
%    of \cs{mathindent} from the prevailing left margin. If the
%    \pkg{amsmath} package is loaded, most of this code will be
%    overridden, but it seems we need it anyway because of the
%    possibility of the \opt{nomath} class option.
%
%    \begin{macrocode}
\DeclareOption{fleqn}{}%
%    \end{macrocode}
%
%  \subsubsection{Dealing with font sizes}
%
%  \begin{macro}{\@mainsize}
%  \begin{macro}{\@ptsize}
%    Instead of the miserly \cs{@ptsize} variable from \latex/'s
%    ancient history that contains only the last digit of the main
%    typesize, we set up a proper variable \cs{@mainsize} that
%    contains all the digits of the main typesize. Just in case it is
%    needed for someone using an old package, we will keep
%    \cs{@ptsize} also.
%    \begin{macrocode}
\newcommand{\@mainsize}{10}
\newcommand{\@ptsize}{0}
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%
%  \begin{macro}{\larger}
%  \begin{macro}{\smaller}
%    This function is an easy byproduct of the work done to fold
%    typesize-specific code into the main class file. The range of font
%    sizes is \cn{normalsize}, \cn{small}, \cn{Small}, \cn{SMALL},
%    \cn{tiny}, \cn{Tiny}, \cn{large}, \cn{Large}, \cn{LARGE},
%    \cn{huge}, \cn{Huge}. Spaces are left at either end of the case
%    statement to accommodate adding \cn{TINY} and \cn{HUGE} in the
%    future but it's not clear that they're really needed.
%    \begin{macrocode}
\newcommand{\larger}[1][1]{%
  \count@\@currsizeindex \advance\count@#1\relax
  \ifnum\count@&lt;\z@ \count@\z@ \else\ifnum\count@&gt;12 \count@12 \fi\fi
%    \end{macrocode}
%    The various size-changing commands \cn{normalsize}, etc., will take
%    care of updating \cs{@currsizeindex}.
%    \begin{macrocode}
  \ifcase\count@
    \Tiny\or\Tiny\or\tiny\or\SMALL\or\Small\or\small
    \or\normalsize
    \or\large\or\Large\or\LARGE\or\huge\or\Huge\else\Huge
  \fi
}
\newcommand{\smaller}[1][1]{\larger[-#1]}
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%
%    The \cs{@adjustvertspacing} function adapts some vertical spacing
%    amounts to the current type size. We don't expect large sections of
%    vertical text to occur in the extraordinarily small or large type
%    sizes, so the \cs{@adjustvertspacing} function is only called in
%    the range between `footnote' size and `Large' size. Notice that no
%    shrinkability is used.
%    \begin{macrocode}
\def\@adjustvertspacing{%
%    \end{macrocode}
%    \cs{big/med/smallskipamount} are generic space values that will be
%    used by the commands \cn{bigskip}, \cn{medskip}, \cn{smallskip}. We
%    also link the spacing around displayed equations to these amounts.
%    \begin{macrocode}
  \bigskipamount.7\baselineskip plus.7\baselineskip
  \medskipamount\bigskipamount \divide\medskipamount\tw@
  \smallskipamount\medskipamount \divide\smallskipamount\tw@
  \abovedisplayskip\medskipamount
  \belowdisplayskip \abovedisplayskip
%    \end{macrocode}
%    The above-display short space is zero but with the same
%    stretchability as the above-display normal space. And the
%    below-display short space is similar, but has a base value equal to
%    \cs{smallskipamount}. Use of the multiplier |1| is an arcane \TeX{}
%    trick that coerces the skip value to a dimen value, i.e., gives us
%    the base value of the skip register without the stretch or shrink
%    values.
%    \begin{macrocode}
  \abovedisplayshortskip\abovedisplayskip
  \advance\abovedisplayshortskip-1\abovedisplayskip
  \belowdisplayshortskip\abovedisplayshortskip
  \advance\belowdisplayshortskip 1\smallskipamount
%    \end{macrocode}
%    The traditional value for \cs{jot} is 3pt, which we generalize
%    to \cs{baselineskip}/4. This is used to adjust interline spacing in
%    multiline displayed equations.
%    \begin{macrocode}
  \jot\baselineskip \divide\jot 4 \relax
}
%    \end{macrocode}%
%
%    We fill out the range of typesize changing commands to a full
%    eleven: five large/huge commands and five small/tiny commands. (The
%    capitalization of the command names suggests that there should
%    actually be thirteen---add \cn{TINY} and \cn{HUGE}---but let's be
%    conservative and leave those out until a real need for them is
%    known to exist.) An unavoidable side effect is that \cn{tiny} now
%    selects 6pt instead of 5pt by default.
%
%    In version 1.1 of \cls{amsart} and \cls{amsbook} \cn{small} was
%    the same as \cn{footnotesize} (\cls{amsproc} didn't exist in v. 1.1).
%
%    The only size-changing command that is predefined by \latex/ is
%    \cn{normalsize}; that's why it's the only one for which we use
%    \cn{renewcommand} below.
%    \begin{macrocode}
\renewcommand\normalsize{\@xsetfontsize\normalsize 6%
  \@adjustvertspacing \let\@listi\@listI}
\DeclareRobustCommand{\Tiny}{\@xsetfontsize\Tiny 1}
\DeclareRobustCommand{\tiny}{\@xsetfontsize\tiny 2}
\DeclareRobustCommand{\SMALL}{\@xsetfontsize\SMALL 3}
\DeclareRobustCommand{\Small}{\@xsetfontsize\Small 4%
  \@adjustvertspacing
  \def\@listi{\topsep\smallskipamount \parsep\z@skip \itemsep\z@skip
    \leftmargin=\leftmargini
    \labelwidth=\leftmargini \advance\labelwidth-\labelsep
  }%
}
\DeclareRobustCommand{\small}{\@xsetfontsize\small 5\@adjustvertspacing}
%    \end{macrocode}
%    For backward compatibility we had better define \cn{footnotesize}
%    and \cn{scriptsize}. Also there is the small discrepancy with
%    \cn{tiny} to worry about.
%    \begin{macrocode}
\def\footnotesize{\Small}
\def\scriptsize{\SMALL}
%    \end{macrocode}
%
%    The sizes above 10pt use magstep values, stored in the functions
%    \cs{@xipt}, \cs{@xiipt}, etc.
%    \begin{macrocode}
\DeclareRobustCommand{\large}{\@xsetfontsize\large 7\@adjustvertspacing}
\DeclareRobustCommand{\Large}{\@xsetfontsize\Large 8\@adjustvertspacing}
\DeclareRobustCommand{\LARGE}{\@xsetfontsize\LARGE 9}
\DeclareRobustCommand{\huge}{\@xsetfontsize\huge{10}}
\DeclareRobustCommand{\Huge}{\@xsetfontsize\Huge{11}}
%\DeclareRobustCommand\HUGE{\@xsetfontsize\HUGE{12}}
%    \end{macrocode}
%
%    So now we had better define the \cs{@xsetfontsize} function.
%    The size-changing commands use \cs{@setfontsize} instead of
%    \cn{fontsize} to (a)~give an error message if used in math mode and
%    (b)~set the \cs{@currsize} variable.
%    \begin{macrocode}
\def\@xsetfontsize#1#2{%
  \chardef\@currsizeindex#2\relax
  \edef\@tempa{\@nx\@setfontsize\@nx#1%
    \@xp\ifcase\@xp\@currsizeindex\@typesizes
%    \end{macrocode}
%    Add nonsense values 99/99 at the end just in case some extreme
%    error turns up.
%    \begin{macrocode}
      \else{99}{99}\fi}%
  \@tempa
}
%    \end{macrocode}
%    For the record let's initialize \cs{@currsizeindex}.
%    \begin{macrocode}
\chardef\@currsizeindex=6
%    \end{macrocode}
%
%    Set page-breaking penalties to prevent all widows, orphans, and
%    hyphens at the end of a page.
%    \begin{macrocode}
\widowpenalty=10000
\clubpenalty=10000
\brokenpenalty=10000
%    \end{macrocode}
%
%    Set some default linespacing values. The variable \cs{linespacing}
%    is usually the normal interline space in the main text. It is used
%    to specify vertical space for elements such as section heads and
%    theorems in proportion to the normal interline space.
%    \begin{macrocode}
\newdimen\linespacing
\lineskip=1pt \lineskiplimit=1pt
\normallineskip=1pt \normallineskiplimit=1pt
\let\baselinestretch=\@empty
%    \end{macrocode}
%
%    Settings for \cn{textheight} and \cn{textwidth}. We start with the
%    value 50.5pc specified in AMS journal specifications as the total
%    height of the type block and then subtract the running head height
%    and adjust for \cs{topskip} to get the proper value for the text
%    block.
%    \begin{macrocode}
\headheight=8pt \headsep=14pt
%&lt;amsbook&gt;\footskip=18pt
%&lt;amsart|amsproc&gt;\footskip=12pt
\textheight=50.5pc \topskip=10pt
\textwidth=30pc
\columnsep=10pt \columnseprule=0pt
%    \end{macrocode}
%    Some settings for marginpars.
%    \begin{macrocode}
\marginparwidth=90pt
\marginparsep=11pt
\marginparpush=5pt
%    \end{macrocode}
%    To avoid setting text before begin-document, we postpone the
%    setting of \cs{footnotesep} using \cs{AtBeginDocument}.
%    \begin{macrocode}
\AtBeginDocument{\settoheight{\footnotesep}{\footnotesize M$^1$}}
%    \end{macrocode}
%
%    \begin{macrocode}
\skip\footins=7pt plus11pt
\skip\@mpfootins=\skip\footins
%    \end{macrocode}
%
%    \begin{macrocode}
\fboxsep=3pt \fboxrule=.4pt
%    \end{macrocode}
%
%    \begin{macrocode}
\arrayrulewidth=.4pt    \doublerulesep=2pt
\labelsep=5pt           \arraycolsep=\labelsep
\tabcolsep=\labelsep    \tabbingsep=\labelsep
%    \end{macrocode}
%
%    \begin{macrocode}
\floatsep=15pt plus 12pt    \dblfloatsep=15pt plus 12pt
\textfloatsep=\floatsep  \dbltextfloatsep=15pt plus 12pt
\intextsep=\floatsep
%    \end{macrocode}
%
%    \begin{macrocode}
\@fptop=0pt plus1fil     \@dblfptop=0pt plus1fil
\@fpbot=0pt plus1fil     \@dblfpbot=0pt plus1fil
\@fpsep=8pt plus2fil     \@dblfpsep=8pt plus2fil\relax
%    \end{macrocode}
%    Note that \cs{parskip} gets no stretch; this is at variance with
%    the generic \latex/ classes.
%    \begin{macrocode}
\parskip=0pt \relax
%    \end{macrocode}
%
%    \cs{@parboxrestore}, used by \cs{@footnotetext}, sets
%    \cs{parindent} to |0pt|; since this is not what we want, we
%    make a new dimen \cs{normalparindent} and after calling
%    \cs{@parboxrestore}, \cs{@footnotetext} resets
%    \cs{parindent} back to normal.
%    \begin{macrocode}
\newdimen\normalparindent
%&lt;amsart&gt;\normalparindent=12pt
%&lt;amsproc|amsbook&gt;\normalparindent=18pt
\parindent=\normalparindent
%    \end{macrocode}
%
%    \begin{macrocode}
\partopsep=0pt \relax \parsep=0pt \relax \itemsep=0pt \relax
%    \end{macrocode}
%
%    \begin{macrocode}
\@lowpenalty=51         \@medpenalty=151        \@highpenalty=301
\@beginparpenalty=-\@lowpenalty
\@endparpenalty=-\@lowpenalty
\@itempenalty=-\@lowpenalty
%    \end{macrocode}
%
%  \subsubsection{Typesize-specific code}
%
%    The class option \opt{12pt} sets the main typesize to 12 pt and
%    makes various adaptations, primarily sliding the size-changing
%    commands up the scale of magsteps. This makes it more likely that
%    someone with bitmapped fonts will have all the fonts and sizes
%    that they need. The \opt{8pt} option is for those who like to
%    conserve paper.
%
%    By parameterizing some aspects it is possible to make a great deal
%    of the typesize-specific code automatically adapt to the selected
%    size. Then there is so little typesize-specific code remaining
%    that it no longer makes sense to put the code in separate \fn{.clo}
%    files. So instead of analogs for the generic \fn{size10,11,12.clo}
%    files we have the code for those options entirely contained in the
%    \fn{.cls} file in the form of declared options.
%
%    Some miscellaneous remarks.
%
%    ---If PostScript fonts are used, it may seem a little strange to
%    use fonts following the magstep'd point sizes 10.95, 14.4, 17.28,
%    20.74, 24.88 instead of simply 11, 14, 17, 21, 25. But it is not
%    easy for us to make that distinction here in the document class
%    definitions of the fontsize changing commands. So we don't try.
%
%    \begin{macrocode}
\DeclareOption{10pt}{\def\@mainsize{10}\def\@ptsize{0}%
  \def\@typesizes{%
%    \end{macrocode}
%    There should be 11 typesize/baselineskip pairs: five below
%    \cn{normalsize} and five above.
%    \begin{macrocode}
    \or{5}{6}\or{6}{7}\or{7}{8}\or{8}{10}\or{9}{11}%
    \or{10}{12}% normalsize
    \or{\@xipt}{13}\or{\@xiipt}{14}\or{\@xivpt}{17}%
    \or{\@xviipt}{20}\or{\@xxpt}{24}}%
  \normalsize \linespacing=\baselineskip
}
%
\DeclareOption{11pt}{\def\@mainsize{11}\def\@ptsize{1}%
  \def\@typesizes{%
    \or{6}{7}\or{7}{8}\or{8}{10}\or{9}{11}\or{10}{12}%
    \or{\@xipt}{13}% normalsize
    \or{\@xiipt}{14}\or{\@xivpt}{17}\or{\@xviipt}{20}%
    \or{\@xxpt}{24}\or{\@xxvpt}{30}}%
  \normalsize \linespacing=\baselineskip
}
%
\DeclareOption{12pt}{\def\@mainsize{12}\def\@ptsize{2}%
  \def\@typesizes{%
    \or{7}{8}\or{8}{10}\or{9}{11}\or{10}{12}\or{\@xipt}{13}%
    \or{\@xiipt}{14}% normalsize
    \or{\@xivpt}{17}\or{\@xviipt}{20}\or{\@xxpt}{24}%
    \or{\@xxvpt}{30}\or{\@xxvpt}{30}}%
  \normalsize \linespacing=\baselineskip
}
%
\DeclareOption{8pt}{\def\@mainsize{8}\def\@ptsize{8}%
  \def\@typesizes{%
    \or{5}{6}\or{5}{6}\or{5}{6}\or{6}{7}\or{7}{8}%
    \or{8}{10}% normalsize
    \or{9}{11}\or{10}{12}\or{\@xipt}{13}%
    \or{\@xiipt}{14}\or{\@xivpt}{17}}%
  \normalsize \linespacing=\baselineskip
}
%
\DeclareOption{9pt}{\def\@mainsize{9}\def\@ptsize{9}%
  \def\@typesizes{%
    \or{5}{6}\or{5}{6}\or{6}{7}\or{7}{8}\or{8}{10}%
    \or{9}{11}% normalsize
    \or{10}{12}\or{\@xipt}{13}\or{\@xiipt}{14}%
    \or{\@xivpt}{17}\or{\@xviipt}{20}}%
  \normalsize \linespacing=\baselineskip
}
%    \end{macrocode}
%
%  \subsubsection{Running heads}
%    The normal application of pagestyle functions \cs{ps@xxx} is to
%    determine the contents of running heads and feet. The function
%    \cs{@mkboth} is used internally by commands \cn{chapter},
%    \cn{section}, and the like to set the running heads.
%    \begin{macrocode}
\def\ps@empty{\let\@mkboth\@gobbletwo
  \let\@oddhead\@empty \let\@evenhead\@empty
  \let\@oddfoot\@empty \let\@evenfoot\@empty
%    \end{macrocode}
%    The current implementation in \cls{amsart}/\cls{amsproc}/\cls{amsbook}
%    of the vertical space at the top of an opening page uses \cs{topskip},
%    which means that we need to do some resetting here.
%    \begin{macrocode}
  \global\topskip\normaltopskip}
%    \end{macrocode}
%    Pagestyle `plain' has the page numbers in the running feet.
%    \begin{macrocode}
\def\ps@plain{\ps@empty
  \def\@oddfoot{\normalfont\scriptsize \hfil\thepage\hfil}%
  \let\@evenfoot\@oddfoot}
%    \end{macrocode}
%
%    Pagestyle `headings' uses text from sectioning commands for
%    running heads.  Empty running feet.
%    \begin{macrocode}
\newswitch{runhead}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\ps@headings{\ps@empty
  \def\@evenhead{%
    \setTrue{runhead}%
    \normalfont\scriptsize
    \rlap{\thepage}\hfil
    \def\thanks{\protect\thanks@warning}%
    \leftmark{}{}\hfil}%
  \def\@oddhead{%
    \setTrue{runhead}%
    \normalfont\scriptsize \hfil
    \def\thanks{\protect\thanks@warning}%
    \rightmark{}{}\hfil \llap{\thepage}}%
  \let\@mkboth\markboth
%&lt;*amsbook&gt;
  \def\partmark{\@secmark\markboth\partrunhead\partname}%
  \def\chaptermark{%
    \@secmark\markboth\chapterrunhead{}}%
  \def\sectionmark{%
    \@secmark\markright\sectionrunhead\sectionname}%
%&lt;/amsbook&gt;
}
%    \end{macrocode}
%
%  \begin{macro}{\sectionname}
%  \begin{macro}{\subsectionname}
%  \begin{macro}{\subsubsectionname}
%  \begin{macro}{\paragraphname}
%  \begin{macro}{\subparagraphname}
%    Initialize section headings.
%    \begin{macrocode}
\let\sectionname\@empty
\let\subsectionname\@empty
\let\subsubsectionname\@empty
\let\paragraphname\@empty
\let\subparagraphname\@empty
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%  \end{macro}
%  \end{macro}
%  \end{macro}
%
%    The default definitions of \cs{leftmark}, \cs{rightmark} are not
%    what we want: the section title (or whatever) reported in the
%    right-hand running head should report the section that is current
%    at the bottom of the right-hand page. And the left-hand running
%    head should report the status at the top of the page.
%    Cf.~\fn{amsppt.sty}.
%    \begin{macrocode}
\def\leftmark{\expandafter\@firstoftwo\topmark{}{}}
\def\rightmark{\expandafter\@secondoftwo\botmark{}{}}
%    \end{macrocode}
%
%    Journal and Proceedings articles require an indication of the first
%    page so the logo and copyright line can appear.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\ps@firstpage{\ps@plain
  \def\@oddfoot{\normalfont\scriptsize \hfil\thepage\hfil
%    \end{macrocode}
%    Stick in the reset of \cs{topskip} here so it only gets executed
%    after the first page is completed.
%    \begin{macrocode}
     \global\topskip\normaltopskip}%
  \let\@evenfoot\@oddfoot
  \def\@oddhead{\@serieslogo\hss}%
  \let\@evenhead\@oddhead % in case an article starts on a left-hand page
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%  \begin{macro}{\@nilgobble}
%    Something that apparently doesn't exist in the kernel?
%    \begin{macrocode}
\long\def\@nilgobble#1\@nil{}
%    \end{macrocode}
%  \end{macro}
%
%    A general section-marking function. Arg 1 is either \cn{markright}
%    or \cn{markboth} indicating which kind of marking action is desired
%    (this gives us some string pool/hash table savings by allowing the
%    \cs{@secmark} function to serve for both cases). Arg 2 is the
%    function that should be called in the running head to process the
%    remaining three args. Arg 3 is normally \cs{xxxname} (but could be
%    empty). Arg 4 is the section-title text. Assumption: whenever
%    \cs{@secmark} is called, the section-number variable
%    \cs{@secnumber} has been set to the value of the current section
%    number (possibly empty, in the case of a |*| section for example).
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\@secmark#1#2#3#4{%
%    \end{macrocode}
%    We want to apply expansion to \cs{xxxname} and \cs{thexxx} but not
%    to the other elements.
%    \begin{macrocode}
  \begingroup \let\protect\@unexpandable@protect
  \edef\@tempa{\endgroup \toks@{\protect#2{#3}{\@secnumber}}}%
  \@tempa
  \toks@\@xp{\the\toks@{#4}}%
%    \end{macrocode}
%    If a \cn{markright} operation is called for, use the current
%    left-mark via \cs{@temptokena}.
%    \begin{macrocode}
  \afterassignment\@nilgobble\@temptokena\@themark{}\@nil
  \edef\@tempa{\@nx\@mkboth{%
    \ifx\markright#1\the\@temptokena\else\the\toks@\fi}{\the\toks@}}%
  \@tempa}
%    \end{macrocode}
%    Init \cs{@secnumber}.
%    \begin{macrocode}
\let\@secnumber\@empty
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%    Fix \cn{markboth} so that \cs{@secmark} can work without too much
%    thrashing.
%    \begin{macrocode}
\def\markboth#1#2{%
  \begingroup
    \@temptokena{{#1}{#2}}\xdef\@themark{\the\@temptokena}%
    \mark{\the\@temptokena}%
  \endgroup
  \if@nobreak\ifvmode\nobreak\fi\fi}
%    \end{macrocode}
%
%    With the myheadings pagestyle, no automatic running heads will be
%    provided by the document class; only running heads specified by
%    the user through explicit \cn{markboth} or \cn{markright}
%    commands will be used.
%    \begin{macrocode}
\def\ps@myheadings{\ps@headings \let\@mkboth\@gobbletwo}
%    \end{macrocode}
%
%    Save normal topskip value in a skip register.
%    \begin{macrocode}
\newskip\normaltopskip
\normaltopskip=10pt \relax
%    \end{macrocode}
%
%    We also want to turn off all section marks.  First-level section
%    heads will be defined in \cs{ps@headings}.
%    \begin{macrocode}
\let\sectionmark\@gobble
\let\subsectionmark\@gobble
\let\subsubsectionmark\@gobble
\let\paragraphmark\@gobble
%    \end{macrocode}

%  \subsubsection{Unrecognized options}
%
%    The \opt{makeidx} option is redundant; everything that it does in
%    the generic \latex/ classes is already done anyway in this class.
%    \begin{macrocode}
\DeclareOption{makeidx}{}
%&lt;/classes&gt;
%    \end{macrocode}
%
%    Unrecognized options for \pkg{amsthm} are treated as references
%    to auxiliary theorem setup (\fn{.thm}) files.  This allows a user
%    to create theorem styles using internal commands (with |@| signs)
%    without having to be concerned about category coding.
%
%    Here is an example from the file \fn{thmtest.tex} which is part
%    of this collection.  See that file for further information.
%\begin{verbatim}
% \begin{filecontents}{exercise.thm}
% \def\th@exercise{%
%   \normalfont % body font
%   \thm@headpunct{:}%
% }
% \end{filecontents}
%\end{verbatim}
%
%    This facility is available only when \pkg{amsthm} is used as an
%    independent package, not as part of an AMS document class.
%    \begin{macrocode}
%&lt;*amsthm&gt;
\DeclareOption*{\input{\CurrentOption .thm}}
\ProcessOptions
%&lt;/amsthm&gt;
%    \end{macrocode}
%
% \subsection{Process options}
%
%    Black boxes for overfull lines are turned off by default (the
%    \opt{final} option). This can be overridden with the \opt{draft}
%    option.
%    \begin{macrocode}
%&lt;*classes&gt;
\ExecuteOptions{leqno,centertags,letterpaper,portrait,%
  10pt,twoside,onecolumn,final}
%    \end{macrocode}
%    Options will be processed in the order of the associated
%    \cs{DeclareOption} commands.
%    \begin{macrocode}
\ProcessOptions\relax
%    \end{macrocode}
%
%    In compatibility  mode, we want to load the frozen version of
%    \fn{amstex.sty} instead of the \pkg{amsmath} package. This is
%    rather a horrible kluge but I can't see anything better at the
%    moment. [mjd,1995/01/27]
%    \begin{macrocode}
\if@compatibility
  \def\@tempa{\RequirePackage{amstex}\relax}%
\else
  \@ifclasswith{\@classname}{nomath}{%
    \let\@tempa\relax
  }{%
    \def\@tempa{\RequirePackage{amsmath}\relax}%
  }%
\fi
\@tempa % load amstex.sty or amsmath.sty
%    \end{macrocode}
%    If the \opt{nomath} option was specified, then \cn{numberwithin}
%    and \cs{@emptytoks} remain to be defined.
%    \begin{macrocode}
\@ifundefined{numberwithin}{%
  \newcommand{\numberwithin}[3][\arabic]{%
    \@ifundefined{c@#2}{\@nocounterr{#2}}{%
      \@ifundefined{c@#3}{\@nocnterr{#3}}{%
        \@addtoreset{#2}{#3}%
        \@xp\xdef\csname the#2\endcsname{%
          \@xp\@nx\csname the#3\endcsname .\@nx#1{#2}}}}%
  }
  \csname newtoks\endcsname\@emptytoks
}{}
%    \end{macrocode}
%
%    If the \opt{noamsfonts} option was called for, skip the
%    \pkg{amsfonts} package load.
%    \begin{macrocode}
\if@compatibility
\else
  \@ifclasswith{\@classname}{noamsfonts}{%
    % amsfonts package is not wanted
  }{%
    % amsfonts package IS wanted; test whether a recent enough version
    % seems to be installed
    \begingroup \fontencoding{U}\fontfamily{msa}\try@load@fontshape\endgroup
    \global\@xp\let\csname U+msa\endcsname\relax % reset
    \@ifundefined{U/msa/m/n}{%
      \ClassError{\@classname}{%
  Package `amsfonts' not installed, or version too old?\MessageBreak
  Unable to get font info for the `msam' fonts in the expected form%
      }{%
  The amsfonts package will not be loaded, to avoid probable\MessageBreak
  incompatibility problems. You can (a) use the `noamsfonts'
      documentclass\MessageBreak
  option next time, or (b) check that the amsfonts package is
      installed\MessageBreak
  correctly, and is not too old to be compatible.%
      }%
    }{%
      \RequirePackage{amsfonts}[1995/01/01]\relax
    }%
  }
\fi % end yesamsfonts branch
%    \end{macrocode}
%
%    \subsection{Basic AMS style features}
%
%    AMS style requires that blank pages between chapters be \emph{really}
%    blank: no running heads, no page numbers.  To accomplish this,
%    redefine \cn{cleardoublepage} to do the right thing.  [bnb, 1999/07/17]
%    \begin{macrocode}
\let\cleardouble@page\cleardoublepage
%    \end{macrocode}
%    Postpone the redefinition of \cs{cleardoublepage} to begin-document
%    to work around difficulties with old versions of \fn{gsm-l.cls}.
%    \begin{macrocode}
\AtBeginDocument{%
  \ifx\cleardouble@page\cleardoublepage
    \def\cleardoublepage{\clearpage{\pagestyle{empty}\cleardouble@page}}
  \fi
}
%    \end{macrocode}
%
%    Now a utility macro to do \cn{uppercase} but sidestep any math, to
%    prevent uppercasing math variables.  In order to be handled properly
%    the |$...$| or |\(...\)| must be on the outer level (not
%    enclosed in braces).  We did not try to handle the possibility
%    |\begin{math}| |...| |\end{math}| in a title at the present time (too
%    complicated).  Also we increase inter-word space in the uppercase
%    text.
%
%    One other little problem: uppercasing of a few special characters
%    like the German {\ss} (\cn{ss}) and the undotted i and j (\cn{i}
%    and \cn{j}), used sometimes with accents. We redefine them to be
%    uppercase equivalents. (Undotted \cn{i} and \cn{j} in math would be
%    typed as \cn{imath} and \cn{jmath}.)
%
%    Spaceskip is changed in accordance with recommendations for
%    increased interword spacing in all-caps text by e.g.\ `Words into
%    Type'.
%    \begin{macrocode}
\newcommand{\uppercasenonmath}[1]{\toks@\@emptytoks
%    Insert an extra \@empty to avoid removing braces around arg \arg{1}.
  \@xp\@skipmath\@xp\@empty#1$$%
%    \end{macrocode}
%    The \cs{protect} here is in case the shorttitle gets used for
%    shortauthors and we get redundant application of \cn{MakeUppercase}.
%    Double braces limit the scope so that later elements in title block
%    aren't uppercased, e.g., \cn{i} in an address.  [bnb, 2004/04/01]
%    \begin{macrocode}
  \edef#1{{\@nx\protect\@nx\@upprep\the\toks@}}%
}
%    \end{macrocode}
%
%  \begin{macro}{\@upprep}
%    Preparations for printing all-caps text.
%    \begin{macrocode}
\newcommand{\@upprep}{%
  \spaceskip1.3\fontdimen2\font plus1.3\fontdimen3\font
  \upchars@}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\upchars@}
%    In all-caps text, esszet should print as SS, dotless i should print
%    as normal cap I, Mc should print with a small-caps (not lowercase)
%    c, and so forth.
%    \begin{macrocode}
\newcommand{\upchars@}{%
  \def\ss{SS}\def\i{I}\def\j{J}\def\ae{\AE}\def\oe{\OE}%
  \def\o{\O}\def\aa{\AA}\def\l{\L}\def\Mc{M{\scshape c}}}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\Mc}
%    The use of \cn{Mc} makes it possible for `Mc' to get special
%    treatment when uppercasing is applied.
%    \begin{macrocode}
\providecommand{\Mc}{Mc}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\@skipmath}
%  \begin{macro}{\@xskipmath}
%    \cs{@skipmath} searches for |$...$| in order to keep from applying
%    \cn{uppercase} to the contents. Then it calls \cs{@xskipmath} to
%    search for |\(...\)|.
%    \begin{macrocode}
\newcommand{\@skipmath}{}
\long\def\@skipmath#1$#2${%
  \@xskipmath#1\(\)%
  \@ifnotempty{#2}{\toks@\@xp{\the\toks@$#2$}\@skipmath\@empty}}%
%
\newcommand{\@xskipmath}{}
\long\def\@xskipmath#1\(#2\){%
%    Expand away the added \@empty
  \uppercase{\toks@\@xp\@xp\@xp{\@xp\the\@xp\toks@#1}}%
  \@ifnotempty{#2}{\toks@\@xp{\the\toks@\(#2\)}\@xskipmath\@empty}}%
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%
%  \begin{macro}{\altucnm}
%    \begin{macrocode}
\def\altucnm#1{%
  \MakeTextUppercase{\toks@{#1}}%
  \edef#1{\the\toks@}%
}
\AtBeginDocument{%
  \@ifundefined{MakeTextUppercase}{}{\let\uppercasenonmath\altucnm}%
}
%    \end{macrocode}
%  \end{macro}
%
%    For older versions of \latex/ this might be needed too:
%    \begin{macrocode}
\@ifundefined{MakeUppercase}{\let\MakeUppercase\uppercase}{}%
%    \end{macrocode}
%
%  \begin{macro}{\today}
%    The command \cn{today} produces today's date in the form most
%    commonly used in the U.S.
%    \begin{macrocode}
\newcommand{\today}{%
  \relax\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\day, \number\year}
%    \end{macrocode}
%  \end{macro}
%
%  \subsection{Old font commands}
%    The \cn{em} command is not redefined here (let's say, to give an
%    `obsolete' warning and recommend instead \cn{emph}) because there
%    is no alternative internal command \cs{emshape}.
%    \begin{macrocode}
\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
%    \end{macrocode}
%
%    This warning might have been a good idea back in 1995 but I don't
%    think we can add it now [mjd,2000/03/10].
%\begin{verbatim}
%%\if@compatibility
%%\else
%%  \def\@obsolete@fontswitch#1#2#3{%
%%    \@latex@warning@no@line{%
%%      Command {\string#1...}\on@line\space is obsolete;\MessageBreak
%%      the LaTeX2e equivalent is \string#3{...}}%
%%    \gdef#1{\@fontswitch\relax#3}%
%%  }
%%  \DeclareRobustCommand*\cal{%
%%    \@xp\@obsolete@fontswitch\csname cal \endcsname\relax\mathcal}
%%  \DeclareRobustCommand*\mit{%
%%    \@xp\@obsolete@fontswitch\csname mit \endcsname\relax\mathnormal}
%%\fi
%\end{verbatim}
%    There's too great a chance that some people out there have
%    documents that begin with
%\begin{verbatim}
%\documentclass{amsart}
%...
%\newcommand{\cal}{\mathcal}
%\end{verbatim}
%    and such documents would now get error messages.
%
%    Since \cs{cal} is not documented as a valid command for \LaTeXe/, I
%    think it is OK to leave the status as is for AMS document classes.
%    If you use \cs{documentstyle}, \cs{cal} will work. If you use
%    \cs{documentclass}, well, it's a good idea to update to
%    \cs{mathcal} instead of leaving old instances of \cs{cal}.
%
%  \subsection{Top matter}
%    For the \cn{title} command, we support an optional argument to give
%    a shortened version of the title for running heads.
%    \begin{macrocode}
\renewcommand*{\title}[2][]{\gdef\shorttitle{#1}\gdef\@title{#2}}
%    \end{macrocode}
%    The default value for the optional argument is `same as the
%    mandatory arg' but there doesn't seem to be an easy way to get that
%    effect with \ncn{[re]newcommand}. Here is how to use \cs{@dblarg}
%    in conjunction with the preceding \cn{newcommand}:
%    \begin{macrocode}
\edef\title{\@nx\@dblarg
  \@xp\@nx\csname\string\title\endcsname}
%    \end{macrocode}
%    The \cn{author} command accepts an optional argument similar to
%    that of the \cn{title} command.
%    Moved update of \cn{addresses} within scope of \cs{else} to avoid
%    adding anything if no authors, and thus avoiding output of ``Author
%    address'' on monograph titlepage.  [bnb, 1996/11/03]
%    \begin{macrocode}
\renewcommand{\author}[2][]{%
  \ifx\@empty\authors
    \gdef\authors{#2}%
  \else
    \g@addto@macro\authors{\and#2}%
    \g@addto@macro\addresses{\author{}}%
  \fi
  \@ifnotempty{#1}{%
    \ifx\@empty\shortauthors
      \gdef\shortauthors{#1}%
    \else
      \g@addto@macro\shortauthors{\and#1}%
    \fi
  }%
}
\edef\author{\@nx\@dblarg
  \@xp\@nx\csname\string\author\endcsname}
%    \end{macrocode}
%    Initialize some variables.
%    \begin{macrocode}
\let\shortauthors\@empty   \let\authors\@empty
%    \end{macrocode}
%
%  \begin{macro}{\contrib}
%
%    Contributors are similar to authors except that they are responsible
%    for only part of a work, e.g., an appendix.  The optional argument
%    for the first contributor of a group identifies what has been
%    contributed.  There can be more than one group of contributors;
%    each group is treated separately, using the same ``and'' conventions
%    within the group as for authors.  Contributor groups are strung
%    together separated by a comma; if the word ``and'' is desired before
%    the final group of contributors, it must be included in the optional
%    argument for that group.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\newif\ifresetcontrib  \resetcontribfalse
\newcommand\contrib[2][]{%
  \def\@tempa{#1}%
  \ifx\@empty\@tempa
  \else
    \ifresetcontrib \@xcontribs
    \else \global\resetcontribtrue
    \fi
  \fi
  \ifx\@empty\contribs
    \gdef\contribs{#1 #2}%
  \else
    \g@addto@macro\contribs{\and#1 #2}%
  \fi
%    \end{macrocode}
%    Accumulate contribs separately for the table of contents.  Here,
%    this is just a dummy; it is fully defined for in-house processing.
%    \begin{macrocode}
  \@wraptoccontribs{#1}{#2}%
}
\def\wraptoccontribs#1#2{}
\def\@xcontribs{%
  \author@andify\contribs
  \ifx\@empty\xcontribs
    \xdef\xcontribs{\contribs}%
  \else
    \xdef\xcontribs{\xcontribs, \contribs}%
  \fi
  \let\contribs\@empty
}
%    \end{macrocode}
%  \end{macro}
%
%    Initialize some more variables.
%    \begin{macrocode}
\let\contribs\@empty  \let\xcontribs\@empty  \let\toccontribs\@empty
%&lt;/amsart|amsproc&gt;
\let\addresses\@empty      \let\thankses\@empty
%    \end{macrocode}
%
%    The optional arguments of \cn{address}, \cn{curraddr}, \cn{email}
%    are to indicate which author the address applies to, if a document
%    has multiple authors and there is not a normal one-to-one
%    correspondence between authors and addresses.
%    \begin{macrocode}
\newcommand{\address}[2][]{\g@addto@macro\addresses{\address{#1}{#2}}}
\newcommand{\curraddr}[2][]{\g@addto@macro\addresses{\curraddr{#1}{#2}}}
\newcommand{\email}[2][]{\g@addto@macro\addresses{\email{#1}{#2}}}
\newcommand{\urladdr}[2][]{\g@addto@macro\addresses{\urladdr{#1}{#2}}}
%    \end{macrocode}
%
%    Someone who does not look closely at the \cls{amsart} documentation
%    is likely to put the \cn{thanks} command inside that argument of
%    \cn{author}.
%    \begin{macrocode}
\long\def\thanks@warning#1{%
  \ClassError{\@classname}{%
    \protect\thanks\space should be given separately, not inside author name.%
  }\@ehb
}
%    \end{macrocode}
%
%    \begin{macrocode}
\renewcommand{\thanks}[1]{%
  \@ifnotempty{#1}{\g@addto@macro\thankses{\thanks{#1}}}%
}
%    \end{macrocode}
%
%    The following example of addresses for three authors of a
%    tri-author paper illustrates the kind of complications that need to
%    be handled.
%\begin{verbatim}
%  \author{Roland Campbell}
%  \address{Department of Mathematics\\
%    Pennsylvania State University\\
%    Pittsburgh, Pennsylvania 13593}
%  \email[R.~Campbell]{campr@@galois.psu.edu}
%
%  \author{Mark M. Dane}
%  % Same address as R. Campbell
%  \curraddr[M.~Dane]{Atmospheric Research Station\\
%    Pala Lundi, Fiji}
%  \email[M.~Dane]{DaneMark@@ffr.choice}
%
%  \author{Jeremiah Jones}
%  \address[J.~Jones]{Department of Philosophy\\
%  Freedman College\\
%  Periwinkle, Colorado 84320}
%  \email[J.~Jones]{id739e@@oseoi44 (Bitnet)}
%\end{verbatim}
%    In an article, typesetting of the address information is done at
%    the end of the document, by calling \cs{@setaddresses}. This is done
%    through a parent function \cs{enddoc@text}, because some AMS journals
%    also print the abstract there instead of at the beginning, and it's
%    easier to redefine \cs{enddoc@text} than to try undoing material
%    already added to the \cs{AtEndDocument} hook.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\enddoc@text{\ifx\@empty\@translators \else\@settranslators\fi
  \ifx\@empty\addresses \else\@setaddresses\fi}
\AtEndDocument{\enddoc@text}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    \begin{macrocode}
\def\curraddrname{{\itshape Current address}}
\def\emailaddrname{{\itshape Email address}}
\def\urladdrname{{\itshape URL}}
\def\@setaddresses{\par
  \nobreak \begingroup
%&lt;amsart|amsproc&gt;\footnotesize
  \def\author##1{\nobreak\addvspace\bigskipamount}%
%    \end{macrocode}
%    Address is supposed to go all on one line, so we redefine |\\|
%    to just insert a comma instead of doing a line break.
%    \begin{macrocode}
  \def\\{\unskip, \ignorespaces}%
%    \end{macrocode}
%    No page breaks in the address section is accomplished by
%    |\interlinepenalty\@M| and by the \cn{nobreak} before the \cn{bigskip}.
%    \begin{macrocode}
  \interlinepenalty\@M
  \def\address##1##2{\begingroup
%    \end{macrocode}
%    If there are two addresses for the same author, add a \cn{bigskip}
%    between them.
%    \begin{macrocode}
    \par\addvspace\bigskipamount\indent
%    \end{macrocode}
%    If the name of the author to whom this address applies
%    was given, typeset it.
%    \begin{macrocode}
    \@ifnotempty{##1}{(\ignorespaces##1\unskip) }%
%    \end{macrocode}
%    Now the main part of the address:
%    \begin{macrocode}
    {\scshape\ignorespaces##2}\par\endgroup}%
%    \end{macrocode}
%    Current address:
%    \begin{macrocode}
  \def\curraddr##1##2{\begingroup
    \@ifnotempty{##2}{\nobreak\indent\curraddrname
      \@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
      ##2\par}\endgroup}%
%    \end{macrocode}
%    And then email. In versions 1.0 and 1.1 |@@| was required to print
%    a single \qc{\@} character; for bulletproofing we convert doubled
%    \qc{\@} characters if found.
%    \begin{macrocode}
  \def\email##1##2{\begingroup
    \@ifnotempty{##2}{\nobreak\indent\emailaddrname
      \@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
      \ttfamily##2\par}\endgroup}%
%    \end{macrocode}
%    URLaddr is simply a replica of the email address, with the
%    addition of a feature to enable |~| to print.
%    \begin{macrocode}
  \def\urladdr##1##2{\begingroup
    \def~{\char`\~}%
    \@ifnotempty{##2}{\nobreak\indent\urladdrname
      \@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
      \ttfamily##2\par}\endgroup}%
  \addresses
  \endgroup
}
%    \end{macrocode}
%
%    Some other administrative info. For \cn{date} we can just use the
%    default definition provided by \latex/, except that we initialize
%    the date to empty instead of to \cn{today}.
%    \begin{macrocode}
\let\@date\@empty
\def\dedicatory#1{\def\@dedicatory{#1}}
\let\@dedicatory=\@empty
\def\keywords#1{\def\@keywords{#1}}
\let\@keywords=\@empty
%    \end{macrocode}
%
%    To allow various versions of the subject classification, accept an
%    optional value to identify the version, provide text for the two
%    currently in use, and give a warning if the version specified is
%    unknown.  Default to 2020 version.
%    \begin{macrocode}
\newcommand*\subjclass[2][2020]{%
  \def\@subjclass{#2}%
  \@ifundefined{subjclassname@#1}{%
    \ClassWarning{\@classname}{Unknown edition (#1) of Mathematics
      Subject Classification; using '2020'.}%
  }{%
    \@xp\let\@xp\subjclassname\csname subjclassname@#1\endcsname
  }%
}
\let\@subjclass=\@empty
%&lt;amsart&gt;\def\commby#1{\def\@commby{(Communicated by #1)}}
%&lt;amsart&gt;\let\@commby=\@empty
%    \end{macrocode}
%
%    We handle translator names like author names, just in case there is
%    more than one translator. [mjd,1994/10/19]
%    \begin{macrocode}
\def\translname{Translated by}
\def\translator#1{%
  \ifx\@empty\@translators \def\@translators{#1}%
  \else\g@addto@macro\@translators{\and#1}\fi}
\let\@translators=\@empty
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\@settranslators{\par\begingroup
  \addvspace{6\p@\@plus9\p@}%
  \hbox to\columnwidth{\hss\normalfont\normalsize
    \translname{ }%
    \andify\@translators \uppercasenonmath\@translators
    \@translators}
  \endgroup
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    The general function to convert a list of items in the form
%\begin{verbatim}
% A\and B\and C\and D
%\end{verbatim}
%    to the form `A, B, C, and D' is \cs{xandlist}:
%\begin{verbatim}
% \xandlist{, }{ and }{, and }{A\and B\and C\and D}
%\end{verbatim}
%    This is a completely expandable macro, with the return value being
%    the converted list. There is also a `no-execute' version whose
%    fourth argument should be a macro; the text to be converted will be
%    taken from that macro and after conversion will be put back as the
%    macro's new replacement text.
%\begin{verbatim}
%      \nxandlist{, }{ and }{, and }\result
%\end{verbatim}
%    I don't think I want to explain this except by recommending that
%    you watch it in operation with \cs{tracingmacros} if you're
%    interested. [mjd,1994/10/19]
%    \begin{macrocode}
\newcommand{\xandlist}[4]{\@andlista{{#1}{#2}{#3}}#4\and\and}
\def\@andlista#1#2\and#3\and{\@andlistc{#2}\@ifnotempty{#3}{%
  \@andlistb#1{#3}}}
\def\@andlistb#1#2#3#4#5\and{%
  \@ifempty{#5}{%
    \@andlistc{#2#4}%
  }{%
    \@andlistc{#1#4}\@andlistb{#1}{#3}{#3}{#5}%
  }}
\let\@andlistc\@iden
\newcommand{\nxandlist}[4]{%
  \def\@andlistc##1{\toks@\@xp{\the\toks@##1}}%
  \toks@{\toks@\@emptytoks \@andlista{{#1}{#2}{#3}}}%
  \the\@xp\toks@#4\and\and
  \edef#4{\the\toks@}%
  \let\@andlistc\@iden}
%    \end{macrocode}
%
%  \begin{macro}{andify}
%
%    The \cs{andify} function is provided as a convenient abbreviation
%    for the most common case.  See also \cs{author@andify} (for
%    \cls{amsart} and \cls{amsproc} only), which gives better results
%    in cases with a large number of authors.  Provide a substitutable
%    text string to simplify language-specific modifications.
%    \begin{macrocode}
\def\@@and{and}
\newcommand{\andify}{%
  \nxandlist{\unskip, }{\unskip{} \@@and~}{\unskip, \@@and~}}
%    \end{macrocode}
%    Override the funny default definition of \cn{and} from \latex/.
%    This is not actually used by AMS classes, however.
%    \begin{macrocode}
\def\and{\unskip{ }\@@and{ }\ignorespaces}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{maketitle}
%
%    Set up the style of an article opening page.  For books, see below.
%    For articles, we must add the copyright info footnote.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\maketitle{\par
  \@topnum\z@ % this prevents figures from falling at the top of page 1
  \@setcopyright
  \thispagestyle{firstpage}% this sets first page specifications
%    \end{macrocode}
%    Do some setup for the running heads here. If there are no author names,
%    we set the left-hand running head to the value of the right-hand running
%    head.
%    \begin{macrocode}
  \uppercasenonmath\shorttitle
  \ifx\@empty\shortauthors \let\shortauthors\shorttitle
  \else \andify\shortauthors
  \fi
%    \end{macrocode}
%    The following hook is used to activate the writing of author and
%    title information to an `issue table of contents' when multiple
%    articles are being processed for a journal issue or a proceedings
%    volume.
%    \begin{macrocode}
  \@maketitle@hook
  \begingroup
  \@maketitle
  \toks@\@xp{\shortauthors}\@temptokena\@xp{\shorttitle}%
  \toks4{\def\\{ \ignorespaces}}% defend against questionable usage
  \edef\@tempa{%
    \@nx\markboth{\the\toks4
      \@nx\MakeUppercase{\the\toks@}}{\the\@temptokena}}%
  \@tempa
  \endgroup
  \c@footnote\z@
  \@cleartopmattertags
}
\def\@cleartopmattertags{%
  \def\do##1{\let##1\relax}%
  \do\maketitle \do\@maketitle \do\title \do\@xtitle \do\@title
  \do\author \do\@xauthor \do\address \do\@xaddress
  \do\contrib \do\contribs \do\xcontribs \do\toccontribs
  \do\email \do\@xemail \do\curraddr \do\@xcurraddr
%&lt;amsart&gt;  \do\commby \do\@commby
  \do\dedicatory \do\@dedicatory \do\thanks \do\thankses
  \do\keywords \do\@keywords \do\subjclass \do\@subjclass
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%  \end{macro}
%
%    The hook \cs{@maketitle@hook} is placed into \cn{maketitle} rather
%    than \cs{@maketitle} because the latter tends to get redefined by
%    derived classes using this one as a base. The initial motivation
%    for this hook is to extract title and author information to an
%    external file, so we can't do it with \cs{AtBeginDocument}:
%    \cn{title} and \cn{author} commands might occur between
%    \verb'\begin{document}' and \cn{maketitle}.
%
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\@maketitle@hook{\global\let\@maketitle@hook\@empty}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    Set up the style of an article opening page.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\@maketitle{%
%    \end{macrocode}
%    Set font to normal, just in case.
%    \begin{macrocode}
  \normalfont\normalsize
%    \end{macrocode}
%    Special footnotes are put here to ensure that they come first at
%    the bottom of the page.
%    \begin{macrocode}
  \@adminfootnotes
%    \end{macrocode}
%    If |\pagestyle{myheadings}| was specified, \cs{@mkboth} will be a no-op.
%    \begin{macrocode}
  \@mkboth{\@nx\shortauthors}{\@nx\shorttitle}%
%&lt;amsproc&gt;  \global\topskip8pc\relax % 10pc to base of first title line
%&lt;amsart&gt;  \global\topskip42\p@\relax % 5.5pc   "   "   "     "     "
  \@settitle
  \ifx\@empty\authors \else \@setauthors \fi
%    \end{macrocode}
%    Likewise with \cs{@dedicatory} and \cs{@date}.
%    \begin{macrocode}
  \ifx\@empty\@dedicatory
  \else
%&lt;amsproc&gt;    \baselineskip26\p@
%&lt;amsart&gt;    \baselineskip18\p@
    \vtop{\centering{\footnotesize\itshape\@dedicatory\@@par}%
      \global\dimen@i\prevdepth}\prevdepth\dimen@i
  \fi
  \@setabstract
%    \end{macrocode}
%    Space before the main text should be 32 + 14 base-to-base; we
%    accomplish this by doing a vskip of that amount with \cs{baselineskip}
%    subtracted.
%    \begin{macrocode}
  \normalsize
  \if@titlepage
    \newpage
  \else
    \dimen@34\p@ \advance\dimen@-\baselineskip
    \vskip\dimen@\relax
  \fi
} % end \@maketitle
%    \end{macrocode}
%
%    Segregate the definitions of administrative footnotes to permit
%    easier customization, especially for translation journals.
%    \begin{macrocode}
\def\@adminfootnotes{%
  \let\@makefnmark\relax  \let\@thefnmark\relax
%&lt;amsart&gt;  \ifx\@empty\@date\else \@footnotetext{\@setdate}\fi
  \ifx\@empty\@subjclass\else \@footnotetext{\@setsubjclass}\fi
  \ifx\@empty\@keywords\else \@footnotetext{\@setkeywords}\fi
%    \end{macrocode}
%    In order to make multiple thanks footnotes work inside a single
%    \cs{@footnotetext} argument we need to make the first \cn{par} be
%    ignored. Cf.~\cs{@setthanks}.
%    \begin{macrocode}
  \ifx\@empty\thankses\else \@footnotetext{%
    \def\par{\let\par\@par}\@setthanks}%
  \fi
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%  \subsection{Journal/series logo for articles}
%
%    \cs{publname} either will be defined by a parent class that is calling
%    \cls{amsart} or \cls{amsproc} as a base class, or will be absent, in
%    which case this can be used as a signal to omit the \cs{@serieslogo}.
%    A typical value for \cs{publname} would be
%\begin{verbatim}
% \def\publname{JOURNAL OF THE\newline
%   AMERICAN MATHEMATICAL SOCIETY}
%\end{verbatim}
%
%    Initialize \cs{publname} and \cs{@serieslogo} to no-op if
%    \cs{publname} is not already defined.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\AtBeginDocument{%
  \@ifundefined{publname}{%
    \let\publname\@empty
    \let\@serieslogo\@empty
  }{%
%&lt;amsart&gt;    \def\@serieslogo{\article@logo}%
%&lt;amsproc&gt;    \def\@serieslogo{\procart@logo}%
  }%
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    The \cs{number} prefix on current issue is to work around
%    inconsistencies in the form of issue numbers as passed in from
%    system level. Sometimes they will get passed in with a leading
%    zero, which we don't want to print if it happens to occur.
%    The |0| prevents an error if \cs{currentissue} happens to be empty.
%    \begin{macrocode}
%&lt;*amsart&gt;
\AtBeginDocument{%
  \@ifundefined{volinfo}{%
    \def\volinfo{%
      Volume \currentvolume, Number \number0\currentissue
%    \end{macrocode}
%    Month/year is not included initially when a journal article is
%    posted on the WWW prior to print publication.
%    \begin{macrocode}
      \if\@printyear , \currentmonth\ \currentyear\fi
    }%
  }{}%
}
\def\@printyear{TF}% boolean false
%&lt;/amsart&gt;
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsproc&gt;
\AtBeginDocument{%
  \@ifundefined{volinfo}{\let\volinfo\@empty}{}
}
%&lt;/amsproc&gt;
%    \end{macrocode}
%
%    Default values for information such as volume, year, and so on are
%    provided as follows.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\issueinfo#1#2#3#4{\def\currentvolume{#1}\def\currentissue{#2}%
  \def\currentmonth{#3}\def\currentyear{#4}}
\issueinfo{00}% volume number
  {0}%        % issue number
  {Xxxx}%     % month
  {XXXX}%     % year
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    Copyright year may be different from issue year. Allow it to be
%    specified separately. It is probably more natural anyway, from the
%    user's perspective, to give the copyright year in the same command
%    when giving the name of the copyright holder.
%    \begin{macrocode}
\newcommand{\copyrightinfo}[2]{%
  \def\copyrightyear{#1}%
  \@ifnotempty{#2}{\def\copyrightholder{#2}}%
}
\copyrightinfo{0000}{(copyright holder)}
%    \end{macrocode}
%
%    Provide page span information. If negative number is given, convert
%    to roman numeral form.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\pagespan#1#2{\setcounter{page}{#1}%
  \ifnum\c@page&lt;\z@ \pagenumbering{roman}\setcounter{page}{-#1}\fi
  \def\start@page{#1}\def\end@page{#2}}
\pagespan{000}{000}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    Formatting for journal page numbers. [bnb, 1996/09/11]
%    \begin{macrocode}
%&lt;*amsart&gt;
\AtBeginDocument{%
  \@ifundefined{pageinfo}{%
    \def\pageinfo{%
      \ifnum\start@page=\z@
        Pages 000--000
      \else
        \ifx\start@page\end@page
          Page \start@page
        \else
          Pages \start@page--\end@page
        \fi
      \fi}%
  }{}%
}
%&lt;/amsart&gt;
%    \end{macrocode}
%
%    Publisher Item Identifier (we started using them in journal logos
%    as of January 1997).
%    \begin{macrocode}
%&lt;amsart&gt;\@ifundefined{ISSN}{\def\ISSN{0000-0000}}{}
%&lt;amsart&gt;\newcommand\PII[1]{\def\@PII{#1}}
%&lt;amsart&gt;\PII{S \ISSN(XX)0000-0}
%    \end{macrocode}
%
%  \subsection{Copyright block}
%
%    Doing the copyright info on the first page is a little tricky. We
%    want it to come at the bottom, after any footnotes and floating
%    inserts, but before the page number. If we simply put it into
%    \cs{@oddfoot} (in \cs{ps@plain}) its height will not be subtracted
%    from the height of the text and then the page number will be lower
%    than we want. So we do it as an insert.
%
%    Through version 1.2, this code was included only for \pkg{amsart}
%    and \pkg{amsproc}; the formatting of some book series requires an
%    insert at the bottom of the text block, so this code has been
%    extended to all AMS document classes. [bnb, 1999/07/14]
%    \begin{macrocode}
\newinsert\copyins
%    \end{macrocode}
%    We set the skip register associated with this insert to the
%    \emph{base-to-base} distance from the bottom of the page contents
%    to the base of the first line in the copyright info. See the
%    definition of \cs{@setcopyright}.
%    \begin{macrocode}
\skip\copyins=1.5pc
\count\copyins=1000 % magnification factor, 1000 = 100%
\dimen\copyins=.5\textheight % maximum allowed per page
%    \end{macrocode}
%    \cn{copyins} is ignored if a float is input on the first page;
%    adding it to \cs{@reinserts} will make the output routine behave.
%    [bnb; 2004/06/09; B-365]
%    \begin{macrocode}
\g@addto@macro\@reinserts{%
  \ifvoid\copyins\else\insert\copyins{\unvbox\copyins}\fi
}
%    \end{macrocode}
%    Put the contents into a \tex/ insert. This information is omitted
%    unless \cs{@serieslogo} is non-null. In other words it will
%    normally not print except when an AMS publication-specific document
%    class such as \cls{tran-l} is used.
%    And even if the series logo is printed, omit the copyright line
%    if requested by |\coprightinfo{}{}|.  [bnb, 1996/10/17]
%    \begin{macrocode}
\def\@copyinsfontsize{\fontsize{6}{7\p@}\normalfont\upshape}
\newif\if@extracrline  \@extracrlinefalse
\let\@extracrline\@empty
\relax
\def\@setcopyright{%
  \ifx\@empty\@serieslogo
  \else\ifx\@empty\copyrightyear
  \else
    \insert\copyins{\hsize\textwidth
      \parfillskip\z@\relax
      \leftskip\z@\@plus.9\textwidth\relax \rightskip\z@\relax
      \@copyinsfontsize
%    \end{macrocode}
%    The spacing between the preceding text and the copyright info is
%    done with a strut of height |\skip\copyins|. (Note that
%    \cs{lineskip} and \cs{baselineskip} are 0 in the \latex/ output
%    routine.) The negative vskip gives an effective distance of 0 from
%    the top of the box to the base of the first line (assuming
%    |\skip\copyins| is greater than the height of that line). Then the
%    apparent total height of the box will work well with \tex/'s
%    calculations involving |\skip\copyins| for how much room to leave
%    for this object.  An extra 6pt is allowed when an additional line
%    is present; this adjustment was found adequate in some borderline
%    cases where tight pages reset with the additional line had text
%    lines moved to the next page, causing the paper length to expand
%    by a page.  [bnb, 2004/05/07-06/24]
%    \begin{macrocode}
      \everypar{}%
      \vskip-\skip\copyins
      \if@extracrline
        \vskip-6pt
      \fi
      \nointerlineskip
      \leavevmode\hfill\vrule\@width\z@\@height\skip\copyins
      \copyright\copyrightyear\ \copyrightholder\ignorespaces
      \if@extracrline \@extracrline \fi
      \par
%    \end{macrocode}
%    This kern of 0pt forces the depth of the last line (if any) to be
%    added to the height of the box.
%    \begin{macrocode}
      \kern\z@}%
  \fi\fi
}
%    \end{macrocode}
%
%    When \cs{@combinefloats} is called, the box \cs{@outputbox} already
%    contains the main text of the page and any footnotes. Then \latex/
%    adds top and bottom figures. We want to add our copyright info at
%    the very bottom, but still inside of the vbox.
%    \begin{macrocode}
\def\@combinefloats{%
  \ifx \@toplist\@empty \else \@cflt \fi
  \ifx \@botlist\@empty \else \@cflb \fi
  \ifvoid\copyins \else \@cflci \fi
}
%    \end{macrocode}
%  \subsubsection{combine-floats-copyright-insert}
%
%    In the twocolumn/firstcolumn case, postpone adding the drop folio.
%    Put an empty box of the same height at the bottom of the left-hand
%    column to make the columns balance.  Allow a smidge of stretch in
%    case the first page of a chapter has no internal stretch, so that
%    the drop folio will be flush to the bottom of the text block;
%    don't do this for a twocolumn page, to avoid an uneven bottom.
%    \begin{macrocode}
\def\@cflci{%
  \setbox\@outputbox\vbox{%
    \unvbox\@outputbox
    \vskip\skip\copyins
    \if@twocolumn \else \vskip\z@ plus\p@ \fi
    \hbox to\columnwidth{%
      \hss\vbox to\z@{\vss
%    \end{macrocode}
%    In two-column layout, put an empty box in the first column
%    instead of the drop folio.
%    \begin{macrocode}
        \if@twocolumn
          \if@firstcolumn \else \unvbox\copyins \fi
        \else
          \unvbox\copyins
        \fi
        }}}%
%    \end{macrocode}
%    Now redo the insert to make sure we get the right amount of space
%    reserved for it in the second column.
%    \begin{macrocode}
  \if@twocolumn \if@firstcolumn
    \insert\copyins{\unvbox\copyins}%
  \fi\fi
%    \end{macrocode}
%    Reset the \cs{copyins} flag so that a subsequent insert
%    (e.g.\ \cs{@dropfolio} in some book series) will work.
%    \begin{macrocode}
  \global\count\copyins=999 \relax
}
%    \end{macrocode}
%    [End of code to support inserts at end of text block.]
%
%    For journals only, provide a switch that indicates the author has
%    agreed to revert copyright to the public domain; this results in
%    an addition to the copyright block on the article.
%    \begin{macrocode}
%&lt;*amsart&gt;
\newif\if@revertcopyright  \@revertcopyrightfalse
\newcommand{\revertcopyright}{%
  \global\@revertcopyrighttrue
  \global\@extracrlinetrue}
%    \end{macrocode}
%    Add notation regarding reversion of copyright to public domain if
%    author has agreed to it.  Permit this to be set in a different
%    size than the copyright line (required for some author packages).
%    \begin{macrocode}
\def\@revertcrfontsize{\fontsize{6}{7\p@}\normalfont\upshape}
\def\@extracrline{%
  \if@revertcopyright
    \unskip\\
    \@revertcrfontsize
    Reverts to public domain 28 years from publication
  \fi
}
%&lt;/amsart&gt;
%    \end{macrocode}
%
%  \subsection{Other top matter info}
%
%    Some name setup.
%    \begin{macrocode}
\newcommand{\abstractname}{Abstract}
\newcommand{\keywordsname}{Key words and phrases}
%    \end{macrocode}
%    Support the most recent versions.  Earlier, unsupported versions
%    were:
%    \begin{itemize}
%    \item \textup{1980} Mathematics Subject Classification
%    \item \textup{1980} Mathematics Subject Classification
%          \textup{(1985} Revision\textup{)}
%    \end{itemize}
%    \begin{macrocode}
\@namedef{subjclassname@1991}{%
  \textup{1991} Mathematics Subject Classification}
\@namedef{subjclassname@2000}{%
  \textup{2000} Mathematics Subject Classification}
\@namedef{subjclassname@2010}{%
  \textup{2010} Mathematics Subject Classification}
\@namedef{subjclassname@2020}{%
  \textup{2020} Mathematics Subject Classification}
%    \end{macrocode}
%    Default to the 2020 edition.
%    \begin{macrocode}
\@xp\let\@xp\subjclassname\csname subjclassname@2020\endcsname
%    \end{macrocode}
%    For the date we have a special little problem: We only want to add
%    the `Received by the editors' text for publication-specific
%    document classes such as \cls{tran-l}.
%    \begin{macrocode}
%&lt;amsbook&gt;\def\@tempb{amsbook}
%&lt;amsproc&gt;\def\@tempb{amsproc}
%&lt;amsart&gt;\def\@tempb{amsart}
\ifx\@classname\@tempb
  \newcommand{\datename}{\textit{Date}:}
\else
  \newcommand{\datename}{Received by the editors}
\fi
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\@settitle{\begin{center}%
%&lt;amsart&gt;  \baselineskip14\p@\relax
%&lt;amsproc&gt; \Large
    \bfseries
%&lt;amsart&gt;\uppercasenonmath\@title
  \@title
  \end{center}%
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    For multiple authors we need to combine the author names into a
%    list of the form Author One, Author Two, \dots, and Author Last.
%    Change line breaking penalties to avoid a line break in the middle of
%    an author name if there are a lot of authors. This should probably
%    better be done by changing spaces within author names to
%    |\nolinebreak[3]\space|, but that would take more work.
%    [mjd,2000/12/27]
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\author@andify{%
  \nxandlist {\unskip ,\penalty-1 \space\ignorespaces}%
    {\unskip {} \@@and~}%
    {\unskip ,\penalty-2 \space \@@and~}%
}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@setauthors{%
  \begingroup
  \def\thanks{\protect\thanks@warning}%
  \trivlist
%&lt;amsart&gt;  \centering\footnotesize \@topsep30\p@\relax
%&lt;amsart&gt;  \advance\@topsep by -\baselineskip
%&lt;amsproc&gt;  \centering \fontsize{11}{13\p@}\selectfont\@topsep13\p@\relax
  \item\relax
  \author@andify\authors
%    \end{macrocode}
%    Make dbl-backslash robust to prevent problems if/when
%    \cs{MakeTextUppercase} expansion is applied.
%    \begin{macrocode}
  \def\\{\protect\linebreak}%
%&lt;amsart&gt;  \MakeUppercase{\authors}%
%&lt;amsproc&gt;  \authors
  \ifx\@empty\contribs
  \else
    ,\penalty-3 \space \@setcontribs
    \@closetoccontribs
  \fi
  \endtrivlist
  \endgroup
}
\def\@closetoccontribs{}
\def\@setcontribs{%
  \@xcontribs
%&lt;amsart&gt;  \MakeUppercase{\xcontribs}%
%&lt;amsproc&gt;  \xcontribs
}
\def\@setdate{\datename\ \@date\@addpunct.}
\def\@setsubjclass{%
  {\itshape\subjclassname.}\enspace\@subjclass\@addpunct.}
\def\@setkeywords{%
  {\itshape \keywordsname.}\enspace \@keywords\@addpunct.}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    The following definitions suffice for all the AMS document classes.
%    \begin{macrocode}
\def\@setthanks{\def\thanks##1{\par##1\@addpunct.}\thankses}
%    \end{macrocode}
%
%    `Abstract' can be changed to, say, `R\'esum\'e' (French) by
%    redefining \cn{abstractname}. This and other control sequence names
%    (\cn{refname}, \cn{contentsname}, \cn{appendixname}, and so on) are
%    compatible with the \pkg{babel} package (the AMS sometimes
%    publishes articles in languages other than English.)
%
%    In AMS document classes, the abstract should be placed before
%    \cn{maketitle} (otherwise the desired ordering of frontmatter
%    elements cannot be ensured in all cases).
%    \begin{macrocode}
\newbox\abstractbox
%    \end{macrocode}
%    We start by checking whether \cn{maketitle} has already been used
%    (in which case it was reset to \cs{relax}); if so, we give a
%    warning that the abstract should be placed before \cn{maketitle}.
%    \begin{macrocode}
\newenvironment{abstract}{%
  \ifx\maketitle\relax
    \ClassWarning{\@classname}{Abstract should precede
      \protect\maketitle\space in AMS document classes; reported}%
  \fi
  \global\setbox\abstractbox=\vtop \bgroup
    \normalfont\Small
    \list{}{\labelwidth\z@
      \leftmargin3pc \rightmargin\leftmargin
      \listparindent\normalparindent \itemindent\z@
      \parsep\z@ \@plus\p@
%    \end{macrocode}
%    In order to get equation numbers indented with the rest of the
%    abstract, we have to do this:
%    \begin{macrocode}
      \let\fullwidthdisplay\relax
    }%
    \item[\hskip\labelsep\scshape\abstractname.]%
}{%
  \endlist\egroup
%    \end{macrocode}
%    If the abstract was supposed to be typeset earlier, then
%    \cs{@setabstract} is now equal to \cs{relax}, and we had better
%    drop the contents of the abstract box onto the page immediately, to
%    salvage the situation as best we can.
%    \begin{macrocode}
  \ifx\@setabstract\relax \@setabstracta \fi
}
%    \end{macrocode}
%
%    Because the abstract might be postponed until the end of an
%    article, we cannot simply use the fact of a preceding
%    \cn{maketitle} to tell whether \cs{endabstract} should immediately
%    put the abstract box contents on the page. So we use an auxiliary
%    function that will be reset to no-op once we have passed the point
%    where the abstract should normally be typeset.
%    \begin{macrocode}
\def\@setabstract{\@setabstracta \global\let\@setabstract\relax}
\def\@setabstracta{%
  \ifvoid\abstractbox
  \else
    \skip@20\p@ \advance\skip@-\lastskip
    \advance\skip@-\baselineskip \vskip\skip@
    \box\abstractbox
    \prevdepth\z@ % because \abstractbox is a vtop
  \fi
}
%    \end{macrocode}
%
%    Title page environment does nothing much; information and
%    formatting to be provided by the user.
%    \begin{macrocode}
\def\titlepage{%
%&lt;amsbook&gt;  \cleardoublepage
%&lt;amsart|amsproc&gt;  \clearpage
  \thispagestyle{empty}\setcounter{page}{0}}
\def\endtitlepage{\newpage}
%    \end{macrocode}
%
%  \subsection{Macros for list labels}
%
%    Through version 1.2, first-level enumerated item labels were formatted
%    with a following period, which is not AMS style.  Effective with
%    version 2.0 these labels are formatted with parentheses.  Anyone
%    requiring the period style will have to redefine \cs{labelenumi}.
%    \begin{macrocode}
\def\labelenumi{(\theenumi)}
\def\theenumi{\@arabic\c@enumi}
\def\labelenumii{(\theenumii)}
\def\theenumii{\@alph\c@enumii}
\def\p@enumii{\theenumi}
\def\labelenumiii{(\theenumiii)}
\def\theenumiii{\@roman\c@enumiii}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{(\theenumiv)}
\def\theenumiv{\@Alph\c@enumiv}
\def\p@enumiv{\p@enumiii\theenumiii}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bfseries --}% \upshape already done by \itemize
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}
%    \end{macrocode}
%
%  \subsection{Verse and quotation environments}
%    \begin{macrocode}
\newenvironment{verse}{\let\\\@centercr
  \list{}{\itemsep\z@ \itemindent -1.5em\listparindent\itemindent
  \rightmargin\leftmargin \advance\leftmargin 1.5em}\item[]%
}{%
  \endlist
}
\let\endverse=\endlist % for efficiency
%    \end{macrocode}
%    The left/right margins of the quotation environment are supposed to
%    be the same as for the abstract environment.
%    \begin{macrocode}
\newenvironment{quotation}{\list{}{%
    \leftmargin3pc \listparindent\normalparindent
    \itemindent\z@
    \rightmargin\leftmargin \parsep\z@ \@plus\p@}%
  \item[]%
}{%
  \endlist
}
\let\endquotation=\endlist % for efficiency
\newenvironment{quote}{%
  \list{}{\rightmargin\leftmargin}\item[]%
}{%
  \endlist
}
\let\endquote=\endlist % for efficiency
%    \end{macrocode}
%
%  \subsection{List environments}
%    Changed definition of \cs{trivlist}, \env{enumerate}, and
%    \env{itemize} in order to have \cn{makelabel} apply \cn{upshape}.
%    \begin{macrocode}
\def\trivlist{\parsep\parskip\@nmbrlistfalse
  \@trivlist \labelwidth\z@ \leftmargin\z@
  \itemindent\z@
  \let\@itemlabel\@empty
  \def\makelabel##1{\upshape##1}}
%    \end{macrocode}
%
%    \begin{macrocode}
\renewenvironment{enumerate}{%
  \ifnum \@enumdepth &gt;3 \@toodeep\else
      \advance\@enumdepth \@ne
      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
      {\csname label\@enumctr\endcsname}{\usecounter
        {\@enumctr}\def\makelabel##1{\hss\llap{\upshape##1}}}\fi
}{%
  \endlist
}
\let\endenumerate=\endlist % for efficiency
%    \end{macrocode}
%
%    \begin{macrocode}
\renewenvironment{itemize}{%
  \ifnum\@itemdepth&gt;3 \@toodeep
  \else \advance\@itemdepth\@ne
    \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
    \list{\csname\@itemitem\endcsname}%
      {\def\makelabel##1{\hss\llap{\upshape##1}}}%
  \fi
}{%
  \endlist
}
\let\enditemize=\endlist % for efficiency
%    \end{macrocode}
%
%    \begin{macrocode}
\newcommand{\descriptionlabel}[1]{\hspace\labelsep \upshape\bfseries #1:}
\newenvironment{description}{\list{}{%
%    \end{macrocode}
%    Adjust the indent of the first line to the desired value:
%    \begin{macrocode}
  \advance\leftmargini6\p@ \itemindent-12\p@
  \labelwidth\z@ \let\makelabel\descriptionlabel}%
}{
  \endlist
}
\let\enddescription=\endlist % for efficiency
%    \end{macrocode}
%
%  \begin{macro}{\upn}
%    The command \cn{upn} can be used to force upright font for
%    punctuation or digits in italic text. For example
%\begin{verbatim}
% ... as numbered by \upn{``A''} or \upn{``1''} hereafter\upn{)}
%\end{verbatim}
%    \begin{macrocode}
\let\upn=\textup
%    \end{macrocode}
%  \end{macro}
%
%    Since these margin settings are dependent on the fonts used, we
%    postpone them until begin-document. (This means that we cannot use
%    the values directly for calculations before begin-document.)  Allow
%    for a reasonable maximum value; 13 = xiii = m should be adequate.
%    \begin{macrocode}
\AtBeginDocument{%
  \labelsep=5pt\relax
  \setcounter{enumi}{13}\setcounter{enumii}{13}%
  \setcounter{enumiii}{13}\setcounter{enumiv}{13}%
  \settowidth\leftmargini{\labelenumi\hskip\labelsep}%
  \advance\leftmargini by \normalparindent
  \settowidth\leftmarginii{\labelenumii\hskip\labelsep}%
  \settowidth\leftmarginiii{\labelenumiii\hskip\labelsep}%
  \settowidth\leftmarginiv{\labelenumiv\hskip\labelsep}%
  \setcounter{enumi}{0}\setcounter{enumii}{0}%
  \setcounter{enumiii}{0}\setcounter{enumiv}{0}%
  \leftmarginv=10pt  \leftmarginvi=\leftmarginv
  \leftmargin=\leftmargini
  \labelwidth=\leftmargini \advance\labelwidth-\labelsep
  \@listi}
%    \end{macrocode}
%
%    In some contexts the space above/below lists needs to be
%    suppressed. So we put it into a variable \cs{listisep}.
%    \begin{macrocode}
\newskip\listisep
\listisep\smallskipamount
\def\@listI{\leftmargin\leftmargini \parsep\z@skip
  \topsep\listisep \itemsep\z@skip
  \listparindent\normalparindent}
\let\@listi\@listI
%    \end{macrocode}
%
%    Is it necessary to reset \cs{parsep}, \cs{partopsep}, \cs{itemsep}
%    to their default values (0) in each of the subordinate list
%    setup functions? I don't believe so, but I leave the settings in
%    the listii function just in case some unusual nesting of
%    environments might cause trouble. [mjd,1994/09/22]
%    \begin{macrocode}
\def\@listii{\leftmargin\leftmarginii
  \labelwidth\leftmarginii \advance\labelwidth-\labelsep
  \topsep\z@skip \parsep\z@skip \partopsep\z@skip \itemsep\z@skip}
\def\@listiii{\leftmargin\leftmarginiii
  \labelwidth\leftmarginiii \advance\labelwidth-\labelsep}
\def\@listiv{\leftmargin\leftmarginiv
  \labelwidth\leftmarginiv \advance\labelwidth-\labelsep}
\def\@listv{\leftmargin\leftmarginv
  \labelwidth\leftmarginv \advance\labelwidth-\labelsep}
\def\@listvi{\leftmargin\leftmarginvi
  \labelwidth\leftmarginvi \advance\labelwidth-\labelsep}
%    \end{macrocode}
%
%  \subsection{Fleqn option}
%
%    \begin{macrocode}
\@ifclasswith{\@classname}{fleqn}{%
  \let\@tempa\@iden
  \AtBeginDocument{\mathindent\leftmargini}%
}{\let\@tempa\@gobble}%
\@ifpackageloaded{amsmath}{\let\@tempa\@gobble}{%
  \@ifpackageloaded{amstex}{\let\@tempa\@gobble}{}%
}
\@tempa{%
  \def\[{\relax
    \ifmmode\@badmath
    \else
      \begin{trivlist}%
      \@beginparpenalty\predisplaypenalty
      \@endparpenalty\postdisplaypenalty
      \item[]\leavevmode
      \hbox to\linewidth\bgroup$\displaystyle
%    \end{macrocode}
%    Note that the \cs{m@th} should go at the end in \cn{]} just in
%    case an embedded small math formula inside \cn{text} occurs in
%    the display.
%
%    Why the extra bgroup here? I think it's not needed.
%    [mjd,3-Feb-1994]
%    \begin{macrocode}
      \hskip\mathindent\bgroup
    \fi}%
  \def\]{\relax
    \ifmmode
      \egroup \m@th$\hfil \egroup
      \end{trivlist}%
    \else \@badmath
    \fi}%
  \renewenvironment{equation}{%
    \@beginparpenalty\predisplaypenalty
    \@endparpenalty\postdisplaypenalty
    \refstepcounter{equation}%
    \@topsep\abovedisplayskip \trivlist
    \item[]\leavevmode
    \hbox to\linewidth\bgroup\hskip\mathindent$\displaystyle
  }{%
    \m@th$\hfil \displaywidth\linewidth \hbox{\@eqnnum}\egroup
    \endtrivlist
  }%
  \renewenvironment{eqnarray}{%
    \stepcounter{equation}\let\@currentlabel\theequation
    \global\@eqnswtrue \global\@eqcnt\z@ \tabskip\mathindent
    \let\\=\@eqncr \abovedisplayskip\topsep
    \ifvmode \advance\abovedisplayskip\partopsep \fi
    \belowdisplayskip\abovedisplayskip
    \belowdisplayshortskip\abovedisplayskip
    \abovedisplayshortskip\abovedisplayskip
    $$\everycr{}\halign to\linewidth\bgroup
      \hskip\@centering
      $\displaystyle\tabskip\z@skip####\m@th$&amp;%
      \@eqnsel \global\@eqcnt\@ne
      \hfil${}####{}\m@th$\hfil&amp;%
      \global\@eqcnt\tw@
      $\displaystyle ####\m@th$\hfil\tabskip\@centering&amp;%
      \global\@eqcnt\thr@@
      \hbox to \z@\bgroup\hss####\egroup\tabskip\z@skip\cr
    }{%
      \@@eqncr \egroup \global\advance\c@equation\m@ne$$%
      \global\@ignoretrue
    }%
  \newdimen\mathindent
  \mathindent\leftmargini
}
%    \end{macrocode}
%
%  \subsection{Redefined internal sectioning commands}
%
%    In amsart.sty \cs{@startsection}, \cs{@sect},
%    and a couple of other things are redefined to fix a few hard-coded
%    things that would interfere with the desired style.  The most
%    noteworthy difference is that all section headings will go into the
%    table of contents (governed by secnumdepth as usual), EVEN WHEN THE
%    |*| FORM IS USED.  The only section heading not listed in the table of
%    contents is the heading for the toc itself.
%
%    A second major departure from standard \latex/ is that when a
%    short form of a section title is given, it is used only for the
%    running heads; the table of contents still gets the full version of
%    the title. This is correct for AMS editorial practice. However if
%    one wants to get a line break into the table of contents it means
%    that the standard \latex/ method cannot be used. See the
%    \cn{except} and \cn{for} commands.
%    \begin{macrocode}
\def\@startsection#1#2#3#4#5#6{%
%    \end{macrocode}
%    Section titles, if they are run-in with the following text, are
%    stored in a box instead of being typeset right away.  They will be
%    typeset by \cs{everypar}, but if one section heading follows
%    right after another, this won't happen.  So by doing
%    \cs{leavevmode} we force this to happen.  (\cs{if@noskipsec}
%    is true if the previous section title has not yet been typeset.)
%    \begin{macrocode}
 \if@noskipsec \leavevmode \fi
 \par \@tempskipa #4\relax
 \@afterindenttrue
 \ifdim \@tempskipa &lt;\z@ \@tempskipa -\@tempskipa \@afterindentfalse\fi
 \if@nobreak \everypar{}\else
     \addpenalty\@secpenalty\addvspace\@tempskipa\fi
%    Don't call \@ssect in the ifstar case:
 \@ifstar{\@dblarg{\@sect{#1}{\@m}{#3}{#4}{#5}{#6}}}%
         {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}%
}
%    \end{macrocode}
%
%    We add \cn{textup} here in order to make section
%    numbers always roman, even if the rest of the section head is
%    italic.
%    \begin{macrocode}
\def\@seccntformat#1{%
  \protect\textup{\protect\@secnumfont
    \csname the#1\endcsname
    \protect\@secnumpunct
  }%
}
%    \end{macrocode}
%
%    Some journals require a different font for section numbers. (As
%    coded here, this option permits only a change of weight, to
%    \cn{bfseries}.)  The \cls{amsart} font is checked again later,
%    when processing \cn{section}, and if there is no section title,
%    it is made bold.
%    \begin{macrocode}
%&lt;amsbook|amsproc&gt;\let\@secnumfont\@empty
%&lt;amsart&gt;\def\@secnumfont{\mdseries}
%    \end{macrocode}
%
%     For reference, here is the argument list for \cs{@sect}.
%\begin{verbatim}
% % #1    #2     #3      #4          #5         #6     #7      #8
% {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}[SHORTT]{TITLE}
%\end{verbatim}
%    \begin{macrocode}
\def\@sect#1#2#3#4#5#6[#7]#8{%
%    \end{macrocode}
%    Define \cs{@toclevel} for for \cs{@tocwrite} (to
%    \cs{@tochangmeasure}).
%    \begin{macrocode}
  \edef\@toclevel{\ifnum#2=\@m 0\else\number#2\fi}%
  \ifnum #2&gt;\c@secnumdepth \let\@secnumber\@empty
  \else \@xp\let\@xp\@secnumber\csname the#1\endcsname\fi
%    \end{macrocode}
%    If the value of afterskip $&gt;0$, then this is not a run-in section
%    heading, and we want to suppress final punctuation.
%    \begin{macrocode}
  \@tempskipa #5\relax
%    \end{macrocode}
%    \cs{@svsec} will be the section number plus some formatting if
%    the star form was not used and if the depth of numbering extends to
%    the current level. The user can change secnumdepth to control how
%    many levels of sectioning will be numbered.
%    \begin{macrocode}
  \ifnum #2&gt;\c@secnumdepth
    \let\@svsec\@empty
  \else
    \refstepcounter{#1}%
%    \end{macrocode}
%    If the section heading is not run-in and there is no title, omit
%    final punctuation and space.  If it is run-in, omit extra space.
%    \begin{macrocode}
    \edef\@secnumpunct{%
      \ifdim\@tempskipa&gt;\z@ % not a run-in section heading
        \@ifnotempty{#8}{.\@nx\enspace}%
      \else
        \@ifempty{#8}{.}{.\@nx\enspace}%
      \fi
    }%
%    \end{macrocode}
%    For \cls{amsart}, if a subsection has no title, make the section
%    number bold; otherwise leave it alone.
%    [bnb; 2004/06/08; per vwa, B-442]
%    \begin{macrocode}
%&lt;amsart&gt;    \@ifempty{#8}{%
%&lt;amsart&gt;      \ifnum #2=\tw@ \def\@secnumfont{\bfseries}\fi}{}%
%    \end{macrocode}
%    If the |*|-form was not used (\arg{2} less than 1000), we add
%    \cn{sectionname} or whatever as a prefix, separated by a space.
%    We need the ifundefined test in order to know whether the space
%    should be added or not.  There must be a better way to do this
%    but I haven't thought of it yet.
%    \begin{macrocode}
    \protected@edef\@svsec{%
      \ifnum#2&lt;\@m
        \@ifundefined{#1name}{}{%
          \ignorespaces\csname #1name\endcsname\space
        }%
      \fi
      \@seccntformat{#1}%
    }%
  \fi
  \ifdim \@tempskipa&gt;\z@ % then this is not a run-in section heading
    \begingroup #6\relax
    \@hangfrom{\hskip #3\relax\@svsec}{\interlinepenalty\@M #8\par}%
    \endgroup
%    \end{macrocode}
%
%    Section headings don't set marks for the running heads in the article
%    style, only in the amsbook style. Assumption: \cs{sectionmark} is
%    defined to call \cs{@secnumber} as its penultimate argument.
%    \begin{macrocode}
%&lt;amsbook&gt;  \csname #1mark\endcsname{#7}%
%    \end{macrocode}
%    If \arg{2} (level) is greater than 1000 then we don't do a table
%    of contents entry. This happens only for the section heading above
%    the table of contents itself.
%    \begin{macrocode}
    \ifnum#2&gt;\@m \else \@tocwrite{#1}{#8}\fi
  \else
%    \end{macrocode}
%    Otherwise we're doing a run-in heading; it is stored as \cs{@svsechd},
%    which will be typeset by \cs{everypar} as soon as some text is
%    encountered.
%    \begin{macrocode}
  \def\@svsechd{#6\hskip #3\@svsec
%    \end{macrocode}
%    To allow for the possibility that the user wants an empty section
%    title, leaving just the section number, we check whether \arg{8}
%    is nonempty before adding the period.
%    \begin{macrocode}
    \@ifnotempty{#8}{\ignorespaces#8\unskip
%    \end{macrocode}
%    The following test is to prevent a period being added if the
%    section title ended in a question mark or other punctuation.
%    \begin{macrocode}
       \@addpunct.}%
    \ifnum#2&gt;\@m \else \@tocwrite{#1}{#8}\fi
  }%
  \fi
%    \end{macrocode}
%    In a previous version of \cls{amsart} \cs{@nobreaktrue} was added to
%    \cs{@xsect} for some reason. Let's keep that just in case it was done to
%    prevent a certain kind of bug. [mjd,17-Aug-1994]
%    \begin{macrocode}
  \global\@nobreaktrue
%    \end{macrocode}
%    \cs{@xsect} does some more stuff based on whether this is a run-in
%    heading or not.
%    \begin{macrocode}
  \@xsect{#5}}
%    \end{macrocode}
%
%    Undefine \cs{@ssect} to save memory; it's not needed in \cls{amsart}.
%    \begin{macrocode}
\let\@ssect\relax
%    \end{macrocode}
%
%  \subsection{Chapters and sections}
%    Allocate counters for sectioning commands. Paragraph and subparagraph
%    counters are allocated but normally not used.
%    \begin{macrocode}
\newcounter{part}
%&lt;amsbook&gt;\newcounter{chapter}
%&lt;amsproc|amsart&gt;\newcounter{section}
%&lt;amsbook&gt;\newcounter{section}[chapter]
%&lt;amsbook&gt;\def\thesection{\arabic{section}}
\newcounter{subsection}[section]
\newcounter{subsubsection}[subsection]
\newcounter{paragraph}[subsubsection]
\newcounter{subparagraph}[paragraph]
%    \end{macrocode}
%    Set numbering style for sectioning commands. In a couple of cases
%    resetting is unnecessary but we include the full list here for
%    completeness.
%    \begin{macrocode}
\renewcommand\thepart          {\arabic{part}}
%&lt;amsbook&gt;\renewcommand\thechapter       {\arabic{chapter}}
\renewcommand\thesection       {\arabic{section}}
\renewcommand\thesubsection    {\thesection.\arabic{subsection}}
\renewcommand\thesubsubsection {\thesubsection .\arabic{subsubsection}}
\renewcommand\theparagraph     {\thesubsubsection.\arabic{paragraph}}
\renewcommand\thesubparagraph  {\theparagraph.\arabic{subparagraph}}
%    \end{macrocode}
%    Depth of section numbering; if \fn{secnumdepth} were 2 instead of
%    3, \cn{subsubsection} would not be numbered.
%    \begin{macrocode}
\setcounter{secnumdepth}{3}
%    \end{macrocode}
%
%    The arguments of \cs{@startsection} are given for reference:
%\begin{verbatim}
% % #1    #2     #3      #4          #5         #6
% {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}
%\end{verbatim}
%
%    \begin{macrocode}
\def\partname{Part}
%&lt;*amsart|amsproc&gt;
\def\part{\@startsection{part}{0}%
  \z@{\linespacing\@plus\linespacing}{.5\linespacing}%
  {\normalfont\bfseries\raggedright}}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    Specialsection correlates to our inhouse Z-head.
%    \begin{macrocode}
\def\specialsection{\@startsection{section}{1}%
%&lt;amsart&gt;  \z@{\linespacing\@plus\linespacing}{.5\linespacing}%
%&lt;amsproc|amsbook&gt;  \z@{2\linespacing\@plus\linespacing}{.5\linespacing}%
%&lt;amsart&gt;  {\normalfont\centering}}
%&lt;amsproc|amsbook&gt;  {\large\scshape\centering}}
%    \end{macrocode}
%
%    In the book class \cn{part} puts the part title on a separate
%    page.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\part{\cleardoublepage \thispagestyle{empty}%
  \null\vfil  \markboth{}{}\secdef\@part\@spart}
%
\def\@part[#1]#2{%
  \ifnum \c@secnumdepth &gt;-2\relax \refstepcounter{part}%
    \addcontentsline{toc}{part}{\partname\ \thepart.
        \protect\enspace\protect\noindent#1}%
  \else
    \addcontentsline{toc}{part}{#1}\fi
  \begingroup\centering
  \ifnum \c@secnumdepth &gt;-2\relax
       {\fontsize{\@xviipt}{22}\bfseries
         \partname\ \thepart} \vskip 20\p@ \fi
  \fontsize{\@xxpt}{25}\bfseries
      #1\vfil\vfil\endgroup \newpage\thispagestyle{empty}}

\def\@spart#1{\addcontentsline{toc}{part}{\protect\noindent#1}%
  \begingroup\centering
  \fontsize{\@xxpt}{25}\bfseries
     #1\vfil\vfil\endgroup \newpage\thispagestyle{empty}}
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%    The arguments of \cs{partrunhead} are \cs{partname},
%    \cs{thepart}, and the text of the part title. The first two were
%    fully expanded during the marking process. Use of a mere
%    interword space between the first two args makes it possible
%    to apply \cn{ignorespaces} and \cn{unskip} as shown here
%    to produce the desired results if one or the other is empty.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\partrunhead#1#2#3{%
  \@ifnotempty{#2}{\uppercase{\ignorespaces#1 #2\unskip}\@ifnotempty{#3}{. }}%
  \def\@tempa{#3}%
  \ifx\@empty\@tempa\else
    \begingroup \def\\{ \ignorespaces}% defend against questionable usage
    \uppercasenonmath\@tempa\@tempa
    \endgroup
  \fi
}
\let\chapterrunhead\partrunhead
\let\sectionrunhead\partrunhead
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%    Section headings in the amsbook style differ from the amsart
%    style in a couple of ways: The ones that aren't centered are
%    indented on the left, instead of flush left; and the first
%    level, \cn{section}, is not small caps but bold.
%    Cf.~the definition of \cn{appendix}.
%    \begin{macrocode}
\def\section{\@startsection{section}{1}%
  \z@{.7\linespacing\@plus\linespacing}{.5\linespacing}%
%&lt;amsart&gt;  {\normalfont\scshape\centering}}
%&lt;amsbook|amsproc&gt;  {\normalfont\bfseries\centering}}
%    \end{macrocode}
%
%    Negative value for \arg{5} is a signal to make a run-in heading instead
%    of doing a vskip after the heading.
%    \begin{macrocode}
\def\subsection{\@startsection{subsection}{2}%
%&lt;amsart&gt;  \z@{.5\linespacing\@plus.7\linespacing}{-.5em}%
%&lt;amsbook|amsproc&gt;  \normalparindent{.5\linespacing\@plus.7\linespacing}{-.5em}%
  {\normalfont\bfseries}}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\subsubsection{\@startsection{subsubsection}{3}%
%&lt;amsart&gt;  \z@{.5\linespacing\@plus.7\linespacing}{-.5em}%
%&lt;amsbook|amsproc&gt;  \normalparindent\z@{-.5em}%
  {\normalfont\itshape}}
%    \end{macrocode}
%
%    Fontdimen 2 of the current font is the ideal interword space of the
%    font. Thus the following spec says that the space after the
%    paragraph heading should be a normal interword space (but
%    nonstretching and nonshrinking).
%    \begin{macrocode}
\def\paragraph{\@startsection{paragraph}{4}%
%&lt;amsart&gt;  \z@\z@{-\fontdimen2\font}%
%&lt;amsbook|amsproc&gt;  \normalparindent\z@{-\fontdimen2\font}%
  \normalfont}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\subparagraph{\@startsection{subparagraph}{5}%
  \z@\z@{-\fontdimen2\font}%
  \normalfont}
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\def\appendix{\par\c@section\z@ \c@subsection\z@
   \let\sectionname\appendixname
   \def\thesection{\@Alph\c@section}}
\def\appendixname{Appendix}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%
%    A slower, but fully expandable definition of \cs{@Roman} to avoid
%    the nonexpandable \cn{uppercase} which is undesirable in certain
%    circumstances.
%    \begin{macrocode}
\def\@Roman#1{\@xp\@slowromancap
  \romannumeral#1@}%
%
\def\@slowromancap#1{\ifx @#1% then terminate
  \else
%    \end{macrocode}
%    Note: \cs{if} is required here, not \cs{ifx}, because
%    \cs{romannumeral} returns category 12 letters!
%    \begin{macrocode}
    \if i#1I\else\if v#1V\else\if x#1X\else\if l#1L\else\if
    c#1C\else\if m#1M\else#1\fi\fi\fi\fi\fi\fi
    \@xp\@slowromancap
  \fi
}
%    \end{macrocode}
%
%  \subsection{Book features}
%    Books (monographs) comprise three distinct sections,
%    \cn{frontmatter}, \cn{mainmatter}, and \cn{backmatter}.  The
%    \cn{frontmatter} would consist of the title page, copyright page,
%    table of contents, preface, etc.  The \cn{mainmatter} would
%    be the body of the book.  The \cn{backmatter} would include the
%    appendix, bibliography, glossary, and index.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\frontmatter{\cleardoublepage\pagenumbering{roman}}
\def\mainmatter{\cleardoublepage\pagenumbering{arabic}}
\def\backmatter{%
  \if@openright\cleardoublepage\else\clearpage\fi
  \let\chaptername\relax}
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%    Book proceedings and monographs allow a signature to print at the
%    end of a preface.
%    \begin{macrocode}
%&lt;*!amsart&gt;
\def\aufm#1{\par\vspace*{12pt}{\flushright #1\par}}
%&lt;/!amsart&gt;
%    \end{macrocode}
%
%    Monographs can have a special exercise environment.
%
%    \begin{macrocode}
%&lt;*amsbook&gt;
\newenvironment{xcb}{%
  \setcounter{enumi}{0}%
  \settowidth{\leftmargini}{\labelenumi\hskip\labelsep}%
  \setcounter{enumii}{4}% letter d
  \settowidth{\leftmarginii}{\labelenumii\hskip\labelsep}%
  \@startsection{section}% counter name; ignored because of the
                                % * below
  {1}% sectioning level
  {\z@}% indent to the left of the section title
  {18\p@\@plus2\p@}% vertical space above
  {1sp}% Space below of 13pt base-to-base, so none needs to be added
      % here; but \z@ would cause the following text to be run-in, so we
      % use 1sp instead.
  {\bfseries}% The font of the subsection title
  *% always unnumbered
}{%
  \par
}
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%  \subsection{Book chapters}
%    The \cn{chapter} command is provided only in the \cls{amsbook} class,
%    not in \cls{amsart} or \cls{amsproc}.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\chapter{%
  \if@openright\cleardoublepage\else\clearpage\fi
  \thispagestyle{plain}\global\@topnum\z@
  \@afterindenttrue \secdef\@chapter\@schapter}
%    \end{macrocode}
%    \cs{@chapter} for numbered chapters.
%    \begin{macrocode}
\def\@chapter[#1]#2{\refstepcounter{chapter}%
  \ifnum\c@secnumdepth&lt;\z@ \let\@secnumber\@empty
  \else \let\@secnumber\thechapter \fi
  \typeout{\chaptername\space\@secnumber}%
  \def\@toclevel{0}%
  \ifx\chaptername\appendixname \@tocwriteb\tocappendix{chapter}{#2}%
  \else \@tocwriteb\tocchapter{chapter}{#2}\fi
  \chaptermark{#1}%
  \addtocontents{lof}{\protect\addvspace{10\p@}}%
  \addtocontents{lot}{\protect\addvspace{10\p@}}%
  \@makechapterhead{#2}\@afterheading}
%    \end{macrocode}
%    \cs{@schapter} for unnumbered chapters.
%    \begin{macrocode}
\def\@schapter#1{\typeout{#1}%
  \let\@secnumber\@empty
  \def\@toclevel{0}%
  \ifx\chaptername\appendixname \@tocwriteb\tocappendix{chapter}{#1}%
  \else \@tocwriteb\tocchapter{chapter}{#1}\fi
  \chaptermark{#1}%
  \addtocontents{lof}{\protect\addvspace{10\p@}}%
  \addtocontents{lot}{\protect\addvspace{10\p@}}%
  \@makeschapterhead{#1}\@afterheading}
%    \end{macrocode}
%
%    \begin{macrocode}
\newcommand\chaptername{Chapter}
\newcommand\appendixname{Appendix}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@makechapterhead#1{\global\topskip 7.5pc\relax
  \begingroup
  \fontsize{\@xivpt}{18}\bfseries\centering
%    \end{macrocode}
%    In order to keep the chapter number ``CHAPTER III'' from
%    getting in the way of the \cs{topskip} we put it inside
%    the paragraph containing the main title.  Then we have to
%    do some laborious \cs{rlap}ing and \cs{hskip}ing to
%    position it correctly.
%    \begin{macrocode}
    \ifnum\c@secnumdepth&gt;\m@ne
      \leavevmode \hskip-\leftskip
      \rlap{\vbox to\z@{\vss
          \centerline{\normalsize\mdseries
              \uppercase\@xp{\chaptername}\enspace\thechapter}
          \vskip 3pc}}\hskip\leftskip\fi
     #1\par \endgroup
  \skip@34\p@ \advance\skip@-\normalbaselineskip
  \vskip\skip@ }
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@makeschapterhead#1{\global\topskip 7.5pc\relax
  \begingroup
  \fontsize{\@xivpt}{18}\bfseries\centering
  #1\par \endgroup
  \skip@34\p@ \advance\skip@-\normalbaselineskip
  \vskip\skip@ }
%&lt;/amsbook&gt;
%    \end{macrocode}
%    The \cn{appendix} command, following the \latex/ book, marks the
%    start of a division after \cn{mainmatter} and before
%    \cn{backmatter} that consists of appendixes.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\appendix{\par
  \c@chapter\z@ \c@section\z@
  \let\chaptername\appendixname
  \def\thechapter{\@Alph\c@chapter}}
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%  \subsection{Table of contents macros}
%
%    \cn{tableofcontents} is like \cn{chapter} or \cn{section} except
%    for no number and no table of contents entry.
%
%    \cs{@pnumwidth} is the maximum width for page numbers in a table of
%    contents.  |1.6em| allows enough room for three digits.
%    \begin{macrocode}
\newcommand{\@pnumwidth}{1.6em}
%    \end{macrocode}
%    \cs{@tocrmarg} is \cs{@pnumwidth} plus the desired minimum
%    space (|1em|) between page numbers and the preceding text.
%    \begin{macrocode}
\newcommand{\@tocrmarg}{2.6em}
%&lt;amsart&gt;\setcounter{tocdepth}{2}
%&lt;amsbook|amsproc&gt;\setcounter{tocdepth}{1}
%    \end{macrocode}
%
%    \begin{macrocode}
\newswitch{toc}
\newswitch{lof}
\newswitch{lot}
%    \end{macrocode}
%
%    Since table of contents, list of figures and list of figures
%    are identical in design as far as the chapter heading and other
%    preliminaries go, we redefine \cs{@starttoc} to do the necessary
%    work, rather than defining a new macro (which would use up another
%    control sequence name).
%
%    We define first the article form of \cs{@starttoc}, then the book
%    form.
%
%    Owing to confusion about what font to use for \cn{contentsname}, a
%    symbolic name has been assigned to provide flexibility.
%    \begin{macrocode}
%&lt;*amsart|amsproc&gt;
\newcommand\contentsnamefont{\scshape}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@starttoc#1#2{\begingroup
  \setTrue{#1}%
%    \end{macrocode}
%    Remove the skip after the abstract so that we can substitute another.
%    \begin{macrocode}
  \par\removelastskip\vskip\z@skip
%    \end{macrocode}
%    The first two arguments of \cs{@startsection} here are special values
%    that cause different internal branches to be taken.
%\begin{verbatim}
%    Arguments: {} = name = empty
%    \@M = no number should be used and no table of contents entry
%    \z@ = indent amount
%    12pt + 12pt = vskip before
%    6pt = vskip after
%    \centering\contentsnamefont = format
%\end{verbatim}
%    \begin{macrocode}
  \@startsection{}\@M\z@{\linespacing\@plus\linespacing}%
    {.5\linespacing}{\centering\contentsnamefont}{#2}%
%    \end{macrocode}
%    If we have a list of figures or list of tables we want to put
%    them in the main table of contents, but we don't want to put an
%    entry there for the main table of contents itself. So we check
%    to see if argument 2 is \cn{contentsname} and if it is then
%    we refrain from doing \cn{addcontentsline}.
%    \begin{macrocode}
  \ifx\contentsname#2%
  \else \addcontentsline{toc}{section}{#2}\fi
  \makeatletter
  \@input{\jobname.#1}%
  \if@filesw
    \@xp\newwrite\csname tf@#1\endcsname
    \immediate\@xp\openout\csname tf@#1\endcsname \jobname.#1\relax
  \fi
  \global\@nobreakfalse \endgroup
  \addvspace{32\p@\@plus14\p@}%
  \let\tableofcontents\relax
}
%&lt;/amsart|amsproc&gt;
%    \end{macrocode}
%    And here is the book form of \cs{@starttoc}.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\@starttoc#1#2{%
  \begingroup
  \setTrue{#1}%
%    \end{macrocode}
%    Inside this group we change \cs{secdef} so that we can call
%    \cn{chapter} and only get the preliminary part of its definition
%    that we need.
%    \begin{macrocode}
  \let\secdef\@gobbletwo \chapter
%    \end{macrocode}
%    If we have a list of figures or list of tables we want to put
%    them in the main table of contents, but we don't want to put an
%    entry there for the main table of contents itself. So we check
%    to see if argument 2 is \cn{contentsname} and if it is then
%    we refrain from doing \cn{addcontentsline}.
%    \begin{macrocode}
  \let\@secnumber\@empty % for \@tocwrite and \chaptermark
  \ifx\contentsname#2%
  \else \@tocwrite{chapter}{#2}\fi
%    \end{macrocode}
%    Now we do the equivalent of \cs{@schapter}. Expand \arg{2} so that
%    it will be easy to apply uppercasing to it. (For \cs{@starttoc} we
%    assume that \arg{2} is always a control such as \cn{contentsname}.)
%    \begin{macrocode}
  \typeout{#2}\@xp\chaptermark\@xp{#2}%
  \@makeschapterhead{#2}\@afterheading
%    \end{macrocode}
%    Protect against document classes that have nonzero \cs{parskip}.
%    \begin{macrocode}
  \parskip\z@skip
%    \end{macrocode}
%    And finally we read in the \fn{.toc} (or whatever) file.
%    \begin{macrocode}
  \makeatletter
  \@input{\jobname.#1}%
  \if@filesw
    \@xp\newwrite\csname tf@#1\endcsname
    \immediate\@xp\openout\csname tf@#1\endcsname \jobname.#1\relax
  \fi
  \global\@nobreakfalse \endgroup
  \newpage
}
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%    Now it is easy to define \cn{tableofcontents} and its relatives.
%    \begin{macrocode}
\def\contentsname{Contents}
\def\listfigurename{List of Figures}
\def\listtablename{List of Tables}
\def\tableofcontents{%
  \@starttoc{toc}\contentsname
}
\def\listoffigures{\@starttoc{lof}\listfigurename}
\def\listoftables{\@starttoc{lot}\listtablename}
%    \end{macrocode}
%
%    In order to automatically leave enough space for the `number' part
%    of toc entries, we compute the maximum width of the `number' part
%    for each sectioning level and pass that information to
%    \cs{@tocline} through the \fn{.aux} file.
%
%    Init the tocindents if they are not yet set (first run).
%    \begin{macrocode}
\AtBeginDocument{%
  \@for\@tempa:=-1,0,1,2,3\do{%
    \@ifundefined{r@tocindent\@tempa}{%
      \@xp\gdef\csname r@tocindent\@tempa\endcsname{0pt}}{}%
  }%
}
%    \end{macrocode}
%
%  \begin{macro}{\@writetocindents}
%    This function writes out the max toc indents to the aux file.
%    \begin{macrocode}
\def\@writetocindents{%
  \begingroup
  \@for\@tempa:=-1,0,1,2,3\do{%
    \immediate\write\@auxout{%
      \string\newlabel{tocindent\@tempa}{%
        \csname r@tocindent\@tempa\endcsname}}%
  }%
  \endgroup}
%
\AtEndDocument{\@writetocindents}
%    \end{macrocode}
%  \end{macro}
%

%  \begin{macro}{\indentlabel}
%    This function is a no-op except in \cs{@tocwrite} where it is a
%    pointer to \cs{@tochangmeasure}.
%    \begin{macrocode}
\let\indentlabel\@empty
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\@tochangmeasure}
%    This function measures the hangindent part of a toc entry and
%    updates the current max for the given sectioning level, if
%    necessary. The max's at the end of the document will be written
%    in the form of a pseudo-label to the \fn{.aux} file by
%    \cs{@writetocindents}.
%
%    We can assume that \cs{@tochangmeasure} is already inside a group
%    when called.
%    \begin{macrocode}
\def\@tochangmeasure#1{\sbox\z@{#1}%
  \ifdim\wd\z@&gt;\csname r@tocindent\@toclevel\endcsname\relax
    \@xp\xdef\csname r@tocindent\@toclevel\endcsname{\the\wd\z@}%
  \fi
}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\@toclevel}
%    Initialize, for the record.
%    \begin{macrocode}
\def\@toclevel{0}
%    \end{macrocode}
%  \end{macro}
%
%    Since we don't have leader dots, we have \cs{@tocline} instead of
%    \cs{@dottedtocline}.
%    \begin{macrocode}
\def\@tocline#1#2#3#4#5#6#7{\relax
  \ifnum #1&gt;\c@tocdepth % then omit
  \else
    \par \addpenalty\@secpenalty\addvspace{#2}%
    \begingroup \hyphenpenalty\@M
    \@ifempty{#4}{%
      \@tempdima\csname r@tocindent\number#1\endcsname\relax
    }{%
      \@tempdima#4\relax
    }%
    \parindent\z@ \leftskip#3\relax \advance\leftskip\@tempdima\relax
    \rightskip\@pnumwidth plus4em \parfillskip-\@pnumwidth
    #5\leavevmode\hskip-\@tempdima #6\nobreak\relax
    \hfil\hbox to\@pnumwidth{\@tocpagenum{#7}}\par
    \nobreak
    \endgroup
  \fi}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@tocpagenum#1{\hss{\mdseries #1}}
%    \end{macrocode}
%
%    The function \cs{@tocwrite} writes the information of a section
%    heading to the \fn{.toc} file in a standard form. It allows
%    different functions to be substituted for \cs{numberline}, to get
%    greater control of toc formatting.
%    \begin{macrocode}
\def\@tocwrite#1{\@xp\@tocwriteb\csname toc#1\endcsname{#1}}
%    \end{macrocode}
%    The \cn{chapter} command uses \cs{@tocwriteb} directly because of
%    the need to write slightly different things to the toc file
%    depending on the current value of \cn{chaptername}.
%    \begin{macrocode}
\def\@tocwriteb#1#2#3{%
  \begingroup
    \def\@tocline##1##2##3##4##5##6{%
      \ifnum##1&gt;\c@tocdepth
      \else \sbox\z@{##5\let\indentlabel\@tochangmeasure##6}\fi}%
    \csname l@#2\endcsname{#1{\csname#2name\endcsname}{\@secnumber}{}}%
  \endgroup
  \addcontentsline{toc}{#2}%
    {\protect#1{\csname#2name\endcsname}{\@secnumber}{#3}}}
%    \end{macrocode}
%
%    Specs for monograph toc are as follows (tocdepth is 1, i.e.,
%    subsections and lower are not listed in toc).
%\begin{verbatim}
% Part: Space above 12pt plus2pt, indent 0pt, "Part" + wordspace +
% number + "." + 1em + title (raggedright, no hangindent) + 1em +
% page number in column 1.6em wide.
%
% Chapter: Space above 8pt, hangindent on ("Chapter 0" + "." + 1em),
% + title (raggedright) + 1em + page number in column 1.6em wide.
%
% Appendix: Same as Chapter except for epithet "Appendix M"
%
% Section: Space above 0pt, hangindent on (1pc + "0.0" + "." + 1em),
% + title (raggedright) + 1em + page number in column 1.6em wide.
%\end{verbatim}
%
%    Specs for article toc are as follows (tocdepth 2):
%\begin{verbatim}
% Section: Same as for monograph.
%
% Subsection: Space above 0pt, hangindent 6pc (number + "." + 1em),
% + title (raggedright) + 1em + page number in column 1.6em wide.
%
% Subsubsection: Same as subsection but hangindent 8pc
%\end{verbatim}
%
%    Typical invocation of \cs{l@chapter}:
%\begin{verbatim}
% \contentsline{chapter}{%
%   \tocchapter{Chapter}{3}{Some title stuff}}{103}
% --&gt;\l@chapter--&gt;
%           #1 #2   #3  #4 #5
% \@tocline{0}{8pt}{0pt}{}{\bfseries}
%    #6           6a      6b 6c                 #7
%   {\tocchapter{Chapter}{3}{Some title stuff}}{103}
%\end{verbatim}%
%    The \cs{tocchapter} is a slightly more useful form than
%    \cs{numberline} that allows control for optionally omitting strings
%    like `Chapter' or changing fonts for subcomponents of the toc
%    entry. Note that it is allowed to have appendix and chapter at the
%    same toc level, with \cs{tocappendix} instead of \cs{tocchapter}
%    written in the \fn{.toc} file.
%
%    The arguments of \cs{@tocline} are as follows:
%\begin{verbatim}
% \@tocline{LEVEL}{VSPACE}{INDENT}{NUMBERWIDTH}{EXTRA}%
%   {TEXT}{PAGENUM}
%\end{verbatim}%
%    where `numberwidth' is the width of the box allotted to contain the
%    section number, including any preceding word like `Chapter' or
%    `Part'. If this width arg is empty then an automatically computed
%    width (max over TOC of the numberwidths for this level) is used.
%    The `extra' argument is formatting such as font changes.
%    The `text' argument contains a section-command specific function
%    like \cs{tocsection} or \cs{tocchapter} which takes in turn three
%    arguments: epithet, number, topic.
%    \begin{macrocode}
\def\l@section{\@tocline{1}{0pt}{1pc}{}{}}
%    \end{macrocode}
%    *** The indents do not agree between in-house and distributed ***\\
%    *** versions; no changes; get specs before revising.          ***\\
%    The use of \cn{ignorespaces} in \cs{tocsection} and its relatives
%    means that if \arg{1} is empty, the following space will be also
%    removed.
%    \begin{macrocode}
\newcommand{\tocsection}[3]{%
  \indentlabel{\@ifnotempty{#2}{\ignorespaces#1 #2.\quad}}#3}
\def\l@subsection{\@tocline{2}{0pt}{1pc}{5pc}{}}
\let\tocsubsection\tocsection
\def\l@subsubsection{\@tocline{3}{0pt}{1pc}{7pc}{}}
\let\tocsubsubsection\tocsection
\let\l@paragraph\l@subsubsection
\let\tocparagraph\tocsection
\let\l@subparagraph\l@subsubsection
\let\tocsubparagraph\tocsection
%
\def\l@part{\@tocline{-1}{12pt plus2pt}{0pt}{}{\bfseries}}
\let\tocpart\tocsection
\def\l@chapter{\@tocline{0}{8pt plus1pt}{0pt}{}{}}
\let\tocchapter\tocsection
%    \end{macrocode}
%    In this case we are pretty sure the word "Appendix" or similar is
%    present, so only check if arg 2 is empty:
%    \begin{macrocode}
\newcommand{\tocappendix}[3]{%
  \indentlabel{#1\@ifnotempty{#2}{ #2}.\quad}#3}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\l@figure{\@tocline{0}{3pt plus2pt}{0pt}{1.5pc}{}}
\let\l@table=\l@figure
%    \end{macrocode}
%
%  \subsection{Bibliography section or chapter}
%
%    Following the \pkg{babel} package, we use \cn{refname} in articles
%    and \cn{bibname} in books.
%    \begin{macrocode}
\def\refname{References}
\def\bibname{Bibliography}
%    \end{macrocode}
%
%    Restudy the following code; \cs{bibsetup} isn't used anywhere
%    although it's defined for the three different bibstyles.
%    Because some publications have different default label styles,
%    separate that out for easy tailoring of packages.
%    \begin{macrocode}
\def\@defaultbiblabelstyle#1{#1.}
\def\bibliographystyle#1{%
    \if@filesw\immediate\write\@auxout{\string\bibstyle{#1}}\fi
    \def\@tempa{#1}%
    \def\@tempb{amsplain}%
    \def\@tempc{}%
    \ifx\@tempa\@tempb
        \def\@biblabel##1{\@defaultbiblabelstyle{##1}}%
        \def\bibsetup{}%
    \else
        \def\bibsetup{\labelsep6\p@}%
        \ifx\@tempa\@tempc
            \def\@biblabel##1{}%
            \def\bibsetup{\labelwidth\z@ \leftmargin24\p@
                \itemindent-\leftmargin
                \labelsep\z@ }%
        \fi
    \fi}
%    \end{macrocode}
%
%    Permit easy change of font size for unusual purpose, e.g., for
%    an author's ``life list'' in collected works.  [bnb, 2004/04/01]
%    \begin{macrocode}
\newcommand{\bibliofont}{\footnotesize}
%    \end{macrocode}
%
%    \env{thebibliography} differs in some author packages only in the
%    shape of the title; make this easy to change.  [bnb, 2004/05/22]
%    \begin{macrocode}
\newcommand{\@bibtitlestyle}{%
%&lt;amsart|amsproc&gt;  \@xp\section\@xp*\@xp{\refname}%
%&lt;amsbook&gt;  \@xp\chapter\@xp*\@xp{\bibname}%
}
\newenvironment{thebibliography}[1]{%
  \@bibtitlestyle
  \normalfont\bibliofont\labelsep .5em\relax
  \renewcommand\theenumiv{\arabic{enumiv}}\let\p@enumiv\@empty
  \list{\@biblabel{\theenumiv}}{\settowidth\labelwidth{\@biblabel{#1}}%
    \leftmargin\labelwidth \advance\leftmargin\labelsep
    \usecounter{enumiv}}%
  \sloppy \clubpenalty\@M \widowpenalty\clubpenalty
  \sfcode`\.=\@m
}{%
%    \end{macrocode}
%    Change error for empty list (no items) to warning, to allow authors
%    to leave their bibliography temporarily empty during writing:
%    \begin{macrocode}
  \def\@noitemerr{\@latex@warning{Empty `thebibliography' environment}}%
  \endlist
}
%    \end{macrocode}
%
%    The \cn{bysame} command prints a horizontal dash indicating
%    repetition of the author's name in consecutive bibliography
%    entries.
%    \begin{macrocode}
\def\bysame{\leavevmode\hbox to3em{\hrulefill}\thinspace}
%    \end{macrocode}
%    We define \cn{newblock} even though it's not needed for AMS
%    publication style, just to avoid error messages when a non-AMS
%    \fn{.bst} file is used. This is a convenience for users; use of
%    \cn{newblock} is not recommended for submissions to the AMS.
%    \begin{macrocode}
\def\newblock{}
%    \end{macrocode}
%
%  \begin{macro}{\MR}
%  \begin{macro}{\MRhref}
%    Provide an MR number for a bibliography item. At the moment
%    [mjd,1995/08/07] this only prints the MR number, but later
%    we expect to extend it to write an HTML \cs{special} to the
%    \fn{.dvi} file.
%
%    The presentation of the MR number has been simplified (from using
%    a bold volume number) coincident with the change in the MathSciNet
%    database to a 7-digit reference number from the volume:number form.
%
%    Ensure that an old-style MR number does not break across lines if
%    it contains a space; editorial request.  [bnb; 2004/04/01]
%    Countermanded, to permit break between reference number and an
%    old-style number following in parentheses.  [bnb; 2004/06/11]
%    \begin{macrocode}
\newcommand\MR[1]{\relax\ifhmode\unskip\spacefactor3000 \space\fi
  MR~\MRhref{#1}{#1}}
%    \end{macrocode}
%
%    \begin{macrocode}
\let\MRhref\@gobble
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%
%  \begin{macro}{\URL}
%  \begin{macro}{\URLhref}
%  \begin{macro}{\@URL}
%    Allows sticking in an arbitrary URL in a bibliography. Leading
%    ``http'' is not assumed. Call \cn{verb} to ensure that special
%    characters in the URL don't cause trouble.
%    \begin{macrocode}
\newcommand\URL{\begingroup
  \def\@sverb##1{%
    \def\@tempa####1##1{\@URL{####1}\egroup\endgroup}%
    \@tempa}%
  \verb}
%    \end{macrocode}
%
%    \begin{macrocode}
\let\URLhref\@gobble
\def\@URL#1{\URLhref{#1}#1}
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%  \end{macro}
%
%  \subsection{Index section or chapter}
%
%    Chapter or section heading for an index. Index is set up to be two
%    columns.
%    \begin{macrocode}
\newif\if@restonecol
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\indexchap#1{\global\topskip 7.5pc\relax
  \twocolumn[{\fontsize{\@xivpt}{18}\bfseries\centering
    \vskip\topskip\hbox{}\vskip-\baselineskip% adjust top space
    #1\par
%    \end{macrocode}
%    After \cs{twocolumn} finishes operating, the top material is left in an
%    insert register, and topskip will now be applied above the
%    following material. So we should set it to the normal
%    after-chapter-title space (34pt)---cf.~\cs{@makeschapterhead}.
%    \begin{macrocode}
   \global\topskip 34\p@\relax
   \ifx\@empty\indexintro
   \else
     \begingroup \normalsize
       \skip@\topskip \advance\skip@ -\baselineskip
       \vskip\skip@
       \parbox[t]{24pc}{\normalfont\indexintro\par}%
     \endgroup
     \global\topskip 24\p@\relax
   \fi
  }]%
}
\newcommand{\indexintro}{}
%&lt;/amsbook&gt;
%    \end{macrocode}
%
%    \env{theindex} differs in some author packages only in the
%    shape of the title; make this easy to change.  [bnb, 2004/05/22]
%    \begin{macrocode}
\newcommand{\@indextitlestyle}{%
%&lt;*amsbook&gt;
  \let\@makeschapterhead\indexchap
  \@xp\chapter\@xp*\@xp{\indexname}%
%&lt;/amsbook&gt;
%&lt;amsart|amsproc&gt;  \twocolumn[\@xp\section\@xp*\@xp{\indexname}]%
}
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
  \columnseprule\z@ \columnsep 35\p@
  \@indextitlestyle
  \thispagestyle{plain}%
  \let\item\@idxitem
  \parindent\z@  \parskip\z@\@plus.3\p@\relax
  \raggedright
  \hyphenpenalty\@M
  \footnotesize}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\indexname{Index}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@idxitem{\par\hangindent 2em}
\def\subitem{\par\hangindent 2em\hspace*{1em}}
\def\subsubitem{\par\hangindent 3em\hspace*{2em}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par\bigskip}
%    \end{macrocode}
%
%  \subsection{Footnotes}
%    In books the footnote counter should reset to 0 at the beginning of
%    each chapter:
%    \begin{macrocode}
%&lt;amsbook&gt;\@addtoreset{footnote}{chapter}
%    \end{macrocode}
%
%    Rule above footnotes is 5 picas wide.
%    \begin{macrocode}
\def\footnoterule{\kern-.4\p@
        \hrule\@width 5pc\kern11\p@\kern-\footnotesep}
%    \end{macrocode}
%
%    A simple superscript doesn't work here; it fails on a minipage,
%    where \cs{itshape} (which is invalid in math mode) is used for the
%    footnote numbers. Cf.~ the definition of \cn{textprime}.
%    \begin{macrocode}
\def\@makefnmark{%
  \leavevmode
  \raise.9ex\hbox{\fontsize\sf@size\z@\normalfont\@thefnmark}%
}
%
\def\@makefntext{\indent\@makefnmark}
%    \end{macrocode}
%    Add \cn{normalfont} before \cn{footnotesize} so that
%    fonts will come out properly using the new font selection scheme.
%    \begin{macrocode}
\long\def\@footnotetext#1{%
  \insert\footins{%
    \normalfont\footnotesize
    \interlinepenalty\interfootnotelinepenalty
    \splittopskip\footnotesep \splitmaxdepth \dp\strutbox
    \floatingpenalty\@MM \hsize\columnwidth
%    \end{macrocode}
%    Mostly \cs{@parboxrestore} does what we want; but not with
%    respect to \cs{parindent} and \cs{tolerance}.
%    \begin{macrocode}
    \@parboxrestore \parindent\normalparindent \sloppy
    \protected@edef\@currentlabel{%
      \csname p@footnote\endcsname\@thefnmark}%
    \@makefntext{%
      \rule\z@\footnotesep\ignorespaces#1\unskip\strut\par}}}
%    \end{macrocode}
%    We change \cn{sloppy} to keep it from overriding our normal value of
%    1pt for \cs{hfuzz} and \cs{vfuzz} with a LESS sloppy value (.5pt).
%    \begin{macrocode}
\hfuzz=1pt \vfuzz=\hfuzz
\def\sloppy{\tolerance9999 \emergencystretch 3em\relax}
%    \end{macrocode}
%
%  \subsection{Float placement parameters}
%    These control the placing of floating objects like tables and
%    figures. We use much more tolerant values than the \latex/ defaults;
%    the \latex/ defaults are geared to fussier page breaks, at a price of
%    requiring more manual intervention to deal with difficult page
%    breaking problems.
%
%    When using \latex/'s twocolumn option, `page' really means `column',
%    for the parameters that don't have a dbl prefix: that is, topnumber
%    is then the maximum number of top figures allowed in each column,
%    and so forth.
% \begin{description}
% \item[topnumber] maximum number of top figures allowed per page
% \item[bottomnumber] maximum number of bottom figures allowed per page
% \item[totalnumber] maximum number of figures (top and bottom) allowed
%    per page
% \item[dbltopnumber] same as topnumber, but for two-column wide
%    figures, when double-column format is used
% \end{description}
%    \begin{macrocode}
\setcounter{topnumber}{4}
\setcounter{bottomnumber}{4}
\setcounter{totalnumber}{4}
\setcounter{dbltopnumber}{4}
%    \end{macrocode}
%    Float fraction parameters.
% \begin{description}
% \item[\cs{topfraction}] maximum part of the page allowed for top
%    figures, expressed as a decimal fraction. The value of .97 means
%    roughly `accept pages that have only two lines of text, and the
%    rest figures'.
% \item[\cs{bottomfraction}] same as \cs{topfraction}, but for bottom
%    figures
% \item[\cs{textfraction}] \emph{minimum} part of the page that must be
%    occupied by text, if the page is to have any text at all. If this
%    value cannot be achieved, \latex/ will turn the current figure or
%    figures into a ``float page'', i.e., a page of figures without any
%    text.
% \item[\cs{floatpagefraction}] minimum amount (that is, total combined
%    height) of figures needed before \latex/ will make a float page. This
%    is expressed as a fraction of the normal page height.
% \item[\cs{dbltopfraction}] like \cs{topfraction}, but applies only to
%    figures that are two columns wide, when double-column format is
%    used.
% \item[\cs{dblfloatpagefraction}] minimum amount of double-column
%    figure material needed before \latex/ will make a two-column wide
%    ``float page''
% \end{description}
%    \begin{macrocode}
\renewcommand{\topfraction}{.97}
\renewcommand{\bottomfraction}{.97}
\renewcommand{\textfraction}{.03}
\renewcommand{\floatpagefraction}{.9}
\renewcommand{\dbltopfraction}{.97}
\renewcommand{\dblfloatpagefraction}{.9}
%    \end{macrocode}
%
%    We also modify the default values for spacing around floating
%    figures: (A) so that figures on a float page will not be
%    vertically centered on the total page height but will
%    be flush at the top of the page, and (B) so that there will
%    be slightly more stretchability around figures, to help find better
%    page breaks in difficult situations.
%
% \begin{description}
% \item[\cs{floatsep}] Space between consecutive figures
% \item[\cs{textfloatsep}] Space between text and top or bottom figures
% \item[\cs{intextsep}] Space above and below a figure in the middle of
%    the text (i.e., placed with the |[h]| option)
% \item[\cs{dblfloatsep}] Space between consecutive figures that are
%    two columns wide (when two-column format is used)
% \item[\cs{dbltextfloatsep}] Space between double-column figures and text
% \item[\cs{@fptop}] Space above the first figure on a float page
% \item[\cs{@fpsep}] Space between figures on a float page
% \item[\cs{@fpbot}] Space below the last figure on a float page
% \item[\cs{@dblfptop}] Space above the first double-column figure on a
%    two-column wide float page
% \item[\cs{@dblfptop}] Space between double-column figures on a  two-column
%    wide float page
% \item[\cs{@dblfptop}] Space below the last double-column figure on a
%    two-column wide float page
% \end{description}
%    \begin{macrocode}
\setlength{\floatsep}{12pt plus 6pt minus 4pt}
\setlength{\textfloatsep}{15pt plus 8pt minus 5pt}
\setlength{\intextsep}{12pt plus 6pt minus 4pt}
\setlength{\dblfloatsep}{12pt plus 6pt minus 4pt}
\setlength{\dbltextfloatsep}{15pt plus 8pt minus 5pt}
\setlength{\@fptop}{0pt}% removed "plus 1fil"
\setlength{\@fpsep}{8pt}% removed "plus 2fil"
\setlength{\@fpbot}{0pt plus 1fil}
\setlength{\@dblfptop}{0pt}% removed "plus 1fil"
\setlength{\@dblfpsep}{8pt}% removed "plus 2fil"
\setlength{\@dblfpbot}{0pt plus 1fil}
%    \end{macrocode}
%
%    \cs{fps@figure}, \cs{fps@table}: placement specifications for
%    \env{figure} and \env{table} environments. `|tbp|' means that a
%    figure will be placed at the top or bottom of a page, or on a
%    separate page with no text. This might be changed to `|tp|', for
%    example, if you never want figures to appear at the bottom of a
%    page.
%    \begin{macrocode}
\newcommand{\fps@figure}{tbp}
\newcommand{\fps@table}{tbp}
%    \end{macrocode}
%
%    Some more setup for figures.
%    \begin{macrocode}
%&lt;amsart|amsproc&gt;\newcounter{figure}
%&lt;amsbook&gt;\newcounter{figure}[chapter]
\def\@captionheadfont{\scshape}
\def\@captionfont{\normalfont}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename\ \thefigure}
\def\figurename{Figure}
\newenvironment{figure}{%
  \@float{figure}%
}{%
  \end@float
}
\newenvironment{figure*}{%
  \@dblfloat{figure}%
}{%
  \end@dblfloat
}
%    \end{macrocode}
%    And similar for tables.
%    \begin{macrocode}
%&lt;amsart|amsproc&gt;\newcounter{table}
%&lt;amsbook&gt;\newcounter{table}[chapter]
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename\ \thetable}
\def\tablename{Table}
\newenvironment{table}{%
  \@float{table}%
}{%
  \end@float
}
\newenvironment{table*}{%
  \@dblfloat{table}%
}{%
  \end@dblfloat
}
%    \end{macrocode}
%
%    Change \cs{@floatboxreset} to add \cn{centering}. Centering is
%    always applied to tables and figures in AMS publications. It should
%    not be necessary to throw in |\begin{center}| \ldots |\end{center}|
%    in every instance to achieve this.
%    \begin{macrocode}
\def\@floatboxreset{\global\@minipagefalse \centering}
%    \end{macrocode}
%
%    This is what we want \cs{@makecaption} to do: If the total width is
%    greater than normal columnwidth we want to break the caption into
%    lines using a line width of $W$ = (columnwidth $-$ 6pc), and center
%    the resulting block between the margins. Otherwise we want to set
%    the caption as a single line, centered between the margins.
%
%    To do this we set the caption as a vbox with line width $W$,
%    except that we allow the last line (which may be the only line) to
%    have width up to full columnwidth by adding a kern of -6pc. If the
%    result is a single hbox (i.e., a single line) we need to unpack the
%    hbox, remove rightskip, parfillskip, and the -6pc kern, and center
%    the remaining material. If the caption is more than one line, then
%    box 1 contains the last line, which we need to unpack in the same
%    way, and run through the paragraphing process again (because this
%    last line may be up to 6 picas wider than the desired width).
%
%    In practice this procedure tends to fail if there are any potential
%    breakpoints near the end of the first line (in the window between
%    short-width and full-width). Then \TeX{} tends to choose a break
%    (depending on spaceskip, tolerance, etc) at the last acceptable
%    breakpoint before short-width is exceeded, \emph{without
%    considering any later material}---in particular, the negative kern.
%    [This was pointed out by Donald Arseneau, May 2000.] Unfortunately,
%    setting parfillskip to a negative value does not work either. I
%    guess this is a special case of the existing limitation on
%    parshape: you cannot specify a parshape in terms of number of lines
%    from the bottom of the paragraph. (We would like to specify a
%    parshape where the last line is 6 picas longer than the others.)
%
%    Finally, if the caption is for a figure, it will be set below the
%    figure, so the separating space goes above the caption;  otherwise
%    the separating space goes below the caption.
%    \begin{macrocode}
\long\def\@makecaption#1#2{%
%    \end{macrocode}
%    Measure the contents of the caption.  If \arg{2} is not
%    empty, then we must add a period and an en-space before
%    typesetting it.  The \cs{@caption} macro adds an extra
%    \cn{ignorespaces} at the beginning of \arg{2}, so in order
%    to find out if the user-typed portion is empty we use
%    \cs{@cdr} to pull off the \cn{ignorespaces}.
%    \begin{macrocode}
%    Use color-safe commands
  \setbox\@tempboxa\vbox{\color@setgroup
    \advance\hsize-2\captionindent\noindent
    \@captionfont\@captionheadfont#1\@xp\@ifnotempty\@xp
        {\@cdr#2\@nil}{.\@captionfont\upshape\enspace#2}%
    \unskip\kern-2\captionindent\par
    \global\setbox\@ne\lastbox\color@endgroup}%
  \ifhbox\@ne % the normal case
    \setbox\@ne\hbox{\unhbox\@ne\unskip\unskip\unpenalty\unkern}%
  \fi
%    \end{macrocode}
%    If \cs{@tempboxa} is not empty at this point then the caption was
%    more than one line long or there was extra vertical mode material,
%    maybe a \cs{write} (from \cn{index} or something).
%    Interestingly, we can't use \cs{ifvoid} to see if
%    \cs{@tempboxa} is empty, because empty is not the same thing
%    as void (as far as the \cs{ifvoid} test is concerned).  So
%    instead we measure the width of \cs{@tempboxa}
%    to see if it's zero; this should suffice for non-bizarre cases.
%    \begin{macrocode}
  \ifdim\wd\@tempboxa=\z@ % this means caption will fit on one line
    \setbox\@ne\hbox to\columnwidth{\hss\kern-2\captionindent\box\@ne\hss}%
  \else % tempboxa contained more than one line
    \setbox\@ne\vbox{\unvbox\@tempboxa\parskip\z@skip
        \noindent\unhbox\@ne\advance\hsize-2\captionindent\par}%
  \fi
  \ifnum\@tempcnta&lt;64 % if the float IS a figure...
    \addvspace\abovecaptionskip
    \hbox to\hsize{\kern\captionindent\box\@ne\hss}%
  \else % if the float IS NOT a figure...
    \hbox to\hsize{\kern\captionindent\box\@ne\hss}%
    \nobreak
    \vskip\belowcaptionskip
  \fi
\relax
}
%    \end{macrocode}
%    Allocate the skip registers for above and below caption space.
%    \begin{macrocode}
\newskip\abovecaptionskip \abovecaptionskip=12pt \relax
\newskip\belowcaptionskip \belowcaptionskip=12pt \relax
\newdimen\captionindent \captionindent=3pc
%    \end{macrocode}
%
%  \subsection{Miscellaneous}
%
%  \begin{macro}{\nonbreakingspace}
%    Change \qc{\~} to be more forgiving of accidental adjacent spaces.
%    Note that this means multiple |~~~...| cannot be used to get
%    multiple spaces in the output.
%    \begin{macrocode}
\def\nonbreakingspace{\unskip\nobreak\ \ignorespaces}
\def~{\protect\nonbreakingspace}
%    \end{macrocode}
%  \end{macro}
%
%    Redefine \cs{@biblabel} to do nothing if the argument is empty. We
%    don't really care what the previous definition was so we don't
%    check it.
%    \begin{macrocode}
\def\@biblabel#1{\@ifnotempty{#1}{[#1]}}
%    \end{macrocode}
%    Changed \cs{@cite} to always use roman/upright, nonbold font, even
%    in italic or bold text (following AMS style).
%    Turn off \cs{mathsurround} just in case there are subscripts in the
%    cite numbers.
%    \begin{macrocode}
\def\@citestyle{\m@th\upshape\mdseries}
%&lt;amsart&gt;\let\citeform\@firstofone
%&lt;amsbook|amsproc&gt;\def\citeform#1{{\bfseries#1}}
\def\@cite#1#2{{%
  \@citestyle[\citeform{#1}\if@tempswa, #2\fi]}}
%    \end{macrocode}
%
%    Make \cn{cite} robust if it isn't already. Too many unsuspecting
%    users get problems from this in a figure or table caption.
%    \begin{macrocode}
\@ifundefined{cite }{%
  \expandafter\let\csname cite \endcsname\cite
  \edef\cite{\@nx\protect\@xp\@nx\csname cite \endcsname}%
}{}
%    \end{macrocode}
%
%  \begin{macro}{\fullwidthdisplay}
%    The function \cs{fullwidthdisplay} makes a displayed equation take
%    up the full column width even if the current context is an indented
%    list.
%    \begin{macrocode}
\def\fullwidthdisplay{\displayindent\z@ \displaywidth\columnwidth}
%    \end{macrocode}
%    And we insert the \cs{fullwidthdisplay} function at the beginning of
%    \cs{everydisplay} just in case any later code in \cs{everydisplay}
%    needs to use the values of \cs{displayindent} or \cs{displaywidth}.
%    \begin{macrocode}
\edef\@tempa{\noexpand\fullwidthdisplay\the\everydisplay}
\everydisplay\expandafter{\@tempa}
%    \end{macrocode}
%  \end{macro}
%
%    A few odds and ends for indexes, based on \pkg{makeindex}.  The
%    definition of \cn{see} as ``see also'' is unfortunate, but of
%    long standing, and cannot be changed without destroying backward
%    compatibility, so an alternate command, \cn{seeonly}, is provided
%    to cover the basic situation.
%    \begin{macrocode}
\newcommand*\seeonlyname{see}
\newcommand*\seename{see also}
\newcommand*\alsoname{see also}
\newcommand*\seeonly[2]{\emph{\seeonlyname} #1}
\newcommand*\see[2]{\emph{\seename} #1}
\newcommand*\seealso[2]{\emph{\alsoname} #1}
\newcommand\printindex{\@input{\jobname.ind}}
%    \end{macrocode}
%
%  \begin{macro}{\textprime}
%    A text prime symbol, for applying primes to numbers such as list
%    numbers or equation numbers that are not really math. Furthermore
%    Cyrillic myagkii znak, or soft sign, is represented by a prime
%    symbol in Russian names when they are transliterated into English.
%
%    \cn{textprime} uses the prime symbol from math, but because it's
%    intended specifically for nonmath use, we avoid going through math
%    mode with \verb'$...$'. We must therefore call \cs{check@mathfonts}
%    to ensure that \verb'scriptfont2' is actually defined. Otherwise,
%    if \cn{textprime} were used in a document before the first math
%    formula, there would be no adequate assignment yet for
%    \verb'\scriptfont2'.
%
%    The raise value of \verb'.8ex' is just a reasonable guess at making
%    the bottom of the prime symbol fall near the top of a preceding
%    lowercase letter but still not fall too low on an uppercase letter.
%    We could look up the \cs{fontdimen} values used in math mode for
%    superscripts but I don't think it's worth the bother.
%
%    Cf.~also the definition of \cs{@makefnmark}. The prime symbol here
%    is not raised quite so high because I think that is desirable for
%    the soft-sign usage.
%    \begin{macrocode}
\DeclareRobustCommand\textprime{\leavevmode
  \raise.8ex\hbox{\check@mathfonts\the\scriptfont2 \char48 }}
%    \end{macrocode}
%  \end{macro}
%
%  \subsection{Book style variations}
%    Here is the layout for a \cn{maketitle} in the \cls{amsbook} class.
%    \begin{macrocode}
%&lt;*amsbook&gt;
\def\maketitle{\par
  \@topnum\z@ % this prevents figures from falling at the top of page 1
  \begingroup
  \@maketitle
  \endgroup
  \c@footnote\z@
  \def\do##1{\let##1\relax}%
  \do\maketitle \do\@maketitle \do\title \do\@xtitle \do\@title
  \do\author \do\@xauthor \do\address \do\@xaddress
  \do\email \do\@xemail \do\curraddr \do\@xcurraddr
  \do\dedicatory \do\@dedicatory \do\thanks \do\thankses
  \do\keywords \do\@keywords \do\subjclass \do\@subjclass
}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\@maketitle{%
  \cleardoublepage \thispagestyle{empty}%
  \begingroup \topskip\z@skip
  \null\vfil
  \begingroup
  \LARGE\bfseries \centering
  \openup\medskipamount
  \@title\par\vspace{24pt}%
  \def\and{\par\medskip}\centering
  \mdseries\authors\par\bigskip
  \endgroup
  \vfil
  \ifx\@empty\addresses \else \@setaddresses \fi
  \vfil
  \ifx\@empty\@dedicatory
  \else \begingroup
    \centering{\footnotesize\itshape\@dedicatory\@@par}%
    \endgroup
  \fi
  \vfill
  \newpage\thispagestyle{empty}
  \begin{center}
    \ifx\@empty\@subjclass\else\@setsubjclass\fi
    \ifx\@empty\@keywords\else\@setkeywords\fi
    \ifx\@empty\@translators\else\vfil\@settranslators\fi
    \ifx\@empty\thankses\else\vfil\@setthanks\fi
  \end{center}
  \vfil
  \@setabstract
  \endgroup}
%    \end{macrocode}
%
%    Define the desired form for translator names.
%    \begin{macrocode}
\def\@settranslators{\par
  \begingroup
  \translname: \andify\@translators \uppercasenonmath\@translators
  \@translators \@@par
  \endgroup}
\def\@setdate{\par\smallskip\@date\par\smallskip}
\def\@setsubjclass{\par\smallskip
  {\itshape\subjclassname.}\enspace\@subjclass\par\smallskip}
\def\@setkeywords{\par\smallskip
  {\itshape \keywordsname.}\enspace \@keywords\par\smallskip}
%&lt;/amsbook&gt;
%&lt;/classes&gt;
%    \end{macrocode}
%
%  \subsection{Setup for theorems, definitions, remarks, proofs}
%  \subsubsection{Intended usage}
%
%    Here are some examples showing the kinds of theorem environment
%    declarations that are possible.
%\begin{verbatim}
% \newtheorem{prop}{Proposition}
% \newtheorem{thm}{Theorem}[section]
% \newtheorem{lem}[thm]{Lemma}
% \newtheorem*{Zorn}{Zorn's Lemma}
%
% \theoremstyle{definition}
% \newtheorem{dfn}{Definition}
%
% \theoremstyle{remark}
% \newtheorem*{rmk}{Remark}
%\end{verbatim}
%
%    The first four statements all define environments using the default
%    theorem style (`plain'), since there is no prefatory
%    \cn{theoremstyle} declaration. The first statement defines an
%    automatically numbered \env{prop} environment whose headings will
%    look like this: Proposition 1, Proposition 2, and so forth. The
%    second statement defines an environment \env{thm} with numbers
%    subordinate to section numbers, so the headings will look like
%    this: Theorem 1.1, Theorem 1.2, Theorem 1.3, \dots, (in section 2:)
%    Theorem 2.1, Theorem 2.2, and so forth. The third statement defines
%    a \env{lem} environment whose numbers will interleave in sequence
%    with the theorem numbers: Theorem 1.3, Lemma 1.4, Lemma 1.5,
%    Theorem 1.6, and so forth. The fourth statement defines a special
%    unnumbered lemma named `Zorn's Lemma'. The remaining two
%    \cn{newtheorem} statements have no special features except for the
%    \cn{theoremstyle} declarations that cause the \env{dfn} and
%    \env{rmk} environments to have some differences in appearance.
%
%    There are three basic styles provided: The `plain' style produces
%    bold headings and italic body text; the `definition' style produces
%    bold headings and normal body text; the `remark' style produces
%    italic headings and normal body text.
%
%    A \cn{swapnumbers} command allows theorem numbers to be swapped to
%    the front of the theorem headings. Putting \cn{swapnumbers} in your
%    document preamble will cause \emph{all following} \cn{newtheorem}
%    statements to produce number-first headings. (To provide maximum
%    control, \cn{swapnumbers} is designed so that it can be used more
%    than once; each time it is used, theorem numbers will be swapped to
%    the opposite side for all following \cn{newtheorem} statements. But
%    rarely will it need to be invoked more than once per document.)
%
% \subsubsection{Custom theorem styles}
%    There is a \cn{newtheoremstyle} command provided to make the
%    creation of custom theoremstyles fairly easy.
%
%    Usage:
%\begin{verbatim}
%                   #1
% \newtheoremstyle{NAME}%
%     #2          #3          #4
%   {ABOVESPACE}{BELOWSPACE}{BODYFONT}%
%     #5      #6        #7         #8
%   {INDENT}{HEADFONT}{HEADPUNCT}{HEADSPACE}%
%     #9
%   {CUSTOM-HEAD-SPEC}
%\end{verbatim}
%    Leaving the `indent' argument empty is equivalent to entering
%    |0pt|. The `headpunct' and `headspace' arguments are for the
%    punctuation and horizontal space between the theorem head and the
%    following text. There are two special values that may be used for
%    `headspace': a single space means that a normal interword space
%    should be used; ``\cn{newline}'' means that there should be a line
%    break after the head instead of horizontal space. The
%    `custom-head-spec' argument follows a special convention: it is
%    interpreted as the replacement text for an internal three-argument
%    function \cn{thmhead}, i.e., as if you were defining
%\begin{verbatim}
% \renewcommand{\thmhead}[3]{...#1...#2...#3...}
%\end{verbatim}
%    but omitting the initial |\renewcommand{\thmhead}[3]|. The three
%    arguments that will be supplied to \cn{thmhead} are the name,
%    number, and optional note components. Within the replacement text
%    you can (and normally will want to) use other special functions
%    \cn{thmname}, \cn{thmnumber}, and \cn{thmnote}. These will print
%    their argument if and only if the corresponding argument of
%    \cn{thmhead} is nonempty. For example
%\begin{verbatim}
% {\thmname{#1}\thmnumber{ #2}\thmnote{ (#3)}}
%\end{verbatim}
%    This would cause the theorem note \arg{3} to be printed with a
%    preceding space and enclosing parentheses, if it is present, and if
%    it is absent, the space and parentheses will be omitted because
%    they are inside the argument of \cn{thmnote}.
%
%    Finally, if you have an extra bit of arbitrary code that you want
%    to slip in somewhere, the best place to do it is in the `body font'
%    argument.
%
%    The \cn{newtheoremstyle} command is designed to provide, through a
%    relatively simple interface, control over the style aspects that
%    are most commonly changed. More complex requirements must be
%    addressed through a separate \latex/ package.
%
%    When you set up custom theorem styles with \cn{newtheoremstyle} you
%    should not use \cn{swapnumbers}. You have full control of the
%    ordering of elements in the theorem head, just place them where you
%    want. Or, if you do use \cn{swapnumbers}, you must look at the
%    definition of \cs{swappedhead} and change it appropriately.

% \subsubsection{Implementation}
%    The \cn{theoremstyle} command is very simple except for the need to
%    warn about an unknown theoremstyle.
%    \begin{macrocode}
%&lt;*amsthm|classes&gt;
\newcommand{\theoremstyle}[1]{%
  \@ifundefined{th@#1}{%
    \PackageWarning{amsthm}{Unknown theoremstyle `#1'}%
    \thm@style{plain}%
  }{%
    \thm@style{#1}%
  }%
}
%    \end{macrocode}
%
%    \begin{macrocode}
\newtoks\thm@style
\thm@style{plain}
%    \end{macrocode}
%
%    What's really needed is a full-fledged systematic approach for
%    specifying the desired order and formatting of the three identified
%    parts of a theorem head (name, number, note).
%    \begin{macrocode}
\newtoks\thm@bodyfont  \thm@bodyfont{\itshape}
\newtoks\thm@headfont  \thm@headfont{\bfseries}
\newtoks\thm@notefont  \thm@notefont{}
\newtoks\thm@headpunct \thm@headpunct{.}
%    \end{macrocode}
%    Vertical spacing: initialize to current value of \cs{topsep}.
%    If a document class loads the \pkg{amsthm} package it
%    should take care to set these variables explicitly, if current
%    \cs{topsep} is not the desired value.
%    \begin{macrocode}
\newskip\thm@preskip \newskip\thm@postskip
%&lt;*classes&gt;
\def\thm@space@setup{%
  \thm@preskip=.5\baselineskip\@plus.2\baselineskip
                             \@minus.2\baselineskip
  \thm@postskip=\thm@preskip
}
%&lt;/classes&gt;
%&lt;*amsthm&gt;
\def\thm@space@setup{%
  \thm@preskip=\topsep \thm@postskip=\thm@preskip
}
%&lt;/amsthm&gt;
%    \end{macrocode}
%    Modify \cn{newtheorem} to add |*| option. If a |*| is found, pass
%    it on to \cs{@xnthm} as the first argument. (This information
%    enables us to handle two different possibilities in a single
%    function \cs{@xnthm} instead of needing two separate functions.)
%    \begin{macrocode}
\renewcommand{\newtheorem}{\@ifstar{\@xnthm *}{\@xnthm \relax}}
%    \end{macrocode}
%
%    Check to see if an optional arg is present after the first
%    mandatory arg (which is \arg{2} at the moment since the |*| or
%    non-|*| is \arg{1}).
%    \begin{macrocode}
\def\@xnthm#1#2{%
  \let\@tempa\relax
  \@xp\@ifdefinable\csname #2\endcsname{%
    \global\@xp\let\csname end#2\endcsname\@endtheorem
    \ifx *#1% unnumbered, need to get one more mandatory arg
      \edef\@tempa##1{%
        \gdef\@xp\@nx\csname#2\endcsname{%
          \@nx\@thm{\@xp\@nx\csname th@\the\thm@style\endcsname}%
            {}{##1}}}%
    \else % numbered theorem, need to check for optional arg
      \def\@tempa{\@oparg{\@ynthm{#2}}[]}%
    \fi
  }%
  \@tempa
}
%    \end{macrocode}
%
%    Environment numbered together with a previously defined
%    environment.
%
%    Arg1: env name, e.g. `thm'\par
%    Arg2: optional sibling counter\par
%    Arg3: heading text e.g. `Theorem'
%    \begin{macrocode}
\def\@ynthm#1[#2]#3{%
%    \end{macrocode}
%    If optional arg \arg{2} is empty, call \cs{@xthm} to look for a
%    possible optional arg in terminal position. Note that
%    the two optional args are mutually exclusive. As \arg{2} is a
%    counter name and must be processed by \cs{csname} anyway,
%    we can use a simpler test instead of \cs{@ifempty}.
%    \begin{macrocode}
  \ifx\relax#2\relax
    \def\@tempa{\@oparg{\@xthm{#1}{#3}}[]}%
  \else
    \@ifundefined{c@#2}{%
      \def\@tempa{\@nocounterr{#2}}%
    }{%
      \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#2\endcsname}%
      \toks@{#3}%
      \@xp\xdef\csname#1\endcsname{%
        \@nx\@thm{%
          \let\@nx\thm@swap
            \if S\thm@swap\@nx\@firstoftwo\else\@nx\@gobble\fi
          \@xp\@nx\csname th@\the\thm@style\endcsname}%
            {#2}{\the\toks@}}%
      \let\@tempa\relax
    }%
  \fi
  \@tempa
}
%    \end{macrocode}
%
%    Environment numbered relative to the counter given as \arg{3}. This
%    function should really be named \cs{@znthm} but we're trying to
%    save a bit of hash table and string pool by reusing one of the
%    command names rendered obsolete by the \pkg{amsthm} package.
%
%    Arg1: env name e.g. `thm';
%    Arg2: heading text e.g. `Theorem';
%    Arg3: parent counter e.g. section.
%    \begin{macrocode}
\def\@xthm#1#2[#3]{%
%    \end{macrocode}
%    Set up the counter \verb'c@#1' and optionally add it to the reset
%    list of counter \arg{3}. As \arg{3} is a
%    counter name and must be processed by \cs{csname} anyway,
%    we can use a simpler test instead of \cs{@ifempty}.
%    \begin{macrocode}
  \ifx\relax#3\relax
    \newcounter{#1}%
  \else
    \newcounter{#1}[#3]%
%    \end{macrocode}
%    Define \cn{thexxx} to be \verb'\theyyy.\arabic{xxx}' (assuming
%    default values of punctuation and numbering style). The use of
%    \cs{xdef} here is inherited from the old \latex/ code, I'm not
%    sure it's a good idea in general, but there should not be any
%    problems unless someone changes the value of \cs{@thmcountersep} or
%    \cs{@thmcounter}.
%    \begin{macrocode}
    \@xp\xdef\csname the#1\endcsname{\@xp\@nx\csname the#3\endcsname
      \@thmcountersep\@thmcounter{#1}}%
  \fi
  \toks@{#2}%
  \@xp\xdef\csname#1\endcsname{%
    \@nx\@thm{%
      \let\@nx\thm@swap
        \if S\thm@swap\@nx\@firstoftwo\else\@nx\@gobble\fi
      \@xp\@nx\csname th@\the\thm@style\endcsname}%
      {#1}{\the\toks@}}%
}
%    \end{macrocode}
%
%    [mjd,1999/10/13] The following code doesn't handle the case where
%    an equation is immediately followed by a theorem with no
%    intervening \cs{par}---then the spacefactor is 1000.
%    \begin{macrocode}
% % \def\thm@check@break{%
% %   \ifhmode \unskip \unskip
% %     \edef\pre@thm@spacefactor{\the\spacefactor}\par
% %     \edef\thm@topbreak{%
% %       \ifnum\pre@thm@spacefactor&lt;\sfcode`\!\relax
% %          % preceding text line did not end with end-of-sentence punctuation
% %         \ifnum\prevgraf=\@ne \penalty\widowpenalty
% %         \else \penalty9999\relax
% %         \fi
% %       \else
% %         \@nx\addpenalty{\@beginparpenalty}%
% %       \fi
% %     }%
% %   \else
% %     \def\thm@topbreak{\addpenalty\@beginparpenalty}%
% %   \fi
% % }
%    \end{macrocode}
%
%    If arg \arg{2} is empty, this is an unnumbered environment;
%    otherwise \arg{2} is the name of a counter. \arg{3} is descriptive
%    name such as ``Theorem'' or ``Lemma''. Arg \arg{1} is the style
%    function, for example \cs{th@plain}.
%    \begin{macrocode}
\def\@thm#1#2#3{%
  \ifhmode\unskip\unskip\par\fi
  \normalfont
  \trivlist
%    \end{macrocode}
%    Explicitly set plain style here, then override parts as necessary
%    in the function provided as \arg{1}.
%    \begin{macrocode}
  \let\thmheadnl\relax
  \let\thm@swap\@gobble
%&lt;amsart&gt;  \let\thm@indent\noindent % no indent
%&lt;amsart&gt;  \thm@headfont{\bfseries}% heading font bold
%&lt;amsbook|amsproc&gt;  \let\thm@indent\indent % indent
%&lt;amsbook|amsproc&gt;  \thm@headfont{\scshape}% heading font small caps
  \thm@notefont{\fontseries\mddefault\upshape}%
  \thm@headpunct{.}% add period after heading
  \thm@headsep 5\p@ plus\p@ minus\p@\relax
  \thm@space@setup
  #1% style overrides
  \@topsep \thm@preskip               % used by thm head
  \@topsepadd \thm@postskip           % used by \@endparenv
  \def\@tempa{#2}\ifx\@empty\@tempa
    \def\@tempa{\@oparg{\@begintheorem{#3}{}}[]}%
  \else
    \refstepcounter{#2}%
    \def\@tempa{\@oparg{\@begintheorem{#3}{\csname the#2\endcsname}}[]}%
  \fi
  \@tempa
}
%    \end{macrocode}
%
%    The internal function \cs{@restorelabelsep} starts out as a no-op.
%    I don't think this is needed any more [mjd,2000/10/26].
%    \begin{macrocode}
\def\@restorelabelsep{\relax}
%    \end{macrocode}
%
%    This variation of the \cs{@thm} command is no longer needed. The
%    variation \cs{@xthm} was commandeered for \cn{newtheorem} use.
%    \begin{macrocode}
\let\@ythm\relax
%    \end{macrocode}
%
%    Init \cn{thmname} etc.
%    \begin{macrocode}
\let\thmname\@iden \let\thmnote\@iden \let\thmnumber\@iden
%    \end{macrocode}
%
%  \begin{macro}{\@upn}
%    The function \cs{\@upn} is used to force theorem numbers and
%    similar elements to be upright even when the current font is
%    italic. If a suitable italic font with upright numbers and
%    punctuation is available, this function should be redefined to be a
%    no-op.
%    \begin{macrocode}
\providecommand\@upn{\textup}
%    \end{macrocode}
%  \end{macro}
%
%    Definitions for theorem heads.
%    \begin{macrocode}
\def\thmhead@plain#1#2#3{%
%    \end{macrocode}
%    To allow for the case where the thmname part is empty and the
%    heading consists only of a number (don't laugh, we have
%    examples from real mathematical manuscripts), we don't add the
%    space at the beginning of thmnumber unless \arg{1} is nonempty.
%    \begin{macrocode}
  \thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2}}%
%    \end{macrocode}
%    In thmnote we always add a leading space, i.e., assuming that
%    at least one of the preceding parts will always be present.
%    \begin{macrocode}
  \thmnote{ {\the\thm@notefont(#3)}}}
\let\thmhead\thmhead@plain
%    \end{macrocode}
%    Swappedhead is for the case where the number precedes the
%    word "Theorem". When the numbers fall on the left, like section
%    numbers, AMS journal style calls for them to be lightface. We get
%    this by invoking \cs{@secnumfont}.
%
%    In handling the punctuation after the number we have to step
%    delicately if we want to successfully handle cases where the
%    theorem name is empty (this is very rare, yet it sometimes arises
%    in practice).
%    \begin{macrocode}
\def\swappedhead#1#2#3{%
%&lt;amsthm&gt;  \thmnumber{#2}%
%&lt;amsthm&gt;  \thmname{\@ifnotempty{#2}{~}#1}%
%&lt;classes&gt;  \thmnumber{\@upn{\@secnumfont#2\@ifnotempty{#1}{.~}}}%
%&lt;classes&gt;  \thmname{#1}%
  \thmnote{ {\the\thm@notefont(#3)}}}
%    \end{macrocode}
%
%    A customized definition of \cs{th@plain} written for version 1.x of
%    the \pkg{amsthm} package might refer to \cs{swappedhead@plain}; this
%    gives it a definition for backward compatibility.
%    \begin{macrocode}
\let\swappedhead@plain=\swappedhead
%    \end{macrocode}
%
%    In \cs{@begintheorem} \cn{thmheadnl} is called after the theorem
%    head: maybe a newline, otherwise a no-op.
%    \begin{macrocode}
\let\thmheadnl\relax
\let\thm@indent\noindent
\let\thm@swap\@gobble
%    \end{macrocode}
%
%    If argument \arg{2} is empty, then this is an unnumbered
%    environment. Otherwise \arg{2} is a numbering command such as
%    \cn{thexyz}. We use \cs{deferred@thm@head} instead of \cs{item} in
%    order to allow line breaking in the optional note argument.
%    \begin{macrocode}
\def\@begintheorem#1#2[#3]{%
  \deferred@thm@head{\the\thm@headfont \thm@indent
%    \end{macrocode}
%    Changes to \cs{thmnumber} and \cs{thmnote} are local to the
%    containing box.
%    \begin{macrocode}
    \@ifempty{#1}{\let\thmname\@gobble}{\let\thmname\@iden}%
    \@ifempty{#2}{\let\thmnumber\@gobble}{\let\thmnumber\@iden}%
    \@ifempty{#3}{\let\thmnote\@gobble}{\let\thmnote\@iden}%
%    \end{macrocode}
%    The \cs{thm@swap} function selects either \cs{swappedhead} or
%    \cs{thmhead}.
%    \begin{macrocode}
    \thm@swap\swappedhead\thmhead{#1}{#2}{#3}%
%    \end{macrocode}
%    I can't think of any example where the after-head punctuation
%    should be omitted so it seems correct not to use \cs{@addpunct}
%    here.
%    \begin{macrocode}
    \the\thm@headpunct
%    \end{macrocode}
%    If this \emph{is} a newline (from a \cn{newtheoremstyle}), it
%    gets lost if there isn't any text following the heading, since
%    \cs{deferred@thm@head} packs the heading into an hbox with
%    \cs{sbox}\cs{@labels}.  Attempting to move the \cs{thmheadnl}
%    outside the scope of \cs{deferred@thm@head} (just outside the
%    ending brace below) results in no improvement if no text follows
%    the heading, and where there is text, runs it in.  Inserting a
%    space following such a heading results in an extra blank line.
%    [bnb, 2004/06/30]
%    \begin{macrocode}
    \thmheadnl % possibly a newline.
    \hskip\thm@headsep
  }%
  \ignorespaces}
%    \end{macrocode}
%
%    \begin{macrocode}
\newskip\thm@headsep
\thm@headsep=5pt plus1pt minus1pt\relax
%    \end{macrocode}
%
%    \begin{macrocode}
\let\adjust@parskip@nobreak=\@nbitem
%    \end{macrocode}
%
%    \begin{macrocode}
\newtoks\dth@everypar
\dth@everypar={%
  \@minipagefalse \global\@newlistfalse
  \@noparitemfalse
  \if@inlabel
    \global\@inlabelfalse
    \begingroup \setbox\z@\lastbox
     \ifvoid\z@ \kern-\itemindent \fi
    \endgroup
    \unhbox\@labels
  \fi
  \if@nobreak \@nobreakfalse \clubpenalty\@M
  \else \clubpenalty\@clubpenalty \everypar{}%
  \fi
}%
%    \end{macrocode}
%
%    \begin{macrocode}
\def\deferred@thm@head#1{%
  \if@inlabel \indent \par \fi % eject a section head if one is pending
  \if@nobreak
%    \end{macrocode}
%    This case normally arises when a theorem follows immediately after
%    a section head. Then we leave the below-section-head space instead
%    of adding above-theorem space; but some adjustment of parskip is
%    needed.
%    \begin{macrocode}
    \adjust@parskip@nobreak
  \else
    \addpenalty\@beginparpenalty
    \addvspace\@topsep
    \addvspace{-\parskip}%
  \fi
  \global\@inlabeltrue
  \everypar\dth@everypar
  \sbox\@labels{\normalfont#1}%
  \ignorespaces
}
%    \end{macrocode}
%
%  \begin{macro}{\nonslanted}
%    The \cn{nonslanted} command changes the current font to
%    \cn{upshape} if it is \cn{itshape} or \cn{slshape}. This is used
%    for document structure numbers that should be consistently upright
%    in all contexts.
%    \begin{macrocode}
\def\nonslanted{\relax
%    \end{macrocode}
%    Can't do a direct \cs{ifx} between \cs{f@shape} and \cs{itdefault}
%    because the latter is \cs{long} (grumble grumble).
%    \begin{macrocode}
  \@xp\let\@xp\@tempa\csname\f@shape shape\endcsname
  \ifx\@tempa\itshape\upshape
  \else\ifx\@tempa\slshape\upshape\fi\fi}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\swapnumbers}
%    The \cn{swapnumbers} command sets a switch \cs{thm@swap} that is
%    used by \cn{newtheorem}. To conserve hash table we load
%    \cs{thm@swap} with two uses; the first one is needed only in
%    \cn{newtheorem} declarations and the second one is needed only in
%    typesetting theorem environments.
%    \begin{macrocode}
\def\swapnumbers{\edef\thm@swap{\if S\thm@swap N\else S\fi}}
\def\thm@swap{N}%
%    \end{macrocode}
%  \end{macro}
%
%    \cs{@opargbegintheorem} not needed, \cs{@oparg} utility serves
%    instead.
%    \begin{macrocode}
\let\@opargbegintheorem\relax
%    \end{macrocode}
%
%    Except for the body font, default values are built into \cs{@thm}.
%    \begin{macrocode}
\def\th@plain{%
%%  \let\thm@indent\noindent % no indent
%%  \thm@headfont{\bfseries}% heading font is bold
%%  \thm@notefont{}% same as heading font
%%  \thm@headpunct{.}% add period after heading
%%  \let\thm@swap\@gobble
%%  \thm@preskip\topsep
%%  \thm@postskip\theorempreskipamount
  \itshape % body font
}
%    \end{macrocode}
%
%    Theorem style `definition' is the same as `plain' except for the
%    body font.
%    \begin{macrocode}
\def\th@definition{%
  \normalfont % body font
}
%    \end{macrocode}
%
%    Theorem style `remark' differs from `plain' in head font and  body
%    font. Also smaller spacing above and below for AMS classes only.
%    \begin{macrocode}
\def\th@remark{%
%&lt;amsart|amsthm&gt;  \thm@headfont{\itshape}%
  \normalfont % body font
%&lt;*amsthm&gt;
  \thm@preskip\topsep \divide\thm@preskip\tw@
  \thm@postskip\thm@preskip
%&lt;/amsthm&gt;
}
%    \end{macrocode}
%
%    The standard definition of \cs{@endtheorem} is just
%    \cs{endtrivlist}, but that doesn't automatically start a new
%    paragraph, so we add \cs{@endpefalse} in order to ensure a new
%    paragraph.  This differs from the basic \latex/ behavior.
%    \begin{macrocode}
\def\@endtheorem{\endtrivlist\@endpefalse }
%    \end{macrocode}
%
%  \begin{macro}{\newtheoremstyle}
%    An easy way to make a not too complicated variant theorem style.
%    Usage:
%\begin{verbatim}
%                   #1
% \newtheoremstyle{NAME}%
%     #2          #3          #4
%   {ABOVESPACE}{BELOWSPACE}{BODYFONT}%
%     #5      #6        #7         #8
%   {INDENT}{HEADFONT}{HEADPUNCT}{HEADSPACE}%
%     #9
%   {CUSTOM-HEAD-SPEC}
%\end{verbatim}
%    \begin{macrocode}
\newcommand{\newtheoremstyle}[9]{%
%    \end{macrocode}
%    Empty or 0pt for \arg{5} is translated to \cs{noindent}.
%    \begin{macrocode}
  \@ifempty{#5}{\dimen@\z@skip}{\dimen@#5\relax}%
  \ifdim\dimen@=\z@
%    \end{macrocode}
%    \arg{4} is body font. Extra code could be included there if
%    necessary.
%    \begin{macrocode}
    \toks@{#4\let\thm@indent\noindent}%
  \else
    \toks@{#4\def\thm@indent{\noindent\hbox to#5{}}}%
  \fi
%    \end{macrocode}
%    Arg \arg{8} is a glue spec for the space after the head. As
%    a proper glue spec for `normal interword space' is rather hard to
%    write, we recognize an argument of |{ }| as a special case and
%    translate internally to the necessary fontdimen equivalent.
%    Furthermore, if \arg{8} consists entirely of \cn{newline}, then we
%    will perform a line break after the theorem head instead of adding
%    horizontal space. At the moment [1995/01/23] this is not perfectly
%    well implemented because of complications with the way \latex/'s
%    \cn{item} adds a heading to the vertical list; for best results
%    there should not be anything (not even a blank line) after the
%    |\begin{xxx}| command.
%    \begin{macrocode}
  \def\@tempa{#8}\ifx\space\@tempa
%    \end{macrocode}
%    Notice that we disregard stretch and shrink for labelsep =
%    interwordspace.
%    \begin{macrocode}
    \toks@\@xp{\the\toks@ \thm@headsep\fontdimen\tw@\font\relax}%
  \else
    \def\@tempb{\newline}%
    \ifx\@tempb\@tempa
      \toks@\@xp{\the\toks@ \thm@headsep\z@skip
        \def\thmheadnl{\newline}}%
    \else
      \toks@\@xp{\the\toks@ \thm@headsep#8\relax}%
    \fi
  \fi
  \begingroup
  \thm@space@setup
  \@defaultunits\@tempskipa#2\thm@preskip\relax\@nnil
  \@defaultunits\@tempskipb#3\thm@postskip\relax\@nnil
  \xdef\@gtempa{\thm@preskip\the\@tempskipa
    \thm@postskip\the\@tempskipb\relax}%
  \endgroup
  \@temptokena\@xp{\@gtempa
    \thm@headfont{#6}\thm@headpunct{#7}%
  }%
  \@ifempty{#9}{%
    \let\thmhead\thmhead@plain
  }{%
    \@namedef{thmhead@#1}##1##2##3{#9}%
    \@temptokena\@xp{\the\@temptokena
      \@xp\let\@xp\thmhead\csname thmhead@#1\endcsname}%
  }%
  \@xp\xdef\csname th@#1\endcsname{\the\toks@ \the\@temptokena}%
}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\qed}
%    Define \cn{qed} for end of proof. This command might
%    occur in math mode, in a displayed equation, but it should never
%    occur in inner math mode in ordinary paragraph text.
%    \begin{macrocode}
\DeclareRobustCommand{\qed}{%
  \ifmmode \mathqed
  \else
    \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
%    \end{macrocode}
%    The hbox is to prevent a line break within the \cn{qedsymbol} if it
%    is defined to be something composite--- e.g., things like
%    \verb"(Corollary 1.2) \openbox" as are occasionally done.
%    \begin{macrocode}
    \quad\hbox{\qedsymbol}%
  \fi
}
%    \end{macrocode}
%  \end{macro}
%
%    Setup for QED stack. We use a dedicated iterator macro \cs{qed@elt}
%    instead of the generic \cs{@elt} because the \latex/ output routine
%    is not safe against changes in \cs{@elt}. Therefore it is not safe
%    to use \cs{@elt} for any processing that might trigger the output
%    routine. Although this does not seem very likely when adding a QED
%    symbol to a horizontal list, we did in fact get a bug report for
%    this kind of failure.
%    \begin{macrocode}
\let\QED@stack\@empty
\let\qed@elt\relax
%    \end{macrocode}
%
%    Puts a QED symbol on the stack:
%    \begin{macrocode}
\newcommand{\pushQED}[1]{%
  \toks@{\qed@elt{#1}}\@temptokena\expandafter{\QED@stack}%
  \xdef\QED@stack{\the\toks@\the\@temptokena}%
}
%    \end{macrocode}
%
%    Pops the QED stack and prints the result.
%    \begin{macrocode}
\newcommand{\popQED}{%
  \begingroup\let\qed@elt\popQED@elt \QED@stack\relax\relax\endgroup
}
%    \end{macrocode}
%
%    \begin{macrocode}
\def\popQED@elt#1#2\relax{#1\gdef\QED@stack{#2}}
%    \end{macrocode}
%
%    Prints the current QED symbol and replaces the top entry on the
%    stack with a null entry.
%    \begin{macrocode}
\newcommand{\qedhere}{%
  \begingroup \let\mathqed\math@qedhere
    \let\qed@elt\setQED@elt \QED@stack\relax\relax \endgroup
}
%    \end{macrocode}
%
%    In case the \pkg{amsmath} or \pkg{amstext} packages are loaded, we
%    need the following two tests. (Redundantly declaring them is
%    harmless.)
%    \begin{macrocode}
\newif\ifmeasuring@
\newif\iffirstchoice@ \firstchoice@true
%    \end{macrocode}
%
%    \begin{macrocode}
\def\setQED@elt#1#2\relax{%
  \ifmeasuring@
  \else \iffirstchoice@ \gdef\QED@stack{\qed@elt{}#2}\fi
  \fi
  #1%
}
%    \end{macrocode}
%
%  \begin{macro}{\mathqed}
%    When a QED occurs inside a math formula, well, it is presumably a
%    displayed equation. In order to find out where to place the QED
%    symbol, we need to check what kind of equation structure we are in.
%
%    \begin{macrocode}
\def\qed@warning{%
  \PackageWarning{amsthm}{The \@nx\qedhere command may not work
    correctly here}%
}
%    \end{macrocode}
%
%    \begin{macrocode}
\newcommand{\mathqed}{\quad\hbox{\qedsymbol}}
%    \end{macrocode}
%
%    The \cs{linebox@qed} function comes into play with the \opt{fleqn}
%    option.
%    \begin{macrocode}
\def\linebox@qed{\hfil\hbox{\qedsymbol}\hfilneg}
%    \end{macrocode}
% \end{macro}
%
%    Two large sections of code follow. One for \fn{amsmath} 2.0 and one
%    for plain \latex/.
%    \begin{macrocode}
\@ifpackageloaded{amsmath}{%
%    \end{macrocode}
%
%    \begin{macrocode}
  \def\math@qedhere{%
    \@ifundefined{\@currenvir @qed}{%
      \qed@warning\quad\hbox{\qedsymbol}%
    }{%
      \@xp\aftergroup\csname\@currenvir @qed\endcsname
    }%
  }
%    \end{macrocode}
%
%    \begin{macrocode}
  \def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \aftergroup\linebox@qed
      \else
        \eqno
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\qedsymbol}%
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }
%    \end{macrocode}
%
%    \begin{macrocode}
  \@xp\let\csname equation*@qed\endcsname\displaymath@qed
%    \end{macrocode}
%
%    If the equation has both an equation number and a qed, we've got
%    trouble, but we can provide half-way decent for the simple cases.
%    \begin{macrocode}
  \def\equation@qed{%
    \iftagsleft@
      \hbox{\phantom{\quad\qedsymbol}}%
      \gdef\alt@tag{%
        \rlap{\hbox to\displaywidth{\hfil\qedsymbol}}%
        \global\let\alt@tag\@empty
      }%
    \else
      \gdef\alt@tag{%
        \global\let\alt@tag\@empty
        \vtop{\ialign{\hfil####\cr
                \tagform@\theequation\cr
                \qedsymbol\cr}}%
        \setbox\z@
      }%
    \fi
  }
%    \end{macrocode}
%
%    \begin{macrocode}
  \def\qed@tag{%
    \global\tag@true \nonumber
    &amp;\omit\setboxz@h {\strut@ \qedsymbol}\tagsleft@false
    \place@tag@gather
    \kern-\tabskip
    \ifst@rred \else \global\@eqnswtrue \fi \global\advance\row@\@ne \cr
  }
%    \end{macrocode}
%
%    \begin{macrocode}
  \def\split@qed{%
    \def\endsplit{\crcr\egroup \egroup \ctagsplit@false \rendsplit@
      \aftergroup\align@qed
    }%
  }
%    \end{macrocode}
%
%    \begin{macrocode}
  \def\align@qed{%
    \ifmeasuring@ \tag*{\qedsymbol}%
    \else \let\math@cr@@@\qed@tag
    \fi
  }
  \@xp\let\csname align*@qed\endcsname\align@qed
  \@xp\let\csname gather*@qed\endcsname\align@qed
%    \end{macrocode}
%
%    \begin{macrocode}
%% Needs some patching up for amsmath 1.2
%    \end{macrocode}
%
%    \begin{macrocode}
}{% end of amsmath branch, start plain LaTeX branch
%    \end{macrocode}
%
%    The \cn{qedhere} handling for generic \latex/ classes (\cls{article},
%    \cls{book}) with the \pkg{amsthm} package (without \pkg{amsmath}) is
%    fairly sketchy. When a qed symbol and an equation number are both
%    applied to a single display, the results may not be entirely
%    satisfactory, particularly when the \opt{fleqn} and/or \opt{leqno}
%    options are used. [mjd,2000/01/17]
%
%    As for \cs{math@qedhere}, it is expected to occur only via
%    \cn{qedhere}, where the \cs{aftergroup} makes sense.
%    \begin{macrocode}
  \def\math@qedhere{%
    \@ifundefined{\@currenvir @qed}{%
      \qed@warning \aftergroup\displaymath@qed
    }{%
      \@xp\aftergroup\csname\@currenvir @qed\endcsname
    }%
  }
%    \end{macrocode}
%
%    The \cs{ifmmode} \cs{ifinner} case is expected to happen with the
%    \opt{fleqn} option, where we have something like:
%\begin{verbatim}
%\hbox to\linewidth{\hbox{$...$}\hfil}
%\end{verbatim}
%    In order to counteract the \cs{hfil} we must jump out two grouping
%    levels.
%    \begin{macrocode}
  \def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \aftergroup\aftergroup\aftergroup\linebox@qed
      \else
        \eqno \def\@badmath{$$}%
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\qedsymbol}%
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }
%    \end{macrocode}
%
%    This definition is a fallback definition that places the qed and
%    then the equation number, on the right-hand side. For \opt{leqno},
%    not so good; but then
%    \begin{macrocode}
  \@ifundefined{ver@leqno.clo}{%
    \def\equation@qed{\displaymath@qed \quad}%
  }{%
    \def\equation@qed{\displaymath@qed}%
  }
%    \end{macrocode}
%
%    If \pkg{amsmath} is not loaded, then we need to do some surgery
%    on the \cn{[} macro. Normally it looks like this:
%\begin{verbatim}
% \[=macro:
% -&gt;\relax \ifmmode \@badmath \else
% \ifvmode \nointerlineskip \makebox [.6\linewidth ]\fi $$\fi
%\end{verbatim}
%
%    If arg 2 is \cs{m@th} when we make this test it indicates that the
%    fleqn option is in effect. Perhaps try to do something there.
%    \begin{macrocode}
    \def\@tempa#1$#2#3\@nil#4{%
        \def#4{#1$#2\def\@currenvir{displaymath}#3}%
    }%
%    \end{macrocode}
% If \cn{[} has already been made robust (by \pkg{fixltx2e} or
% a \LaTeX\ format from 2015 or later), patch the internal macro
% \cs{[&lt;space&gt;} instead.
%    \begin{macrocode}
    \expandafter\ifx\csname[ \endcsname\relax
        \expandafter\@tempa\[\@nil\[%
    \else
        \expandafter\expandafter\expandafter\@tempa\csname[
        \expandafter\endcsname\expandafter\@nil
        \csname[ \endcsname
    \fi
}
%    \end{macrocode}
%
%    If an older version of \pkg{amsmath} is in use, we need to fall
%    back to a simpler definition of \cs{math@qedhere}.
%    \begin{macrocode}
\@ifpackageloaded{amstex}{%
  \def\@tempa{TT}%
}{%
  \@ifpackageloaded{amsmath}{%
    \def\@tempb#1 v#2.#3\@nil{#2}%
    \ifnum\@xp\@xp\@xp\@tempb\csname ver@amsmath.sty\endcsname v0.0\@nil
       &lt;\tw@
      \def\@tempa{TT}%
    \else
      \def\@tempa{TF}%
    \fi
  }{%
    \def\@tempa{TF}
  }%
}
\if\@tempa
  \renewcommand{\math@qedhere}{\quad\hbox{\qedsymbol}}%
\fi
%    \end{macrocode}
%
%    The reason that we do not simply use the \cn{square} symbol from
%    \fn{msam} for the open-box qed symbol is that we want to avoid
%    requiring users to have the AMSFonts font package. And the \fn{lasy}
%    \cn{Box} is too large.
%    \begin{macrocode}
\newcommand{\openbox}{\leavevmode
%    \end{macrocode}
%    I think I got these numbers from measuring \fn{msam}'s \cn{square}
%    but I forgot to make notes at the time. [mjd,1995/01/25]
%    \begin{macrocode}
  \hbox to.77778em{%
  \hfil\vrule
  \vbox to.675em{\hrule width.6em\vfil\hrule}%
  \vrule\hfil}}
%    \end{macrocode}
%
%    \begin{macrocode}
\DeclareRobustCommand{\textsquare}{%
  \begingroup \usefont{U}{msa}{m}{n}\thr@@\endgroup
}
%    \end{macrocode}
%
%    \begin{macrocode}
%&lt;*classes&gt;
\@ifclasswith{\@classname}{noamsfonts}{%
  \providecommand{\qedsymbol}{\openbox}%
}{}
\providecommand{\qedsymbol}{\textsquare}
%&lt;/classes&gt;
%&lt;amsthm&gt;\providecommand{\qedsymbol}{\openbox}
%    \end{macrocode}
%
%    The proof environment is never numbered, and has a \cn{qed} at the
%    end, which makes it inconvenient to use \cn{newtheorem} for
%    defining it. Also authors frequently need to substitute an
%    alternative heading text (e.g.\ `Proof of Lemma 4.3')
%    instead of the default `Proof'. For all these reasons we define the
%    proof environment here instead of leaving it for authors to define.
%    Text after the end of a proof, like that after the end of a theorem,
%    begins a new paragraph.  This differs from basic \latex/ behavior.
%    [bnb, 1999/09/27]
%    \begin{macrocode}
\newenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
%&lt;amsbook|amsproc&gt;  \itemindent\normalparindent
  \item[\hskip\labelsep
%&lt;amsbook|amsproc&gt;        \scshape
%&lt;amsart|amsthm&gt;        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
%    \end{macrocode}
%    Default for \cn{proofname}:
%    \begin{macrocode}
\providecommand{\proofname}{Proof}
%    \end{macrocode}
%
%    For reference:
%\begin{verbatim}
% From: tycchow@math.mit.edu (Timothy Y. Chow)
% Subject: Suppressing theorem numbering in LaTeX
% Message-ID: &lt;1994Aug11.234754.22523@galois.mit.edu&gt;
% Date: Thu, 11 Aug 94 23:47:54 GMT
% To: tex-news@SHSU.EDU
%
% A friend of mine wants numbering of theorems, conjectures, and so on
% suppressed if there is only one of them in his article.  In other words
% he wants "Conjecture 1" to appear as simply "Conjecture" if there is no
% Conjecture 2.  What is the best way to go about doing this?
% ...
%\end{verbatim}
%    Maybe something clever can be done to make the desired behavior
%    happen automatically. Note that this would seem to be a general
%    numbering problem rather than a theorem-specific one, because
%    similar behavior would be desirable for appendixes: according to
%    standard publishing practice, if there's only one it is titled just
%    `Appendix', and if there are more than one they are titled
%    `Appendix A', `Appendix B', and so on.
%
%    \begin{macrocode}
%&lt;/amsthm|classes&gt;
%&lt;*classes&gt;
%    \end{macrocode}
%
%  \subsection{Utility commands used with AMS author packages}
%
%  \begin{macro}{\bb@skip}
%    Skip to result in base-to-base distance from previous to next box.
%    \begin{macrocode}
\def\bb@skip#1{%
  \skip@#1\relax \advance\skip@-\prevdepth \advance\skip@-\baselineskip
  \vskip\skip@}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\markleft}
%    Basic \latex/ has \cn{markright} and \cn{markboth}, but sometimes
%    it's necessary to change just the left running head.  This macro
%    completes the set.  From the \pkg{altxext.sty} module of Klaus
%    Lagally's \pkg{arabtex}.  [bnb, 2004/03/25]
%    \begin{macrocode}
\def\markleft#1{{\let\protect\noexpand
    \let\label\relax \let\index\relax \let\glossary\relax
    \expandafter\@markleft\@themark{#1}%
    \mark{\@themark}}%
  \if@nobreak\ifvmode\nobreak\fi\fi}
\def\@markleft#1#2#3{\gdef\@themark{{#3}{#2}}}
%    \end{macrocode}
%  \end{macro}
%
%  \begin{macro}{\DH}
%  \begin{macro}{\dh}
%  \begin{macro}{\DJ}
%  \begin{macro}{\dj}
%    The Icelandic thorn and eth and the Croatian barred D are part of
%    the T1 font encoding, but aren't available in OT1.  However, they
%    are needed (rarely) in the author names or bibliographies.  Provide
%    emulations, using the thorn in \fn{msbm} or D's barred with a macron.
%    The lowercase eth requires an \cs{edef} to access \fn{msbm} properly.
%    Define it separately to permit checking for small caps.  [bnb, 2004/04/05]
%    \begin{macrocode}
\@ifundefined{symAMSb}{%
  \def\@dh{dh}%
  \ClassWarning{\@classname}{\string\dh\space unavailable without amsfonts;
    replaced by 'dh'}%
}{%
  \edef\@dh{\noexpand\mathhexbox{\hexnumber@\symAMSb}67}%
}
\DeclareTextCommand{\dh}{OT1}{%
  \edef\@tempb{\scdefault}%
  \ifx\f@shape\@tempb
    \leavevmode
    \raisebox{-.8ex}{\makebox[\z@][l]{\hskip-.08em\accent"16\hss}}d%
  \else
    \@dh
  \fi
}
\DeclareTextCommand{\DH}{OT1}{%
  \leavevmode\raisebox{-.5ex}{\makebox[\z@][l]{\hskip-.07em\accent"16\hss}}D}
\DeclareTextCommand{\DJ}{OT1}{%
  \leavevmode\raisebox{-.5ex}{\makebox[\z@][l]{\hskip-.07em\accent"16\hss}}D}
\DeclareTextCommand{\dj}{OT1}{%
  \edef\@tempa{\f@shape}\edef\@tempb{\scdefault}%
  \ifx\@tempa\@tempb
    \leavevmode
    \raisebox{-.75ex}{\makebox[\z@][l]{\hskip-.08em\accent"16\hss}}d%
  \else
    \leavevmode\raisebox{.02ex}{\makebox[\z@][l]{\hskip.1em\accent"16\hss}}d%
  \fi}
%    \end{macrocode}
%  \end{macro}
%  \end{macro}
%  \end{macro}
%  \end{macro}
%
%  \subsection{Hyphenation exceptions}
%    Some common hyphenation exceptions, based on the listing in
%    TUGboat vol 10, no 3, November 1989, pp.~336--341. Many words from
%    the TUGboat list that seemed less likely to occur in mathematical
%    text have been omitted because hyphenation exceptions use up memory
%    (most versions of \tex/ currently have a limit of 307 on hyphenation
%    exceptions; each added hyphenation exception uses up something like
%    2 extra words of main memory as well). The list of hyphenations for
%    proper names could be expanded forever if room permitted; we
%    restrict ourselves to a rather short, extremely arbitrary list.
%    Note that the hyphenation rules of British English differ in some
%    particulars from the US rules, so some of the hyphenations
%    given below may need to be overridden for proper UK hyphenation.
%
%    \begin{macrocode}
\hyphenation{acad-e-my acad-e-mies af-ter-thought anom-aly anom-alies
an-ti-deriv-a-tive an-tin-o-my an-tin-o-mies apoth-e-o-ses
apoth-e-o-sis ap-pen-dix ar-che-typ-al as-sign-a-ble as-sist-ant-ship
as-ymp-tot-ic asyn-chro-nous at-trib-uted at-trib-ut-able bank-rupt
bank-rupt-cy bi-dif-fer-en-tial blue-print busier busiest
cat-a-stroph-ic cat-a-stroph-i-cally con-gress cross-hatched data-base
de-fin-i-tive de-riv-a-tive dis-trib-ute dri-ver dri-vers eco-nom-ics
econ-o-mist elit-ist equi-vari-ant ex-quis-ite ex-tra-or-di-nary
flow-chart for-mi-da-ble forth-right friv-o-lous ge-o-des-ic
ge-o-det-ic geo-met-ric griev-ance griev-ous griev-ous-ly
hexa-dec-i-mal ho-lo-no-my ho-mo-thetic ideals idio-syn-crasy
in-fin-ite-ly in-fin-i-tes-i-mal ir-rev-o-ca-ble key-stroke
lam-en-ta-ble light-weight mal-a-prop-ism man-u-script mar-gin-al
meta-bol-ic me-tab-o-lism meta-lan-guage me-trop-o-lis
met-ro-pol-i-tan mi-nut-est mol-e-cule mono-chrome mono-pole
mo-nop-oly mono-spline mo-not-o-nous mul-ti-fac-eted mul-ti-plic-able
non-euclid-ean non-iso-mor-phic non-smooth par-a-digm par-a-bol-ic
pa-rab-o-loid pa-ram-e-trize para-mount pen-ta-gon phe-nom-e-non
post-script pre-am-ble pro-ce-dur-al pro-hib-i-tive pro-hib-i-tive-ly
pseu-do-dif-fer-en-tial pseu-do-fi-nite pseu-do-nym qua-drat-ic
quad-ra-ture qua-si-smooth qua-si-sta-tion-ary qua-si-tri-an-gu-lar
quin-tes-sence quin-tes-sen-tial re-arrange-ment rec-tan-gle
ret-ri-bu-tion retro-fit retro-fit-ted right-eous right-eous-ness
ro-bot ro-bot-ics sched-ul-ing se-mes-ter semi-def-i-nite
semi-ho-mo-thet-ic set-up se-vere-ly side-step sov-er-eign spe-cious
spher-oid spher-oid-al star-tling star-tling-ly sta-tis-tics
sto-chas-tic straight-est strange-ness strat-a-gem strong-hold
sum-ma-ble symp-to-matic syn-chro-nous topo-graph-i-cal tra-vers-a-ble
tra-ver-sal tra-ver-sals treach-ery turn-around un-at-tached
un-err-ing-ly white-space wide-spread wing-spread wretch-ed
wretch-ed-ly Eng-lish Euler-ian Feb-ru-ary Gauss-ian
Hamil-ton-ian Her-mit-ian Jan-u-ary Japan-ese Kor-te-weg
Le-gendre Mar-kov-ian Noe-ther-ian No-vem-ber Rie-mann-ian Sep-tem-ber}
%    \end{macrocode}
%
%  \subsection{Initialization}
%    We define a function to do the normal calculations that we want for
%    \cn{textheight} and \cn{textwidth}
%
%  \begin{macro}{\calclayout}
%    Subtract the height of the running heads:
%    \begin{macrocode}
\def\calclayout{\advance\textheight -\headheight
  \advance\textheight -\headsep
%    \end{macrocode}
%    We set \cn{oddsidemargin} and \cn{evensidemargin} to
%    center the text on the page.
%    \begin{macrocode}
  \oddsidemargin\paperwidth
  \advance\oddsidemargin -\textwidth
  \divide\oddsidemargin\tw@
%    \end{macrocode}
%    Now we subtract the default margin provided by standard DVI
%    drivers.  But first we make sure that the final margin will
%    be at least .5 inch.
%    \begin{macrocode}
  \ifdim\oddsidemargin&lt;.5truein \oddsidemargin.5truein \fi
  \advance\oddsidemargin -1truein
  \evensidemargin\oddsidemargin
%    \end{macrocode}
%     And we set \cn{topmargin} to get vertical centering as well.
%    \begin{macrocode}
  \topmargin\paperheight \advance\topmargin -\textheight
  \advance\topmargin -\headheight \advance\topmargin -\headsep
%    \end{macrocode}
%    Height of running foot ignored: not present.
%    \begin{macrocode}
  \divide\topmargin\tw@
%    \end{macrocode}
%    We provide a minimum of .5in (after compensating for the default
%    margin---see next step).
%    \begin{macrocode}
  \ifdim\topmargin&lt;.5truein \topmargin.5truein \fi
%    \end{macrocode}
%    Now subtract the default margin provided by standard DVI
%    drivers.
%    \begin{macrocode}
  \advance\topmargin -1truein\relax
}
%    \end{macrocode}
%    \end{macro}
%
%    Initialize the dimensions, page numbering, etc.  For inhouse use,
%    administrative stuff is isolated in separate files.
%    \begin{macrocode}
%&lt;amsart&gt;\InputIfFileExists{amsart.cfg}{}{%
%&lt;amsproc&gt;\InputIfFileExists{amsproc.cfg}{}{%
%&lt;amsbook&gt;\InputIfFileExists{amsbook.cfg}{}{%
  \calclayout % initialize
  \pagenumbering{arabic}%
  \pagestyle{headings}%
  \thispagestyle{plain}%
}
%    \end{macrocode}
%
%    If we are in compatibility mode, add some backward compatibility
%    stuff below. Otherwise quit here.
%    \begin{macrocode}
\if@compatibility \else\endinput\fi
%    \end{macrocode}
%
%    Compensate for changed meaning of \cn{tiny}:
%    \begin{macrocode}
\def\tiny{\Tiny}
%    \end{macrocode}
%
%    The macro \cn{defaultfont} was provided in version 1.1 of amsart;
%    retained for compatibility as a synonym of \cn{normalfont}. Resets
%    everything except for size.
%    \begin{macrocode}
\def\defaultfont{\normalfont}
%    \end{macrocode}
%
%    Macro for making non-slanted numbers and punctuation in italic
%    or slanted text.  This is to avoid visual inconsistencies
%    between numbers or parentheses in math and adjacent numbers or
%    parentheses in text.
%    \begin{macrocode}
\def\rom{\textup}
%    \end{macrocode}
%
%    For backward compatibility with version 1.1 of \cls{amsart}, we
%    define \env{pf}, \env{pf*} environments. And undefine \cn{proof}
%    just in case an existing document contains a \cn{newenvironment} or
%    \cn{newcommand} for it, as that would now cause an error.
%    \begin{macrocode}
\let\@newpf\proof \let\proof\relax \let\endproof\relax
\newenvironment{pf}{\@newpf[\proofname]}{\popQED\endtrivlist}
\newenvironment{pf*}[1]{\@newpf[#1]}{\popQED\endtrivlist}
%    \end{macrocode}
%
%    The usual \cn{endinput} to ensure that random garbage at the end of
%    the file doesn't get copied by \fn{docstrip}.
%    \begin{macrocode}
\endinput
%&lt;/classes&gt;
%    \end{macrocode}
%
% \changes{v1.2a}{1995/02/01}{Added global init for @secnumber}
% \changes{v1.2a}{1995/02/01}{Made psamsfonts option pass cmex10 to
%   amsmath}
% \changes{v1.2a}{1995/02/01}{Added missing endpar after authors in
%   amsbook @maketitle}
%
% \changes{v1.2b}{1995/02/20}{Improve handling of abstract}
% \changes{v1.2b}{1995/02/20}{Allow titlepage option for articles}
% \changes{v1.2b}{1995/02/20}{Suppress logo and copyright info for
%   generic AMS classes}
% \changes{v1.2b}{1995/02/20}{Use `Date' instead of `Received by...' in
%   the generic AMS classes}
%
% \changes{v2.13}{2002/12/06}{Added a warning for thanks inside author}
%
% \Finale
</pre></body></html>