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amsart.cls
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%%
%% This is file `amsart.cls',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% amsclass.dtx (with options: `amsart,classes')
%%
%% This is a generated file.
%%
%% Copyright 1995, 1999, 2004, 2009, 2015, 2017, 2020 American
%% Mathematical Society.
%%
%% American Mathematical Society
%% Technical Support
%% Publications Technical Group
%% 201 Charles Street
%% Providence, RI 02904
%% USA
%% tel: (401) 455-4080
%% (800) 321-4267 (USA and Canada only)
%% fax: (401) 331-3842
%% email: [email protected]
%%
%% Unlimited copying and redistribution of this file are permitted as
%% long as this file is not modified. Modifications, and distribution
%% of modified versions, are permitted, but only if the resulting file
%% is renamed.
%%
\NeedsTeXFormat{LaTeX2e}% LaTeX 2.09 can't be used (nor non-LaTeX)
[1995/06/01]% LaTeX date must be June 1995 or later
\ProvidesClass{amsart}[2020/05/21 v2.20.5]
\global\expandafter\let\csname [email protected]\expandafter\endcsname
\csname ver@\@currname.\@currext\endcsname
\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>\@m \else#1\fi
\fi}
\def\nopunct{\spacefactor 1007 }
\def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
\sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
\def\@tempa#1#2\@nil{\edef\@classname{#1}}
\expandafter\@tempa\@currnamestack{}{}{}\@nil
\ifx\@classname\@empty \edef\@classname{\@currname}\fi
\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
}
\newswitch{}
\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
}
\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}
\DeclareOption{a4paper}{\paperheight 297mm\paperwidth 210mm
\textheight 54.5pc }
\DeclareOption{letterpaper}{\paperheight 11in\paperwidth 8.5in }
\DeclareOption{landscape}{\@tempdima\paperheight
\paperheight\paperwidth \paperwidth\@tempdima}
\DeclareOption{portrait}{}
\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}
\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}
\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@ }
\def\dateposted#1{\def\@dateposted{#1}}%
\let\@dateposted\@empty
\def\@setdateposted{%
\newline Article electronically published on \@dateposted}
\def\article@logo{%
\set@logo{%
\publname
\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
}%
}
\def\@logofont{\fontsize{6}{7\p@}\selectfont}
\long\def\set@logo#1{%
\vbox to\headheight{%
\@parboxrestore \@logofont
\noindent#1\par\vss
}%
}
\DeclareOption{e-only}{%
\def\volinfo{Volume \currentvolume}%
\dateposted{Xxxx XX, XXXX}%
\def\@setdateposted{\ (\@dateposted)}%
\let\article@logo\eonly@logo
}
\newif\if@titlepage
\DeclareOption{titlepage}{\@titlepagetrue}
\DeclareOption{notitlepage}{\@titlepagefalse}
\DeclareOption{onecolumn}{\@twocolumnfalse}
\DeclareOption{twocolumn}{\@twocolumntrue}
\DeclareOption{nomath}{}
\DeclareOption{noamsfonts}{}
\DeclareOption{psamsfonts}{%
\PassOptionsToPackage{psamsfonts}{amsfonts}%
\PassOptionsToPackage{cmex10}{amsmath}}
\newif\iftagsleft@
\DeclareOption{leqno}{%
\tagsleft@true \PassOptionsToPackage{leqno}{amsmath}}
\DeclareOption{reqno}{%
\tagsleft@false \PassOptionsToPackage{reqno}{amsmath}}
\newif\ifctagsplit@
\DeclareOption{centertags}{%
\ctagsplit@true \PassOptionsToPackage{centertags}{amsmath}}
\DeclareOption{tbtags}{%
\ctagsplit@false \PassOptionsToPackage{tbtags}{amsmath}}
\DeclareOption{fleqn}{}%
\newcommand{\@mainsize}{10}
\newcommand{\@ptsize}{0}
\newcommand{\larger}[1][1]{%
\count@\@currsizeindex \advance\count@#1\relax
\ifnum\count@<\z@ \count@\z@ \else\ifnum\count@>12 \count@12 \fi\fi
\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]}
\def\@adjustvertspacing{%
\bigskipamount.7\baselineskip plus.7\baselineskip
\medskipamount\bigskipamount \divide\medskipamount\tw@
\smallskipamount\medskipamount \divide\smallskipamount\tw@
\abovedisplayskip\medskipamount
\belowdisplayskip \abovedisplayskip
\abovedisplayshortskip\abovedisplayskip
\advance\abovedisplayshortskip-1\abovedisplayskip
\belowdisplayshortskip\abovedisplayshortskip
\advance\belowdisplayshortskip 1\smallskipamount
\jot\baselineskip \divide\jot 4 \relax
}
\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}
\def\footnotesize{\Small}
\def\scriptsize{\SMALL}
\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}}
\def\@xsetfontsize#1#2{%
\chardef\@currsizeindex#2\relax
\edef\@tempa{\@nx\@setfontsize\@nx#1%
\@xp\ifcase\@xp\@currsizeindex\@typesizes
\else{99}{99}\fi}%
\@tempa
}
\chardef\@currsizeindex=6
\widowpenalty=10000
\clubpenalty=10000
\brokenpenalty=10000
\newdimen\linespacing
\lineskip=1pt \lineskiplimit=1pt
\normallineskip=1pt \normallineskiplimit=1pt
\let\baselinestretch=\@empty
\headheight=8pt \headsep=14pt
\footskip=12pt
\textheight=50.5pc \topskip=10pt
\textwidth=30pc
\columnsep=10pt \columnseprule=0pt
\marginparwidth=90pt
\marginparsep=11pt
\marginparpush=5pt
\AtBeginDocument{\settoheight{\footnotesep}{\footnotesize M$^1$}}
\skip\footins=7pt plus11pt
\skip\@mpfootins=\skip\footins
\fboxsep=3pt \fboxrule=.4pt
\arrayrulewidth=.4pt \doublerulesep=2pt
\labelsep=5pt \arraycolsep=\labelsep
\tabcolsep=\labelsep \tabbingsep=\labelsep
\floatsep=15pt plus 12pt \dblfloatsep=15pt plus 12pt
\textfloatsep=\floatsep \dbltextfloatsep=15pt plus 12pt
\intextsep=\floatsep
\@fptop=0pt plus1fil \@dblfptop=0pt plus1fil
\@fpbot=0pt plus1fil \@dblfpbot=0pt plus1fil
\@fpsep=8pt plus2fil \@dblfpsep=8pt plus2fil\relax
\parskip=0pt \relax
\newdimen\normalparindent
\normalparindent=12pt
\parindent=\normalparindent
\partopsep=0pt \relax \parsep=0pt \relax \itemsep=0pt \relax
\@lowpenalty=51 \@medpenalty=151 \@highpenalty=301
\@beginparpenalty=-\@lowpenalty
\@endparpenalty=-\@lowpenalty
\@itempenalty=-\@lowpenalty
\DeclareOption{10pt}{\def\@mainsize{10}\def\@ptsize{0}%
\def\@typesizes{%
\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
}
\def\ps@empty{\let\@mkboth\@gobbletwo
\let\@oddhead\@empty \let\@evenhead\@empty
\let\@oddfoot\@empty \let\@evenfoot\@empty
\global\topskip\normaltopskip}
\def\ps@plain{\ps@empty
\def\@oddfoot{\normalfont\scriptsize \hfil\thepage\hfil}%
\let\@evenfoot\@oddfoot}
\newswitch{runhead}
\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
}
\let\sectionname\@empty
\let\subsectionname\@empty
\let\subsubsectionname\@empty
\let\paragraphname\@empty
\let\subparagraphname\@empty
\def\leftmark{\expandafter\@firstoftwo\topmark{}{}}
\def\rightmark{\expandafter\@secondoftwo\botmark{}{}}
\def\ps@firstpage{\ps@plain
\def\@oddfoot{\normalfont\scriptsize \hfil\thepage\hfil
\global\topskip\normaltopskip}%
\let\@evenfoot\@oddfoot
\def\@oddhead{\@serieslogo\hss}%
\let\@evenhead\@oddhead % in case an article starts on a left-hand page
}
\long\def\@nilgobble#1\@nil{}
\def\markboth#1#2{%
\begingroup
\@temptokena{{#1}{#2}}\xdef\@themark{\the\@temptokena}%
\mark{\the\@temptokena}%
\endgroup
\if@nobreak\ifvmode\nobreak\fi\fi}
\def\ps@myheadings{\ps@headings \let\@mkboth\@gobbletwo}
\newskip\normaltopskip
\normaltopskip=10pt \relax
\let\sectionmark\@gobble
\let\subsectionmark\@gobble
\let\subsubsectionmark\@gobble
\let\paragraphmark\@gobble
\DeclareOption{makeidx}{}
\ExecuteOptions{leqno,centertags,letterpaper,portrait,%
10pt,twoside,onecolumn,final}
\ProcessOptions\relax
\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
\@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
}{}
\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
\let\cleardouble@page\cleardoublepage
\AtBeginDocument{%
\ifx\cleardouble@page\cleardoublepage
\def\cleardoublepage{\clearpage{\pagestyle{empty}\cleardouble@page}}
\fi
}
\newcommand{\uppercasenonmath}[1]{\toks@\@emptytoks
\@xp\@skipmath\@xp\@empty#1$$%
\edef#1{{\@nx\protect\@nx\@upprep\the\toks@}}%
}
\newcommand{\@upprep}{%
\spaceskip1.3\fontdimen2\font plus1.3\fontdimen3\font
\upchars@}
\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}}}
\providecommand{\Mc}{Mc}
\newcommand{\@skipmath}{}
\long\def\@skipmath#1$#2${%
\@xskipmath#1\(\)%
\@ifnotempty{#2}{\toks@\@xp{\the\toks@$#2$}\@skipmath\@empty}}%
\newcommand{\@xskipmath}{}
\long\def\@xskipmath#1\(#2\){%
\uppercase{\toks@\@xp\@xp\@xp{\@xp\the\@xp\toks@#1}}%
\@ifnotempty{#2}{\toks@\@xp{\the\toks@\(#2\)}\@xskipmath\@empty}}%
\def\altucnm#1{%
\MakeTextUppercase{\toks@{#1}}%
\edef#1{\the\toks@}%
}
\AtBeginDocument{%
\@ifundefined{MakeTextUppercase}{}{\let\uppercasenonmath\altucnm}%
}
\@ifundefined{MakeUppercase}{\let\MakeUppercase\uppercase}{}%
\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}
\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}
%%\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
\renewcommand*{\title}[2][]{\gdef\shorttitle{#1}\gdef\@title{#2}}
\edef\title{\@nx\@dblarg
\@xp\@nx\csname\string\title\endcsname}
\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}
\let\shortauthors\@empty \let\authors\@empty
\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
\@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
}
\let\contribs\@empty \let\xcontribs\@empty \let\toccontribs\@empty
\let\addresses\@empty \let\thankses\@empty
\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}}}
\long\def\thanks@warning#1{%
\ClassError{\@classname}{%
\protect\thanks\space should be given separately, not inside author name.%
}\@ehb
}
\renewcommand{\thanks}[1]{%
\@ifnotempty{#1}{\g@addto@macro\thankses{\thanks{#1}}}%
}
\def\enddoc@text{\ifx\@empty\@translators \else\@settranslators\fi
\ifx\@empty\addresses \else\@setaddresses\fi}
\AtEndDocument{\enddoc@text}
\def\curraddrname{{\itshape Current address}}
\def\emailaddrname{{\itshape Email address}}
\def\urladdrname{{\itshape URL}}
\def\@setaddresses{\par
\nobreak \begingroup
\footnotesize
\def\author##1{\nobreak\addvspace\bigskipamount}%
\def\\{\unskip, \ignorespaces}%
\interlinepenalty\@M
\def\address##1##2{\begingroup
\par\addvspace\bigskipamount\indent
\@ifnotempty{##1}{(\ignorespaces##1\unskip) }%
{\scshape\ignorespaces##2}\par\endgroup}%
\def\curraddr##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\indent\curraddrname
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
##2\par}\endgroup}%
\def\email##1##2{\begingroup
\@ifnotempty{##2}{\nobreak\indent\emailaddrname
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
\ttfamily##2\par}\endgroup}%
\def\urladdr##1##2{\begingroup
\def~{\char`\~}%
\@ifnotempty{##2}{\nobreak\indent\urladdrname
\@ifnotempty{##1}{, \ignorespaces##1\unskip}\/:\space
\ttfamily##2\par}\endgroup}%
\addresses
\endgroup
}
\let\@date\@empty
\def\dedicatory#1{\def\@dedicatory{#1}}
\let\@dedicatory=\@empty
\def\keywords#1{\def\@keywords{#1}}
\let\@keywords=\@empty
\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
\def\commby#1{\def\@commby{(Communicated by #1)}}
\let\@commby=\@empty
\def\translname{Translated by}
\def\translator#1{%
\ifx\@empty\@translators \def\@translators{#1}%
\else\g@addto@macro\@translators{\and#1}\fi}
\let\@translators=\@empty
\def\@settranslators{\par\begingroup
\addvspace{6\p@\@plus9\p@}%
\hbox to\columnwidth{\hss\normalfont\normalsize
\translname{ }%
\andify\@translators \uppercasenonmath\@translators
\@translators}
\endgroup
}
\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}
\def\@@and{and}
\newcommand{\andify}{%
\nxandlist{\unskip, }{\unskip{} \@@and~}{\unskip, \@@and~}}
\def\and{\unskip{ }\@@and{ }\ignorespaces}
\def\maketitle{\par
\@topnum\z@ % this prevents figures from falling at the top of page 1
\@setcopyright
\thispagestyle{firstpage}% this sets first page specifications
\uppercasenonmath\shorttitle
\ifx\@empty\shortauthors \let\shortauthors\shorttitle
\else \andify\shortauthors
\fi
\@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
\do\commby \do\@commby
\do\dedicatory \do\@dedicatory \do\thanks \do\thankses
\do\keywords \do\@keywords \do\subjclass \do\@subjclass
}
\def\@maketitle@hook{\global\let\@maketitle@hook\@empty}
\def\@maketitle{%
\normalfont\normalsize
\@adminfootnotes
\@mkboth{\@nx\shortauthors}{\@nx\shorttitle}%
\global\topskip42\p@\relax % 5.5pc " " " " "
\@settitle
\ifx\@empty\authors \else \@setauthors \fi
\ifx\@empty\@dedicatory
\else
\baselineskip18\p@
\vtop{\centering{\footnotesize\itshape\@dedicatory\@@par}%
\global\dimen@i\prevdepth}\prevdepth\dimen@i
\fi
\@setabstract
\normalsize
\if@titlepage
\newpage
\else
\dimen@34\p@ \advance\dimen@-\baselineskip
\vskip\dimen@\relax
\fi
} % end \@maketitle
\def\@adminfootnotes{%
\let\@makefnmark\relax \let\@thefnmark\relax
\ifx\@empty\@date\else \@footnotetext{\@setdate}\fi
\ifx\@empty\@subjclass\else \@footnotetext{\@setsubjclass}\fi
\ifx\@empty\@keywords\else \@footnotetext{\@setkeywords}\fi
\ifx\@empty\thankses\else \@footnotetext{%
\def\par{\let\par\@par}\@setthanks}%
\fi
}
\AtBeginDocument{%
\@ifundefined{publname}{%
\let\publname\@empty
\let\@serieslogo\@empty
}{%
\def\@serieslogo{\article@logo}%
}%
}
\AtBeginDocument{%
\@ifundefined{volinfo}{%
\def\volinfo{%
Volume \currentvolume, Number \number0\currentissue
\if\@printyear , \currentmonth\ \currentyear\fi
}%
}{}%
}
\def\@printyear{TF}% boolean false
\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
\newcommand{\copyrightinfo}[2]{%
\def\copyrightyear{#1}%
\@ifnotempty{#2}{\def\copyrightholder{#2}}%
}
\copyrightinfo{0000}{(copyright holder)}
\def\pagespan#1#2{\setcounter{page}{#1}%
\ifnum\c@page<\z@ \pagenumbering{roman}\setcounter{page}{-#1}\fi
\def\start@page{#1}\def\end@page{#2}}
\pagespan{000}{000}
\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}%
}{}%
}
\@ifundefined{ISSN}{\def\ISSN{0000-0000}}{}
\newcommand\PII[1]{\def\@PII{#1}}
\PII{S \ISSN(XX)0000-0}
\newinsert\copyins
\skip\copyins=1.5pc
\count\copyins=1000 % magnification factor, 1000 = 100%
\dimen\copyins=.5\textheight % maximum allowed per page
\g@addto@macro\@reinserts{%
\ifvoid\copyins\else\insert\copyins{\unvbox\copyins}\fi
}
\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
\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
\kern\z@}%
\fi\fi
}
\def\@combinefloats{%
\ifx \@toplist\@empty \else \@cflt \fi
\ifx \@botlist\@empty \else \@cflb \fi
\ifvoid\copyins \else \@cflci \fi
}
\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
\if@twocolumn
\if@firstcolumn \else \unvbox\copyins \fi
\else
\unvbox\copyins
\fi
}}}%
\if@twocolumn \if@firstcolumn
\insert\copyins{\unvbox\copyins}%
\fi\fi
\global\count\copyins=999 \relax
}
\newif\if@revertcopyright \@revertcopyrightfalse
\newcommand{\revertcopyright}{%
\global\@revertcopyrighttrue
\global\@extracrlinetrue}
\def\@revertcrfontsize{\fontsize{6}{7\p@}\normalfont\upshape}
\def\@extracrline{%
\if@revertcopyright
\unskip\\
\@revertcrfontsize
Reverts to public domain 28 years from publication
\fi
}
\newcommand{\abstractname}{Abstract}
\newcommand{\keywordsname}{Key words and phrases}
\@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}
\@xp\let\@xp\subjclassname\csname subjclassname@2020\endcsname
\def\@tempb{amsart}
\ifx\@classname\@tempb
\newcommand{\datename}{\textit{Date}:}
\else
\newcommand{\datename}{Received by the editors}
\fi
\def\@settitle{\begin{center}%
\baselineskip14\p@\relax
\bfseries
\uppercasenonmath\@title
\@title
\end{center}%
}
\def\author@andify{%
\nxandlist {\unskip ,\penalty-1 \space\ignorespaces}%
{\unskip {} \@@and~}%
{\unskip ,\penalty-2 \space \@@and~}%
}
\def\@setauthors{%
\begingroup
\def\thanks{\protect\thanks@warning}%
\trivlist
\centering\footnotesize \@topsep30\p@\relax
\advance\@topsep by -\baselineskip
\item\relax
\author@andify\authors
\def\\{\protect\linebreak}%
\MakeUppercase{\authors}%
\ifx\@empty\contribs
\else
,\penalty-3 \space \@setcontribs
\@closetoccontribs
\fi
\endtrivlist
\endgroup
}
\def\@closetoccontribs{}
\def\@setcontribs{%
\@xcontribs
\MakeUppercase{\xcontribs}%
}
\def\@setdate{\datename\ \@date\@addpunct.}
\def\@setsubjclass{%
{\itshape\subjclassname.}\enspace\@subjclass\@addpunct.}
\def\@setkeywords{%
{\itshape \keywordsname.}\enspace \@keywords\@addpunct.}
\def\@setthanks{\def\thanks##1{\par##1\@addpunct.}\thankses}
\newbox\abstractbox
\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@
\let\fullwidthdisplay\relax
}%
\item[\hskip\labelsep\scshape\abstractname.]%
}{%
\endlist\egroup
\ifx\@setabstract\relax \@setabstracta \fi
}
\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
}
\def\titlepage{%
\clearpage
\thispagestyle{empty}\setcounter{page}{0}}
\def\endtitlepage{\newpage}
\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}
\def\labelitemi{$\m@th\bullet$}
\def\labelitemii{\bfseries --}% \upshape already done by \itemize
\def\labelitemiii{$\m@th\ast$}
\def\labelitemiv{$\m@th\cdot$}
\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
\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
\def\trivlist{\parsep\parskip\@nmbrlistfalse
\@trivlist \labelwidth\z@ \leftmargin\z@
\itemindent\z@
\let\@itemlabel\@empty
\def\makelabel##1{\upshape##1}}
\renewenvironment{enumerate}{%
\ifnum \@enumdepth >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
\renewenvironment{itemize}{%
\ifnum\@itemdepth>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
\newcommand{\descriptionlabel}[1]{\hspace\labelsep \upshape\bfseries #1:}
\newenvironment{description}{\list{}{%
\advance\leftmargini6\p@ \itemindent-12\p@
\labelwidth\z@ \let\makelabel\descriptionlabel}%
}{
\endlist
}
\let\enddescription=\endlist % for efficiency
\let\upn=\textup
\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}
\newskip\listisep
\listisep\smallskipamount
\def\@listI{\leftmargin\leftmargini \parsep\z@skip
\topsep\listisep \itemsep\z@skip
\listparindent\normalparindent}
\let\@listi\@listI
\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}
\@ifclasswith{\@classname}{fleqn}{%
\let\@tempa\@iden
\AtBeginDocument{\mathindent\leftmargini}%
}{\let\@tempa\@gobble}%
\@ifpackageloaded{amsmath}{\let\@tempa\@gobble}{%
\@ifpackageloaded{amstex}{\let\@tempa\@gobble}{}%
}
\@tempa{%
\def\[{\relax
\ifmmode\@badmath
\else
\begin{trivlist}%
\@beginparpenalty\predisplaypenalty
\@endparpenalty\postdisplaypenalty
\item[]\leavevmode
\hbox to\linewidth\bgroup$\displaystyle
\hskip\mathindent\bgroup
\fi}%
\def\]{\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
}%