%% This is file `amsppt.sty' generated from `amsppt.doc'
%% on 22-JAN-1992 by the docstrip.ams utility (1.2).
%%
%% @texfile{
%%     filename="amsppt.sty",
\def\filename{amsppt.sty}
%%     version="2.1a",
\def\fileversion{2.1a}
%%     date="22-JAN-1992",
\def\filedate{22-JAN-1992}
%%     filetype="AMS-TeX: documentstyle",
%%     copyright="Copyright (C) American Mathematical Society,
%%            all rights reserved.  Copying of this file is
%%            authorized only if either:
%%            (1) you make absolutely no changes to your copy
%%                including name; OR
%%            (2) if you do make changes, you first rename it to some
%%                other name.",
%%     author="American Mathematical Society",
%%     address="American Mathematical Society,
%%            Technical Support Group,
%%            P. O. Box 6248,
%%            Providence, RI 02940,
%%            USA",
%%     telephone="401-455-4080 or (in the USA) 800-321-4AMS",
%%     email="Internet: [email protected]",
%%     codetable="ISO/ASCII",
%%     checksumtype="line count",
%%     checksum="1133",
%%     keywords="amstex, ams-tex, tex",
%%     abstract="This file is a documentstyle for use with
%%       AMS-TeX 2.1. It exists in two forms: amsppt.doc, which
%%       is the full form containing all technical documentation,
%%       and amsppt.sty, which is identical except that all lines
%%       beginning with a single percent sign are removed, to
%%       make the file more rapid-loading when processed by
%%       TeX."
%%     }
\expandafter\ifx\csname amsppt.sty\endcsname\endinput
 \expandafter\def\csname amsppt.sty\endcsname{2.1 (1-JUL-1991)}\fi
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\expandafter\ifx\csname\filename\endcsname\fileversiontest
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\expandafter\ifx\csname\filename\endcsname\relax % file not yet loaded
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    now to load version \fileversiontest}\fi
\expandafter\xdef\csname\filename\endcsname{%
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 \expandafter\gdef\csname\filename\endcsname{%
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\catcode`\@=11
\message{version \fileversion\space(\filedate):}
\expandafter\ifx\csname styname\endcsname\relax
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\fi
\message{Loading utility definitions,}
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\def\thethanks@{}
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\def\thesubjclass@{}
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  \edef\thesubjclass@{\the\toks@
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\newbox\abstractbox@
\def\abstract{\let\savedef@\abstract
\def\abstract{\let\abstract\savedef@
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\def\widestnumber{\begingroup \let\head\relax\let\subhead\relax
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      \setboxz@h{\refsfont@\keyformat{#2}}%
      \refindentwd\wd\z@
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      \setboxz@h{\refsfont@\keyformat{#2}}%
      \refindentwd\wd\z@
  \else\ifx#1\page\setbox\z@\hbox{\quad\bf#2}%
      \pagenumwd\wd\z@
  \else\ifx#1\item
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      \revert@\expandafter{\next@}%
      \setboxz@h{(#2)}\rosteritemwd\wdz@
  \else\message{\string\widestnumber\space not defined for this
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\fi\fi\fi\fi\fi\fi\fi}
\newif\ifmonograph@
\def\Monograph{\monograph@true \let\headmark\rightheadtext
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 \def\remarkheadfont@{\smc}}
\let\varindent@\noindent
\newbox\tocheadbox@    \newbox\tocsubheadbox@
\newbox\tocbox@
\newdimen\pagenumwd
\def\toc{\toc@{Contents}}
\def\newtocdefs{%
  \def \title##1\endtitle
      {\penaltyandskip@\z@\smallskipamount
       \hangindent\wd\tocheadbox@\noindent{\bf##1}}%
  \def \chapter##1{%
       Chapter \uppercase\expandafter{%
             \romannumeral##1.\unskip}\enspace}%
  \def \specialhead##1\endspecialhead
      {\par\hangindent\wd\tocheadbox@ \noindent##1\par}%
  \def \head##1 ##2\endhead
      {\par\hangindent\wd\tocheadbox@ \noindent
       \if\notempty{##1}\hbox to\wd\tocheadbox@{\hfil##1\enspace}\fi
       ##2\par}%
  \def \subhead##1 ##2\endsubhead
      {\par\vskip-\parskip {\normalbaselines
       \advance\leftskip\wd\tocheadbox@
       \hangindent\wd\tocsubheadbox@ \noindent
       \if\notempty{##1}%
             \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
        ##2\par}}%
  \def \subsubhead##1 ##2\endsubsubhead
      {\par\vskip-\parskip {\normalbaselines
       \advance\leftskip\wd\tocheadbox@
       \hangindent\wd\tocsubheadbox@ \noindent
       \if\notempty{##1}%
             \hbox to\wd\tocsubheadbox@{##1\unskip\hfil}\fi
       ##2\par}}}
\def\toc@#1{\relaxnext@
\DN@{\ifx\next\nofrills\DN@\nofrills{\nextii@}%
     \else\DN@{\nextii@{{#1}}}\fi
     \next@}%
\DNii@##1{%
\ifmonograph@\bgroup\else\setbox\tocbox@\vbox\bgroup
  \centerline{\headfont@\ignorespaces##1\unskip}\nobreak
  \vskip\belowheadskip \fi
  \def\page####1%
      {\unskip\penalty\z@\null\hfil
       \rlap{\hbox to\pagenumwd{\quad\hfil####1}}%
             \hfilneg\penalty\@M}%
  \setbox\tocheadbox@\hbox{0.\enspace}%
  \setbox\tocsubheadbox@\hbox{0.0.\enspace}%
  \leftskip\indenti \rightskip\leftskip
  \setboxz@h{\bf\quad000}\pagenumwd\wd\z@
  \advance\rightskip\pagenumwd
  \newtocdefs
}%
\FN@\next@}
\def\endtoc{\par\egroup}
\let\pretitle\relax
\let\preauthor\relax
\let\preaffil\relax
\let\predate\relax
\let\preabstract\relax
\let\prepaper\relax
\def\dedicatory #1\enddedicatory{\def\preabstract{{\medskip
 \eightpoint\it \raggedcenter@#1\endgraf}}}
\def\thetranslator@{}
\def\translator{%
 \let\savedef@\translator
 \def\translator##1\endtranslator{\let\translator\savedef@
   \edef\thetranslator@{\noexpand\nobreak\noexpand\medskip
     \noexpand\line{\noexpand\eightpoint\hfil
     \frills@{Translated by \uppercase}{##1}\qquad\qquad}%
      \noexpand\nobreak}}%
 \nofrillscheck\translator}
\outer\def\endtopmatter{\add@missing\endabstract
\edef\next{\the\leftheadtoks}\ifx\next\empty
 \expandafter\leftheadtext\expandafter{\the\rightheadtoks}\fi
\ifmonograph@\else
  \ifx\thesubjclass@\empty\else \makefootnote@{}{\thesubjclass@}\fi
  \ifx\thekeywords@\empty\else \makefootnote@{}{\thekeywords@}\fi
  \ifx\thethanks@\empty\else \makefootnote@{}{\thethanks@}\fi
\fi
 \pretitle
 \begingroup % to localize variant topskip
 \ifmonograph@ \topskip7pc \else \topskip4pc \fi
 \box\titlebox@
 \endgroup
 \preauthor
 \ifvoid\authorbox@\else \vskip2.5pcplus1pc\unvbox\authorbox@\fi
 \preaffil
 \ifvoid\affilbox@\else \vskip1pcplus.5pc\unvbox\affilbox@\fi
 \predate
 \ifx\thedate@\empty\else
      \vskip1pcplus.5pc\line{\hfil\thedate@\hfil}\fi
 \preabstract
 \ifvoid\abstractbox@\else
      \vskip1.5pcplus.5pc\unvbox\abstractbox@ \fi
 \ifvoid\tocbox@\else\vskip1.5pcplus.5pc\unvbox\tocbox@\fi
 \prepaper
 \vskip2pcplus1pc\relax
}
\def\document{\let\fontlist@\relax\let\alloclist@\relax
 \tenpoint}
\message{section heads,}
\newskip\aboveheadskip       \aboveheadskip\bigskipamount
\newdimen\belowheadskip      \belowheadskip6\p@
\def\headfont@{\smc}
\def\penaltyandskip@#1#2{\par\skip@#2\relax
 \ifdim\lastskip<\skip@\relax\removelastskip
     \ifnum#1=\z@\else\penalty@#1\relax\fi\vskip\skip@
 \else\ifnum#1=\z@\else\penalty@#1\relax\fi\fi}
\def\nobreak{\penalty\@M
 \ifvmode\gdef\penalty@{\global\let\penalty@\penalty\count@@@}%
 \everypar{\global\let\penalty@\penalty\everypar{}}\fi}
\let\penalty@\penalty
\def\heading#1\endheading{\head#1\endhead}
\def\subheading{\DN@{\ifx\next\nofrills
   \expandafter\subheading@
 \else \expandafter\subheading@\expandafter\empty
 \fi}%
 \FN@\next@
}
\def\subheading@#1#2{\subhead#1#2\endsubhead}
\def\specialheadfont@{\bf}
\outer\def\specialhead{%
 \add@missing\endroster \add@missing\enddefinition
 \add@missing\enddemo \add@missing\endexample
 \add@missing\endproclaim
 \penaltyandskip@{-200}\aboveheadskip
 \begingroup\interlinepenalty\@M\rightskip\z@ plus\hsize
 \let\\\linebreak
 \specialheadfont@\noindent}
\def\endspecialhead{\par\endgroup\nobreak\vskip\belowheadskip}
\outer\def\head#1\endhead{%
 \add@missing\endroster \add@missing\enddefinition
 \add@missing\enddemo \add@missing\endexample
 \add@missing\endproclaim
 \penaltyandskip@{-200}\aboveheadskip
 {\headfont@\raggedcenter@\interlinepenalty\@M
 #1\endgraf}\headmark{#1}%
 \nobreak
 \vskip\belowheadskip}
\let\headmark\eat@
\def\restoredef@#1{\relax\let#1\savedef@\let\savedef@\relax}
\newskip\subheadskip       \subheadskip\medskipamount
\def\subheadfont@{\bf}
\outer\def\subhead{%
 \add@missing\endroster \add@missing\enddefinition
 \add@missing\enddemo \add@missing\endexample
 \add@missing\endproclaim
 \let\savedef@\subhead \let\subhead\relax
 \def\subhead##1\endsubhead{\restoredef@\subhead
   \penaltyandskip@{-100}\subheadskip
   \varindent@{\def\usualspace{{\subheadfont@\enspace}}%
   \subheadfont@\ignorespaces##1\unskip\frills@{.\enspace}}%
   \ignorespaces}%
 \nofrillscheck\subhead}
\outer\def\subsubhead{%
 \add@missing\endroster \add@missing\enddefinition
 \add@missing\enddemo
 \add@missing\endexample \add@missing\endproclaim
 \let\savedef@\subsubhead \let\subsubhead\relax
 \def\subsubhead##1\endsubsubhead{\restoredef@\subsubhead
   \penaltyandskip@{-50}\medskipamount
     {\def\usualspace{\/{\it\enspace}}%
   \it##1\unskip\frills@{.\enspace}}}%
 \nofrillscheck\subsubhead}
\message{theorems/proofs/definitions/remarks,}
\def\proclaimheadfont@{\bf}
\outer\def\proclaim{%
 \let\savedef@\proclaim \let\proclaim\relax
 \add@missing\endroster \add@missing\enddefinition
 \add@missing\endproclaim \envir@stack\endproclaim
\def\proclaim##1{\restoredef@\proclaim
  \penaltyandskip@{-100}\medskipamount\varindent@
  \def\usualspace{{\proclaimheadfont@\enspace}}\proclaimheadfont@
  \ignorespaces##1\unskip\frills@{.\enspace}%
 \sl\ignorespaces}%
\nofrillscheck\proclaim}
\def\endproclaim{\revert@envir\endproclaim \par\rm
 \penaltyandskip@{55}\medskipamount}
\def\remarkheadfont@{\it}
\def\remark{\let\savedef@\remark \let\remark\relax
 \add@missing\endroster \add@missing\endproclaim
 \envir@stack\endremark
 \def\remark##1{\restoredef@\remark
   \penaltyandskip@\z@\medskipamount
 {\def\usualspace{{\remarkheadfont@\enspace}}%
 \varindent@\remarkheadfont@\ignorespaces##1\unskip%
 \frills@{.\enspace}}\rm
 \ignorespaces}\nofrillscheck\remark}
\def\endremark{\par\revert@envir\endremark}
\ifx\undefined\square
 \def\square{\vrule width.6em height.5em depth.1em\relax}\fi
\def\qed{\ifhmode\unskip\nobreak\fi\quad
 \ifmmode\square\else$\m@th\square$\fi}
\def\demo{\DN@{\ifx\next\nofrills
   \DN@####1####2{\remark####1{####2}\envir@stack\enddemo
     \ignorespaces}%
 \else
   \DN@####1{\remark{####1}\envir@stack\enddemo\ignorespaces}%
 \fi
 \next@}%
\FN@\next@}

\def\enddemo{\par\revert@envir\enddemo \endremark\medskip}
\def\definition{\let\savedef@\definition \let\definition\relax
 \add@missing\endproclaim \add@missing\endroster
 \add@missing\enddefinition \envir@stack\enddefinition
  \def\definition##1{\restoredef@\definition
    \penaltyandskip@{-100}\medskipamount
       {\def\usualspace{{\proclaimheadfont@\enspace}}%
       \varindent@\proclaimheadfont@\ignorespaces##1\unskip
       \frills@{.\proclaimheadfont@\enspace}}%
       \rm \ignorespaces}%
 \nofrillscheck\definition}
\def\enddefinition{\revert@envir\enddefinition
 \par\medskip}
\def\example{\DN@{\ifx\next\nofrills
   \DN@####1####2{\definition####1{####2}\envir@stack\endexample
     \ignorespaces}%
 \else
   \DN@####1{\definition{####1}\envir@stack\endexample\ignorespaces}%
 \fi
 \next@}%
\FN@\next@}
\def\endexample{\revert@envir\endexample \enddefinition }
\message{rosters,}
\newdimen\rosteritemwd
\rosteritemwd16pt % approximately the width of (iii) in 10 point text
\newcount\rostercount@
\newif\iffirstitem@
\let\plainitem@\item
\newtoks\everypartoks@
\def\par@{\everypartoks@\expandafter{\the\everypar}\everypar{}}
\def\leftskip@{}
\def\roster{%
 \envir@stack\endroster
\edef\leftskip@{\leftskip\the\leftskip}%
\relaxnext@
\rostercount@\z@% Initialize \rostercount@ to 0.
\def\item{\FN@\rosteritem@}%      \item, now redefined, has
\DN@{\ifx\next\runinitem\let\next@\nextii@\else
 \let\next@\nextiii@\fi\next@}%
\DNii@\runinitem% If \runinitem occurs, \nextii@ must kill it off.
 {\unskip% This unskips any space before the original \roster.
  \DN@{\ifx\next[\let\next@\nextii@\else
   \ifx\next"\let\next@\nextiii@\else\let\next@\nextiv@\fi\fi\next@}%
  \DNii@[####1]{\rostercount@####1\relax
   \enspace\therosteritem{\number\rostercount@}~\ignorespaces}%
  \def\nextiii@"####1"{\enspace{\rm####1}~\ignorespaces}%
  \def\nextiv@{\enspace\therosteritem1\rostercount@\@ne~}%
  \par@\firstitem@false% Before doing any of this we still change
  \FN@\next@}%      End of definition of \nextii@\runinitem.
\def\nextiii@{\par\par@% End the present paragraph, change \everypar
 \penalty\@m\smallskip\vskip-\parskip
 \firstitem@true}
\FN@\next@}
\def\rosteritem@{\iffirstitem@\firstitem@false
 \else\par\vskip-\parskip\fi
\leftskip\rosteritemwd \advance\leftskip\normalparindent
\advance\leftskip.5em \noindent
\DNii@[##1]{\rostercount@##1\relax\itembox@}%
\def\nextiii@"##1"{\def\therosteritem@{\rm##1}\itembox@}%
\def\nextiv@{\advance\rostercount@\@ne\itembox@}%
\def\therosteritem@{\therosteritem{\number\rostercount@}}%
\ifx\next[\let\next@\nextii@\else\ifx\next"\let\next@\nextiii@\else
 \let\next@\nextiv@\fi\fi\next@}
\def\itembox@{\llap{\hbox to\rosteritemwd{\hss
 \kern\z@ % kern to thwart \unskip in \rom
 \therosteritem@}\enspace}\ignorespaces}
\def\therosteritem#1{\rom{(\ignorespaces#1\unskip)}}
\newif\ifnextRunin@
\def\endroster{\relaxnext@
\revert@envir\endroster % restore \envir@end
\par\leftskip@% End the paragraph, and restore the \leftskip.
\global\rosteritemwd16\p@ % restore default value
\penalty-50 \vskip-\parskip\smallskip% Add a good break and
\DN@{\ifx\next\Runinitem\let\next@\relax
 \else\nextRunin@false\let\item\plainitem@% Otherwise, set
  \ifx\next\par% moreover, if \endroster is followed by \par,
   \DN@\par{\everypar\expandafter{\the\everypartoks@}}%
  \else% but if the \endroster isn't followed by a new paragraph,
   \DN@{\noindent\everypar\expandafter{\the\everypartoks@}}%
 \fi\fi\next@}%
\FN@\next@}
\newcount\rosterhangafter@
\def\Runinitem#1\roster\runinitem{\relaxnext@
 \envir@stack\endroster
\rostercount@\z@
\def\item{\FN@\rosteritem@}%
\def\runinitem@{#1}%
\DN@{\ifx\next[\let\next\nextii@\else\ifx\next"\let\next\nextiii@
 \else\let\next\nextiv@\fi\fi\next}%
\DNii@[##1]{\rostercount@##1\relax
 \def\item@{\therosteritem{\number\rostercount@}}\nextv@}%
\def\nextiii@"##1"{\def\item@{{\rm##1}}\nextv@}%
\def\nextiv@{\advance\rostercount@\@ne
 \def\item@{\therosteritem{\number\rostercount@}}\nextv@}%
\def\nextv@{\setbox\z@\vbox
 {\ifnextRunin@\noindent\fi
 \runinitem@\unskip\enspace\item@~\par
 \global\rosterhangafter@\prevgraf}%
 \firstitem@false% Set \firstitem@false for future \item's.
 \ifnextRunin@\else\par\fi
 \hangafter\rosterhangafter@\hangindent3\normalparindent
 \ifnextRunin@\noindent\fi
 \runinitem@\unskip\enspace%  Put in all the stored stuff
 \item@~\ifnextRunin@\else\par@\fi% and the \item@, and
 \nextRunin@true\ignorespaces}%% Here's where we set \nextRunin@true.
\FN@\next@}
\message{footnotes,}
\def\footmarkform@#1{$\m@th^{#1}$}
\let\thefootnotemark\footmarkform@
\def\makefootnote@#1#2{\insert\footins
{\interlinepenalty\interfootnotelinepenalty
\eightpoint\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox
\floatingpenalty\@MM\leftskip\z@\rightskip\z@
\spaceskip\z@\xspaceskip\z@
\leavevmode{#1}\footstrut\ignorespaces#2\unskip\lower\dp\strutbox
\vbox to\dp\strutbox{}}}
\newcount\footmarkcount@
\footmarkcount@\z@
\def\footnotemark{\let\@sf\empty\relaxnext@
\ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
\DN@{\ifx[\next\let\next@\nextii@\else
 \ifx"\next\let\next@\nextiii@\else
 \let\next@\nextiv@\fi\fi\next@}%
\DNii@[##1]{\footmarkform@{##1}\@sf}%
\def\nextiii@"##1"{{##1}\@sf}%
\def\nextiv@{\iffirstchoice@\global\advance\footmarkcount@\@ne\fi
 \footmarkform@{\number\footmarkcount@}\@sf}%
\FN@\next@}
\def\footnotetext{\relaxnext@
\DN@{\ifx[\next\let\next@\nextii@\else
 \ifx"\next\let\next@\nextiii@\else
 \let\next@\nextiv@\fi\fi\next@}%
\DNii@[##1]##2{\makefootnote@{\footmarkform@{##1}}{##2}}%
\def\nextiii@"##1"##2{\makefootnote@{##1}{##2}}%
\def\nextiv@##1{\makefootnote@{\footmarkform@%
 {\number\footmarkcount@}}{##1}}%
\FN@\next@}
\def\footnote{\let\@sf\empty\relaxnext@
\ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
\DN@{\ifx[\next\let\next@\nextii@\else
 \ifx"\next\let\next@\nextiii@\else
 \let\next@\nextiv@\fi\fi\next@}%
\DNii@[##1]##2{\footnotemark[##1]\footnotetext[##1]{##2}}%
\def\nextiii@"##1"##2{\footnotemark"##1"\footnotetext"##1"{##2}}%
\def\nextiv@##1{\footnotemark\footnotetext{##1}}%
\FN@\next@}
\def\adjustfootnotemark#1{\advance\footmarkcount@#1\relax}
\def\footnoterule{\kern-3\p@
 \hrule width5pc\kern 2.6\p@}%      the \hrule is .4pt high
\message{figures and captions,}
\def\captionfont@{\smc}
\def\topcaption#1#2\endcaption{%
 {\dimen@\hsize \advance\dimen@-\captionwidth@
  \rm\raggedcenter@ \advance\leftskip.5\dimen@ \rightskip\leftskip
 {\captionfont@#1}%
 \if\notempty{#2}.\enspace\ignorespaces#2\fi
 \endgraf}\nobreak\bigskip}
\def\botcaption#1#2\endcaption{%
 \nobreak\bigskip
 \setboxz@h{\captionfont@#1\if\notempty{#2}.\enspace\rm#2\fi}%
 {\dimen@\hsize \advance\dimen@-\captionwidth@
  \leftskip.5\dimen@ \rightskip\leftskip
  \noindent \ifdim\wdz@>\captionwidth@
  \else\hfil\fi
 {\captionfont@#1}%
 \if\notempty{#2}.\enspace\rm#2\fi\endgraf}}
\def\@ins{\par\begingroup\def\vspace##1{\vskip##1\relax}%
 \def\captionwidth##1{\captionwidth@##1\relax}%
 \setbox\z@\vbox\bgroup} % start a \vbox
\message{miscellaneous,}
\def\block{\RIfMIfI@\nondmatherr@\block\fi
      \else\ifvmode\noindent$$\predisplaysize\hsize
        \else$$\fi
 \def\endblock{\par\egroup$$}\fi
 \vbox\bgroup\advance\hsize-2\indenti\noindent}
\def\endblock{\par\egroup}
\def\cite#1{\rom{[{\citefont@\m@th#1}]}}
\def\citefont@{\rm}
\def\rom#1{\leavevmode\skip@\lastskip\unskip\/%
       \ifdim\skip@=\z@\else\hskip\skip@\fi{\rm#1}}
\message{references,}
\def\refsfont@{\eightpoint}
\newdimen\refindentwd
\setboxz@h{\refsfont@ 00.\enspace}
\refindentwd\wdz@
\outer\def\Refs{\add@missing\endroster \add@missing\endproclaim
\let\savedef@\Refs \let\Refs\relax % because of \outer-ness
\def\Refs##1{\restoredef@\Refs
  \if\notempty{##1}\penaltyandskip@{-200}\aboveheadskip
    \begingroup \raggedcenter@\headfont@
      \ignorespaces##1\endgraf\endgroup
    \penaltyandskip@\@M\belowheadskip
  \fi
  \begingroup\def\envir@end{\endRefs}\refsfont@\sfcode`\.\@m
  }%
\nofrillscheck{\csname Refs\expandafter\endcsname
 \frills@{{References}}}}
\def\endRefs{\par % This will check for a missing \endref, also
 \endgroup}
\newif\ifbook@ \newif\ifprocpaper@
\def\nofrills{%
 \expandafter\ifx\envir@end\endref
   \let\do\relax
   \xdef\nofrills@list{\nofrills@list\do\curbox}%
 \else\errmessage{\Invalid@@ \string\nofrills}%
 \fi}%
\def\defaultreftexts{\gdef\edtext{ed.}\gdef\pagestext{pp.}%
 \gdef\voltext{vol.}\gdef\issuetext{no.}}
\defaultreftexts
\def\ref{\par
 \begingroup \def\envir@end{\endref}%
 \noindent\hangindent\refindentwd
 \def\par{\add@missing\endref}%
 \global\let\nofrills@list\empty
 \refbreaks
 \procpaper@false \book@false
 \def\curbox{\z@}\setbox\z@\vbox\bgroup
}
\let\keyhook@\empty
\def\endref{%
 \setbox\tw@\box\thr@@
 \makerefbox?\thr@@{\endgraf\egroup}%
 \endref@
 \endgraf
 \endgroup
 \keyhook@
 \global\let\keyhook@\empty % \global to conserve save stack
}
\def\key{\gdef\key{\makerefbox\key\keybox@\empty}\key} \newbox\keybox@
\def\no{\gdef\no{\makerefbox\no\keybox@\empty}%
 \gdef\keyhook@{\refstyle C}\no}
\def\by{\makerefbox\by\bybox@\empty} \newbox\bybox@
\let\manyby\by % for backward compatibility
\def\bysame{\by\hbox to3em{\hrulefill}\thinspace\kern\z@}
\def\paper{\makerefbox\paper\paperbox@\it} \newbox\paperbox@
\def\paperinfo{\makerefbox\paperinfo\paperinfobox@\empty}%
 \newbox\paperinfobox@
\def\jour{\makerefbox\jour\jourbox@
 {\aftergroup\book@false \aftergroup\procpaper@false}} \newbox\jourbox@
\def\issue{\makerefbox\issue\issuebox@\empty} \newbox\issuebox@
\def\yr{\makerefbox\yr\yrbox@\empty} \newbox\yrbox@
\def\pages{\makerefbox\pages\pagesbox@\empty} \newbox\pagesbox@
\def\page{\gdef\pagestext{p.}\makerefbox\page\pagesbox@\empty}
\def\ed{\makerefbox\ed\edbox@\empty} \newbox\edbox@
\def\eds{\gdef\edtext{eds.}\makerefbox\eds\edbox@\empty}
\def\book{\makerefbox\book\bookbox@
 {\it\aftergroup\book@true \aftergroup\procpaper@false}}
 \newbox\bookbox@
\def\bookinfo{\makerefbox\bookinfo\bookinfobox@\empty}%
 \newbox\bookinfobox@
\def\publ{\makerefbox\publ\publbox@\empty} \newbox\publbox@
\def\publaddr{\makerefbox\publaddr\publaddrbox@\empty}%
 \newbox\publaddrbox@
\def\inbook{\makerefbox\inbook\bookbox@
 {\aftergroup\procpaper@true \aftergroup\book@false}}
\def\procinfo{\makerefbox\procinfo\procinfobox@\empty}%
 \newbox\procinfobox@
\def\finalinfo{\makerefbox\finalinfo\finalinfobox@\empty}%
 \newbox\finalinfobox@
\def\miscnote{\makerefbox\miscnote\miscnotebox@\empty}%
 \newbox\miscnotebox@
\def\toappear{\miscnote to appear}
\def\lang{\makerefbox\lang\langbox@\empty} \newbox\langbox@
\newbox\morerefbox@
\def\vol{\makerefbox\vol\volbox@{\ifbook@ \else
 \ifprocpaper@\else\bf\fi\fi}}
\newbox\volbox@
\newbox\holdoverbox
\def\makerefbox#1#2#3{\endgraf
 \setbox\z@\lastbox
 \global\setbox\@ne\hbox{\unhbox\holdoverbox
   \ifvoid\z@\else\unhbox\z@\unskip\unskip\unpenalty\fi}%
 \egroup
 \setbox\curbox\box\ifdim\wd\@ne>\z@ \@ne \else\voidb@x\fi
 \ifvoid#2\else\Err@{Redundant \string#1; duplicate use, or
    mutually exclusive information already given}\fi
 \def\curbox{#2}\setbox\curbox\vbox\bgroup \hsize\maxdimen \noindent
 #3}
\def\refbreaks{%
 \def\refconcat##1{\setbox\z@\lastbox \setbox\holdoverbox\hbox{%
      \unhbox\holdoverbox \unhbox\z@\unskip\unskip\unpenalty##1}}%
 \def\holdover##1{%
   \RIfM@
     \penalty-\@M\null
     \hfil$\clubpenalty\z@\widowpenalty\z@\interlinepenalty\z@
     \offinterlineskip\endgraf
     \setbox\z@\lastbox\unskip \unpenalty
     \refconcat{##1}%
     \noindent
     $\hfil\penalty-\@M
   \else
     \endgraf\refconcat{##1}\noindent
   \fi}%
 \def\break{\holdover{\penalty-\@M}}%
 \let\vadjust@\vadjust
 \def\vadjust##1{\holdover{\vadjust@{##1}}}%
 \def\newpage{\vadjust{\vfill\break}}%
}
\def\refstyle#1{\uppercase{%
 \if#1A\relax \def\keyformat##1{[##1]\enspace\hfil}%
 \else\if#1B\relax
   \def\keyformat##1{\aftergroup\kern
             \aftergroup-\aftergroup\refindentwd}%
   \refindentwd\parindent
\else\if#1C\relax
  \def\keyformat##1{\hfil##1.\enspace}%
\fi\fi\fi}% end of \uppercase
}
\refstyle{A}
\def\finalpunct{\ifnum\lastkern=\m@ne\unkern\else.\fi
      \refquotes@\refbreak@}%
\def\continuepunct#1#2#3#4{}%
\def\endref@{%
 \keyhook@
 \def\nofrillscheck##1{%
   \def\do####1{\ifx##1####1\let\frills@\eat@\fi}%
   \let\frills@\identity@ \nofrills@list}%
 \ifvoid\bybox@
   \ifvoid\edbox@
   \else\setbox\bybox@\hbox{\unhbox\edbox@\breakcheck
     \nofrillscheck\edbox@\frills@{\space(\edtext)}\refbreak@}\fi
 \fi
 \ifvoid\keybox@\else\hbox to\refindentwd{%
      \keyformat{\unhbox\keybox@}}\fi
 \commaunbox@\morerefbox@
 \ppunbox@\empty\empty\bybox@\empty
 \ifbook@ % Case 1: \book etc.
   \commaunbox@\bookbox@ \commaunbox@\bookinfobox@
   \ppunbox@\empty{ (}\procinfobox@)%
   \ppunbox@,{ vol.~}\volbox@\empty
   \ppunbox@\empty{ (}\edbox@{, \edtext)}%
   \commaunbox@\publbox@ \commaunbox@\publaddrbox@
   \commaunbox@\yrbox@
   \ppunbox@,{ \pagestext~}\pagesbox@\empty
 \else
   \commaunbox@\paperbox@ \commaunbox@\paperinfobox@
   \ifprocpaper@ % Case 2: \paper ... \inbook
     \commaunbox@\bookbox@
     \ppunbox@\empty{ (}\procinfobox@)%
     \ppunbox@\empty{ (}\edbox@{, \edtext)}%
     \commaunbox@\bookinfobox@
     \ppunbox@,{ \voltext~}\volbox@\empty
     \commaunbox@\publbox@ \commaunbox@\publaddrbox@
     \commaunbox@\yrbox@
     \ppunbox@,{ \pagestext~}\pagesbox@\empty
   \else % Case 3: \paper ... \jour
     \commaunbox@\jourbox@
     \ppunbox@\empty{ }\volbox@\empty
     \ppunbox@\empty{ (}\yrbox@)%
     \ppunbox@,{ \issuetext~}\issuebox@\empty
     \commaunbox@\publbox@ \commaunbox@\publaddrbox@
     \commaunbox@\pagesbox@
   \fi
 \fi
 \commaunbox@\finalinfobox@
 \ppunbox@\empty{ (}\miscnotebox@)%
 \finalpunct\ppunbox@\empty{ (}\langbox@)%
 \defaultreftexts
}
\def\punct@#1{#1}
\def\ppunbox@#1#2#3#4{\ifvoid#3\else
 \ifnum\lastkern=\m@ne\unkern\let\punct@\eat@\fi
 \nofrillscheck#3%
 \punct@{#1}\refquotes@\refbreak@
 \let\punct@\identity@
 \frills@{#2\eat@}\space
 \unhbox#3\breakcheck
 \frills@{#4\eat@}{\kern\m@ne sp}\fi}
\def\commaunbox@#1{\ppunbox@,\space{#1}\empty}
\def\breakcheck{\edef\refbreak@{\ifnum\lastpenalty=\z@\else
 \penalty\the\lastpenalty\relax\fi}\unpenalty}
\def\endquotes{\def\refquotes@{''\let\refquotes@\empty}}
\let\refquotes@\empty
\let\refbreak@\empty
\def\moreref{%
 \setbox\tw@\box\thr@@
 \makerefbox?\thr@@{\endgraf\egroup}%
 \let\savedef@\finalpunct  \let\finalpunct\empty
 \endref@
 \def\punct@##1##2{##2;}%
 \global\let\nofrills@list\empty % global, to conserve save stack
 \let\finalpunct\savedef@
 \def\curbox{\morerefbox@}%
 \setbox\morerefbox@\vbox\bgroup \hsize\maxdimen \noindent
}
\def\transl{\moreref}
\message{end of document,}
\outer\def\enddocument{\par% \par will do a runaway check for \endref
 \add@missing\endRefs
 \add@missing\endroster \add@missing\endproclaim
 \add@missing\enddefinition
 \add@missing\enddemo \add@missing\endremark \add@missing\endexample
\ifmonograph@ % do nothing
\else
\nobreak
\thetranslator@
\count@\z@ \loop\ifnum\count@<\addresscount@\advance\count@\@ne
\csname address\number\count@\endcsname
\csname email\number\count@\endcsname
\repeat
\fi
\vfill\supereject\end}
\message{output routine,}
\def\folio{{\foliofont@\ifnum\pageno<\z@ \romannumeral-\pageno
\else\number\pageno \fi}}
\def\foliofont@{\eightrm}
\def\headlinefont@{\eightpoint}
\def\leftheadline{\rlap{\folio}\hfill \iftrue\topmark\fi \hfill}
\def\rightheadline{\hfill \expandafter\iffalse\botmark\fi
 \hfill \llap{\folio}}
\newtoks\leftheadtoks
\newtoks\rightheadtoks
\def\leftheadtext{\let\savedef@\leftheadtext
 \def\leftheadtext##1{\let\leftheadtext\savedef@
   \leftheadtoks\expandafter{\frills@\uppercasetext@{##1}}%
   \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}
   \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
       \headlinefont@##1}\fi}%
 \nofrillscheck\leftheadtext}
\def\rightheadtext{\let\savedef@\rightheadtext
 \def\rightheadtext##1{\let\rightheadtext\savedef@
   \rightheadtoks\expandafter{\frills@\uppercasetext@{##1}}%
   \mark{\the\leftheadtoks\noexpand\else\the\rightheadtoks}%
   \ifsyntax@\setboxz@h{\def\\{\unskip\space\ignorespaces}%
       \headlinefont@##1}\fi}%
 \nofrillscheck\rightheadtext}
\headline={\def\chapter#1{\chapterno@. }%
 \def\\{\unskip\space\ignorespaces}\headlinefont@
 \ifodd\pageno \rightheadline \else \leftheadline\fi}
\def\NoRunningHeads{\global\runheads@false\global\let\headmark\eat@}
\def\NoPageNumbers{\gdef\folio{}}
\def\logo@{\baselineskip2pc \hbox to\hsize{\hfil\eightpoint Typeset by
\AmSTeX}}
\newif\iffirstpage@     \firstpage@true
\newif\ifrunheads@      \runheads@true
\output={\output@}
\def\output@{\shipout\vbox{%
\iffirstpage@ \global\firstpage@false
 \pagebody \logo@ \makefootline%
\else \ifrunheads@ \makeheadline \pagebody
      \else \pagebody \makefootline \fi
\fi}%
\advancepageno \ifnum\outputpenalty>-\@MM\else\dosupereject\fi}
\message{hyphenation exceptions (U.S. English)}
\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 Brown-ian Eng-lish Euler-ian Feb-ru-ary Gauss-ian
Grothen-dieck Hamil-ton-ian Her-mit-ian Jan-u-ary Japan-ese Kor-te-weg
Le-gendre Lip-schitz Lip-schitz-ian Mar-kov-ian Noe-ther-ian
No-vem-ber Rie-mann-ian Schwarz-schild Sep-tem-ber}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\tenpoint
\W@{}
\csname amsppt.sty\endcsname
\endinput
%%
%% End of file `amsppt.sty'.