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amstex.tex
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amstex.tex
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% Version of amstex.tex downloaded on 15.6.05
% For my own changes look for the string DHF
\DHFamstexloadedtrue %DHF 15.6.05
%% @texfile{
%% filename = "amstex.tex",
%% version = "2.2",
%% date = "2001/10/04",
%% time = "09:08:48 EDT",
%% checksum = "54330 1806 2947 78920",
%% filetype = "AMS-TeX: documentstyle",
%% author = "American Mathematical Society",
%% copyright = "Copyright 1985, 1990, 1991, 2001
%% American Mathematical Society,
%% all rights reserved. Copying of this file is
%% authorized only if either:
%% (1) you make absolutely no changes to your copy
%% including name; OR
%% (2) if you do make changes, you first rename it
%% to some other name.",
%% address = "American Mathematical Society,
%% Technical Support,
%% Publications Technical Group,
%% P. O. Box 6248,
%% Providence, RI 02940,
%% USA",
%% telephone = "401-455-4080 or (in the USA and Canada)
%% 800-321-4AMS (321-4267)",
%% FAX = "401-331-3842",
%% email = "tech-support@ams.org (Internet)",
%% codetable = "ISO/ASCII",
%% keywords = "amstex, ams-tex, tex",
%% abstract = "This file contains the AMS-TeX Version 2.2
%% macro package. It is intended to be used in
%% conjunction with plain TeX. The macros defined
%% herein are chiefly oriented to the construction
%% of mathematical formulas, both display and
%% nondisplay, using AMS conventions for fonts,
%% spacing, and other details."
%% docstring = "The checksum field above contains a CRC-16
%% checksum as the first value, followed by the
%% equivalent of the standard UNIX wc (word
%% count) utility output of lines, words, and
%% characters. This is produced by Robert
%% Solovay's checksum utility.",
%% }
%% ====================================================================
\def\fmtname{AmS-TeX}
\let\plainfmtversion\fmtversion
\def\fmtversion{2.2}
\catcode`\@=11
\ifx\amstexloaded@\relax\catcode`\@=\active
\endinput\else\let\amstexloaded@\relax\fi
\newlinechar=`\^^J
\def\W@{\immediate\write\sixt@@n}
\def\CR@{\W@{^^J\fmtname - Version \fmtversion^^J}}
\CR@ \everyjob{\CR@}
\message{Loading definitions for}
\message{misc utility macros,}
\toksdef\toks@@=2
\long\def\rightappend@#1\to#2{\toks@{\\{#1}}\toks@@
=\expandafter{#2}\xdef#2{\the\toks@@\the\toks@}\toks@{}\toks@@{}}
\def\alloclist@{}
\newif\ifalloc@
\def\showallocations{{\def\\{\immediate\write\m@ne}\alloclist@}\alloc@true}
\def\alloc@#1#2#3#4#5{\global\advance\count1#1by\@ne
\ch@ck#1#4#2\allocationnumber=\count1#1
\global#3#5=\allocationnumber
\edef\next@{\string#5=\string#2\the\allocationnumber}%
\expandafter\rightappend@\next@\to\alloclist@}
\newcount\count@@
\newcount\count@@@
\def\FN@{\futurelet\next}
\def\DN@{\def\next@}
\def\DNii@{\def\nextii@}
\def\RIfM@{\relax\ifmmode}
\def\RIfMIfI@{\relax\ifmmode\ifinner}
\def\setboxz@h{\setbox\z@\hbox}
\def\wdz@{\wd\z@}
\def\boxz@{\box\z@}
\def\setbox@ne{\setbox\@ne}
\def\wd@ne{\wd\@ne}
\def\iterate{\body\expandafter\iterate\else\fi}
\def\err@#1{\errmessage{AmS-TeX error: #1}}
\newhelp\defaulthelp@{Sorry, I already gave what help I could...^^J
Maybe you should try asking a human?^^J
An error might have occurred before I noticed any problems.^^J
``If all else fails, read the instructions.''}
\def\Err@{\errhelp\defaulthelp@\err@}
\def\eat@#1{}
\def\in@#1#2{\def\in@@##1#1##2##3\in@@{\ifx\in@##2\in@false\else\in@true\fi}%
\in@@#2#1\in@\in@@}
\newif\ifin@
\def\space@.{\futurelet\space@\relax}
\space@. %
\newhelp\athelp@
{Only certain combinations beginning with @ make sense to me.^^J
Perhaps you wanted \string\@\space for a printed @?^^J
I've ignored the character or group after @.}
{\catcode`\~=\active % just in case
\lccode`\~=`\@ \lowercase{\gdef~{\FN@\at@}}}
\def\at@{\let\next@\at@@
\ifcat\noexpand\next a\else\ifcat\noexpand\next0\else
\ifcat\noexpand\next\relax\else
\let\next\at@@@\fi\fi\fi
\next@}
\def\at@@#1{\expandafter
\ifx\csname\space @\string#1\endcsname\relax
\expandafter\at@@@ \else
\csname\space @\string#1\expandafter\endcsname\fi}
\def\at@@@#1{\errhelp\athelp@ \err@{\Invalid@@ @}}%%
\def\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}%%
\newhelp\defahelp@{If you typed \string\define\space cs instead of
\string\define\string\cs\space^^J
I've substituted an inaccessible control sequence so that your^^J
definition will be completed without mixing me up too badly.^^J
If you typed \string\define{\string\cs} the inaccessible control sequence^^J
was defined to be \string\cs, and the rest of your^^J
definition appears as input.}
\newhelp\defbhelp@{I've ignored your definition, because it might^^J
conflict with other uses that are important to me.}
\def\define{\FN@\define@}
\def\define@{\ifcat\noexpand\next\relax
\expandafter\define@@\else\errhelp\defahelp@ %1
\err@{\string\define\space must be followed by a control
sequence}\expandafter\def\expandafter\nextii@\fi} %2
\def\undefined@@@@@@@@@@{}
\def\preloaded@@@@@@@@@@{}
\def\next@@@@@@@@@@{}
\def\define@@#1{\ifx#1\relax\errhelp\defbhelp@ %1
\err@{\string#1\space is already defined}\DN@{\DNii@}\else
\expandafter\ifx\csname\expandafter\eat@\string %2
#1@@@@@@@@@@\endcsname\undefined@@@@@@@@@@\errhelp\defbhelp@
\err@{\string#1\space can't be defined}\DN@{\DNii@}\else
\expandafter\ifx\csname\expandafter\eat@\string#1\endcsname\relax %3
\global\let#1\undefined\DN@{\def#1}\else\errhelp\defbhelp@
\err@{\string#1\space is already defined}\DN@{\DNii@}\fi
\fi\fi\next@}
\let\redefine\def
\def\predefine#1#2{\let#1#2}
\def\undefine#1{\let#1\undefined}
\message{page layout,}
\newdimen\captionwidth@
\captionwidth@\hsize
\advance\captionwidth@-1.5in
\def\pagewidth#1{\hsize#1\relax
\captionwidth@\hsize\advance\captionwidth@-1.5in}
\def\pageheight#1{\vsize#1\relax}
\def\hcorrection#1{\advance\hoffset#1\relax}
\def\vcorrection#1{\advance\voffset#1\relax}
\message{accents/punctuation,}
\def\tie{\unskip\nobreak\ }
\let\graveaccent\`
\let\acuteaccent\'
\let\tildeaccent\~
\let\hataccent\^
\let\underscore\_
\let\B\=
\let\D\.
\let\ic@\/
\def\/{\unskip\ic@}
\def\textfonti{\the\textfont\@ne}
\def\t#1#2{{\edef\next@{\the\font}\textfonti\accent"7F \next@#1#2}}
\def~{\unskip\nobreak\ \ignorespaces}
\def\.{.\spacefactor\@m}
\atdef@;{\leavevmode\null;}
\atdef@:{\leavevmode\null:}
\atdef@?{\leavevmode\null?}
\edef\@{\string @}
\def\relaxnext@{\let\next\relax}
\atdef@-{\relaxnext@\leavevmode
\DN@{\ifx\next-\DN@-{\FN@\nextii@}\else
\DN@{\leavevmode\hbox{-}}\fi\next@}%
\DNii@{\ifx\next-\DN@-{\leavevmode\hbox{---}}\else
\DN@{\leavevmode\hbox{--}}\fi\next@}%
\FN@\next@}
\def\srdr@{\kern.16667em}
\def\drsr@{\kern.02778em}
\def\sldl@{\drsr@}
\def\dlsl@{\srdr@}
\atdef@"{\unskip\relaxnext@
\DN@{\ifx\next\space@\DN@. {\FN@\nextii@}\else
\DN@.{\FN@\nextii@}\fi\next@.}%
\DNii@{\ifx\next`\DN@`{\FN@\nextiii@}\else
\ifx\next\lq\DN@\lq{\FN@\nextiii@}\else
\DN@####1{\FN@\nextiv@}\fi\fi\next@}%
\def\nextiii@{\ifx\next`\DN@`{\sldl@``}\else\ifx\next\lq
\DN@\lq{\sldl@``}\else\DN@{\dlsl@`}\fi\fi\next@}%
\def\nextiv@{\ifx\next'\DN@'{\srdr@''}\else
\ifx\next\rq\DN@\rq{\srdr@''}\else\DN@{\drsr@'}\fi\fi\next@}%
\FN@\next@}
\def\flushpar{\par\noindent}
\def\textfontii{\the\textfont\tw@}
\def\lbrace@{\delimiter"4266308 }
\def\rbrace@{\delimiter"5267309 }
\def\{{\RIfM@\lbrace@\else{\textfontii f}\spacefactor\@m\fi}
\def\}{\RIfM@\rbrace@\else
\let\@sf\empty\ifhmode\edef\@sf{\spacefactor\the\spacefactor}\fi
{\textfontii g}\@sf\relax\fi}
\let\lbrace\{
\let\rbrace\}
\def\AmSTeX{{\textfontii A\kern-.1667em%
\lower.5ex\hbox{M}\kern-.125emS}-\TeX\spacefactor1000 }
\message{line and page breaks,}
\def\vmodeerr@#1{\Err@{\string#1\space not allowed between paragraphs}}
\def\mathmodeerr@#1{\Err@{\string#1\space not allowed in math mode}}
\def\linebreak{\RIfM@\mathmodeerr@\linebreak\else
\ifhmode\unskip\unkern\break\else\vmodeerr@\linebreak\fi\fi}
\def\slash{\unskip/\penalty\exhyphenpenalty}
\newskip\saveskip@
\def\allowlinebreak{\RIfM@\mathmodeerr@\allowlinebreak\else
\ifhmode\saveskip@\lastskip\unskip
\allowbreak\ifdim\saveskip@>\z@\hskip\saveskip@\fi
\else\vmodeerr@\allowlinebreak\fi\fi}
\def\nolinebreak{\RIfM@\mathmodeerr@\nolinebreak\else
\ifhmode\saveskip@\lastskip\unskip
\nobreak\ifdim\saveskip@>\z@\hskip\saveskip@\fi
\else\vmodeerr@\nolinebreak\fi\fi}
\def\newline{\relaxnext@
\DN@{\RIfM@\expandafter\mathmodeerr@\expandafter\newline\else
\ifhmode\ifx\next\par\else
\expandafter\unskip\expandafter\null\expandafter\hfill\expandafter\break\fi
\else
\expandafter\vmodeerr@\expandafter\newline\fi\fi}%
\FN@\next@}
\def\dmatherr@#1{\Err@{\string#1\space not allowed in display math mode}}
\def\nondmatherr@#1{\Err@{\string#1\space not allowed in non-display math
mode}}
\def\onlydmatherr@#1{\Err@{\string#1\space allowed only in display math mode}}
\def\nonmatherr@#1{\Err@{\string#1\space allowed only in math mode}}
\def\mathbreak{\RIfMIfI@\break\else
\dmatherr@\mathbreak\fi\else\nonmatherr@\mathbreak\fi}
\def\nomathbreak{\RIfMIfI@\nobreak\else
\dmatherr@\nomathbreak\fi\else\nonmatherr@\nomathbreak\fi}
\def\allowmathbreak{\RIfMIfI@\allowbreak\else
\dmatherr@\allowmathbreak\fi\else\nonmatherr@\allowmathbreak\fi}
\def\pagebreak{\RIfM@
\ifinner\nondmatherr@\pagebreak\else\postdisplaypenalty-\@M\fi
\else\ifvmode\removelastskip\break\else\vadjust{\break}\fi\fi}
\def\nopagebreak{\RIfM@
\ifinner\nondmatherr@\nopagebreak\else\postdisplaypenalty\@M\fi
\else\ifvmode\nobreak\else\vadjust{\nobreak}\fi\fi}
\def\nonvmodeerr@#1{\Err@{\string#1\space not allowed within a paragraph
or in math}}
\def\vnonvmode@#1#2{\relaxnext@\DNii@{\ifx\next\par\DN@{#1}\else
\DN@{#2}\fi\next@}%
\ifvmode\DN@{#1}\else
\DN@{\FN@\nextii@}\fi\next@}
\def\newpage{\vnonvmode@{\vfill\break}{\nonvmodeerr@\newpage}}
\def\smallpagebreak{\vnonvmode@\smallbreak{\nonvmodeerr@\smallpagebreak}}
\def\medpagebreak{\vnonvmode@\medbreak{\nonvmodeerr@\medpagebreak}}
\def\bigpagebreak{\vnonvmode@\bigbreak{\nonvmodeerr@\bigpagebreak}}
\def\NoBlackBoxes{\global\overfullrule\z@}
\def\BlackBoxes{\global\overfullrule5\p@}
\def\Invalid@#1{\def#1{\Err@{\Invalid@@\string#1}}}
\def\Invalid@@{Invalid use of }
\message{figures,}
\Invalid@\caption
\Invalid@\captionwidth
\newdimen\smallcaptionwidth@
\def\topspace{\mid@false\ins@}
\def\midspace{\mid@true\ins@}
\newif\ifmid@
\def\captionfont@{}
\def\ins@#1{\relaxnext@\allowbreak
\smallcaptionwidth@\captionwidth@\gdef\thespace@{#1}%
\DN@{\ifx\next\space@\DN@. {\FN@\nextii@}\else
\DN@.{\FN@\nextii@}\fi\next@.}%
\DNii@{\ifx\next\caption\DN@\caption{\FN@\nextiii@}%
\else\let\next@\nextiv@\fi\next@}%
\def\nextiv@{\vnonvmode@
{\ifmid@\expandafter\midinsert\else\expandafter\topinsert\fi
\vbox to\thespace@{}\endinsert}
{\ifmid@\nonvmodeerr@\midspace\else\nonvmodeerr@\topspace\fi}}%
\def\nextiii@{\ifx\next\captionwidth\expandafter\nextv@
\else\expandafter\nextvi@\fi}%
\def\nextv@\captionwidth##1##2{\smallcaptionwidth@##1\relax\nextvi@{##2}}%
\def\nextvi@##1{\def\thecaption@{\captionfont@##1}%
\DN@{\ifx\next\space@\DN@. {\FN@\nextvii@}\else
\DN@.{\FN@\nextvii@}\fi\next@.}%
\FN@\next@}%
\def\nextvii@{\vnonvmode@
{\ifmid@\expandafter\midinsert\else
\expandafter\topinsert\fi\vbox to\thespace@{}\nobreak\smallskip
\setboxz@h{\noindent\ignorespaces\thecaption@\unskip}%
\ifdim\wdz@>\smallcaptionwidth@\centerline{\vbox{\hsize\smallcaptionwidth@
\noindent\ignorespaces\thecaption@\unskip}}%
\else\centerline{\boxz@}\fi\endinsert}
{\ifmid@\nonvmodeerr@\midspace
\else\nonvmodeerr@\topspace\fi}}%
\FN@\next@}
\message{comments,}
\def\newcodes@{\catcode`\\12\catcode`\{12\catcode`\}12\catcode`\#12%
\catcode`\%12\relax}
\def\oldcodes@{\catcode`\\0\catcode`\{1\catcode`\}2\catcode`\#6%
\catcode`\%14\relax}
\def\comment{\newcodes@\endlinechar=10 \comment@}
{\lccode`\0=`\\
\lowercase{\gdef\comment@#1^^J{\comment@@#10endcomment\comment@@@}%
\gdef\comment@@#10endcomment{\FN@\comment@@@}%
\gdef\comment@@@#1\comment@@@{\ifx\next\comment@@@\let\next\comment@
\else\def\next{\oldcodes@\endlinechar=`\^^M\relax}%
\fi\next}}}
\def\pr@m@s{\ifx'\next\DN@##1{\prim@s}\else\let\next@\egroup\fi\next@}
\def\prime{{\null\prime@\null}}
\mathchardef\prime@="0230
\let\dsize\displaystyle
\let\tsize\textstyle
\let\ssize\scriptstyle
\let\sssize\scriptscriptstyle
\message{math spacing,}
\def\,{\RIfM@\mskip\thinmuskip\relax\else\kern.16667em\fi}
\def\!{\RIfM@\mskip-\thinmuskip\relax\else\kern-.16667em\fi}
\let\thinspace\,
\let\negthinspace\!
\def\medspace{\RIfM@\mskip\medmuskip\relax\else\kern.222222em\fi}
\def\negmedspace{\RIfM@\mskip-\medmuskip\relax\else\kern-.222222em\fi}
\def\thickspace{\RIfM@\mskip\thickmuskip\relax\else\kern.27777em\fi}
\let\;\thickspace
\def\negthickspace{\RIfM@\mskip-\thickmuskip\relax\else
\kern-.27777em\fi}
\atdef@,{\RIfM@\mskip.1\thinmuskip\else\leavevmode\null,\fi}
\atdef@!{\RIfM@\mskip-.1\thinmuskip\else\leavevmode\null!\fi}
\atdef@.{\RIfM@&&\else\leavevmode.\spacefactor3000 \fi}
\def\and{\DOTSB\;\mathchar"3026 \;}
\def\implies{\DOTSB\;\Longrightarrow\;}
\def\impliedby{\DOTSB\;\Longleftarrow\;}
\message{fractions,}
\def\frac#1#2{{#1\over#2}}
\def\dfrac#1#2{{\displaystyle{#1\over#2}}}
\def\tfrac#1#2{{\textstyle{#1\over#2}}}
\newdimen\ex@
\ex@.2326ex
\Invalid@\thickness
\def\thickfrac{\relaxnext@
\DN@{\ifx\next\thickness\let\next@\nextii@\else
\DN@{\nextii@\thickness1}\fi\next@}%
\DNii@\thickness##1##2##3{{##2\above##1\ex@##3}}%
\FN@\next@}
\def\fracwithdelims#1#2#3#4{{#3\overwithdelims#1#2#4}}
\def\thickfracwithdelims#1#2{\relaxnext@\def\ldelim@{#1}\def\rdelim@{#2}%
\DN@{\ifx\next\thickness\let\next@\nextii@\else
\DN@{\nextii@\thickness1}\fi\next@}%
\DNii@\thickness##1##2##3{{##2\abovewithdelims
\ldelim@\rdelim@##1\ex@##3}}%
\FN@\next@}
\def\binom#1#2{{#1\choose#2}}
\def\dbinom#1#2{{\displaystyle{#1\choose#2}}}
\def\tbinom#1#2{{\textstyle{#1\choose#2}}}
\def\:{\nobreak\hskip.1111em\mathpunct{}\nonscript\mkern-\thinmuskip{:}\hskip
.3333emplus.0555em\relax}
\def\snug{\unskip\kern-\mathsurround}
\message{smash commands,}
\def\topsmash{\top@true\bot@false\smash@}
\def\botsmash{\top@false\bot@true\smash@}
\newif\iftop@
\newif\ifbot@
\def\smash{\top@true\bot@true\smash@}
\def\smash@{\RIfM@\expandafter\mathpalette\expandafter\mathsm@sh\else
\expandafter\makesm@sh\fi}
\def\finsm@sh{\iftop@\ht\z@\z@\fi\ifbot@\dp\z@\z@\fi\leavevmode\boxz@}
\message{large operator symbols,}
\def\LimitsOnSums{\global\let\slimits@\displaylimits}
\def\NoLimitsOnSums{\global\let\slimits@\nolimits}
\LimitsOnSums
\mathchardef\coprod@="1360 \def\coprod{\DOTSB\coprod@\slimits@}
\mathchardef\bigvee@="1357 \def\bigvee{\DOTSB\bigvee@\slimits@}
\mathchardef\bigwedge@="1356 \def\bigwedge{\DOTSB\bigwedge@\slimits@}
\mathchardef\biguplus@="1355 \def\biguplus{\DOTSB\biguplus@\slimits@}
\mathchardef\bigcap@="1354 \def\bigcap{\DOTSB\bigcap@\slimits@}
\mathchardef\bigcup@="1353 \def\bigcup{\DOTSB\bigcup@\slimits@}
\mathchardef\prod@="1351 \def\prod{\DOTSB\prod@\slimits@}
\mathchardef\sum@="1350 \def\sum{\DOTSB\sum@\slimits@}
\mathchardef\bigotimes@="134E \def\bigotimes{\DOTSB\bigotimes@\slimits@}
\mathchardef\bigoplus@="134C \def\bigoplus{\DOTSB\bigoplus@\slimits@}
\mathchardef\bigodot@="134A \def\bigodot{\DOTSB\bigodot@\slimits@}
\mathchardef\bigsqcup@="1346 \def\bigsqcup{\DOTSB\bigsqcup@\slimits@}
\message{integrals,}
\def\LimitsOnInts{\global\let\ilimits@\displaylimits}
\def\NoLimitsOnInts{\global\let\ilimits@\nolimits}
\NoLimitsOnInts
\def\int{\DOTSI\intop\ilimits@}
\def\oint{\DOTSI\ointop\ilimits@}
\def\intic@{\mathchoice{\hskip.5em}{\hskip.4em}{\hskip.4em}{\hskip.4em}}
\def\negintic@{\mathchoice
{\hskip-.5em}{\hskip-.4em}{\hskip-.4em}{\hskip-.4em}}
\def\intkern@{\mathchoice{\!\!\!}{\!\!}{\!\!}{\!\!}}
\def\intdots@{\mathchoice{\plaincdots@}
{{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}
{{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}
{{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
\newcount\intno@
\def\iint{\DOTSI\intno@\tw@\FN@\ints@}
\def\iiint{\DOTSI\intno@\thr@@\FN@\ints@}
\def\iiiint{\DOTSI\intno@4 \FN@\ints@}
\def\idotsint{\DOTSI\intno@\z@\FN@\ints@}
\def\ints@{\findlimits@\ints@@}
\newif\iflimtoken@
\newif\iflimits@
\def\findlimits@{\limtoken@true\ifx\next\limits\limits@true
\else\ifx\next\nolimits\limits@false\else
\limtoken@false\ifx\ilimits@\nolimits\limits@false\else
\ifinner\limits@false\else\limits@true\fi\fi\fi\fi}
\def\multint@{\int\ifnum\intno@=\z@\intdots@ %1
\else\intkern@\fi %2
\ifnum\intno@>\tw@\int\intkern@\fi %3
\ifnum\intno@>\thr@@\int\intkern@\fi %4
\int} %5
\def\multintlimits@{\intop\ifnum\intno@=\z@\intdots@\else\intkern@\fi
\ifnum\intno@>\tw@\intop\intkern@\fi
\ifnum\intno@>\thr@@\intop\intkern@\fi\intop}
\def\ints@@{\iflimtoken@ %1
\def\ints@@@{\iflimits@\negintic@\mathop{\intic@\multintlimits@}\limits %2
\else\multint@\nolimits\fi %3
\eat@} %4
\else %5
\def\ints@@@{\iflimits@\negintic@
\mathop{\intic@\multintlimits@}\limits\else
\multint@\nolimits\fi}\fi\ints@@@}
\def\LimitsOnNames{\global\let\nlimits@\displaylimits}
\def\NoLimitsOnNames{\global\let\nlimits@\nolimits@}
\LimitsOnNames
\def\nolimits@{\relaxnext@
\DN@{\ifx\next\limits\DN@\limits{\nolimits}\else
\let\next@\nolimits\fi\next@}%
\FN@\next@}
\message{operator names,}
\def\newmcodes@{\mathcode`\'"27\mathcode`\*"2A\mathcode`\."613A%
\mathcode`\-"2D\mathcode`\/"2F\mathcode`\:"603A }
\def\operatorname#1{\mathop{\newmcodes@\kern\z@\fam\z@#1}\nolimits@}
\def\operatornamewithlimits#1{\mathop{\newmcodes@\kern\z@\fam\z@#1}\nlimits@}
\def\qopname@#1{\mathop{\fam\z@#1}\nolimits@}
\def\qopnamewl@#1{\mathop{\fam\z@#1}\nlimits@}
\def\arccos{\qopname@{arccos}}
\def\arcsin{\qopname@{arcsin}}
\def\arctan{\qopname@{arctan}}
\def\arg{\qopname@{arg}}
\def\cos{\qopname@{cos}}
\def\cosh{\qopname@{cosh}}
\def\cot{\qopname@{cot}}
\def\coth{\qopname@{coth}}
\def\csc{\qopname@{csc}}
\def\deg{\qopname@{deg}}
\def\det{\qopnamewl@{det}}
\def\dim{\qopname@{dim}}
\def\exp{\qopname@{exp}}
\def\gcd{\qopnamewl@{gcd}}
\def\hom{\qopname@{hom}}
\def\inf{\qopnamewl@{inf}}
\def\injlim{\qopnamewl@{inj\,lim}}
\def\ker{\qopname@{ker}}
\def\lg{\qopname@{lg}}
\def\lim{\qopnamewl@{lim}}
\def\liminf{\qopnamewl@{lim\,inf}}
\def\limsup{\qopnamewl@{lim\,sup}}
\def\ln{\qopname@{ln}}
\def\log{\qopname@{log}}
\def\max{\qopnamewl@{max}}
\def\min{\qopnamewl@{min}}
\def\Pr{\qopnamewl@{Pr}}
\def\projlim{\qopnamewl@{proj\,lim}}
\def\sec{\qopname@{sec}}
\def\sin{\qopname@{sin}}
\def\sinh{\qopname@{sinh}}
\def\sup{\qopnamewl@{sup}}
\def\tan{\qopname@{tan}}
\def\tanh{\qopname@{tanh}}
\def\varinjlim{\mathop{\vtop{\ialign{##\crcr
\hfil\rm lim\hfil\crcr\noalign{\nointerlineskip}\rightarrowfill\crcr
\noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
\def\varprojlim{\mathop{\vtop{\ialign{##\crcr
\hfil\rm lim\hfil\crcr\noalign{\nointerlineskip}\leftarrowfill\crcr
\noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
\def\varliminf{\mathop{\underline{\vrule height\z@ depth.2exwidth\z@
\hbox{\rm lim}}}}
\def\varlimsup{\mathop{\overline{\hbox{\rm lim}}}}
\newdimen\buffer@
\buffer@\fontdimen13 \tenex
\newdimen\buffer
\buffer\buffer@
\def\ChangeBuffer#1{\fontdimen13 \tenex#1\relax
\global\buffer\fontdimen13 \tenex}
\def\ResetBuffer{\fontdimen13 \tenex\buffer@\global\buffer\buffer@}
\def\shave#1{\mathop{\hbox{$\m@th\fontdimen13 \tenex\z@ %1
\displaystyle{#1}$}}\fontdimen13 \tenex\buffer}
\def\topshave#1{\mathop{\topsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}}
\def\botshave#1{\mathop{\botsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}}
\message{multilevel sub/superscripts,}
\Invalid@\\
\def\Let@{\relax\iffalse{\fi\let\\=\cr\iffalse}\fi}
\Invalid@\vspace
\def\vspace@{\def\vspace##1{\crcr\noalign{\vskip##1\relax}}}
\def\multilimits@{\bgroup\vspace@\Let@
\baselineskip\fontdimen10 \scriptfont\tw@
\advance\baselineskip\fontdimen12 \scriptfont\tw@
\lineskip\thr@@\fontdimen8 \scriptfont\thr@@
\lineskiplimit\lineskip
\vbox\bgroup\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil\crcr}
\def\Sb{_\multilimits@}
\def\endSb{\crcr\egroup\egroup\egroup}
\def\Sp{^\multilimits@}
\let\endSp\endSb
\def\spreadlines#1{\RIfMIfI@\onlydmatherr@\spreadlines\else
\openup#1\relax\fi\else\onlydmatherr@\spreadlines\fi}
\def\Mathstrut@{\copy\Mathstrutbox@}
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@\null
\setboxz@h{$\m@th($}
\ht\Mathstrutbox@\ht\z@
\dp\Mathstrutbox@\dp\z@
\message{matrices,}
\newdimen\spreadmlines@
\def\spreadmatrixlines#1{\RIfMIfI@
\onlydmatherr@\spreadmatrixlines\else
\spreadmlines@#1\relax\fi\else\onlydmatherr@\spreadmatrixlines\fi}
\def\matrix{\null\,\vcenter\bgroup\Let@\vspace@
\normalbaselines\openup\spreadmlines@\ialign
\bgroup\hfil$\m@th##$\hfil&&\quad\hfil$\m@th##$\hfil\crcr
\Mathstrut@\crcr\noalign{\kern-\baselineskip}}
\def\endmatrix{\crcr\Mathstrut@\crcr\noalign{\kern-\baselineskip}\egroup
\egroup\,}
\def\format{\crcr\egroup\iffalse{\fi\ifnum`}=0 \fi\format@}
\newtoks\hashtoks@
\hashtoks@{#}
\def\format@#1\\{\def\preamble@{#1}%
\def\l{$\m@th\the\hashtoks@$\hfil}%
\def\c{\hfil$\m@th\the\hashtoks@$\hfil}%
\def\r{\hfil$\m@th\the\hashtoks@$}%
\edef\preamble@@{\preamble@}\ifnum`{=0 \fi\iffalse}\fi
\ialign\bgroup\span\preamble@@\crcr}
\def\smallmatrix{\null\,\vcenter\bgroup\vspace@\Let@
\baselineskip9\ex@\lineskip\ex@
\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil&&\thickspace\hfil
$\m@th\scriptstyle{##}$\hfil\crcr}
\def\endsmallmatrix{\crcr\egroup\egroup\,}
\def\pmatrix{\left(\matrix}
\def\endpmatrix{\endmatrix\right)}
\def\bmatrix{\left[\matrix}
\def\endbmatrix{\endmatrix\right]}
\def\vmatrix{\left|\matrix}
\def\endvmatrix{\endmatrix\right|}
\def\Vmatrix{\left\|\matrix}
\def\endVmatrix{\endmatrix\right\|}
\def\hdots{\mathinner{\ldotp\ldotp\ldotp}}
\newmuskip\dotsspace@
\dotsspace@1.5mu
\def\strip@#1 {#1}
\def\spacehdots#1\for#2{\multispan{#2}\xleaders
\hbox{$\m@th\mkern\strip@#1 \dotsspace@.\mkern\strip@#1 \dotsspace@$}\hfill}
\def\hdotsfor#1{\spacehdots\@ne\for{#1}}
\def\multispan@#1{\omit\mscount#1\unskip\loop\ifnum\mscount>\@ne\sp@n\repeat}
\def\spaceinnerhdots#1\for#2\after#3{\multispan@{\strip@#2 }#3\xleaders
\hbox{$\m@th\mkern\strip@#1 \dotsspace@.\mkern\strip@#1 \dotsspace@$}\hfill}
\def\innerhdotsfor#1\after#2{\spaceinnerhdots\@ne\for#1\after{#2}}
\def\cases{\bgroup\spreadmlines@\jot\left\{\,\matrix\format\l&\quad\l\\}
\def\endcases{\endmatrix\right.\egroup}
\message{multiline displays,}
\newif\ifinany@
\newif\ifinalign@
\newif\ifingather@
\def\strut@{\copy\strutbox@}
\newbox\strutbox@
\setbox\strutbox@\hbox{\vrule height8\p@ depth3\p@ width\z@}
\def\topaligned{\null\,\vtop\aligned@}
\def\botaligned{\null\,\vbox\aligned@}
\def\aligned{\null\,\vcenter\aligned@}
\def\aligned@{\bgroup\vspace@\Let@
\ifinany@\else\openup\jot\fi\ialign
\bgroup\hfil\strut@$\m@th\displaystyle{##}$&
$\m@th\displaystyle{{}##}$\hfil\crcr}
\def\endaligned{\crcr\egroup\egroup}
\let\endtopaligned\endaligned
\let\endbotaligned\endaligned
\def\alignedat#1{\null\,\vcenter\bgroup\doat@{#1}\vspace@\Let@
\ifinany@\else\openup\jot\fi\ialign\bgroup\span\preamble@@\crcr}
\newcount\atcount@
\def\doat@#1{\toks@{\hfil\strut@$\m@th
\displaystyle{\the\hashtoks@}$&$\m@th\displaystyle
{{}\the\hashtoks@}$\hfil}% %1
\atcount@#1\relax\advance\atcount@\m@ne %2
\loop\ifnum\atcount@>\z@\toks@=\expandafter{\the\toks@&\hfil$\m@th
\displaystyle{\the\hashtoks@}$&$\m@th
\displaystyle{{}\the\hashtoks@}$\hfil}\advance
\atcount@\m@ne\repeat %3
\xdef\preamble@{\the\toks@}\xdef\preamble@@{\preamble@}}
\let\endalignedat\endaligned
\def\gathered{\null\,\vcenter\bgroup\vspace@\Let@
\ifinany@\else\openup\jot\fi\ialign
\bgroup\hfil\strut@$\m@th\displaystyle{##}$\hfil\crcr}
\def\endgathered{\crcr\egroup\egroup}
\newif\iftagsleft@
\def\TagsOnLeft{\global\tagsleft@true}
\def\TagsOnRight{\global\tagsleft@false}
\TagsOnLeft
\newif\ifmathtags@
\def\TagsAsMath{\global\mathtags@true}
\def\TagsAsText{\global\mathtags@false}
\TagsAsText
\def\tagform@#1{\hbox{\rm(\ignorespaces#1\unskip)}}
\def\thetag{\leavevmode\tagform@}
\def\tag#1$${\iftagsleft@\leqno\else\eqno\fi %1
\maketag@#1\maketag@ %2
$$} %3
\def\maketag@{\FN@\maketag@@}
\def\maketag@@{\ifx\next"\expandafter\maketag@@@\else\expandafter\maketag@@@@
\fi}
\def\maketag@@@"#1"#2\maketag@{\hbox{\rm#1}} %1
\def\maketag@@@@#1\maketag@{\ifmathtags@\tagform@{$\m@th#1$}\else
\tagform@{#1}\fi}
\interdisplaylinepenalty\@M
\def\allowdisplaybreaks{\RIfMIfI@
\onlydmatherr@\allowdisplaybreaks\else
\interdisplaylinepenalty\z@\fi\else\onlydmatherr@\allowdisplaybreaks\fi}
\Invalid@\allowdisplaybreak
\Invalid@\displaybreak
\Invalid@\intertext
\def\allowdisplaybreak@{\def\allowdisplaybreak{\crcr\noalign{\allowbreak}}}
\def\displaybreak@{\def\displaybreak{\crcr\noalign{\break}}}
\def\intertext@{\def\intertext##1{\crcr\noalign{%
\penalty\postdisplaypenalty \vskip\belowdisplayskip
\vbox{\normalbaselines\noindent##1}%
\penalty\predisplaypenalty \vskip\abovedisplayskip}}}
\newskip\centering@
\centering@\z@ plus\@m\p@
\def\align{\relax\ifingather@\DN@{\csname align (in
\string\gather)\endcsname}\else
\ifmmode\ifinner\DN@{\onlydmatherr@\align}\else
\let\next@\align@\fi
\else\DN@{\onlydmatherr@\align}\fi\fi\next@}
\newhelp\andhelp@
{An extra & here is so disastrous that you should probably exit^^J
and fix things up.}
\newif\iftag@
\newcount\and@
\def\align@{\inalign@true\inany@true
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\def\tag{\global\tag@true\ifnum\and@=\z@\DN@{&&}\else
\DN@{&}\fi\next@}%
\iftagsleft@\DN@{\csname align \endcsname}\else
\DN@{\csname align \space\endcsname}\fi\next@}
\def\Tag@{\iftag@\else\errhelp\andhelp@\err@{Extra & on this line}\fi}
\newdimen\lwidth@
\newdimen\rwidth@
\newdimen\maxlwidth@
\newdimen\maxrwidth@
\newdimen\totwidth@
\def\measure@#1\endalign{\lwidth@\z@\rwidth@\z@\maxlwidth@\z@\maxrwidth@\z@
\global\and@\z@ %1
\setbox@ne\vbox %2
{\everycr{\noalign{\global\tag@false\global\and@\z@}}\Let@ %3
\halign{\setboxz@h{$\m@th\displaystyle{\@lign##}$}% %4
\global\lwidth@\wdz@ %5
\ifdim\lwidth@>\maxlwidth@\global\maxlwidth@\lwidth@\fi %6
\global\advance\and@\@ne %7
&\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}\global\rwidth@\wdz@ %8
\ifdim\rwidth@>\maxrwidth@\global\maxrwidth@\rwidth@\fi %9
\global\advance\and@\@ne %10
&\Tag@
\eat@{##}\crcr#1\crcr}}% %11
\totwidth@\maxlwidth@\advance\totwidth@\maxrwidth@} %12
\def\displ@y@{\global\dt@ptrue\openup\jot
\everycr{\noalign{\global\tag@false\global\and@\z@\ifdt@p\global\dt@pfalse
\vskip-\lineskiplimit\vskip\normallineskiplimit\else
\penalty\interdisplaylinepenalty\fi}}}
\def\black@#1{\noalign{\ifdim#1>\displaywidth
\dimen@\prevdepth\nointerlineskip %1
\vskip-\ht\strutbox@\vskip-\dp\strutbox@ %2
\vbox{\noindent\hbox to#1{\strut@\hfill}}% %3
\prevdepth\dimen@ %4
\fi}}
\expandafter\def\csname align \space\endcsname#1\endalign
{\measure@#1\endalign\global\and@\z@ %1
\ifingather@\everycr{\noalign{\global\and@\z@}}\else\displ@y@\fi %2
\Let@\tabskip\centering@ %3
\halign to\displaywidth
{\hfil\strut@\setboxz@h{$\m@th\displaystyle{\@lign##}$}% %4
\global\lwidth@\wdz@\boxz@\global\advance\and@\@ne %5
\tabskip\z@skip %6
&\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}% %7
\global\rwidth@\wdz@\boxz@\hfill\global\advance\and@\@ne %8
\tabskip\centering@ %9
&\setboxz@h{\@lign\strut@\maketag@##\maketag@}% %10
\dimen@\displaywidth\advance\dimen@-\totwidth@
\divide\dimen@\tw@\advance\dimen@\maxrwidth@\advance\dimen@-\rwidth@ %11
\ifdim\dimen@<\tw@\wdz@\llap{\vtop{\normalbaselines\null\boxz@}}% %12
\else\llap{\boxz@}\fi %13
\tabskip\z@skip %14
\crcr#1\crcr %15
\black@\totwidth@}} %16
\newdimen\lineht@
\expandafter\def\csname align \endcsname#1\endalign{\measure@#1\endalign
\global\and@\z@
\ifdim\totwidth@>\displaywidth\let\displaywidth@\totwidth@\else
\let\displaywidth@\displaywidth\fi %1
\ifingather@\everycr{\noalign{\global\and@\z@}}\else\displ@y@\fi
\Let@\tabskip\centering@\halign to\displaywidth
{\hfil\strut@\setboxz@h{$\m@th\displaystyle{\@lign##}$}%
\global\lwidth@\wdz@\global\lineht@\ht\z@ %2
\boxz@\global\advance\and@\@ne
\tabskip\z@skip&\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
\global\rwidth@\wdz@\ifdim\ht\z@>\lineht@\global\lineht@\ht\z@\fi %3
\boxz@\hfil\global\advance\and@\@ne
\tabskip\centering@&\kern-\displaywidth@ %4
\setboxz@h{\@lign\strut@\maketag@##\maketag@}%
\dimen@\displaywidth\advance\dimen@-\totwidth@
\divide\dimen@\tw@\advance\dimen@\maxlwidth@\advance\dimen@-\lwidth@
\ifdim\dimen@<\tw@\wdz@
\rlap{\vbox{\normalbaselines\boxz@\vbox to\lineht@{}}}\else
\rlap{\boxz@}\fi
\tabskip\displaywidth@\crcr#1\crcr\black@\totwidth@}}
\expandafter\def\csname align (in \string\gather)\endcsname
#1\endalign{\vcenter{\align@#1\endalign}}
\Invalid@\endalign
\newif\ifxat@
\def\alignat{\RIfMIfI@\DN@{\onlydmatherr@\alignat}\else
\DN@{\csname alignat \endcsname}\fi\else
\DN@{\onlydmatherr@\alignat}\fi\next@}
\newif\ifmeasuring@
\newbox\savealignat@
\expandafter\def\csname alignat \endcsname#1#2\endalignat %1
{\inany@true\xat@false
\def\tag{\global\tag@true\count@#1\relax\multiply\count@\tw@
\xdef\tag@{}\loop\ifnum\count@>\and@\xdef\tag@{&\tag@}\advance\count@\m@ne
\repeat\tag@}%
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y@\measuring@true %2
\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
\attag@{#1}% %3
\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
\measuring@false %4
\Let@\attag@{#1}% %5
\tabskip\centering@\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr %6
\black@{\wd\savealignat@}}} %7
\Invalid@\endalignat
\def\xalignat{\RIfMIfI@
\DN@{\onlydmatherr@\xalignat}\else
\DN@{\csname xalignat \endcsname}\fi\else
\DN@{\onlydmatherr@\xalignat}\fi\next@}
\expandafter\def\csname xalignat \endcsname#1#2\endxalignat
{\inany@true\xat@true
\def\tag{\global\tag@true\def\tag@{}\count@#1\relax\multiply\count@\tw@
\loop\ifnum\count@>\and@\xdef\tag@{&\tag@}\advance\count@\m@ne\repeat\tag@}%
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y@\measuring@true\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
\attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
\measuring@false\Let@
\attag@{#1}\tabskip\centering@\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\def\attag@#1{\let\Maketag@\maketag@\let\TAG@\Tag@ %1
\let\Tag@=0\let\maketag@=0% %2
\ifmeasuring@\def\llap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}%
\def\rlap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}\else
\let\llap@\llap\let\rlap@\rlap\fi %3
\toks@{\hfil\strut@$\m@th\displaystyle{\@lign\the\hashtoks@}$\tabskip\z@skip
\global\advance\and@\@ne&$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil
\ifxat@\tabskip\centering@\fi\global\advance\and@\@ne}% %4
\iftagsleft@
\toks@@{\tabskip\centering@&\Tag@\kern-\displaywidth
\rlap@{\@lign\maketag@\the\hashtoks@\maketag@}%
\global\advance\and@\@ne\tabskip\displaywidth}\else
\toks@@{\tabskip\centering@&\Tag@\llap@{\@lign\maketag@
\the\hashtoks@\maketag@}\global\advance\and@\@ne\tabskip\z@skip}\fi %5
\atcount@#1\relax\advance\atcount@\m@ne
\loop\ifnum\atcount@>\z@
\toks@=\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\@lign
\the\hashtoks@}$\global\advance\and@\@ne
\tabskip\z@skip&$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil\ifxat@
\tabskip\centering@\fi\global\advance\and@\@ne}\advance\atcount@\m@ne
\repeat %6
\xdef\preamble@{\the\toks@\the\toks@@}% %7
\xdef\preamble@@{\preamble@}% %8
\let\maketag@\Maketag@\let\Tag@\TAG@} %9
\Invalid@\endxalignat
\def\xxalignat{\RIfMIfI@
\DN@{\onlydmatherr@\xxalignat}\else\DN@{\csname xxalignat
\endcsname}\fi\else
\DN@{\onlydmatherr@\xxalignat}\fi\next@}
\expandafter\def\csname xxalignat \endcsname#1#2\endxxalignat{\inany@true
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
\xxattag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}%
\Let@\xxattag@{#1}\tabskip\z@skip\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
\def\xxattag@#1{\toks@{\tabskip\z@skip\hfil\strut@
$\m@th\displaystyle{\the\hashtoks@}$&%
$\m@th\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\centering@&}%
\atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
\toks@=\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\the\hashtoks@}$%
\tabskip\z@skip&$\m@th\displaystyle{{}\the\hashtoks@}$\hfil
\tabskip\centering@}\advance\atcount@\m@ne\repeat
\xdef\preamble@{\the\toks@\tabskip\z@skip}\xdef\preamble@@{\preamble@}}
\Invalid@\endxxalignat
\newdimen\gwidth@
\newdimen\gmaxwidth@
\def\gmeasure@#1\endgather{\gwidth@\z@\gmaxwidth@\z@\setbox@ne\vbox{\Let@
\halign{\setboxz@h{$\m@th\displaystyle{##}$}\global\gwidth@\wdz@
\ifdim\gwidth@>\gmaxwidth@\global\gmaxwidth@\gwidth@\fi
&\eat@{##}\crcr#1\crcr}}}
\def\gather{\RIfMIfI@\DN@{\onlydmatherr@\gather}\else
\ingather@true\inany@true\def\tag{&}%
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y\Let@
\iftagsleft@\DN@{\csname gather \endcsname}\else
\DN@{\csname gather \space\endcsname}\fi\fi
\else\DN@{\onlydmatherr@\gather}\fi\next@}
\expandafter\def\csname gather \space\endcsname#1\endgather
{\gmeasure@#1\endgather\tabskip\centering@
\halign to\displaywidth{\hfil\strut@\setboxz@h{$\m@th\displaystyle{##}$}%
\global\gwidth@\wdz@\boxz@\hfil&
\setboxz@h{\strut@{\maketag@##\maketag@}}%
\dimen@\displaywidth\advance\dimen@-\gwidth@
\ifdim\dimen@>\tw@\wdz@\llap{\boxz@}\else
\llap{\vtop{\normalbaselines\null\boxz@}}\fi
\tabskip\z@skip\crcr#1\crcr\black@\gmaxwidth@}}
\newdimen\glineht@
\expandafter\def\csname gather \endcsname#1\endgather{\gmeasure@#1\endgather
\ifdim\gmaxwidth@>\displaywidth\let\gdisplaywidth@\gmaxwidth@\else
\let\gdisplaywidth@\displaywidth\fi\tabskip\centering@\halign to\displaywidth
{\hfil\strut@\setboxz@h{$\m@th\displaystyle{##}$}%
\global\gwidth@\wdz@\global\glineht@\ht\z@\boxz@\hfil&\kern-\gdisplaywidth@
\setboxz@h{\strut@{\maketag@##\maketag@}}%
\dimen@\displaywidth\advance\dimen@-\gwidth@
\ifdim\dimen@>\tw@\wdz@\rlap{\boxz@}\else
\rlap{\vbox{\normalbaselines\boxz@\vbox to\glineht@{}}}\fi
\tabskip\gdisplaywidth@\crcr#1\crcr\black@\gmaxwidth@}}
\newif\ifctagsplit@
\def\CenteredTagsOnSplits{\global\ctagsplit@true}
\def\TopOrBottomTagsOnSplits{\global\ctagsplit@false}
\TopOrBottomTagsOnSplits
\def\split{\relax\ifinany@\let\next@\insplit@\else
\ifmmode\ifinner\def\next@{\onlydmatherr@\split}\else
\let\next@\outsplit@\fi\else
\def\next@{\onlydmatherr@\split}\fi\fi\next@}
\def\insplit@{\global\setbox\z@\vbox\bgroup\vspace@\Let@\ialign\bgroup
\hfil\strut@$\m@th\displaystyle{##}$&$\m@th\displaystyle{{}##}$\hfill\crcr}
\def\endsplit{\crcr\egroup\egroup\iftagsleft@\expandafter\lendsplit@\else
\expandafter\rendsplit@\fi}
\def\rendsplit@{\global\setbox9 \vbox
{\unvcopy\z@\global\setbox8 \lastbox\unskip}% %1
\setbox@ne\hbox{\unhcopy8 \unskip\global\setbox\tw@\lastbox
\unskip\global\setbox\thr@@\lastbox}% %2
\global\setbox7 \hbox{\unhbox\tw@\unskip}% %3
\ifinalign@\ifctagsplit@ %4
\gdef\split@{\hbox to\wd\thr@@{}&
\vcenter{\vbox{\moveleft\wd\thr@@\boxz@}}}% %5
\else\gdef\split@{&\vbox{\moveleft\wd\thr@@\box9}\crcr
\box\thr@@&\box7}\fi %6
\else %7
\ifctagsplit@\gdef\split@{\vcenter{\boxz@}}\else
\gdef\split@{\box9\crcr\hbox{\box\thr@@\box7}}\fi
\fi
\split@} %8
\def\lendsplit@{\global\setbox9\vtop{\unvcopy\z@}% %1
\setbox@ne\vbox{\unvcopy\z@\global\setbox8\lastbox}% %2
\setbox@ne\hbox{\unhcopy8\unskip\setbox\tw@\lastbox
\unskip\global\setbox\thr@@\lastbox}% %3
\ifinalign@\ifctagsplit@ %4
\gdef\split@{\hbox to\wd\thr@@{}&
\vcenter{\vbox{\moveleft\wd\thr@@\box9}}}% %5
\else %6
\gdef\split@{\hbox to\wd\thr@@{}&\vbox{\moveleft\wd\thr@@\box9}}\fi
\else
\ifctagsplit@\gdef\split@{\vcenter{\box9}}\else
\gdef\split@{\box9}\fi
\fi\split@}
\def\outsplit@#1$${\align\insplit@#1\endalign$$}
\newdimen\multlinegap@
\multlinegap@1em
\newdimen\multlinetaggap@
\multlinetaggap@1em
\def\MultlineGap#1{\global\multlinegap@#1\relax}
\def\multlinegap#1{\RIfMIfI@\onlydmatherr@\multlinegap\else
\multlinegap@#1\relax\fi\else\onlydmatherr@\multlinegap\fi}
\def\nomultlinegap{\multlinegap{\z@}}
\def\multline{\RIfMIfI@
\DN@{\onlydmatherr@\multline}\else
\DN@{\multline@}\fi\else
\DN@{\onlydmatherr@\multline}\fi\next@}
\newif\iftagin@
\def\tagin@#1{\tagin@false\in@\tag{#1}\ifin@\tagin@true\fi}
\def\multline@#1$${\inany@true\vspace@\allowdisplaybreak@\displaybreak@
\tagin@{#1}\iftagsleft@\DN@{\multline@l#1$$}\else
\DN@{\multline@r#1$$}\fi\next@}
\newdimen\mwidth@
\def\rmmeasure@#1\endmultline{%
\def\shoveleft##1{##1}\def\shoveright##1{##1}% %1
\setbox@ne\vbox{\Let@\halign{\setboxz@h
{$\m@th\@lign\displaystyle{}##$}\global\mwidth@\wdz@
\crcr#1\crcr}}}
\newdimen\mlineht@
\newif\ifzerocr@
\newif\ifonecr@
\def\lmmeasure@#1\endmultline{\global\zerocr@true\global\onecr@false
\everycr{\noalign{\ifonecr@\global\onecr@false\fi
\ifzerocr@\global\zerocr@false\global\onecr@true\fi}}% %1
\def\shoveleft##1{##1}\def\shoveright##1{##1}%
\setbox@ne\vbox{\Let@\halign{\setboxz@h
{$\m@th\@lign\displaystyle{}##$}\ifonecr@\global\mwidth@\wdz@
\global\mlineht@\ht\z@\fi\crcr#1\crcr}}}
\newbox\mtagbox@
\newdimen\ltwidth@
\newdimen\rtwidth@
\def\multline@l#1$${\iftagin@\DN@{\lmultline@@#1$$}\else
\DN@{\setbox\mtagbox@\null\ltwidth@\z@\rtwidth@\z@
\lmultline@@@#1$$}\fi\next@}
\def\lmultline@@#1\endmultline\tag#2$${%
\setbox\mtagbox@\hbox{\maketag@#2\maketag@}% %1
\lmmeasure@#1\endmultline\dimen@\mwidth@\advance\dimen@\wd\mtagbox@
\advance\dimen@\multlinetaggap@ %2
\ifdim\dimen@>\displaywidth\ltwidth@\z@\else\ltwidth@\wd\mtagbox@\fi %3
\lmultline@@@#1\endmultline$$}
\def\lmultline@@@{\displ@y
\def\shoveright##1{##1\hfilneg\hskip\multlinegap@}%
\def\shoveleft##1{\setboxz@h{$\m@th\displaystyle{}##1$}%
\setbox@ne\hbox{$\m@th\displaystyle##1$}%
\hfilneg
\iftagin@
\ifdim\ltwidth@>\z@\hskip\ltwidth@\hskip\multlinetaggap@\fi
\else\hskip\multlinegap@\fi\hskip.5\wd@ne\hskip-.5\wdz@##1}% %1
\halign\bgroup\Let@\hbox to\displaywidth
{\strut@$\m@th\displaystyle\hfil{}##\hfil$}\crcr
\hfilneg %2
\iftagin@ %3
\ifdim\ltwidth@>\z@ %4
\box\mtagbox@\hskip\multlinetaggap@ %5
\else
\rlap{\vbox{\normalbaselines\hbox{\strut@\box\mtagbox@}%
\vbox to\mlineht@{}}}\fi %6
\else\hskip\multlinegap@\fi} %7
\def\multline@r#1$${\iftagin@\DN@{\rmultline@@#1$$}\else
\DN@{\setbox\mtagbox@\null\ltwidth@\z@\rtwidth@\z@
\rmultline@@@#1$$}\fi\next@}
\def\rmultline@@#1\endmultline\tag#2$${\ltwidth@\z@
\setbox\mtagbox@\hbox{\maketag@#2\maketag@}%
\rmmeasure@#1\endmultline\dimen@\mwidth@\advance\dimen@\wd\mtagbox@
\advance\dimen@\multlinetaggap@
\ifdim\dimen@>\displaywidth\rtwidth@\z@\else\rtwidth@\wd\mtagbox@\fi
\rmultline@@@#1\endmultline$$}
\def\rmultline@@@{\displ@y
\def\shoveright##1{##1\hfilneg\iftagin@\ifdim\rtwidth@>\z@
\hskip\rtwidth@\hskip\multlinetaggap@\fi\else\hskip\multlinegap@\fi}%
\def\shoveleft##1{\setboxz@h{$\m@th\displaystyle{}##1$}%
\setbox@ne\hbox{$\m@th\displaystyle##1$}%
\hfilneg\hskip\multlinegap@\hskip.5\wd@ne\hskip-.5\wdz@##1}%
\halign\bgroup\Let@\hbox to\displaywidth
{\strut@$\m@th\displaystyle\hfil{}##\hfil$}\crcr
\hfilneg\hskip\multlinegap@}
\def\endmultline{\iftagsleft@\expandafter\lendmultline@\else
\expandafter\rendmultline@\fi}
\def\lendmultline@{\hfilneg\hskip\multlinegap@\crcr\egroup}
\def\rendmultline@{\iftagin@ %1
\ifdim\rtwidth@>\z@ %2
\hskip\multlinetaggap@\box\mtagbox@ %3
\else\llap{\vtop{\normalbaselines\null\hbox{\strut@\box\mtagbox@}}}\fi %4
\else\hskip\multlinegap@\fi %5
\hfilneg\crcr\egroup}
\def\bmod{\mskip-\medmuskip\mkern5mu\mathbin{\fam\z@ mod}\penalty900
\mkern5mu\mskip-\medmuskip}
\def\pmod#1{\allowbreak\ifinner\mkern8mu\else\mkern18mu\fi
({\fam\z@ mod}\,\,#1)}
\def\pod#1{\allowbreak\ifinner\mkern8mu\else\mkern18mu\fi(#1)}
\def\mod#1{\allowbreak\ifinner\mkern12mu\else\mkern18mu\fi{\fam\z@ mod}\,\,#1}
\message{continued fractions,}
\newcount\cfraccount@
\def\cfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut
\iffalse{\fi\def\\{\over\displaystyle}\iffalse}\fi}
\def\lcfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut
\iffalse{\fi\def\\{\hfill\over\displaystyle}\iffalse}\fi}
\def\rcfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut\hfill
\iffalse{\fi\def\\{\over\displaystyle}\iffalse}\fi}
\def\gloop@#1\repeat{\gdef\body{#1}\iterate}
\def\endcfrac{\gloop@\ifnum\cfraccount@>\z@\global\advance\cfraccount@\m@ne
\egroup\hskip-\nulldelimiterspace\egroup\repeat}
\message{compound symbols,}
\def\binrel@#1{\setboxz@h{\thinmuskip0mu
\medmuskip\m@ne mu\thickmuskip\@ne mu$#1\m@th$}%
\setbox@ne\hbox{\thinmuskip0mu\medmuskip\m@ne mu\thickmuskip
\@ne mu${}#1{}\m@th$}%
\setbox\tw@\hbox{\hskip\wd@ne\hskip-\wdz@}}
\def\overset#1\to#2{\binrel@{#2}\ifdim\wd\tw@<\z@
\mathbin{\mathop{\kern\z@#2}\limits^{#1}}\else\ifdim\wd\tw@>\z@
\mathrel{\mathop{\kern\z@#2}\limits^{#1}}\else
{\mathop{\kern\z@#2}\limits^{#1}}{}\fi\fi}
\def\underset#1\to#2{\binrel@{#2}\ifdim\wd\tw@<\z@
\mathbin{\mathop{\kern\z@#2}\limits_{#1}}\else\ifdim\wd\tw@>\z@
\mathrel{\mathop{\kern\z@#2}\limits_{#1}}\else
{\mathop{\kern\z@#2}\limits_{#1}}{}\fi\fi}
\def\oversetbrace#1\to#2{\overbrace{#2}^{#1}}
\def\undersetbrace#1\to#2{\underbrace{#2}_{#1}}
\def\sideset#1\and#2\to#3{%
\setbox@ne\hbox{$\dsize{\vphantom{#3}}#1{#3}\m@th$}%
\setbox\tw@\hbox{$\dsize{#3}#2\m@th$}%
\hskip\wd@ne\hskip-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wd@ne
{\vphantom{#3}}#1{#3}#2}}
\def\rightarrowfill@#1{\setboxz@h{$#1-\m@th$}\ht\z@\z@
$#1\m@th\copy\z@\mkern-6mu\cleaders
\hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
\mkern-6mu\mathord\rightarrow$}