trunk/required/amsmath/amstex.sty

   1 %
   2 % \iffalse meta-comment
   3 %
   4 % Copyright 1995, 1999 American Mathematical Society.
   5 % Copyright 2016 LaTeX3 Project and American Mathematical Society.
   6 %
   7 % This work may be distributed and/or modified under the
   8 % conditions of the LaTeX Project Public License, either version 1.3c
   9 % of this license or (at your option) any later version.
  10 % The latest version of this license is in
  11 %   http://www.latex-project.org/lppl.txt
  12 % and version 1.3c or later is part of all distributions of LaTeX
  13 % version 2005/12/01 or later.
  14 %
  15 % This work has the LPPL maintenance status `maintained'.
  16 %
  17 % The Current Maintainer of this work is the LaTeX3 Project.
  18 %
  19 % \fi
  20 %
  21 %    This file was generated from version 1.2beta of amstex.dtx and then
  22 %    underwent additional hand-editing.
  23 \if@compatibility \else \catcode`\%=9 \fi
  24 %\PackageError{amstex}{%
  25 %Package `amstex' is obsolete, substituting `amsmath'}{You
  26 %should use \string\usepackage{amsmath} instead. If
  27 %that does not give satisfactory results, rename your previous copy
  28 %of amstex.sty to amstex12beta.sty and call it with
  29 %\string\usepackage{amstex12beta}.}
  30 %\catcode`\%=14 \relax \input{amsmath.sty}\endinput
  31 %
  32 \ProvidesPackage{amstex}[1999/11/15 v1.2f AMS extra math features]
  33 \let\@amsfonts=T
  34 \DeclareOption{noamsfonts}{\let\@amsfonts=F}
  35 \DeclareOption{psamsfonts}{\let\@amsfonts=P}
  36 \DeclareOption{intlimits}{\let\ilimits@\displaylimits}
  37 \DeclareOption{nointlimits}{\let\ilimits@\nolimits}
  38 \DeclareOption{sumlimits}{\let\slimits@\displaylimits}
  39 \DeclareOption{nosumlimits}{\let\slimits@\nolimits}
  40 \DeclareOption{namelimits}{\let\nlimits@\displaylimits}
  41 \DeclareOption{nonamelimits}{\let\nlimits@\nolimits}
  42 \newif\ifctagsplit@
  43 \newif\iftagsleft@
  44 \DeclareOption{leqno}{\tagsleft@true}
  45 \DeclareOption{reqno}{\tagsleft@false}
  46 \DeclareOption{centertags}{\ctagsplit@true}
  47 \DeclareOption{tbtags}{\ctagsplit@false}
  48 \newif\if@fleqn
  49 \newskip\@mathmargin
  50 \@mathmargin\@centering
  51 \DeclareOption{fleqn}{%
  52     \@fleqntrue
  53     \@mathmargin\m@ne sp
  54     \AtBeginDocument{%
  55         \ifdim\@mathmargin=\m@ne sp
  56             \@mathmargin\leftmargini
  57         \fi
  58     }%
  59 }
  60 \DeclareOption{righttag}{\tagsleft@false}
  61 \DeclareOption{ctagsplt}{\ctagsplit@true}
  62 \DeclareOption{intlim}{\let\ilimits@\displaylimits}
  63 \DeclareOption{nosumlim}{\let\slimits@\nolimits}
  64 \DeclareOption{nonamelm}{\let\nlimits@\nolimits}
  65 \ExecuteOptions{nointlimits,sumlimits,namelimits,centertags}
  66 \ProcessOptions
  67 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  68 %% In this section \RequirePackage statements were replaced with the
  69 %% contents of the referenced files.
  70 %%%     filename        = "amsgen.dtx",
  71 %%%     version         = "1.2beta",
  72 %%%     date            = "1994/12/13",
  73 \providecommand{\@saveprimitive}[2]{\begingroup\escapechar`\\\relax
  74   \edef\@tempa{\string#1}\edef\@tempb{\meaning#1}%
  75   \ifx\@tempa\@tempb \global\let#2#1%
  76   \else
  77     \edef\@tempb{\meaning#2}%
  78     \ifx\@tempa\@tempb
  79     \else
  80       \@latex@error{Unable to properly define \string#2; primitive
  81       \noexpand#1no longer primitive}\@eha
  82     \fi
  83   \fi
  84   \endgroup}
  85 \let\@xp=\expandafter
  86 \let\@nx=\noexpand
  87 \newtoks\@emptytoks
  88 \def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
  89 \def\@ifempty#1{\@xifempty#1@@..\@nil}
  90 \long\def\@xifempty#1#2@#3#4#5\@nil{%
  91   \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
  92 \long\def\@ifnotempty#1{\@ifempty{#1}{}}
  93 \def\FN@{\futurelet\@let@token}
  94 \def\DN@{\def\next@}
  95 \def\RIfM@{\relax\ifmmode}
  96 \def\setboxz@h{\setbox\z@\hbox}
  97 \def\wdz@{\wd\z@}
  98 \def\boxz@{\box\z@}
  99 \def\relaxnext@{\let\@let@token\relax}
 100 \def\new@ifnextchar#1#2#3{%
 101   \let\@tempe #1\def\@tempa{#2}\def\@tempb{#3}\futurelet
 102     \@tempc\new@ifnch}
 103 \def\new@ifnch{\ifx\@tempc \@tempe \let\@tempd\@tempa
 104              \else\let\@tempd\@tempb\fi\@tempd}
 105 \def\new@ifstar#1#2{\new@ifnextchar *{\def\@tempa*{#1}\@tempa}{#2}}
 106 \@ifundefined{every@math@size}{%
 107 \let\every@math@size=\every@size
 108 \def\glb@settings{%
 109      \expandafter\ifx\csname S@\f@size\endcsname\relax
 110        \calculate@math@sizes
 111      \fi
 112      \csname S@\f@size\endcsname
 113       \ifmath@fonts
 114         \begingroup
 115           \escapechar\m@ne
 116           \csname mv@\math@version \endcsname
 117           \globaldefs\@ne
 118           \let \glb@currsize \f@size
 119           \math@fonts
 120         \endgroup
 121         \the\every@math@size
 122       \else
 123       \fi
 124 }
 125 \def\set@fontsize#1#2#3{%
 126     \@defaultunits\@tempdimb#2pt\relax\@nnil
 127     \edef\f@size{\strip@pt\@tempdimb}%
 128     \@defaultunits\@tempskipa#3pt\relax\@nnil
 129     \edef\f@baselineskip{\the\@tempskipa}%
 130     \edef\f@linespread{#1}%
 131     \let\baselinestretch\f@linespread
 132       \def\size@update{%
 133         \baselineskip\f@baselineskip\relax
 134         \baselineskip\f@linespread\baselineskip
 135         \normalbaselineskip\baselineskip
 136         \setbox\strutbox\hbox{%
 137           \vrule\@height.7\baselineskip
 138                 \@depth.3\baselineskip
 139                 \@width\z@}%
 140 %%%     \the\every@size
 141         \let\size@update\relax}%
 142   }
 143 }{}% end \@ifundefined test
 144 \newdimen\ex@
 145 \addto@hook\every@math@size{\compute@ex@}
 146 \def\compute@ex@{%
 147   \begingroup
 148   \dimen@-\f@size\p@
 149   \ifdim\dimen@<-20\p@
 150     \global\ex@ 1.5\p@
 151   \else
 152     \advance\dimen@10\p@ \multiply\dimen@\tw@
 153     \edef\@tempa{\ifdim\dimen@>\z@ -\fi}%
 154     \dimen@ \ifdim\dimen@<\z@ -\fi \dimen@
 155     \advance\dimen@-\@m sp % fudge factor
 156     \vfuzz\p@
 157     \def\do{\ifdim\dimen@>\z@
 158       \vfuzz=.97\vfuzz
 159       \advance\dimen@ -\p@
 160       \@xp\do \fi}%
 161     \do
 162     \dimen@\p@ \advance\dimen@-\vfuzz
 163     \global\ex@\p@
 164     \global\advance\ex@ \@tempa\dimen@
 165   \fi
 166   \endgroup
 167 }
 168 \def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}
 169 \def\frenchspacing{\sfcode`\.1006\sfcode`\?1005\sfcode`\!1004%
 170   \sfcode`\:1003\sfcode`\;1002\sfcode`\,1001 }
 171 \def\@mathmeasure#1#2#3{\setbox#1\hbox{\frozen@everymath\@emptytoks
 172   \m@th$#2#3$}}
 173 \def\nomath@env{\PackageError{amstex}{%
 174   \string\begin{\@currenvir} allowed only in paragraph mode%
 175 }\@ehb% "You've lost some text"
 176 }
 177 \def\Invalid@@{Invalid use of \string}
 178 \def\nonmatherr@#1{\PackageError{amsfonts}%
 179     {\noexpand#1allowed only in math mode}\@ehd}
 180 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 181 %%%     filename        = "amstext.dtx",
 182 %%%     version         = "1.2beta",
 183 %%%     date            = "1994/12/13",
 184 \DeclareRobustCommand{\text}{%
 185   \ifmmode\expandafter\text@\else\expandafter\mbox\fi}
 186 \let\nfss@text\text
 187 \def\text@#1{\mathchoice
 188   {\textdef@\displaystyle\f@size{#1}}%
 189   {\textdef@\textstyle\tf@size{\firstchoice@false #1}}%
 190   {\textdef@\textstyle\sf@size{\firstchoice@false #1}}%
 191   {\textdef@\textstyle \ssf@size{\firstchoice@false #1}}%
 192   \check@mathfonts
 193 }
 194 \def\textdef@#1#2#3{\hbox{{%
 195                     \everymath{#1}%
 196                     \let\f@size#2\selectfont
 197                     #3}}}
 198 \newif\iffirstchoice@
 199 \firstchoice@true
 200 \def\stepcounter#1{%
 201   \iffirstchoice@
 202      \global\expandafter\advance\csname c@#1\endcsname \@ne
 203      \begingroup
 204          \let\@elt\@stpelt
 205          \csname cl@#1\endcsname
 206      \endgroup
 207   \fi}
 208 \toks@{\iffirstchoice@\else\@xp\@gobblefour\fi\protect}
 209 \edef\GenericInfo{\the\toks@
 210   \@xp\@nx\csname GenericInfo \endcsname}
 211 \edef\GenericWarning{\the\toks@
 212   \@xp\@nx\csname GenericWarning \endcsname}
 213 \toks@{\iffirstchoice@\else
 214   \@xp\@xp\@xp\@gobblefour
 215   \@xp\@gobbletwo\fi\protect}
 216 \edef\GenericError{\the\toks@
 217   \@xp\@nx\csname GenericError \endcsname}
 218 \def\label#1{\@bsphack\iffirstchoice@\if@filesw {\let\thepage\relax
 219    \def\protect{\noexpand\noexpand\noexpand}%
 220 \xdef\@gtempa{\write\@auxout{\string
 221       \newlabel{#1}{{\@currentlabel}{\thepage}}}}}\@gtempa
 222    \if@nobreak \ifvmode\nobreak\fi\fi\fi\fi\@esphack}
 223 \begingroup \catcode`\"=12
 224 \gdef\mathhexbox#1#2#3{\text{$\m@th\mathchar"#1#2#3$}}
 225 \endgroup
 226 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 227 %%%     filename        = "amsfonts.dtx",
 228 %%%     version         = "1.2beta",
 229 %%%     date            = "1994/12/13",
 230 \newbox\Mathstrutbox@
 231 \setbox\Mathstrutbox@=\hbox{}
 232 \def\Mathstrut@{\copy\Mathstrutbox@}
 233 \addto@hook\every@math@size{\setbox\z@\hbox{\normalfont(}%
 234   \ht\Mathstrutbox@\ht\z@ \dp\Mathstrutbox@\dp\z@}
 235 \newbox\strutbox@
 236 \def\strut@{\copy\strutbox@}
 237 \addto@hook\every@math@size{%
 238   \global\setbox\strutbox@\hbox{\lower.5\normallineskiplimit
 239          \vbox{\kern-\normallineskiplimit\copy\strutbox}}}
 240 \def\big{\bBigg@\@ne}
 241 \def\Big{\bBigg@{1.5}}
 242 \def\bigg{\bBigg@\tw@}
 243 \def\Bigg{\bBigg@{2.5}}
 244 \def\bBigg@#1#2{%
 245    {%
 246     \hbox{$\left#2\vcenter to#1\big@size{}\right.%
 247            \n@space
 248      $}}}
 249 \addto@hook\every@math@size{%
 250   \global\big@size 1.2\ht\Mathstrutbox@
 251   \global\advance\big@size 1.2\dp\Mathstrutbox@ }
 252 \newdimen\big@size
 253 %% msam, msbm, eufm fonts dealt with at end of file
 254 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 255 %%%     filename        = "amsbsy.dtx",
 256 %%%     version         = "1.2beta",
 257 %%%     date            = "1994/10/27",
 258 \DeclareRobustCommand{\boldsymbol}[1]{%
 259   \begingroup
 260   \let\@nomath\@gobble \mathversion{bold}%
 261   \math@atom{#1}{%
 262   \mathchoice%
 263     {\hbox{$\m@th\displaystyle#1$}}%
 264     {\hbox{$\m@th\textstyle#1$}}%
 265     {\hbox{$\m@th\scriptstyle#1$}}%
 266     {\hbox{$\m@th\scriptscriptstyle#1$}}}%
 267   \endgroup}
 268 \def\math@atom#1#2{%
 269    \binrel@{#1}\binrel@@{#2}}
 270 \DeclareRobustCommand{\pmb}{%
 271   \ifmmode\else \expandafter\pmb@@\fi\mathpalette\pmb@}
 272 \def\pmb@@#1#2#3{\leavevmode\setboxz@h{#3}%
 273    \dimen@-\wdz@
 274    \kern-.5\ex@\copy\z@
 275    \kern\dimen@\kern.25\ex@\raise.4\ex@\copy\z@
 276    \kern\dimen@\kern.25\ex@\box\z@
 277 }
 278 \newdimen\pmbraise@
 279 \def\pmb@#1#2{\setbox8\hbox{$\m@th#1{#2}$}%
 280   \setboxz@h{$\m@th#1\mkern.5mu$}\pmbraise@\wdz@
 281   \binrel@{#2}%
 282   \dimen@-\wd8 %
 283   \binrel@@{%
 284     \mkern-.8mu\copy8 %
 285     \kern\dimen@\mkern.4mu\raise\pmbraise@\copy8 %
 286     \kern\dimen@\mkern.4mu\box8 }%
 287 }
 288 \def\binrel@#1{\begingroup
 289   \setboxz@h{\thinmuskip0mu
 290     \medmuskip\m@ne mu\thickmuskip\@ne mu
 291     \setbox\tw@\hbox{$#1\m@th$}\kern-\wd\tw@
 292     ${}#1{}\m@th$}%
 293   \edef\@tempa{\endgroup\let\noexpand\binrel@@
 294     \ifdim\wdz@<\z@ \mathbin
 295     \else\ifdim\wdz@>\z@ \mathrel
 296     \else \relax\fi\fi}%
 297   \@tempa
 298 }
 299 \let\binrel@@\relax
 300 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 301 \def\AmSTeX{\protect\AmS-\protect\TeX{}}
 302 \def\AmS{{\protect\AmSfont
 303   A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
 304 \def\AmSfont{%
 305   \usefont{OMS}{cmsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}
 306 \def\prim@s{\prime\futurelet\@let@token\pr@m@s}
 307 \def\pr@m@s{%
 308   \ifx\@let@token'\DN@##1{\prim@s}\else\let\next@\egroup\fi\next@}
 309 \let\@prime=\prime
 310 \renewcommand{\prime}{{\kern\z@\@prime}}
 311 \DeclareRobustCommand{\mspace}[3]{%
 312   \ifmmode\mskip#1#2\else\kern#1#3\fi\relax}
 313 \renewcommand{\,}{\mspace+\thinmuskip{.1667em}}
 314 \let\thinspace\,
 315 \renewcommand{\!}{\mspace-\thinmuskip{.1667em}}
 316 \let\negthinspace\!
 317 \renewcommand{\:}{\mspace+\medmuskip{.2222em}}
 318 \let\medspace\:
 319 \newcommand{\negmedspace}{\mspace-\medmuskip{.2222em}}
 320 \renewcommand{\;}{\mspace+\thickmuskip{.2777em}}
 321 \let\thickspace\;
 322 \newcommand{\negthickspace}{\mspace-\thickmuskip{.2777em}}
 323 \def\implies{\DOTSB\;\Longrightarrow\;}
 324 \def\impliedby{\DOTSB\;\Longleftarrow\;}
 325 \begingroup \catcode`\"=12 % in case activated by a preceding package
 326 \gdef\And{\DOTSB\;\mathchar"3026 \;}
 327 \gdef\lvert{\delimiter"426A30C }
 328 \gdef\rvert{\delimiter"526A30C }
 329 \gdef\lVert{\delimiter"426B30D }
 330 \gdef\rVert{\delimiter"526B30D }
 331 \endgroup % restore "
 332 \DeclareRobustCommand{\frac}{\new@ifnextchar[{\frfrac{}}{\frfrac{}[]}}
 333 \def\frfrac#1[#2]#3#4{\def\next@{#2}%
 334   \ifx\next@\@empty \def\next@{#1{#3\over#4}}%
 335   \else \def\next@{{#1{#3\above#2\relax#4}}}%
 336   \fi
 337   \next@}
 338 \def\dfrac{\protect\frfrac\displaystyle[]}
 339 \def\tfrac{\protect\frfrac\textstyle[]}
 340 \DeclareRobustCommand{\binom}{\frbinom{}}
 341 \def\frbinom#1#2#3{{#1{#2\atopwithdelims()#3}}}
 342 \def\dbinom{\protect\frbinom\displaystyle}
 343 \def\tbinom{\protect\frbinom\textstyle}
 344 \def\colon{\nobreak\mskip2mu\mathpunct{}\nonscript
 345   \mkern-\thinmuskip{:}\mskip6muplus1mu\relax}
 346 \begingroup \catcode`\"=12
 347 \DeclareMathSymbol{\coprod@}{\mathop}{largesymbols}{"60}
 348 \gdef\coprod{\DOTSB\coprod@\slimits@}
 349 \DeclareMathSymbol{\bigvee@}{\mathop}{largesymbols}{"57}
 350 \gdef\bigvee{\DOTSB\bigvee@\slimits@}
 351 \DeclareMathSymbol{\bigwedge@}{\mathop}{largesymbols}{"56}
 352 \gdef\bigwedge{\DOTSB\bigwedge@\slimits@}
 353 \DeclareMathSymbol{\biguplus@}{\mathop}{largesymbols}{"55}
 354 \gdef\biguplus{\DOTSB\biguplus@\slimits@}
 355 \DeclareMathSymbol{\bigcap@}{\mathop}{largesymbols}{"54}
 356 \gdef\bigcap{\DOTSB\bigcap@\slimits@}
 357 \DeclareMathSymbol{\bigcup@}{\mathop}{largesymbols}{"53}
 358 \gdef\bigcup{\DOTSB\bigcup@\slimits@}
 359 \DeclareMathSymbol{\prod@}{\mathop}{largesymbols}{"51}
 360 \gdef\prod{\DOTSB\prod@\slimits@}
 361 \DeclareMathSymbol{\sum@}{\mathop}{largesymbols}{"50}
 362 \gdef\sum{\DOTSB\sum@\slimits@}
 363 \DeclareMathSymbol{\bigotimes@}{\mathop}{largesymbols}{"4E}
 364 \gdef\bigotimes{\DOTSB\bigotimes@\slimits@}
 365 \DeclareMathSymbol{\bigoplus@}{\mathop}{largesymbols}{"4C}
 366 \gdef\bigoplus{\DOTSB\bigoplus@\slimits@}
 367 \DeclareMathSymbol{\bigodot@}{\mathop}{largesymbols}{"4A}
 368 \gdef\bigodot{\DOTSB\bigodot@\slimits@}
 369 \DeclareMathSymbol{\bigsqcup@}{\mathop}{largesymbols}{"46}
 370 \gdef\bigsqcup{\DOTSB\bigsqcup@\slimits@}
 371 \endgroup
 372 \def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 373  \hbox{\normalfont ...}\vss}}}}
 374 \def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 375  \hbox{\normalfont....}\vss}}}}
 376 \def~{\nobreakspace}
 377 \DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
 378 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 379 \newif\if@display
 380 \everydisplay\expandafter{\the\everydisplay \@displaytrue}
 381 \def\int{\DOTSI\intop\ilimits@}
 382 \def\oint{\DOTSI\ointop\ilimits@}
 383 \def\intkern@{\mkern-6mu\mathchoice{\mkern-3mu}{}{}{}}
 384 \def\intdots@{\mathchoice{\@cdots}%
 385  {{\cdotp}\mkern1.5mu{\cdotp}\mkern1.5mu{\cdotp}}%
 386  {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}%
 387  {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
 388
 389 \def\iint{\DOTSI\protect\ints@\tw@}
 390 \def\iiint{\DOTSI\protect\ints@\thr@@}
 391 \def\iiiint{\DOTSI\protect\ints@{4}}
 392 \def\idotsint{\DOTSI\protect\ints@\z@}
 393
 394 \def\ints@#1{%
 395   \mkern-7mu\mathchoice{\mkern-2mu}{}{}{}%
 396   \mathop{\mkern7mu\mathchoice{\mkern2mu}{}{}{}%
 397     \intop\ifnum#1=\z@\intdots@
 398     \else\intkern@\fi
 399     \ifnum#1>\tw@\intop\intkern@\fi
 400     \ifnum#1>\thr@@\intop\intkern@\fi
 401     \intop
 402   }\ilimits@
 403 }
 404 \def\nolimits@{%
 405   \DN@{\nolimits\ifx\@let@token\limits\expandafter\@gobble\fi}%
 406   \FN@\next@}
 407 \begingroup \catcode`\"=12
 408 \gdef\newmcodes@{\mathcode`\'39\mathcode`\*42\mathcode`\."613A%
 409  \mathcode`\-45\mathcode`\/47\mathcode`\:"603A\relax}
 410 \endgroup
 411 \DeclareRobustCommand{\operatorname}{%
 412   \@ifstar{\qopname\newmcodes@ n}%
 413           {\qopname\newmcodes@{no}}}%
 414 \DeclareRobustCommand{\qopname}[3]{\mathop{#1\kern\z@\operator@font#3}%
 415   \csname #2limits@\endcsname}
 416 \def\arccos{\qopname\relax{no}{arccos}}
 417 \def\arcsin{\qopname\relax{no}{arcsin}}
 418 \def\arctan{\qopname\relax{no}{arctan}}
 419 \def\arg{\qopname\relax{no}{arg}}
 420 \def\cos{\qopname\relax{no}{cos}}
 421 \def\cosh{\qopname\relax{no}{cosh}}
 422 \def\cot{\qopname\relax{no}{cot}}
 423 \def\coth{\qopname\relax{no}{coth}}
 424 \def\csc{\qopname\relax{no}{csc}}
 425 \def\deg{\qopname\relax{no}{deg}}
 426 \def\det{\qopname\relax n{det}}
 427 \def\dim{\qopname\relax{no}{dim}}
 428 \def\exp{\qopname\relax{no}{exp}}
 429 \def\gcd{\qopname\relax n{gcd}}
 430 \def\hom{\qopname\relax{no}{hom}}
 431 \def\inf{\qopname\relax n{inf}}
 432 \def\injlim{\qopname\relax n{inj\,lim}}
 433 \def\ker{\qopname\relax{no}{ker}}
 434 \def\lg{\qopname\relax{no}{lg}}
 435 \def\lim{\qopname\relax n{lim}}
 436 \def\liminf{\qopname\relax n{lim\,inf}}
 437 \def\limsup{\qopname\relax n{lim\,sup}}
 438 \def\ln{\qopname\relax{no}{ln}}
 439 \def\log{\qopname\relax{no}{log}}
 440 \def\max{\qopname\relax n{max}}
 441 \def\min{\qopname\relax n{min}}
 442 \def\Pr{\qopname\relax n{Pr}}
 443 \def\projlim{\qopname\relax n{proj\,lim}}
 444 \def\sec{\qopname\relax{no}{sec}}
 445 \def\sin{\qopname\relax{no}{sin}}
 446 \def\sinh{\qopname\relax{no}{sinh}}
 447 \def\sup{\qopname\relax n{sup}}
 448 \def\tan{\qopname\relax{no}{tan}}
 449 \def\tanh{\qopname\relax{no}{tanh}}
 450 \def\operator@font{\mathgroup\symoperators}
 451 \def\operatornamewithlimits{\operatorname*}
 452 \def\varlim@#1#2{\mathop{\vtop{\ialign{##\crcr
 453  \hfil$#1\m@th\operator@font lim$\hfil\crcr
 454  \noalign{\nointerlineskip\kern\ex@}#2#1\crcr
 455  \noalign{\nointerlineskip\kern-\ex@}\crcr}}}}
 456 \def\varinjlim{\mathpalette\varlim@\rightarrowfill@}
 457 \def\varprojlim{\mathpalette\varlim@\leftarrowfill@}
 458 \def\varliminf{\mathpalette\varliminf@{}}
 459 \def\varliminf@#1{\mathop{\@@underline{\vrule\@depth.2\ex@\@width\z@
 460    \hbox{$#1\m@th\operator@font lim$}}}}
 461 \def\varlimsup{\mathpalette\varlimsup@{}}
 462 \def\varlimsup@#1{\mathop{\@@overline
 463   {\hbox{$#1\m@th\operator@font lim$}}}}
 464 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 465 \def\numberwithin#1#2{\@ifundefined{c@#1}{\@nocounterr{#1}}{%
 466   \@ifundefined{c@#2}{\@nocnterr{#2}}{%
 467   \@addtoreset{#1}{#2}%
 468   \toks@\expandafter\expandafter\expandafter{\csname the#1\endcsname}%
 469   \expandafter\xdef\csname the#1\endcsname
 470     {\expandafter\noexpand\csname the#2\endcsname
 471      .\the\toks@}}}}
 472 \def\eqref#1{\textup{\tagform@{\ref{#1}}}}
 473 \def\bmod{\mskip-\medmuskip\mkern5mu\mathbin
 474   {\operator@font mod}\penalty900
 475   \mkern5mu\mskip-\medmuskip}
 476 \def\pod#1{\allowbreak\if@display\mkern18mu\else\mkern8mu\fi(#1)}
 477 \def\pmod#1{\pod{{\operator@font mod}\mkern6mu#1}}
 478 \def\mod#1{\allowbreak\if@display\mkern18mu
 479   \else\mkern12mu\fi{\operator@font mod}\,\,#1}
 480 \newcommand{\cfrac}[3][c]{{\displaystyle\frac{%
 481   \strut\ifx r#1\hfill\fi#2\ifx l#1\hfill\fi}{#3}}%
 482   \kern-\nulldelimiterspace}
 483 \def\lcfrac{\cfrac[l]}
 484 \def\rcfrac{\cfrac[r]}
 485 \def\overset#1#2{\binrel@{#2}%
 486   \binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
 487 \def\underset#1#2{\binrel@{#2}%
 488   \binrel@@{\mathop{\kern\z@#2}\limits_{#1}}}
 489 \def\sideset#1#2#3{%
 490   \setbox\z@\hbox{$\displaystyle{\vphantom{#3}}#1{#3}\m@th$}%
 491   \setbox\tw@\hbox{$\displaystyle{#3}#2\m@th$}%
 492   \hskip\wd\z@\hskip-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wd\z@
 493   {\vphantom{#3}}#1{#3}#2}}
 494 \renewcommand{\smash}[2][tb]{%
 495   \def\smash@{#1}%
 496   \ifmmode\expandafter\mathpalette\expandafter\mathsm@sh\else
 497         \expandafter\makesm@sh\fi{#2}}
 498 \def\finsm@sh{\def\mb@t{\ht\z@\z@}\def\mb@b{\dp\z@\z@}%
 499   \def\mb@tb{\mb@t\mb@b}%
 500   {\csname mb@\smash@\endcsname}%
 501   \leavevmode\boxz@}
 502 \def\rightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
 503   $#1\copy\z@\mkern-6mu\cleaders
 504   \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
 505   \mkern-6mu\mathord\rightarrow$}
 506 \def\leftarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
 507   $#1\mathord\leftarrow\mkern-6mu\cleaders
 508   \hbox{$#1\mkern-2mu\copy\z@\mkern-2mu$}\hfill
 509   \mkern-6mu\box\z@$}
 510 \def\leftrightarrowfill@#1{\m@th\setboxz@h{$#1\relbar$}\ht\z@\z@
 511   $#1\mathord\leftarrow\mkern-6mu\cleaders
 512   \hbox{$#1\mkern-2mu\box\z@\mkern-2mu$}\hfill
 513   \mkern-6mu\mathord\rightarrow$}
 514 \def\overarrow@#1#2#3{\vbox{\ialign{##\crcr#1#2\crcr
 515  \noalign{\kern-\ex@\nointerlineskip}$\m@th\hfil#2#3\hfil$\crcr}}}
 516 \def\overrightarrow{\mathpalette{\overarrow@\rightarrowfill@}}
 517 \def\overleftarrow{\mathpalette{\overarrow@\leftarrowfill@}}
 518 \def\overleftrightarrow{\mathpalette{\overarrow@\leftrightarrowfill@}}
 519 \def\underarrow@#1#2#3{%
 520  \vtop{\ialign{##\crcr$\m@th\hfil#2#3\hfil$\crcr
 521  \noalign{\nointerlineskip\kern-.5\ex@}#1#2\crcr}}}
 522 \def\underrightarrow{\mathpalette{\underarrow@\rightarrowfill@}}
 523 \def\underleftarrow{\mathpalette{\underarrow@\leftarrowfill@}}
 524 \def\underleftrightarrow{\mathpalette{\underarrow@\leftrightarrowfill@}}
 525 \let\ifgtest@\iffalse                              % initial value
 526 \def\gtest@true{\global\let\ifgtest@\iftrue}
 527 \def\gtest@false{\global\let\ifgtest@\iffalse}
 528 \let\DOTSI\relax
 529 \let\DOTSB\relax
 530 \let\DOTSX\relax
 531 {\uccode`7=`\\ \uccode`8=`m \uccode`9=`a \uccode`0=`t \uccode`!=`h
 532  \uppercase{%
 533   \gdef\math@#1#2#3#4#5#6\math@{\gtest@false\ifx 7#1\ifx 8#2%
 534   \ifx 9#3\ifx 0#4\ifx !#5\xdef\meaning@{#6}\gtest@true
 535   \fi\fi\fi\fi\fi}}}
 536 {\uccode`7=`c \uccode`8=`h \uccode`9=`\"
 537  \uppercase{\gdef\mathch@#1#2#3#4#5#6\mathch@{\gtest@false
 538   \ifx 7#1\ifx 8#2\ifx 9#5\gtest@true\xdef\meaning@{9#6}\fi\fi\fi}}}
 539 \newcount\classnum@
 540 \def\getmathch@#1.#2\getmathch@{\classnum@#1 \divide\classnum@4096
 541  \ifcase\number\classnum@\or\or\gdef\thedots@{\dotsb@}\or
 542  \gdef\thedots@{\dotsb@}\fi}
 543 {\uccode`4=`b \uccode`5=`i \uccode`6=`n
 544  \uppercase{\gdef\mathbin@#1#2#3{\relaxnext@
 545   \def\nextii@##1\mathbin@{\ifx\@sptoken\@let@token\gtest@true\fi}%
 546   \gtest@false\DN@##1\mathbin@{}%
 547  \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
 548 {\uccode`4=`r \uccode`5=`e \uccode`6=`l
 549  \uppercase{\gdef\mathrel@#1#2#3{\relaxnext@
 550   \def\nextii@##1\mathrel@{\ifx\@sptoken\@let@token\gtest@true\fi}%
 551  \gtest@false\DN@##1\mathrel@{}%
 552  \ifx 4#1\ifx 5#2\ifx 6#3\DN@{\FN@\nextii@}\fi\fi\fi\next@}}}
 553 {\uccode`5=`m \uccode`6=`a \uccode`7=`c
 554  \uppercase{\gdef\macro@#1#2#3#4\macro@{\gtest@false
 555   \ifx 5#1\ifx 6#2\ifx 7#3\gtest@true
 556   \xdef\meaning@{\macro@@#4\macro@@}\fi\fi\fi}}}
 557 \def\macro@@#1->#2\macro@@{#2}
 558 \newcount\DOTSCASE@
 559 {\uccode`6=`\\ \uccode`7=`D \uccode`8=`O \uccode`9=`T \uccode`0=`S
 560  \uppercase{\gdef\DOTS@#1#2#3#4#5{\gtest@false\DN@##1\DOTS@{}%
 561   \ifx 6#1\ifx 7#2\ifx 8#3\ifx 9#4\ifx 0#5\let\next@\DOTS@@
 562   \fi\fi\fi\fi\fi
 563   \next@}}}
 564 {\uccode`3=`B \uccode`4=`I \uccode`5=`X
 565  \uppercase{\gdef\DOTS@@#1{\relaxnext@
 566   \def\nextii@##1\DOTS@{\ifx\@sptoken\@let@token\gtest@true\fi}%
 567   \DN@{\FN@\nextii@}%
 568   \ifx 3#1\global\DOTSCASE@\z@\else
 569   \ifx 4#1\global\DOTSCASE@\@ne\else
 570   \ifx 5#1\global\DOTSCASE@\tw@\else\DN@##1\DOTS@{}%
 571   \fi\fi\fi\next@}}}
 572 {\uccode`5=`\\ \uccode`6=`n \uccode`7=`o \uccode`8=`t
 573  \uppercase{\gdef\not@#1#2#3#4{\relaxnext@
 574   \def\nextii@##1\not@{\ifx\@sptoken\@let@token\gtest@true\fi}%
 575  \gtest@false\DN@##1\not@{}%
 576  \ifx 5#1\ifx 6#2\ifx 7#3\ifx 8#4\DN@{\FN@\nextii@}\fi\fi\fi
 577  \fi\next@}}}
 578 \def\keybin@{\gtest@true
 579   \ifx\@let@token+\else\ifx\@let@token=\else\ifx\@let@token<%
 580   \else\ifx\@let@token>\else\ifx\@let@token-\else\ifx\@let@token*%
 581   \else\ifx\@let@token:\else\gtest@false\fi\fi\fi\fi\fi\fi\fi}
 582 \@ifundefined{@ldots}{\def\@ldots{\mathellipsis}}{}
 583 \DeclareRobustCommand{\dots}{\relax
 584   \csname\ifmmode m\else t\fi dots@\endcsname}
 585 \def\tdots@{\leavevmode\unskip\relaxnext@
 586  \DN@{$\m@th\@ldots\,
 587    \ifx\@let@token,\,$\else\ifx\@let@token.\,$\else\ifx\@let@token;\,$%
 588    \else\ifx\@let@token:\,$\else\ifx\@let@token?\,$%
 589    \else\ifx\@let@token!\,$\else$ \fi\fi\fi\fi\fi\fi}%
 590  \ \FN@\next@}
 591 \def\mdots@{\FN@\mdots@@}
 592 \def\mdots@@{\gdef\thedots@{\dotso@}%
 593  \ifx\@let@token\boldsymbol\gdef\thedots@\boldsymbol{\boldsymboldots@}%
 594  \else\ifx,\@let@token\gdef\thedots@{\dotsc}%
 595  \else\ifx\not\@let@token\gdef\thedots@{\dotsb@}%
 596  \else\keybin@
 597  \ifgtest@\gdef\thedots@{\dotsb@}%
 598  \else\xdef\meaning@{\meaning\@let@token..........}%
 599   \xdef\meaning@@{\meaning@}%
 600   \expandafter\math@\meaning@\math@
 601   \ifgtest@
 602    \expandafter\mathch@\meaning@\mathch@
 603    \ifgtest@\expandafter\getmathch@\meaning@\getmathch@\fi
 604   \else\expandafter\macro@\meaning@@\macro@
 605   \ifgtest@
 606    \expandafter\not@\meaning@\not@\ifgtest@\gdef\thedots@{\dotsb@}%
 607   \else\expandafter\DOTS@\meaning@\DOTS@
 608   \ifgtest@
 609    \ifcase\number\DOTSCASE@\gdef\thedots@{\dotsb@}%
 610     \or\gdef\thedots@{\dotsi}\else\fi
 611   \else\expandafter\math@\meaning@\math@
 612   \ifgtest@\expandafter\mathbin@\meaning@\mathbin@
 613   \ifgtest@\gdef\thedots@{\dotsb@}%
 614   \else\expandafter\mathrel@\meaning@\mathrel@
 615   \ifgtest@\gdef\thedots@{\dotsb@}%
 616   \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
 617  \thedots@}
 618 \def\boldsymboldots@#1{%
 619  \bold@true\let\@let@token=#1\let\delayed@=#1\mdots@@
 620  \boldsymbol#1\bold@false}
 621 \def\@cdots{\mathinner{\cdotp\cdotp\cdotp}}
 622 \def\dotsi{\!\@cdots}
 623 \let\dotsb@\@cdots
 624 \def\rightdelim@{\gtest@true
 625  \ifx\@let@token)\else
 626  \ifx\@let@token]\else
 627  \ifx\@let@token\rbrack\else
 628  \ifx\@let@token\}\else
 629  \ifx\@let@token\rbrace\else
 630  \ifx\@let@token\rangle\else
 631  \ifx\@let@token\rceil\else
 632  \ifx\@let@token\rfloor\else
 633  \ifx\@let@token\rgroup\else
 634  \ifx\@let@token\rmoustache\else
 635  \ifx\@let@token\right\else
 636  \ifx\@let@token\bigr\else
 637  \ifx\@let@token\biggr\else
 638  \ifx\@let@token\Bigr\else
 639  \ifx\@let@token\Biggr\else\gtest@false
 640  \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}
 641 \def\extra@{%
 642  \rightdelim@\ifgtest@
 643  \else\ifx\@let@token$\gtest@true
 644  \else\xdef\meaning@{\meaning\@let@token..........}%
 645  \expandafter\macro@\meaning@\macro@\ifgtest@
 646  \expandafter\DOTS@\meaning@\DOTS@
 647  \ifgtest@
 648  \ifnum\DOTSCASE@=\tw@\gtest@true\else\gtest@false
 649  \fi\fi\fi\fi\fi}
 650 \newif\ifbold@
 651 \def\dotso@{\relaxnext@
 652  \ifbold@
 653   \let\@let@token\delayed@
 654   \def\nextii@{\extra@\@ldots\ifgtest@\,\fi}%
 655  \else
 656   \def\nextii@{\DN@{\extra@\@ldots\ifgtest@\,\fi}\FN@\next@}%
 657  \fi
 658  \nextii@}
 659 \def\extrap@#1{%
 660  \DN@{#1\,}%
 661  \ifx\@let@token,\else
 662  \ifx\@let@token;\else
 663  \ifx\@let@token.\else\extra@
 664  \ifgtest@\else
 665  \let\next@#1\fi\fi\fi\fi\next@}
 666 \DeclareRobustCommand{\ldots}{\relax
 667   \ifmmode \DN@{\extrap@\@ldots}%
 668   \else \let\next@\tdots@\fi
 669   \FN@\next@}
 670 \DeclareRobustCommand{\cdots}{\DN@{\extrap@\@cdots}\FN@\next@}
 671 \let\dotso\ldots
 672 \let\dotsb\cdots
 673 \let\dotsm\dotsb
 674 \DeclareRobustCommand{\dotsc}{%
 675   \DN@{\ifx\@let@token;\@ldots\,%
 676        \else \ifx\@let@token.\@ldots\,%
 677        \else \extra@\@ldots \ifgtest@\,\fi
 678        \fi\fi}%
 679   \FN@\next@}
 680 \def\longrightarrow{\DOTSB\relbar\joinrel\rightarrow}
 681 \def\Longrightarrow{\DOTSB\Relbar\joinrel\Rightarrow}
 682 \def\longleftarrow{\DOTSB\leftarrow\joinrel\relbar}
 683 \def\Longleftarrow{\DOTSB\Leftarrow\joinrel\Relbar}
 684 \def\longleftrightarrow{\DOTSB\leftarrow\joinrel\rightarrow}
 685 \def\Longleftrightarrow{\DOTSB\Leftarrow\joinrel\Rightarrow}
 686 \def\mapsto{\DOTSB\mapstochar\rightarrow}
 687 \def\longmapsto{\DOTSB\mapstochar\longrightarrow}
 688 \def\hookrightarrow{\DOTSB\lhook\joinrel\rightarrow}
 689 \def\hookleftarrow{\DOTSB\leftarrow\joinrel\rhook}
 690 \def\doteq{\DOTSB\buildrel\textstyle.\over=}
 691 \def\iff{\DOTSB\;\Longleftrightarrow\;}
 692 \begingroup \catcode`\"=12
 693 \mathchardef\@tempa="7000
 694 \ifx\@tempa\Gamma
 695   \DeclareMathSymbol{\Gamma}{\mathord}{operators}{"00}
 696   \DeclareMathSymbol{\Delta}{\mathord}{operators}{"01}
 697   \DeclareMathSymbol{\Theta}{\mathord}{operators}{"02}
 698   \DeclareMathSymbol{\Lambda}{\mathord}{operators}{"03}
 699   \DeclareMathSymbol{\Xi}{\mathord}{operators}{"04}
 700   \DeclareMathSymbol{\Pi}{\mathord}{operators}{"05}
 701   \DeclareMathSymbol{\Sigma}{\mathord}{operators}{"06}
 702   \DeclareMathSymbol{\Upsilon}{\mathord}{operators}{"07}
 703   \DeclareMathSymbol{\Phi}{\mathord}{operators}{"08}
 704   \DeclareMathSymbol{\Psi}{\mathord}{operators}{"09}
 705   \DeclareMathSymbol{\Omega}{\mathord}{operators}{"0A}
 706   \DeclareMathSymbol{\varGamma}{\mathord}{letters}{"00}
 707   \DeclareMathSymbol{\varDelta}{\mathord}{letters}{"01}
 708   \DeclareMathSymbol{\varTheta}{\mathord}{letters}{"02}
 709   \DeclareMathSymbol{\varLambda}{\mathord}{letters}{"03}
 710   \DeclareMathSymbol{\varXi}{\mathord}{letters}{"04}
 711   \DeclareMathSymbol{\varPi}{\mathord}{letters}{"05}
 712   \DeclareMathSymbol{\varSigma}{\mathord}{letters}{"06}
 713   \DeclareMathSymbol{\varUpsilon}{\mathord}{letters}{"07}
 714   \DeclareMathSymbol{\varPhi}{\mathord}{letters}{"08}
 715   \DeclareMathSymbol{\varPsi}{\mathord}{letters}{"09}
 716   \DeclareMathSymbol{\varOmega}{\mathord}{letters}{"0A}
 717 \fi
 718 \endgroup
 719 \def\accentclass@{7}
 720 \def\noaccents@{\def\accentclass@{0}}
 721 \DeclareFontEncoding{OML}{}{\noaccents@}
 722 \DeclareFontEncoding{OMS}{}{\noaccents@}
 723 \edef\@tempa#1#2{\def#1{\mathaccent\string"\noexpand\accentclass@#2 }}
 724 \@tempa\hat{05E}\@tempa\check{014}\@tempa\tilde{07E}\@tempa\acute{013}
 725 \@tempa\grave{012}\@tempa\dot{05F}\@tempa\ddot{07F}\@tempa\breve{015}
 726 \@tempa\bar{016}
 727 \newcount\skewcharcount@
 728 \newcount\familycount@
 729 \def\theskewchar@{\familycount@\@ne
 730  \global\skewcharcount@\the\skewchar\textfont\@ne
 731  \ifnum\mathgroup>\m@ne\ifnum\mathgroup<16
 732   \global\familycount@\the\mathgroup\relax
 733   \global\skewcharcount@\the\skewchar\textfont\the\mathgroup\relax\fi\fi
 734  \ifnum\skewcharcount@>\m@ne
 735   \ifnum\skewcharcount@<128
 736   \multiply\familycount@256
 737   \global\advance\skewcharcount@\familycount@
 738   \global\advance\skewcharcount@28672
 739   \mathchar\skewcharcount@\else
 740   \global\skewcharcount@\m@ne\fi\else
 741  \global\skewcharcount@\m@ne\fi}
 742 \newcount\pointcount@
 743 \def\getpoints@#1.#2\getpoints@{\pointcount@#1 }
 744 \newdimen\accentdimen@
 745 \newcount\accentmu@
 746 \def\dimentomu@{\multiply\accentdimen@ 100
 747  \expandafter\getpoints@\the\accentdimen@\getpoints@
 748  \multiply\pointcount@18
 749  \divide\pointcount@\@m
 750  \global\accentmu@\pointcount@}
 751 \def\mathaccent@#1#2{\ifnum\mathgroup=\m@ne\xdef\thefam@{1}\else
 752  \xdef\thefam@{\the\mathgroup}\fi
 753  \accentdimen@\z@
 754  \setboxz@h{\unbracefonts@$\m@th\mathgroup\thefam@\relax#2$}%
 755  \ifdim\accentdimen@=\z@\DN@{\mathaccent#1{#2}}%
 756   \setbox\@ne\hbox{\unbracefonts@
 757     $\m@th\mathgroup\thefam@\relax#2\theskewchar@$}
 758   \setbox\tw@\hbox{$\m@th\ifnum\skewcharcount@=\m@ne\else
 759    \mathchar\skewcharcount@\fi$}%
 760   \global\accentdimen@\wd\@ne\global\advance\accentdimen@-\wdz@
 761   \global\advance\accentdimen@-\wd\tw@
 762   \global\multiply\accentdimen@\tw@
 763   \dimentomu@\global\advance\accentmu@\@ne
 764  \else\DN@{{\mathaccent#1{#2\mkern\accentmu@ mu}%
 765     \mkern-\accentmu@ mu}{}}\fi
 766  \next@}
 767 \def\unbracefonts@{\let\math@bgroup\@empty\let\math@egroup\@empty}
 768 \begingroup \catcode`\"=12
 769 \def\@tempa#1#2{\gdef#1{\RIfM@\DN@{\mathaccent@{"\accentclass@#2 }}%
 770   \else\DN@{\nonmatherr@{#1}}\fi\next@}}
 771 \@tempa\Hat{05E}\@tempa\Check{014}\@tempa\Tilde{07E}\@tempa\Acute{013}
 772 \@tempa\Grave{012}\@tempa\Dot{05F}\@tempa\Ddot{07F}\@tempa\Breve{015}
 773 \@tempa\Bar{016}
 774 \gdef\Vec{\RIfM@\DN@{\mathaccent@{"017E }}\else
 775  \DN@{\nonmatherr@\Vec}\fi\next@}
 776 \endgroup
 777 \begingroup \catcode`\"=12
 778 \gdef\@@sqrt#1{\radical"270370 {#1}}
 779 \endgroup
 780 \@saveprimitive\overline\@@overline
 781 \def\overline#1{\@@overline{#1}}
 782 \def\boxed#1{\fbox{\m@th$\displaystyle#1$}}
 783 \def\setb@ck{\iffirstchoice@\global\advance\c@equation\m@ne\fi}
 784 \newcount\dspbrk@lvl
 785 \dspbrk@lvl=-1
 786 \interdisplaylinepenalty\@M
 787 \def\allowdisplaybreaks{%
 788   \new@ifnextchar[\allowdspbrks@{\allowdspbrks@[4]}}
 789 \def\allowdspbrks@[#1]{%
 790   \interdisplaylinepenalty\getdsp@pen{#1}}
 791 \def\getdsp@pen#1{%
 792   \ifcase #1\relax \@M
 793     \or 9999
 794     \or 6999
 795     \or 2999
 796     \or \z@\fi}
 797 \def\displaybreak{\PackageError{amstex}{\Invalid@@\displaybreak}\@eha}
 798 \def\displaybreak@{%
 799   \def\displaybreak{\new@ifnextchar[\dspbrk@{\dspbrk@[4]}}}
 800 \def\dspbrk@[#1]{\global\dspbrk@lvl #1\relax}
 801 \def\math@cr{{\ifnum0=`}\fi
 802   \new@ifstar{\global\@eqpen\@M\math@cr@}%
 803           {\global\@eqpen
 804              \ifnum\dspbrk@lvl <\z@ \interdisplaylinepenalty
 805               \else -\@getpen\dspbrk@lvl \fi
 806            \math@cr@}}
 807 \def\math@cr@{\new@ifnextchar[\math@cr@@{\math@cr@@[\z@]}}
 808 \def\math@cr@@[#1]{\ifnum0=`{\fi}\math@cr@@@
 809   \noalign{\vskip#1\relax}}
 810 \def\Let@{\let\\\math@cr}
 811 \def\restore@math@cr{\def\math@cr@@@{\cr}}
 812 \restore@math@cr
 813 \def\intertext{\PackageError{amstex}{\Invalid@@\intertext}\@eha}
 814 \def\intertext@{\def\intertext##1{\noalign{%
 815   \penalty\postdisplaypenalty\vskip\belowdisplayskip
 816   \vbox{\normalbaselines\noindent##1}%
 817   \penalty\predisplaypenalty\vskip\abovedisplayskip}}}
 818 \newhelp\tag@help
 819   {tag cannot be used at this point.\space
 820    If you don't understand why^^Jyou should consult
 821    the documentation.^^JBut don't worry: just continue, and I'll
 822    forget what happened.}
 823 \def\gobble@tag{\new@ifstar\@gobble\@gobble}
 824 \def\invalid@tag#1{\PackageError{amstex}{#1}{\the\tag@help}\gobble@tag}
 825 \def\dft@tag{\invalid@tag{\string\tag\space not allowed here}}
 826 \def\default@tag{\let\tag\dft@tag}
 827 \default@tag
 828 \def\maketag@@{\new@ifstar\maketag@@@\tagform@}
 829 \def\maketag@@@#1{\hbox{\m@th\normalfont#1}}
 830 \def\tagform@#1{\maketag@@@{(\ignorespaces#1\unskip)}}
 831 \def\thetag{\leavevmode\tagform@}
 832 \def\make@df@tag{\new@ifstar\make@df@tag@@\make@df@tag@@@}
 833 \def\make@df@tag@@#1{%
 834   \def\@currentlabel{#1}%
 835   \gdef\df@tag{\maketag@@@{#1}}}
 836 \def\make@df@tag@@@#1{\@seteqlabel{#1}\gdef\df@tag{\tagform@{#1}}}
 837 \def\@seteqlabel#1{\toks@\@xp{\p@equation{#1}}%
 838   \edef\@currentlabel{\the\toks@}}
 839 \def\notag{\nonumber}
 840 \iftagsleft@
 841 \def\@eqnnum{\hbox to1sp{}\rlap{\normalfont
 842     \hskip -\displaywidth\tagform@\theequation}}
 843 \fi
 844
 845 \let\@adjusttag\@empty
 846
 847 \def\adjusttag#1{\skip@#1\relax\gdef\@adjusttag{#1}}
 848
 849 \def\@movetag{%
 850     \ifx\@adjusttag\@empty \else
 851         \vskip\@adjusttag\relax
 852         \global\let\@adjusttag\@empty
 853     \fi
 854 }
 855 \def\multilimits@{\bgroup
 856   \Let@
 857   \restore@math@cr
 858   \default@tag
 859  \baselineskip\fontdimen10 \scriptfont\tw@
 860  \advance\baselineskip\fontdimen12 \scriptfont\tw@
 861  \lineskip\thr@@\fontdimen8 \scriptfont\thr@@
 862  \lineskiplimit\lineskip
 863  \vbox\bgroup\ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil\crcr}
 864 \def\Sb{_\multilimits@}
 865 \def\Sp{^\multilimits@}
 866 \def\endSb{\crcr\egroup\egroup\egroup}
 867 \let\endSp=\endSb
 868 \def\smallmatrix{\null\,\vcenter\bgroup
 869  \Let@\restore@math@cr\default@tag
 870  \baselineskip6\ex@ \lineskip1.5\ex@ \lineskiplimit\lineskip
 871  \ialign\bgroup\hfil$\m@th\scriptstyle{##}$\hfil&&\thickspace\hfil
 872  $\m@th\scriptstyle{##}$\hfil\crcr}
 873 \def\endsmallmatrix{\crcr\egroup\egroup\,}
 874 \newcount\c@MaxMatrixCols
 875 \c@MaxMatrixCols=10
 876
 877 \def\matrix{\hskip -\arraycolsep\array{*\c@MaxMatrixCols c}}
 878 \def\endmatrix{\endarray \hskip -\arraycolsep}
 879 \@ifundefined{prepnext@tok}{%
 880   \def\@array[#1]#2{%
 881     \setbox\@arstrutbox\hbox{\vrule\@height\arraystretch\ht\strutbox
 882        \@depth\arraystretch\dp\strutbox \@width\z@}%
 883     \@mkpream{#2}\edef\@preamble{\ialign \noexpand\@halignto
 884     \bgroup \tabskip\z@ \@arstrut \@preamble \tabskip\z@ \cr}%
 885     \let\@startpbox\@@startpbox \let\@endpbox\@@endpbox
 886     \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
 887     \bgroup \let\par\@empty
 888     \let\@sharp##\let\protect\relax
 889     \lineskip\z@\baselineskip\z@\@preamble}%
 890 \begingroup \lccode`\~=`\@ \catcode`\~=\active % just to be sure!
 891 \lowercase{%
 892 \gdef\@xexpast#1*#2#3#4\@@{\begingroup
 893   \def~{@}\edef\reserved@a{#1}\@tempcnta#2\relax
 894   \ifnum\@tempcnta >\z@
 895     \@whilenum\@tempcnta >\z@\do
 896       {\edef\reserved@a{\reserved@a#3}\advance\@tempcnta \m@ne}%
 897     \let\reserved@b\@xexpast
 898   \else \let\reserved@b\@xexnoop\fi
 899   \expandafter\reserved@b \reserved@a #4\@@
 900   \expandafter\endgroup
 901   \expandafter\def\expandafter\reserved@a\expandafter{\reserved@a}%
 902   \let\@tempa\reserved@a
 903 }% End of \@xexpast
 904 }% End of \lowercase
 905 \endgroup
 906 }{}% End of \@ifundefined test.
 907 \def\pmatrix{\left(\matrix}
 908 \def\endpmatrix{\endmatrix\right)}
 909 \def\bmatrix{\left[\matrix}
 910 \def\endbmatrix{\endmatrix\right]}
 911 \def\vmatrix{\left|\matrix}
 912 \def\endvmatrix{\endmatrix\right|}
 913 \def\Vmatrix{\left\|\matrix}
 914 \def\endVmatrix{\endmatrix\right\|}
 915 \let\hdots\@ldots
 916 \def\hdotsfor#1{\if\noexpand#1[\expandafter\shdots@for\else
 917                 \hdots@for\@ne{#1}\fi}
 918 \newmuskip\dotsspace@
 919 \def\shdots@for#1]{\hdots@for{#1}}
 920 \def\hdots@for#1#2{\multicolumn{#2}c%
 921   {\m@th\dotsspace@1.5mu\mkern-#1\dotsspace@
 922    \xleaders\hbox{$\m@th\mkern#1\dotsspace@.\mkern#1\dotsspace@$}%
 923            \hfill
 924    \mkern-#1\dotsspace@}%
 925    }
 926 \def\cases{\left\{\def\arraystretch{1.2}\hskip-\arraycolsep
 927   \array{l@{\quad}l}}
 928 \def\endcases{\endarray\hskip-\arraycolsep\right.}
 929 \newif\ifinany@
 930 \newif\ifinalign@
 931 \newif\ifingather@
 932 \newcount\and@
 933 \newif\iftag@
 934 \newhelp\andhelp@
 935 {An extra & here is so disastrous that you should probably exit^^J
 936 and fix things up.}
 937 \newif\ifst@rred
 938 \newtoks\@envbody
 939 \def\addto@envbody#1{\@envbody\expandafter{\the\@envbody#1}}
 940 \def\collect@body#1{%
 941   \@envbody{}%
 942   \def\process@envbody{%
 943     \expandafter#1\expandafter{\the\@envbody}}%
 944   \expandafter\let\csname\@currenvir\endcsname\collect@@body
 945   \csname\@currenvir\endcsname}
 946 \def\collect@@body#1\end#2{%
 947   \def\@tempa{#2}%
 948   \ifx\@tempa\@currenvir
 949     \addto@envbody{#1}%
 950     \expandafter\edef\csname\@currenvir\endcsname
 951       {\noexpand\process@envbody\noexpand\end{\@tempa}}%
 952   \else
 953     \addto@envbody{#1\end{#2}}%
 954   \fi
 955   \csname\@currenvir\endcsname}
 956 \newenvironment{aligned}{%
 957   \relax\ifmmode\else\nonmatherr@{\begin{aligned}}\fi
 958   \null\,\new@ifnextchar[{\aligned@}{\aligned@[c]}%
 959 }{%
 960   \crcr\egroup\egroup
 961 }
 962 \def\aligned@[#1]{%
 963   \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
 964   \bgroup
 965    \Let@\restore@math@cr
 966    \default@tag
 967    \ifinany@\else\openup\jot\fi
 968    \ialign\bgroup\hfil\strut@$\m@th\displaystyle{##}$&%
 969     $\m@th\displaystyle{{}##}$\hfil\crcr}
 970 \newtoks\hashtoks@
 971 \hashtoks@{#}
 972 \newcount\atcount@
 973 \def\doat@#1{\toks@{\hfil\strut@$\m@th
 974   \displaystyle{\the\hashtoks@}$&$\m@th\displaystyle
 975   {{}\the\hashtoks@}$\hfil}%
 976  \atcount@#1\relax\advance\atcount@\m@ne
 977  \loop\ifnum\atcount@>\z@\toks@\expandafter{\the\toks@&\hfil$\m@th
 978   \displaystyle{\the\hashtoks@}$&$\m@th
 979   \displaystyle{{}\the\hashtoks@}$\hfil}\advance
 980  \atcount@\m@ne\repeat
 981  \xdef\preamble@{\the\toks@}\xdef\preamble@@{\preamble@}}
 982 \newenvironment{alignedat}[2][c]{%
 983   \null\,%
 984   \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
 985   \bgroup\doat@{#2}\Let@ \restore@math@cr\default@tag
 986   \ifinany@\else\openup\jot\fi\ialign\bgroup\span\preamble@@\crcr
 987 }{%
 988   \endaligned
 989 }
 990 \newenvironment{gathered}[1][c]{%
 991   \relax\ifmmode\else\nonmatherr@{\begin{gathered}}\fi
 992   \null\,%
 993   \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi
 994   \bgroup\Let@\restore@math@cr
 995   \ifinany@\else\openup\jot\fi\ialign
 996   \bgroup\hfil\strut@$\m@th\displaystyle##$\hfil\crcr
 997 }{%
 998   \endaligned
 999 }
1000 \def\tag@in@align{\relax
1001   \iftag@\DN@{\invalid@tag{Multiple \string\tag}}\else
1002    \global\tag@true
1003    \if@eqnsw\global\@eqnswfalse\fi
1004    \let\next@\make@df@tag\fi
1005   \next@}
1006 \def\math@cr@@@align{%
1007   \if@eqnsw\global\tag@true\fi
1008   \iftag@
1009    \ifcase\and@
1010     \DN@{&&}\else
1011     \DN@{&}\fi\else
1012     \let\next@\relax\fi
1013   \next@
1014   \relax
1015   \if@eqnsw\tagform@\theequation\stepcounter{equation}\else
1016   \iftag@\df@tag\fi\fi
1017   \global\@eqnswtrue\cr}
1018 \def\Tag@{\relax\iftag@\else\firstchoice@true
1019   \PackageError{amstex}{%
1020   Extra & on this line%
1021   }{\the\andhelp@% "An extra & here is disastrous"
1022 }\fi}
1023 \newdimen\lwidth@
1024 \newdimen\rwidth@
1025 \newdimen\maxlwidth@
1026 \newdimen\maxrwidth@
1027 \newdimen\totwidth@
1028 \def\measure@#1{\lwidth@\z@\rwidth@\z@\maxlwidth@\z@\maxrwidth@\z@
1029  \global\and@\z@
1030  \setbox\@ne\vbox{%
1031    \everycr{\noalign{\global\tag@false\global\and@\z@}}\Let@
1032    \let\tag\gobble@tag
1033    \let\notag\@empty \let\nonumber\@empty
1034    \firstchoice@false
1035     \halign{\setboxz@h{$\m@th\displaystyle{\@lign##}$}%
1036      \global\lwidth@\wdz@
1037      \ifdim\lwidth@>\maxlwidth@\global\maxlwidth@\lwidth@\fi
1038      \global\advance\and@\@ne
1039      &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
1040      \global\rwidth@\wdz@
1041      \ifdim\rwidth@>\maxrwidth@\global\maxrwidth@\rwidth@\fi
1042      \global\advance\and@\@ne
1043      &\Tag@\@gobble{##}\crcr#1\crcr}}%
1044  \totwidth@\maxlwidth@\advance\totwidth@\maxrwidth@}
1045 \def\displ@y{\global\dt@ptrue\openup\jot\m@th
1046   \everycr{\noalign{\ifdt@p \global\dt@pfalse
1047       \vskip-\lineskiplimit \vskip\normallineskiplimit
1048       \else \penalty\@eqpen \fi}}}
1049 \def\displ@y@{\global\dt@ptrue\openup\jot
1050   \everycr{\noalign{\global\tag@false
1051                    \global\and@\z@
1052                    \global\dspbrk@lvl\m@ne
1053                    \ifdt@p\global\dt@pfalse
1054       \vskip-\lineskiplimit\vskip\normallineskiplimit\else
1055       \penalty\@eqpen\fi}}}
1056 \def\black@#1{\noalign{\ifdim#1>\displaywidth
1057  \dimen@\prevdepth\nointerlineskip
1058  \vskip-\ht\strutbox@\vskip-\dp\strutbox@
1059  \vbox{\noindent\hbox to#1{\strut@\hfill}}%
1060  \prevdepth\dimen@
1061  \fi}}
1062 \def\align{\ifingather@
1063   {\ifnum0=`}\fi
1064   \DN@{\@nameuse{align (in \string\gather)}}%
1065   \else \ifmmode\nomath@env
1066     \DN@{\let\endalign\relax\@gobble}\else
1067   $$\stepcounter{equation}%
1068   \st@rredfalse\let\next@\align@\fi\fi
1069  \collect@body\next@}
1070 \@namedef{align*}{\ifingather@
1071   {\ifnum0=`}\fi
1072   \DN@{\@nameuse{align* (in \string\gather)}}\else
1073    \ifmmode\nomath@env
1074     \DN@{\@namedef{endalign*}{}\@gobble}\else
1075    $$\st@rredtrue
1076   \let\next@\align@\fi\fi
1077  \collect@body\next@}
1078 \newdimen\lineht@
1079 \def\align@{\inalign@true\inany@true
1080  \displaybreak@\intertext@
1081  \let\math@cr@@@\math@cr@@@align
1082  \let\tag\tag@in@align
1083  \global\and@\z@\global\dspbrk@lvl\m@ne
1084  \iftagsleft@\DN@{\@nameuse{align }}\else
1085   \DN@{\@nameuse{align \space}}\fi\next@}
1086 \@namedef{align }#1{%
1087     \measure@{#1}%
1088     \global\and@\z@
1089     \global\dspbrk@lvl\m@ne
1090     \if@fleqn %%*F
1091         \advance\totwidth@\@mathmargin %%*F
1092     \fi %%*F
1093     \ifdim\totwidth@>\displaywidth
1094         \let\displaywidth@\totwidth@
1095     \else
1096         \let\displaywidth@\displaywidth
1097     \fi
1098     \ifingather@
1099         \everycr{%
1100             \noalign{%
1101                 \global\and@\z@
1102                 \global\dspbrk@lvl\m@ne
1103             }%
1104         }%
1105     \else
1106         \displ@y@
1107     \fi
1108     \Let@
1109     \ifst@rred\else\@seteqlabel\theequation\fi
1110     \tabskip\@mathmargin %%*F
1111     \dimen@\displaywidth %%*F
1112     \if@fleqn %%*F
1113         \ifingather@ %%*F
1114             \tabskip\z@skip %%*F
1115             \advance\dimen@-\@mathmargin %%*F
1116         \fi %%*F
1117     \fi %%*F
1118     \halign to\dimen@\bgroup %%*F
1119         \ifst@rred\nonumber\fi
1120         \hfil
1121         \strut@
1122         \setboxz@h{\global\tag@false$\m@th\displaystyle{\@lign##}$}%
1123         \global\lwidth@\wdz@
1124         \global\lineht@\ht\z@
1125         \boxz@
1126         \global\advance\and@\@ne
1127         \tabskip\z@skip
1128        &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
1129         \global\rwidth@\wdz@
1130         \ifdim\ht\z@>\lineht@
1131             \global\lineht@\ht\z@
1132         \fi
1133         \boxz@
1134         \hfil
1135         \global\advance\and@\@ne
1136         \tabskip\@centering
1137        &\kern-\displaywidth@
1138         \setboxz@h{\@lign\strut@{##}}%
1139         \if@fleqn %%*F
1140             \dimen@\@mathmargin %%*F
1141             \advance\dimen@\maxlwidth@ %%*F
1142             \advance\dimen@-\lwidth@ %%*F
1143         \else %%*F
1144             \dimen@\displaywidth
1145             \advance\dimen@-\totwidth@
1146             \divide\dimen@\tw@
1147             \advance\dimen@\maxlwidth@
1148             \advance\dimen@-\lwidth@
1149         \fi %%*F
1150         \ifdim\dimen@<\tw@\wdz@
1151             \rlap{\vbox{\normalbaselines\boxz@\vbox to\lineht@{}}}%
1152         \else
1153             \rlap{\boxz@}%
1154         \fi
1155         \tabskip\displaywidth@
1156         \crcr
1157         #1%
1158 }
1159 \@namedef{align \space}#1{%
1160     \measure@{#1}%
1161     \if@fleqn %%*F
1162         \advance\totwidth@\@mathmargin %%*F
1163     \fi %%*F
1164     \global\and@\z@
1165     \global\dspbrk@lvl\m@ne
1166     \ifingather@
1167         \everycr{\noalign{\global\and@\z@\global\dspbrk@lvl\m@ne}}%
1168     \else
1169         \displ@y@
1170     \fi
1171     \Let@
1172     \ifst@rred\else\@seteqlabel\theequation\fi
1173     \tabskip\@mathmargin %%*F
1174     \dimen@\displaywidth %%*F
1175     \if@fleqn %%*
1176         \ifingather@ %%*F
1177             \tabskip\z@skip %%*F
1178             \advance\dimen@-\@mathmargin %%*F
1179         \fi %%*F
1180     \fi %%*F
1181      \halign to\dimen@\bgroup %%*F
1182         \ifst@rred\nonumber\fi
1183         \hfil
1184         \strut@
1185         \setboxz@h{\global\tag@false$\m@th\displaystyle{\@lign##}$}%
1186         \global\lwidth@\wdz@\boxz@
1187         \global\advance\and@\@ne
1188         \tabskip\z@skip
1189        &\setboxz@h{$\m@th\displaystyle{{}\@lign##}$}%
1190         \global\rwidth@\wdz@
1191         \boxz@
1192         \hfill
1193         \global\advance\and@\@ne
1194         \tabskip\@centering
1195        &\setboxz@h{\@lign\strut@{##}}%
1196         \dimen@\displaywidth
1197         \advance\dimen@-\totwidth@
1198         \divide\dimen@\tw@
1199         \advance\dimen@\maxrwidth@
1200         \advance\dimen@-\rwidth@
1201         \ifdim\dimen@<\tw@\wdz@
1202             \llap{\vtop{\@movetag\normalbaselines\null\boxz@}}%%*T
1203         \else
1204             \llap{\boxz@}%
1205         \fi
1206         \tabskip\z@skip
1207         \crcr#1%
1208 }
1209 \def\endalign{\math@cr@@@align
1210   \black@\totwidth@
1211   \egroup$$\global\@ignoretrue\setb@ck}
1212
1213 \@namedef{endalign*}{\math@cr@@@align\black@\totwidth@
1214   \egroup$$\global\@ignoretrue}
1215 \@namedef{align (in \string\gather)}{%
1216   \ifst@rred\stepcounter{equation}\fi
1217   \def\endalign{\@nameuse{endalign (in \string\gather)}\ifnum0=`{\fi}}%
1218   \vcenter\bgroup\st@rredfalse
1219     \collect@body\align@}
1220 \@namedef{endalign (in \string\gather)}{%
1221   \math@cr@@@align\black@\totwidth@
1222   \egroup\egroup
1223   \ifst@rred\setb@ck\fi% this ifst@rred is set by the enclosing gather
1224   \global\tag@false\global\@eqnswfalse}
1225 \@namedef{align* (in \string\gather)}{%
1226   \@namedef{endalign*}{\@nameuse{endalign* (in \string\gather)}%
1227                        \ifnum0=`{\fi}}%
1228   \vcenter\bgroup\st@rredtrue
1229     \collect@body\align@}
1230 \@namedef{endalign* (in \string\gather)}{%
1231   \math@cr@@@align\black@\totwidth@\egroup\egroup
1232   \global\tag@false\global\@eqnswfalse}
1233 \newif\ifxat@
1234 \def\alignat#1{%
1235  \ifmmode\nomath@env\DN@{\let\endalignat\relax\@gobble}\else$$%
1236  \st@rredfalse\stepcounter{equation}\@seteqlabel\theequation
1237  \DN@{\@nameuse{alignat }#1}\fi
1238  \collect@body\next@}
1239 \@namedef{alignat*}#1{%
1240  \ifmmode\nomath@env\DN@{\@namedef{endalignat*}{}\@gobble}\else$$%
1241  \st@rredtrue
1242  \DN@{\@nameuse{alignat }#1}\fi
1243  \collect@body\next@}
1244 \newif\ifmeasuring@
1245 \newbox\savealignat@
1246 \def\math@cr@@@alignat{%
1247   \if@eqnsw\global\tag@true\fi
1248   \iftag@
1249    \multiply\count@\tw@
1250    \xdef\next@{}\loop\ifnum\count@>\and@\xdef\next@{&\next@}%
1251     \advance\count@\m@ne\repeat\else
1252    \let\next@\relax\fi
1253   \next@
1254   \relax
1255   \if@eqnsw\tagform@\theequation\stepcounter{equation}\else
1256   \iftag@\df@tag\fi\fi
1257   \global\@eqnswtrue\cr}%
1258 \@namedef{alignat }#1#2{%
1259     \inany@true
1260     \xat@false
1261     \let\tag\tag@in@align
1262     \def\math@cr@@@{\count@#1\relax \math@cr@@@alignat}%
1263     \displaybreak@
1264     \intertext@
1265     \displ@y@
1266     \ifst@rred
1267         \global\@eqnswfalse
1268     \else
1269         \global\@eqnswtrue
1270     \fi
1271     \measuring@true
1272     \setbox\savealignat@\hbox{%
1273         $\m@th\displaystyle\Let@
1274         \attag@{#1}%
1275         \vbox{\firstchoice@false\halign{\span\preamble@@\crcr#2\crcr}}$%
1276     }%
1277     \measuring@false
1278     \Let@
1279     \attag@{#1}%
1280     \tabskip\@mathmargin %%*F
1281     \halign to\displaywidth\bgroup
1282         \span\preamble@@\crcr
1283         #2%
1284 }
1285 \def\endalignat{\math@cr@@@\black@{\wd\savealignat@}%
1286      \egroup\setb@ck$$\global\@ignoretrue}
1287 \@namedef{endalignat*}{\math@cr@@@\black@{\wd\savealignat@}\egroup
1288   $$\global\@ignoretrue}
1289 \def\xalignat#1{%
1290  \ifmmode\nomath@env\DN@{\let\endxalignat\relax\@gobble}\else$$%
1291  \st@rredfalse\stepcounter{equation}\@seteqlabel\theequation
1292  \DN@{\@nameuse{xalignat }#1}\fi
1293  \collect@body\next@}
1294 \@namedef{xalignat*}#1{%
1295  \ifmmode\nomath@env\DN@{\@namedef{endxalignat*}{}\@gobble}\else$$%
1296  \st@rredtrue
1297  \DN@{\@nameuse{xalignat }#1}\fi
1298  \collect@body\next@}
1299 \let\endxalignat=\endalignat
1300
1301 \expandafter\let\csname endxalignat*\expandafter
1302   \endcsname\csname endalignat*\endcsname
1303 \@namedef{xalignat }#1#2{%
1304     \inany@true
1305     \xat@true
1306     \let\tag\tag@in@align
1307     \def\math@cr@@@{\count@#1\relax\math@cr@@@alignat}%
1308     \displaybreak@
1309     \intertext@
1310     \displ@y@
1311     \measuring@true
1312     \setbox\savealignat@\hbox{%
1313         $\m@th\displaystyle\Let@
1314         \attag@{#1}%
1315         \vbox{%
1316             \firstchoice@false
1317             \halign{\span\preamble@@\crcr#2\crcr}%
1318         }%
1319         $%
1320     }%
1321     \measuring@false
1322     \Let@
1323     \attag@{#1}%
1324     \tabskip\@mathmargin %%*F
1325     \halign to\displaywidth\bgroup
1326         \span\preamble@@\crcr#2%
1327 }
1328 \def\attag@#1{%
1329  \let\TAG@\Tag@\let\Tag@0%
1330  \ifmeasuring@\def\llap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}%
1331   \def\rlap@##1{\setboxz@h{##1}\hbox to\tw@\wdz@{}}\else
1332   \let\llap@\llap\let\rlap@\rlap\fi
1333  \toks@{\hfil\strut@$\m@th\displaystyle{\@lign\the\hashtoks@}$%
1334   \tabskip\z@skip
1335   \global\advance\and@\@ne
1336   &$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil
1337   \ifxat@\tabskip\@centering\fi\global\advance\and@\@ne}%
1338  \iftagsleft@
1339   \@temptokena{\tabskip\@centering&\Tag@\kern-\displaywidth
1340    \rlap@{\@lign
1341      \the\hashtoks@
1342     }%
1343    \global\advance\and@\@ne\tabskip\displaywidth}\else
1344   \@temptokena{\tabskip\@centering&\Tag@\llap@{\@lign
1345    \the\hashtoks@
1346   }\global\advance\and@\@ne\tabskip\z@skip}\fi
1347  \atcount@#1\relax\advance\atcount@\m@ne
1348  \loop\ifnum\atcount@>\z@
1349  \toks@\expandafter{\the\toks@&\hfil$\m@th\displaystyle{\@lign
1350   \the\hashtoks@}$\global\advance\and@\@ne
1351   \tabskip\z@skip
1352   &$\m@th\displaystyle{{}\@lign\the\hashtoks@}$\hfil\ifxat@
1353   \tabskip\@centering\fi\global\advance\and@\@ne}\advance\atcount@\m@ne
1354  \repeat
1355  \xdef\preamble@{\the\toks@\the\@temptokena}%
1356  \xdef\preamble@@{\ifst@rred\noexpand\nonumber\fi\preamble@}%
1357  \let\Tag@\TAG@}
1358 \def\xxalignat#1{%
1359  \ifmmode\nomath@env\DN@{\let\endxxalignat\relax\@gobble}\else$$%
1360  \DN@{\@nameuse{xxalignat }#1}\fi
1361  \collect@body\next@}
1362 \@namedef{xxalignat }#1#2{\inany@true
1363  \displaybreak@\intertext@
1364  \displ@y\setbox\savealignat@\hbox{$\m@th\displaystyle\Let@
1365  \xxattag@{#1}%
1366  \vbox{\firstchoice@false\halign{\span\preamble@@\crcr#2\crcr}}$}%
1367  \Let@\xxattag@{#1}\tabskip\z@skip\halign to\displaywidth\bgroup
1368   \span\preamble@@\crcr#2}
1369 \expandafter\let\expandafter\endxxalignat\csname endxalignat*\endcsname
1370 \def\xxattag@#1{\toks@{\tabskip\z@skip\hfil\strut@
1371  $\m@th\displaystyle{\the\hashtoks@}$&%
1372  $\m@th\displaystyle{{}\the\hashtoks@}$\hfil\tabskip\@centering&}%
1373  \atcount@#1\relax\advance\atcount@\m@ne\loop\ifnum\atcount@>\z@
1374  \toks@
1375   \expandafter
1376    {\the\toks@&\hfil$\m@th\displaystyle{\the\hashtoks@}$%
1377   \tabskip\z@skip&$\m@th\displaystyle{{}\the\hashtoks@}$\hfil
1378   \tabskip\@centering}\advance\atcount@\m@ne\repeat
1379  \xdef\preamble@{\the\toks@\tabskip\z@skip}\xdef\preamble@@{\preamble@}}
1380 \newdimen\gwidth@
1381 \newdimen\gmaxwidth@
1382 \def\gmeasure@#1{\gwidth@\z@\gmaxwidth@\z@\setbox\@ne\vbox{\Let@
1383  \firstchoice@false\let\tag\gobble@tag
1384  \halign{\setboxz@h{$\m@th\displaystyle{##}$}\global\gwidth@\wdz@
1385  \ifdim\gwidth@>\gmaxwidth@\global\gmaxwidth@\gwidth@\fi
1386  &\@gobble{##}\crcr#1\crcr}}}
1387 \def\math@cr@@@gather{%
1388   \if@eqnsw\global\tag@true\fi
1389   \iftag@
1390     \DN@{&\relax \if@eqnsw
1391                     \tagform@\theequation \stepcounter{equation}%
1392                  \else\iftag@\df@tag\fi\fi}%
1393   \else
1394     \expandafter\@gobble\fi
1395   \next@
1396   \global\@eqnswtrue\cr}
1397 \def\gather{%
1398  \ifmmode\nomath@env\DN@{\let\endgather\relax\@gobble}\else $$%
1399   \ingather@true\inany@true
1400   \stepcounter{equation}%
1401   \let\tag\tag@in@align\st@rredfalse
1402   \displaybreak@\intertext@
1403   \displ@y
1404   \Let@\@seteqlabel\theequation
1405   \let\math@cr@@@\math@cr@@@gather
1406   \iftagsleft@\DN@{\@nameuse{gather }}\else
1407    \DN@{\@nameuse{gather \space}}\fi\fi
1408  \collect@body\next@}
1409 \@namedef{gather*}{%
1410  \ifmmode\nomath@env\DN@{\@namedef{endgather*}{}\@gobble}\else $$%
1411   \ingather@true\inany@true
1412   \let\tag\tag@in@align\st@rredtrue
1413   \displaybreak@\intertext@
1414   \displ@y\Let@
1415   \let\math@cr@@@\math@cr@@@gather
1416   \iftagsleft@\DN@{\@nameuse{gather }}\else
1417    \DN@{\@nameuse{gather \space}}\fi\fi
1418  \collect@body\next@}
1419 \newdimen\glineht@
1420 \@namedef{gather \space}#1{%
1421     \gmeasure@{#1}%
1422     \if@fleqn %%*F
1423         \advance\gmaxwidth@\@mathmargin %%*F
1424     \fi %%*F
1425     \global\dt@ptrue
1426     \tabskip\@mathmargin %%*F
1427     \halign to\displaywidth\bgroup
1428         \ifst@rred\nonumber\else\global\@eqnswtrue\fi
1429         \if@fleqn\else\hfil\fi %%*F
1430         \strut@
1431         \setboxz@h{\global\tag@false$\m@th\displaystyle{##}$}%
1432         \global\gwidth@\wdz@\boxz@
1433         \hfil
1434         \tabskip\@centering %%*F
1435        &\setboxz@h{\strut@{##}}%
1436         \dimen@\displaywidth
1437         \advance\dimen@-\gwidth@
1438         \if@fleqn %%*F
1439             \advance\dimen@-\@mathmargin %%*F
1440         \else %%*F
1441             \divide\dimen@\tw@ %%*B
1442         \fi %%*F
1443         \ifdim\dimen@<\tw@\wdz@ %%*
1444             \llap{\vtop{\@movetag\normalbaselines\null\boxz@}}%%*T %%*
1445         \else
1446             \llap{\boxz@}% %%*
1447         \fi
1448         \tabskip\z@skip
1449         \crcr
1450         #1%
1451 }
1452 \def\endgather{\math@cr
1453   \black@\gmaxwidth@\egroup $$\setb@ck\global\@ignoretrue}
1454
1455 \@namedef{endgather*}{\math@cr
1456   \black@\gmaxwidth@\egroup $$\global\@ignoretrue}
1457 \@namedef{gather }#1{%
1458     \gmeasure@{#1}%
1459     \global\dt@ptrue
1460     \if@fleqn %%*F
1461         \advance\gmaxwidth@\@mathmargin %%*F
1462     \fi %%*F
1463     \ifdim\gmaxwidth@>\displaywidth
1464         \let\gdisplaywidth@\gmaxwidth@
1465     \else
1466         \let\gdisplaywidth@\displaywidth
1467     \fi
1468     \tabskip\@mathmargin %%*F
1469     \halign to\displaywidth\bgroup
1470         \ifst@rred\nonumber\else\global\@eqnswtrue\fi
1471         \if@fleqn\else\hfil\fi %%*F
1472         \strut@
1473         \setboxz@h{\global\tag@false$\m@th\displaystyle{##}$}%
1474         \global\gwidth@\wdz@
1475         \global\glineht@\ht\z@
1476         \boxz@
1477         \hfil
1478         \tabskip\@centering %%*F
1479        &\kern-\gdisplaywidth@
1480         \setboxz@h{\strut@{##}}%
1481         \if@fleqn %%*F
1482             \dimen@\@mathmargin %%*F
1483         \else %%*F
1484             \dimen@\displaywidth
1485             \advance\dimen@-\gwidth@
1486             \divide\dimen@\tw@ %%*B
1487         \fi %%*F
1488         \ifdim\dimen@<\tw@\wdz@ %%*
1489             \rlap{\vbox{\normalbaselines\boxz@\vbox to\glineht@{}}}% %%*
1490         \else
1491             \rlap{\boxz@}% %%*
1492         \fi
1493         \tabskip\gdisplaywidth@
1494         \crcr
1495         #1%
1496 }
1497 \def\split{%
1498  \ifinany@\let\next@\insplit@\else
1499   \DN@{\PackageError{amstex}{\string\begin{split} is not allowed
1500     here.  Try the `aligned' environment.}\@ehb}\fi
1501  \next@}
1502 \def\insplit@{\global\setbox\z@\vbox\bgroup
1503   \Let@ \restore@math@cr \default@tag % disallow use of \tag here
1504   \ialign\bgroup \hfil\strut@
1505    $\m@th\displaystyle{##}$&$\m@th\displaystyle{{}##}$\hfill\crcr}
1506 \def\endsplit{\crcr\egroup\egroup
1507  \iftagsleft@\expandafter\lendsplit@\else
1508   \expandafter\rendsplit@\fi}
1509 \def\rendsplit@{\global\setbox9 \vbox
1510  {\unvcopy\z@\global\setbox8 \lastbox\unskip}%
1511  \setbox\@ne\hbox{\unhcopy8 \unskip\global\setbox\tw@\lastbox
1512  \unskip\global\setbox\thr@@\lastbox}%
1513  \global\setbox7 \hbox{\unhbox\tw@\unskip}%
1514  \ifinalign@\ifctagsplit@
1515   \gdef\split@{\hbox to\wd\thr@@{}&
1516    \vcenter{\vbox{\moveleft\wd\thr@@\boxz@}}}%
1517  \else\gdef\split@{&\vbox{\moveleft\wd\thr@@\box9}\crcr
1518   \box\thr@@&\box7}\fi
1519  \else
1520   \ifctagsplit@\gdef\split@{\vcenter{\boxz@}}\else
1521   \gdef\split@{\box9\crcr\hbox{\box\thr@@\box7}}\fi
1522  \fi
1523  \aftergroup\split@}
1524 \def\lendsplit@{\global\setbox9\vtop{\unvcopy\z@}%
1525  \setbox\@ne\vbox{\unvcopy\z@\global\setbox8\lastbox}%
1526  \setbox\@ne\hbox{\unhcopy8\unskip\setbox\tw@\lastbox
1527   \unskip\global\setbox\thr@@\lastbox}%
1528  \ifinalign@\ifctagsplit@
1529   \gdef\split@{\hbox to\wd\thr@@{}&
1530   \vcenter{\vbox{\moveleft\wd\thr@@\box9}}}%
1531   \else
1532   \gdef\split@{\hbox to\wd\thr@@{}&\vbox{\moveleft\wd\thr@@\box9}}\fi
1533  \else
1534   \ifctagsplit@\gdef\split@{\vcenter{\box9}}\else
1535   \gdef\split@{\box9}\fi
1536  \fi\aftergroup\split@}
1537 \newdimen\multlinegap
1538 \multlinegap10pt
1539 \newdimen\multlinetaggap@
1540 \multlinetaggap@10pt
1541 \def\multline{%
1542  \ifmmode\nomath@env\DN@{\let\endmultline\relax\@gobble}%
1543  \else $$\DN@{\collect@body\multline@}\fi
1544  \st@rredfalse\@eqnswtrue \@seteqlabel\theequation
1545  \stepcounter{equation}\next@}
1546 \@namedef{multline*}{%
1547  \ifmmode\nomath@env\DN@{\@namedef{endmultline*}{}\@gobble}%
1548  \else $$\DN@{\collect@body\multline@}\fi
1549  \st@rredtrue\@eqnswfalse \let\@currentlabel\@empty
1550  \next@}
1551 \def\multline@{\inany@true\displaybreak@
1552  \global\tag@false
1553  \def\tag{\ifst@rred\else
1554    \global\advance\c@equation\m@ne\fi\tag@in@align}%
1555  \iftagsleft@
1556   \expandafter\lmultline@@\else
1557   \expandafter\rmultline@@\fi}
1558 \newdimen\mwidth@
1559 \def\rmmeasure@#1{%
1560  \def\shoveleft##1{##1}\def\shoveright##1{##1}%
1561  \setbox\@ne\vbox{\firstchoice@false\Let@\halign{\setboxz@h
1562   {$\m@th\@lign\displaystyle{}##$}\global\mwidth@\wdz@
1563   \crcr#1\crcr}}}
1564 \newdimen\mlineht@
1565 \newif\ifzerocr@
1566 \newif\ifonecr@
1567 \def\lmmeasure@#1{\global\zerocr@true\global\onecr@false
1568  \everycr{\noalign{\ifonecr@\global\onecr@false\fi
1569   \ifzerocr@\global\zerocr@false\global\onecr@true\fi}}%
1570   \def\shoveleft##1{##1}\def\shoveright##1{##1}%
1571  \setbox\@ne\vbox{\Let@\firstchoice@false\halign{\setboxz@h
1572   {$\m@th\@lign\displaystyle{}##$}\ifonecr@\global\mwidth@\wdz@
1573   \global\mlineht@\ht\z@\fi\crcr#1\crcr}}}
1574 \newbox\mtagbox@
1575 \newdimen\ltwidth@
1576 \newdimen\rtwidth@
1577 \def\lmultline@@#1{%
1578     \lmmeasure@{#1}%
1579     \setbox\mtagbox@\hbox{%
1580         \iftag@
1581             \df@tag
1582         \else
1583             \if@eqnsw
1584                 \global\tag@true
1585                 \tagform@\theequation
1586             \fi
1587         \fi
1588     }%
1589     \dimen@\mwidth@
1590     \advance\dimen@\wd\mtagbox@
1591     \advance\dimen@\multlinetaggap@
1592     \if@fleqn %%*F
1593         \advance\dimen@\@mathmargin %%*F
1594     \fi %%*F
1595     \ifdim\dimen@>\displaywidth
1596         \ltwidth@\z@
1597     \else
1598         \ltwidth@\wd\mtagbox@
1599     \fi
1600     \lmultline@@@#1
1601 }
1602 \def\lmultline@@@{%
1603     \displ@y
1604     \def\shoveright##1{##1\hfilneg\hskip\multlinegap}%
1605     \if@fleqn %%*F
1606         \def\shoveleft##1{##1}% %%*F
1607     \else %%*F
1608         \def\shoveleft##1{%
1609                 \setboxz@h{$\m@th\displaystyle{}##1$}%
1610                 \setbox\@ne\hbox{$\m@th\displaystyle##1$}%
1611                 \hfilneg
1612                 \iftag@
1613                     \ifdim\ltwidth@>\z@
1614                         \hskip\ltwidth@
1615                         \hskip\multlinetaggap@
1616                     \fi
1617                 \else
1618                     \hskip\multlinegap
1619                 \fi
1620                 \hskip.5\wd\@ne
1621                 \hskip-.5\wdz@##1%
1622         }%
1623     \fi %%*F
1624     \if@fleqn %%*F
1625         \tabskip\@mathmargin %%*F
1626     \else %%*F
1627         \tabskip\z@skip %%*
1628     \fi %%*F
1629     \totwidth@\displaywidth %%*F
1630     \if@fleqn %%*F
1631         \advance\totwidth@-\@mathmargin %%*F
1632     \fi %%*F
1633     \halign\bgroup
1634         \Let@
1635         \let\tag\gobble@tag
1636         \hbox to\totwidth@{% %%*F
1637             \strut@$\m@th\displaystyle
1638             \if@fleqn %%*F
1639                 \hskip 0pt plus 1000pt %%*F
1640             \else %%*F
1641                 \hfil
1642             \fi %%*F
1643             {}##\hfil$%
1644         }%
1645         \crcr
1646         \if@fleqn %%*F
1647             \hskip-\@mathmargin %%*F
1648         \else %%*F
1649             \hfilneg
1650         \fi %%*F
1651         \iftag@
1652             \ifdim\ltwidth@>\z@
1653                 \box\mtagbox@
1654                 \hskip\multlinetaggap@
1655             \else
1656                 \rlap{%
1657                     \vbox{%
1658                         \normalbaselines
1659                         \hbox{\strut@\box\mtagbox@}%
1660                         \vbox to\mlineht@{}%
1661                     }%
1662                 }%
1663                 \hskip\multlinegap %%*
1664             \fi
1665         \else
1666             \hskip\multlinegap
1667         \fi
1668 }
1669 \def\rmultline@@#1{%
1670     \rmmeasure@{#1}%
1671     \setbox\mtagbox@\hbox{%
1672         \iftag@
1673             \df@tag
1674         \else
1675             \if@eqnsw
1676                 \global\tag@true
1677                 \tagform@\theequation
1678             \fi
1679         \fi
1680     }%
1681     \dimen@\mwidth@
1682     \advance\dimen@\wd\mtagbox@
1683     \advance\dimen@\multlinetaggap@
1684     \if@fleqn %%*F
1685         \advance\dimen@\@mathmargin %%*F
1686     \fi %%*F
1687     \ifdim\dimen@>\displaywidth
1688         \rtwidth@\z@
1689     \else
1690         \rtwidth@\wd\mtagbox@
1691     \fi
1692     \rmultline@@@#1
1693 }
1694 \def\rmultline@@@{%
1695     \displ@y
1696     \def\shoveright##1{%
1697         ##1%
1698         \hfilneg
1699         \iftag@
1700             \ifdim\rtwidth@>\z@
1701                 \hskip\rtwidth@
1702                 \hskip\multlinetaggap@
1703             \fi
1704         \else
1705             \hskip\multlinegap
1706         \fi
1707     }%
1708     \if@fleqn %%*F
1709         \def\shoveleft##1{##1}% %%*F
1710     \else %%*F
1711         \def\shoveleft##1{%
1712             \setboxz@h{$\m@th\displaystyle{}##1$}%
1713             \setbox\@ne\hbox{$\m@th\displaystyle##1$}%
1714             \hfilneg
1715             \hskip\multlinegap
1716             \hskip.5\wd\@ne
1717             \hskip-.5\wdz@
1718             ##1%
1719         }%
1720     \fi %%*F
1721     \if@fleqn %%*F
1722         \tabskip\@mathmargin %%*F
1723     \else %%*F
1724         \tabskip\z@skip %%*
1725     \fi %%*F
1726     \totwidth@\displaywidth %%*F
1727     \if@fleqn %%*F
1728         \advance\totwidth@-\@mathmargin %%*F
1729     \fi %%*F
1730     \halign\bgroup
1731         \Let@
1732         \let\tag\gobble@tag
1733         \hbox to\totwidth@{%
1734             \strut@$\m@th\displaystyle
1735             \if@fleqn %%*F
1736                 \hskip 0pt plus 1000pt %%*F
1737             \else %%*F
1738                 \hfil
1739             \fi %%*F
1740             {}##\hfil$%
1741         }%
1742         \crcr
1743         \if@fleqn %%*F
1744             \hskip-\@mathmargin %%*F
1745         \else %%*F
1746             \hfilneg
1747         \fi %%*F
1748         \hskip\multlinegap
1749 }
1750 \def\endmultline{\iftagsleft@\expandafter\lendmultline@\else
1751   \expandafter\rendmultline@\fi\global\@ignoretrue}
1752 \expandafter\let\csname endmultline*\endcsname=\endmultline
1753 \def\lendmultline@{\hfilneg\hskip\multlinegap\crcr\egroup$$}
1754 \def\rendmultline@{%
1755     \iftag@
1756         \ifdim\rtwidth@>\z@
1757             \hskip\multlinetaggap@
1758             \box\mtagbox@
1759         \else
1760             \hskip\multlinegap %%*
1761             \llap{%
1762                 \vtop{%
1763                     \@movetag %%*T
1764                     \normalbaselines\null\hbox{\strut@\box\mtagbox@}%
1765                 }%
1766             }%
1767         \fi
1768     \else
1769         \hskip\multlinegap
1770     \fi
1771     \hfilneg
1772     \crcr
1773     \egroup$$%
1774 }
1775 \expandafter\def
1776  \expandafter\@arrayparboxrestore
1777   \expandafter{\@arrayparboxrestore
1778                \inany@false\ingather@false\inalign@false
1779    \default@tag}
1780 \def\equation{\gather\def\\{\PackageError{amstex}{\Invalid@@\\}\@eha}}
1781 \def\endequation{\endgather}
1782 \newenvironment{equation*}{%
1783   \equation
1784 }{%
1785   \nonumber\endequation
1786 }
1787 \newcounter{parentequation}% Counter for ``parent equation''.
1788 \newenvironment{subequations}{%
1789   \refstepcounter{equation}%
1790   \begingroup % conservative approach
1791   \let\protect\@nx
1792   \edef\@tempa{\def\@nx\theparentequation{\theequation}}%
1793   \@xp\endgroup\@tempa
1794   \setcounter{parentequation}{\value{equation}}%
1795   \setcounter{equation}{0}%
1796   \def\theequation{\theparentequation\alph{equation}}%
1797   \ignorespaces
1798 }{%
1799   \setcounter{equation}{\value{parentequation}}%
1800   \global\@ignoretrue
1801 }
1802 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1803 \def\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}
1804 \begingroup \catcode`\@=\active
1805 \gdef @{\Iat}
1806 \endgroup
1807 \DeclareRobustCommand{\Iat}{\FN@\at@}
1808 \def\at@{\let\next@\at@@
1809  \ifcat\noexpand\@let@token a\else
1810  \ifcat\noexpand\@let@token0\else
1811  \ifcat\noexpand\@let@token\relax\else
1812  \let\@let@token@\at@@@\fi\fi\fi\next@}
1813 \def\at@@#1{\expandafter
1814   \@ifundefined{ @\string#1}%
1815     {\DN@{\at@@@#1}}%
1816     {\DN@{\csname\space @\string#1\endcsname}}%
1817   \next@}%
1818 \def\at@@@{\PackageError{amstex}{\Invalid@@ @}%
1819   {\the\athelp@}% "I'll assume you wanted @@"
1820   \char64\relax}
1821 \newhelp\athelp@
1822 {Only certain combinations beginning with @ make sense to me.^^J%
1823 I'll assume you wanted @@ for a printed @.}
1824 \atdef@ @{{\atchar}}% to define @@
1825 \chardef\atchar=64
1826 \def\makeatother{\catcode64=\active}
1827 \def\@tempa#1#2#3#4#5#6{%
1828   {#1}{#2}\ifnum0#6=0{13}\@xp\@gobblefour
1829   \else{#3}\fi\@tempa{#4}{#5}{#6}}%
1830 \xdef\@currnamestack{\@xp\@tempa\@currnamestack{}{}{0}}
1831 {\def\@makeother{\noexpand\@makeother\noexpand}
1832 \xdef\@sanitize{\@sanitize\@makeother\@}}
1833 {\def\do{\noexpand\do\noexpand}
1834 \xdef\dospecials{\dospecials\do\@}}
1835 \atdef@,{\ifmmode\mskip.1\thinmuskip\else \nonmatherr@{@,}\fi}
1836 \atdef@!{\RIfM@\mskip-.1\thinmuskip\else \nonmatherr@{@!}\fi}
1837
1838 \@ifpackageloaded{amscd}{%
1839 }{%
1840 \atdef@>#1>#2>{%
1841   \global\bigaw@\minaw@
1842   \setboxz@h{$\m@th\scriptstyle\;{#1}\;\;$}%
1843   \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
1844   \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;{#2}\;\;$}%
1845     \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
1846    \mathrel{\mathop{\hbox to\bigaw@{\rightarrowfill@\displaystyle}}%
1847      \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
1848 }% end of @>>>
1849 \atdef@<#1<#2<{%
1850   \global\bigaw@\minaw@
1851   \setboxz@h{$\m@th\scriptstyle\;\;{#1}\;$}%
1852   \ifdim\wdz@>\bigaw@ \global\bigaw@\wdz@ \fi
1853   \@ifnotempty{#2}{\setbox\@ne\hbox{$\m@th\scriptstyle\;\;{#2}\;$}%
1854     \ifdim\wd\@ne>\bigaw@ \global\bigaw@\wd\@ne \fi}%
1855   \mathrel{\mathop{\hbox to\bigaw@{\leftarrowfill@\displaystyle}}%
1856       \limits^{#1}\@ifnotempty{#2}{_{#2}}}%
1857 }% end of @<<<
1858 }% end of @ifpackageloaded
1859 \@ifundefined{minaw@}{\newdimen\minaw@}{}
1860 \minaw@11.111pt
1861 \@ifundefined{bigaw@}{\newdimen\bigaw@}{}
1862 \atdef@-{\let\next-%%
1863   \DN@{\ifx\next-%%
1864     \def\next-{\setbox\z@\hbox{-}\unhbox\z@\FN@\next@}%%
1865     \expandafter\next \else\nobreak\fi}%%
1866   \next@-}%%
1867 \def\leftroot{\PackageError{amstex}{\Invalid@@\leftroot}\@eha}
1868 \def\uproot{\PackageError{amstex}{\Invalid@@\uproot}\@eha}
1869 \newcount\uproot@
1870 \newcount\leftroot@
1871 \def\root{\relaxnext@
1872   \DN@{\ifx\@let@token\uproot\let\next@\nextii@\else
1873    \ifx\@let@token\leftroot\let\next@\nextiii@\else
1874    \let\next@\plainroot@\fi\fi\next@}%
1875   \def\nextii@\uproot##1{\uproot@##1\relax\FN@\nextiv@}%
1876   \def\nextiv@{\ifx\@let@token\@sptoken\DN@. {\FN@\nextv@}\else
1877    \DN@.{\FN@\nextv@}\fi\next@.}%
1878   \def\nextv@{\ifx\@let@token\leftroot\let\next@\nextvi@\else
1879    \let\next@\plainroot@\fi\next@}%
1880   \def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
1881    \def\nextiii@\leftroot##1{\leftroot@##1\relax\FN@\nextvii@}%
1882   \def\nextvii@{\ifx\@let@token\@sptoken
1883    \DN@. {\FN@\nextviii@}\else
1884    \DN@.{\FN@\nextviii@}\fi\next@.}%
1885   \def\nextviii@{\ifx\@let@token\uproot\let\next@\nextix@\else
1886    \let\next@\plainroot@\fi\next@}%
1887   \def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
1888   \bgroup\uproot@\z@\leftroot@\z@\FN@\next@}
1889 \def\plainroot@#1\of#2{\setbox\rootbox\hbox{%
1890  $\m@th\scriptscriptstyle{#1}$}%
1891  \mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
1892  {\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
1893 \def\r@@t#1#2{\setboxz@h{$\m@th#1\@@sqrt{#2}$}%
1894  \dimen@\ht\z@\advance\dimen@-\dp\z@
1895  \setbox\@ne\hbox{$\m@th#1\mskip\uproot@ mu$}%
1896  \advance\dimen@ by1.667\wd\@ne
1897  \mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
1898  \mkern-10mu\mkern\leftroot@ mu\boxz@}
1899 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1900 %% Fragment from old amsfonts.sty to deal with msam, msbm, eufm fonts;
1901 %% omit if `noamsfonts' option was specified.
1902 \ifx F\@amsfonts \endinput \fi
1903 \DeclareSymbolFont{AMSa}{U}{msa}{m}{n}
1904 \DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
1905 \ifx P\@amsfonts
1906   \DeclareFontFamily{U}{msa}{}%
1907   \DeclareFontShape{U}{msa}{m}{n}{<-6>msam5<6-8>msam7<8->msam10}{}%
1908   \DeclareFontFamily{U}{msb}{}%
1909   \DeclareFontShape{U}{msb}{m}{n}{<-6>msbm5<6-8>msbm7<8->msbm10}{}%
1910   \DeclareFontFamily{U}{euf}{}%
1911   \DeclareFontShape{U}{euf}{m}{n}{<-6>eufm5<6-8>eufm7<8->eufm10}{}%
1912   \DeclareFontShape{U}{euf}{b}{n}{<-6>eufb5<6-8>eufb7<8->eufb10}{}%
1913 \fi
1914 \@ifundefined{yen}{%
1915   \edef\yen{\noexpand\mathhexbox{\hexnumber@\symAMSa}55}
1916 }{}
1917 \@ifundefined{checkmark}{%
1918   \edef\checkmark{\noexpand\mathhexbox{\hexnumber@\symAMSa}58}
1919 }{}
1920 \@ifundefined{circledR}{%
1921   \edef\circledR{\noexpand\mathhexbox{\hexnumber@\symAMSa}72}
1922 }{}
1923 \@ifundefined{maltese}{%
1924   \edef\maltese{\noexpand\mathhexbox{\hexnumber@\symAMSa}7A}
1925 }{}
1926 \begingroup \catcode`\"=12
1927 \DeclareMathDelimiter\ulcorner{\mathopen} {AMSa}{"70}{AMSa}{"70}
1928 \DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{"71}{AMSa}{"71}
1929 \DeclareMathDelimiter\llcorner{\mathopen} {AMSa}{"78}{AMSa}{"78}
1930 \DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{"79}{AMSa}{"79}
1931 \xdef\widehat#1{\noexpand\@mathmeasure\z@\textstyle{#1}%
1932   \noexpand\ifdim\noexpand\wdz@>\tw@ em%
1933   \mathaccent"0\hexnumber@\symAMSb 5B{#1}%
1934   \noexpand\else\mathaccent"0362{#1}\noexpand\fi}
1935 \xdef\widetilde#1{\noexpand\@mathmeasure\z@\textstyle{#1}%
1936   \noexpand\ifdim\noexpand\wdz@>\tw@ em%
1937   \mathaccent"0\hexnumber@\symAMSb 5D{#1}%
1938   \noexpand\else\mathaccent"0365{#1}\noexpand\fi}
1939 \DeclareMathSymbol\dabar@{\mathord}{AMSa}{"39}
1940 \xdef\dashrightarrow{\mathrel{\dabar@\dabar@
1941                               \mathchar"0\hexnumber@\symAMSa 4B}}%
1942 \xdef\dashleftarrow{\mathrel{\mathchar"0\hexnumber@\symAMSa 4C\dabar@
1943                               \dabar@}}%
1944 \global\let\dasharrow\dashrightarrow
1945 \global\let\rightleftharpoons\undefined
1946 \DeclareMathSymbol\rightleftharpoons{\mathrel}{AMSa}{"0A}
1947 \global\let\angle\undefined
1948 \DeclareMathSymbol\angle            {\mathord}{AMSa}{"5C}
1949 \global\let\hbar\undefined
1950 \DeclareMathSymbol\hbar             {\mathord}{AMSb}{"7E}
1951 \global\let\sqsubset\undefined
1952 \DeclareMathSymbol\sqsubset         {\mathrel}{AMSa}{"40}
1953 \global\let\sqsupset\undefined
1954 \DeclareMathSymbol\sqsupset         {\mathrel}{AMSa}{"41}
1955 \global\let\mho\undefined
1956 \DeclareMathSymbol\mho              {\mathord}{AMSb}{"66}
1957 \DeclareMathSymbol\square           {\mathord}{AMSa}{"03}
1958 \DeclareMathSymbol\lozenge          {\mathord}{AMSa}{"06}
1959 \DeclareMathSymbol\vartriangleright {\mathrel}{AMSa}{"42}
1960 \DeclareMathSymbol\vartriangleleft  {\mathrel}{AMSa}{"43}
1961 \DeclareMathSymbol\trianglerighteq  {\mathrel}{AMSa}{"44}
1962 \DeclareMathSymbol\trianglelefteq   {\mathrel}{AMSa}{"45}
1963 \DeclareMathSymbol\rightsquigarrow  {\mathrel}{AMSa}{"20}
1964 \def\@tempa{\not@base\lhd}
1965 \ifx\lhd\@tempa
1966  \global\let\lhd\vartriangleleft
1967  \global\let\unlhd\trianglelefteq
1968  \global\let\rhd\vartriangleright
1969  \global\let\unrhd\trianglerighteq
1970  \global\let\Box\square
1971  \global\let\Diamond\lozenge
1972  \global\let\leadsto\rightsquigarrow
1973 \xdef\Join{\mathrel{\mathchar"0\hexnumber@\symAMSb 6F\mkern-13.8mu%
1974   \mathchar"0\hexnumber@\symAMSb 6E}}
1975 \fi
1976 \endgroup
1977 \DeclareMathAlphabet\mathfrak{U}{euf}{m}{n}
1978 \SetMathAlphabet\mathfrak{bold}{U}{euf}{b}{n}
1979 \DeclareSymbolFontAlphabet{\mathbb}{AMSb}
1980 \DeclareFontEncodingDefaults{\relax}{\def\accentclass@{7}}
1981 \def\frak{\mathfrak}
1982 \def\Bbb{\mathbb}
1983 \def\bold{\mathbf}
1984 \begingroup \catcode`\"=12 \relax
1985 \gdef\newsymbol#1#2#3#4#5{%
1986   \@ifdefinable#1{%
1987      \edef\next@
1988        {\ifcase #2 \or
1989           \hexnumber@\symAMSa\or
1990           \hexnumber@\symAMSb\fi}%
1991      \ifx\next@\@empty
1992        \PackageError{amsfonts}{\Invalid@@\newsymbol}\@ehd%
1993      \else
1994       \global\mathchardef#1"#3\next@#4#5
1995      \fi}}
1996 \endgroup
1997 %%   Some odds and ends
1998 \def\sphat{^{\mathchoice{}{}%
1999  {\,\,\smash[b]{\hbox{\lower4\ex@\hbox{$\m@th\widehat{\null}$}}}}%
2000  {\,\smash[b]{\hbox{\lower3\ex@\hbox{$\m@th\hat{\null}$}}}}}}
2001 \def\spcheck{^\vee}
2002 \def\sptilde{^\sim}
2003 \def\spdot{^{\hbox{\raise\ex@\hbox{\normalfont .}}}}
2004 \def\spddot{^{\hbox{\raise\ex@\hbox{\normalfont ..}}}}
2005 \def\spdddot{^{\hbox{\raise\ex@\hbox{\normalfont...}}}}
2006 \def\spbreve{^{\!\smash[b]{\hbox{\lower4\ex@\hbox{\u{}}}}}}
2007 \def\fracwithdelims#1#2{\new@ifnextchar[{\fracwithdelims@#1#2}%
2008   {\fracwithdelims@#1#2[\@empty]}}
2009 \def\fracwithdelims@#1#2[#3]#4#5{\relax
2010   \ifx\@empty#3{#4\overwithdelims#1#2#5}\else
2011   {#4\abovewithdelims#1#2#3\relax#5}\fi}
2012 \def\accentedsymbol#1#2{%
2013   \expandafter\newbox
2014     \csname\expandafter\@gobble\string#1@box\endcsname
2015   \expandafter\setbox
2016     \csname\expandafter\@gobble\string#1@box\endcsname
2017       \hbox{$\m@th#2$}%
2018   \newcommand{#1}{%
2019     \expandafter\copy
2020       \csname\expandafter\@gobble\string#1@box\endcsname{}}%
2021 }
2022 \def~{\nobreakspace}
2023 \DeclareRobustCommand{\nobreakspace}{\unskip\nobreak\ \ignorespaces}
2024 %%
2025 %% End of file `amstex.sty'.