%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%% This file is part of the AMS-LaTeX Version 1.0 distribution       %% 
%%    American Mathematical Society, Technical Support Group,        %% 
%%    P. O. Box 6248, Providence, RI 02940                           %% 
%%    800-321-4AMS (321-4267) or 401-455-4080                        %% 
%%    Internet: Tech-Support@Math.AMS.com                            %% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%% This is file `AMSFONTS.STY',
%% generated on August 29, 1990 from `amsfonts.doc'
%% using the stripb utility (v0.9---derived from docstrip.tex).
%% 
\def\fileversion{v1.0a}
\def\filedate{29-AUG-1990}
\def\docdate {7-JUN-1990}

%% \CheckSum{507}
%% \CharacterTable
%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
%%
\@ifundefined{msa@group}{}{\endinput}
\immediate\write\sixt@@n{Style Option: `amsfonts'
 \fileversion\space <\filedate>  (FMi, RmS; MJD)}
\immediate\write\sixt@@n{English Documentation
 \space\@spaces\@spaces  <\docdate>  (FMi, RmS; MJD)}
\@ifundefined{RIfM@}{
  \def\RIfM@{\relax\protect\ifmmode}
    \let\boxz@\fi % \if \fi matching hack
  \def\boxz@{\box\z@}
  \def\setboxz@h{\setbox\z@\hbox}
  \def\wdz@{\wd\z@}
  \def\noaccents@{\def\accentclass@{0}}
  \def\Invalid@@{Invalid use of \string}
  \def\nonmatherr@#1{\err@
    {\string#1\space allowed only in math mode}\@ehd}
  \def\err@{\@latexerr}
}{}
 \new@mathgroup\msa@group
 \new@mathgroup\msb@group
\define@mathgroup\mv@normal\msa@group{msa}{m}{n}
\define@mathgroup\mv@normal\msb@group{msb}{m}{n}
\define@mathgroup\mv@bold\msa@group{msa}{m}{n}
\define@mathgroup\mv@bold\msb@group{msb}{m}{n}
{\catcode`\"=12
\edef\@tempa{\hexnumber@\msa@group}%
\edef\@tempb{\hexnumber@\msb@group}%
\xdef\ulcorner{\delimiter"4\@tempa 70\@tempa 70 }
\xdef\urcorner{\delimiter"5\@tempa 71\@tempa 71 }
\xdef\llcorner{\delimiter"4\@tempa 78\@tempa 78 }
\xdef\lrcorner{\delimiter"5\@tempa 79\@tempa 79 }
\xdef\yen      {\noexpand\mathhexbox\@tempa 55 }
\xdef\checkmark{\noexpand\mathhexbox\@tempa 58 }
\xdef\circledR {\noexpand\mathhexbox\@tempa 72 }
\xdef\maltese  {\noexpand\mathhexbox\@tempa 7A }
\xdef\widehat#1{\noexpand\setboxz@h{$\noexpand\m@th#1$}%
 \noexpand\ifdim\noexpand\wdz@>\tw@ em\mathaccent"0\@tempb5B{#1}%
 \noexpand\else\mathaccent"0362{#1}\noexpand\fi}

\xdef\widetilde#1{\noexpand\setboxz@h{$\noexpand\m@th#1$}%
 \noexpand\ifdim\noexpand\wdz@>\tw@ em\mathaccent"0\@tempb5D{#1}%
 \noexpand\else\mathaccent"0365{#1}\noexpand\fi}
\mathchardef\dabar@="0\@tempa39
\xdef\dashrightarrow{\mathrel{\dabar@\dabar@\mathchar"0\@tempa4B}}%
\xdef\dashleftarrow{\mathrel{\mathchar"0\@tempa4C\dabar@\dabar@}}%

\global\let\dasharrow\dashrightarrow
\gdef\newsymbol#1#2#3#4#5{%
    \@ifdefinable#1{%
       \edef\next@
         {\ifcase #2 \or
            \hexnumber@{\msa@group}\or
            \hexnumber@{\msb@group}\fi}%
       \ifx\next@\@empty
         \err@{\Invalid@@\newsymbol}\@ehd%
       \else
        \global\mathchardef#1"#3\next@#4#5
       \fi}}
}
\let\rightleftharpoons\undefined \newsymbol\rightleftharpoons 130A
\let\angle\undefined             \newsymbol\angle             105C
\let\hbar\undefined              \newsymbol\hbar              207E
\let\sqsubset\undefined          \newsymbol\sqsubset          1340
\let\sqsupset\undefined          \newsymbol\sqsupset          1341
\let\mho\undefined               \newsymbol\mho               2066
\def\frak{\protect\pfrak}
\def\pfrak{\RIfM@\expandafter\frak@\else
                 \expandafter\nonmatherr@\expandafter\frak\fi}
\newmathalphabet\frak@
\addtoversion{normal}\frak@{euf}{m}{n}
\addtoversion{bold}\frak@{euf}{b}{n}
\def\bold{\protect\pbold}
\def\pbold{\RIfM@\expandafter\bold@\else
                 \expandafter\nonmatherr@\expandafter\bold\fi}
\newmathalphabet*\bold@{cmr}{bx}{n}
\def\Bbb{\protect\pBbb}
\def\pBbb{\RIfM@\expandafter\Bbb@\else
                 \expandafter\nonmatherr@\expandafter\Bbb\fi}

\edef\Bbb@{\noexpand\use@mathgroup
          \expandafter\noexpand\csname =msb\endcsname
          \msb@group}
\def\goth{\family{euf}\selectfont\frak@}
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@\null
\def\Mathstrut@{\copy\Mathstrutbox@}
\newbox\@tempbox@every@size
\addto@hook\every@size{%
        \setbox\@tempbox@every@size\hbox{$\m@th($}%
        \ht\Mathstrutbox@\ht\@tempbox@every@size
        \dp\Mathstrutbox@\dp\@tempbox@every@size}
\newbox\strutbox@
\def\strut@{\copy\strutbox@}
\addto@hook\every@size{%
    \setbox\strutbox@\hbox{\lower.5\normallineskiplimit
         \vbox{\kern-\normallineskiplimit\copy\strutbox}}}
\def\big{\bBigg@\@ne}
\def\Big{\bBigg@{1.5}}
\def\bigg{\bBigg@\tw@}
\def\Bigg{\bBigg@{2.5}}
\def\bBigg@#1#2{%
   {%
    \hbox{$\left#2\vcenter to#1\big@size{}\right.%
                         \nulldelimiterspace\z@ \m@th$}}}
\addto@hook\every@size{\setbox\@tempbox@every@size
       \vbox{\hbox{$($}\kern\z@}\big@size 1.2\ht\@tempbox@every@size}
\newdimen\big@size
\newdimen\ex@
\addto@hook\every@size{\ex@.2326\fontdimen5\textfont\@ne}
\newdimen\minaw@
\addto@hook\every@size{\minaw@11.11128\ex@}
\addto@hook\every@size{\jot\thr@@\ex@}
\newmuskip\dotsspace@
\dotsspace@1.5mu
\def\smash{\@ifnextchar[\@xsmash{\@xsmash[tb]}}
\def\@xsmash[#1]{\def\smash@{#1}%
  \ifmmode\expandafter\mathpalette\expandafter\mathsm@sh\else
        \expandafter\makesm@sh\fi}
\def\finsm@sh{\def\mb@t{\ht\z@\z@}\def\mb@b{\dp\z@\z@}%
   \expandafter\@tfor\expandafter\@tempa
         \expandafter:\expandafter=\smash@\do
      {\csname mb@\@tempa\endcsname}%
   \leavevmode\boxz@}
\def\default@mextra{\def\accentclass@{7}}
\extra@def{cmm}{\skewchar#1'177}{\noaccents@}
\extra@def{cmsy}{\skewchar#1'60}{\noaccents@}
\new@fontshape{msa}{m}{n}{%
   <5>msam5%
   <6>msam6%
   <7>msam7%
   <8>msam8%
   <9>msam9%
   <10>msam10%
   <11>msam10 at10.95pt%
   <12>msam10 at12pt%
   <14>msam10 at14.4pt%
   <17>msam10 at17.28pt%
   <20>msam10 at20.74pt%
   <25>msam10 at24.88pt}{}
\extra@def{msa}{}{}
\new@fontshape{msb}{m}{n}{%
   <5>msbm5%
   <6>msbm6%
   <7>msbm7%
   <8>msbm8%
   <9>msbm9%
   <10>msbm10%
   <11>msbm10 at10.95pt%
   <12>msbm10 at12pt%
   <14>msbm10 at14.4pt%
   <17>msbm10 at17.28pt%
   <20>msbm10 at20.74pt%
   <25>msbm10 at24.88pt}{}
\extra@def{msb}{}{\noaccents@}
\new@fontshape{euf}{m}{n}{%
   <5>eufm5%
   <6>eufm6%
   <7>eufm7%
   <8>eufm8%
   <9>eufm9%
   <10>eufm10%
   <11>eufm10 at10.95pt%
   <12>eufm10 at12pt%
   <14>eufm10 at14.4pt%
   <17>eufm10 at17.28pt%
   <20>eufm10 at20.74pt%
   <25>eufm10 at24.88pt}{}

\new@fontshape{euf}{b}{n}{%
   <5>eufb5%
   <6>eufb6%
   <7>eufb7%
   <8>eufb8%
   <9>eufb9%
   <10>eufb10%
   <11>eufb10 at10.95pt%
   <12>eufb10 at12pt%
   <14>eufb14%
   <17>eufb14 at17.28pt%
   <20>eufb14 at20.74pt%
   <25>eufb14 at24.88pt}{}
\extra@def{euf}{\hyphenchar#1\m@ne
       \@tempdima\fontdimen2#1%
       \fontdimen3#1.4\@tempdima
       \fontdimen4#1.3\@tempdima}
      {\noaccents@}
\new@fontshape{cmm}{b}{it}{%
      <5>cmmib5%
      <6>cmmib6%
      <7>cmmib7%
      <8>cmmib8%
      <9>cmmib9%
      <10>cmmib10%
      <11>cmmib10 at10.95pt%
      <12>cmmib10 at12pt%
      <14>cmmib10 at14.4pt%
      <17>cmmib10 at17.28pt%
      <20>cmmib10 at20.74pt%
      <25>cmmib10 at24.88pt%
      }{}
\new@fontshape{cmsy}{b}{n}{%
      <5>cmbsy5%
      <6>cmbsy6%
      <7>cmbsy7%
      <8>cmbsy8%
      <9>cmbsy9%
      <10>cmbsy10%
      <11>cmbsy10 at10.95pt%
      <12>cmbsy10 at12pt%
      <14>cmbsy10 at14.4pt%
      <17>cmbsy10 at17.28pt%
      <20>cmbsy10 at20.74pt%
      <25>cmbsy10 at24.88pt%
      }{}
\def\unbracefonts@{\let\math@bgroup\@empty\let\math@egroup\@empty}
\def\operator@font{\mathgroup\z@}
\endinput
%% 
%% End of file `amsfonts.sty'.
