%% amsfonts.sty, temporary patch version 1.1x, 10-Mar-1994
%% American Mathematical Society, Technical Support Department,
%%   P. O. Box 6248, Providence, RI 02940, USA
%% 401-455-4080, 800-321-4AMS
%% tech-support@math.ams.org
%%
\expandafter\ifx\csname ds@amsfonts\endcsname\relax
\global\let\ds@amsfonts\@empty
\else\message{---already loaded}\endinput\fi
\def\filename{amsfonts.sty}
\def\fileversion{2.0x} \def\filedate{10-Mar-1994}
\immediate\write16{%
AMS-LaTeX option `\filename' (\fileversion, \filedate)}
%%% end of file header
\begingroup \newlinechar`\/
\errhelp{/%
Options:/%
1. Ask the person who installed LaTeX on your system for more help./%
2. If you installed LaTeX yourself, ask for help from the company/%
   from which you bought LaTeX./%
3. If you obtained LaTeX from a noncommercial source, consult the/%
   installation documentation./%
4. Try contacting one of the TeX user groups listed in your TeX/%
   system documentation./}
\expandafter\ifx\csname renewenvironment\endcsname\relax
\errmessage{%
  Non-LaTeX format file; amsfonts.sty can only be used with LaTeX./%
! Enter h if you need more information%
}
\fi
\expandafter\ifx\csname extract@font\endcsname\relax
\errmessage{%
  The style option `amsfonts' requires NFSS, which is not present in/%
! the current LaTeX format file. Enter h if you need more information%
}
\aftergroup\stop
\fi
\endgroup
\def\RIfM@{\relax\protect\ifmmode}
\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@
    {\noexpand#1allowed only in math mode}\@ehd}
\@ifundefined{err@}{\def\err@{\@latexerr}}{}
\DeclareSymbolFont{AMSa}{U}{msa}{m}{n}
\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}
%    Add definition of \newsymbol for backward compatibility
%    [mjd,23-Feb-1994]
\def\newsymbol#1#2#3#4#5{%
    \@ifdefinable#1{%
       \edef\next@
         {\ifcase #2 \or
            \hexnumber@\symAMSa\or
            \hexnumber@\symAMSb\fi}%
       \ifx\next@\@empty
         \err@{\Invalid@@\newsymbol}\@ehd%
       \else
        \global\mathchardef#1"#3\next@#4#5
       \fi}}%
\begingroup
\catcode`\"=12
\DeclareMathDelimiter\ulcorner{\mathopen} {AMSa}{"70}{AMSa}{"70}
\DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{"71}{AMSa}{"71}
\DeclareMathDelimiter\llcorner{\mathopen} {AMSa}{"78}{AMSa}{"78}
\DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{"79}{AMSa}{"79}
\xdef\yen      {\noexpand\mathhexbox\hexnumber@\symAMSa 55 }
\xdef\checkmark{\noexpand\mathhexbox\hexnumber@\symAMSa 58 }
\xdef\circledR {\noexpand\mathhexbox\hexnumber@\symAMSa 72 }
\xdef\maltese  {\noexpand\mathhexbox\hexnumber@\symAMSa 7A }
\xdef\widehat#1{\noexpand\setboxz@h{$\noexpand\m@th#1$}%
 \noexpand\ifdim\noexpand\wdz@>\tw@ em%
 \mathaccent"0\hexnumber@\symAMSb 5B{#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%
 \hexnumber@\symAMSb 5D{#1}%
 \noexpand\else\mathaccent"0365{#1}\noexpand\fi}
\DeclareMathSymbol\dabar@{\mathord}{AMSa}{"39}
\xdef\dashrightarrow{\mathrel{\dabar@\dabar@
                              \mathchar"0\hexnumber@\symAMSa 4B}}%
\xdef\dashleftarrow{\mathrel{\mathchar"0\hexnumber@\symAMSa 4C\dabar@
                              \dabar@}}%
\global\let\dasharrow\dashrightarrow
\global\let\rightleftharpoons\undefined
\DeclareMathSymbol\rightleftharpoons{\mathrel}{AMSa}{"0A}
\global\let\angle\undefined
\DeclareMathSymbol\angle            {\mathord}{AMSa}{"5C}
\global\let\hbar\undefined
\DeclareMathSymbol\hbar             {\mathord}{AMSb}{"7E}
\global\let\sqsubset\undefined
\DeclareMathSymbol\sqsubset         {\mathrel}{AMSa}{"40}
\global\let\sqsupset\undefined
\DeclareMathSymbol\sqsupset         {\mathrel}{AMSa}{"41}
\global\let\mho\undefined
\DeclareMathSymbol\mho              {\mathord}{AMSb}{"66}

\DeclareMathSymbol\square           {\mathord}{AMSa}{"03}

\DeclareMathSymbol\lozenge          {\mathord}{AMSa}{"06}

\DeclareMathSymbol\vartriangleright {\mathrel}{AMSa}{"42}
\DeclareMathSymbol\vartriangleleft  {\mathrel}{AMSa}{"43}
\DeclareMathSymbol\trianglerighteq  {\mathrel}{AMSa}{"44}
\DeclareMathSymbol\trianglelefteq   {\mathrel}{AMSa}{"45}

\DeclareMathSymbol\rightsquigarrow  {\mathrel}{AMSa}{"20}

\def\@tempa{\not@base\lhd}
\ifx\lhd\@tempa
 \global\let\lhd\vartriangleright
 \global\let\unlhd\vartriangleleft
 \global\let\rhd\trianglerighteq
 \global\let\unrhd\trianglelefteq
 \global\let\Box\square
 \global\let\Diamond\lozenge
 \global\let\leadsto\rightsquigarrow
\xdef\Join{\mathrel{\mathchar"0\hexnumber@\symAMSb 6F\mkern-13.8mu%
  \mathchar"0\hexnumber@\symAMSb 6E}}
\fi
\endgroup
\DeclareMathAlphabet\frak{U}{euf}{m}{n}
\SetMathAlphabet \frak{bold}{U}{euf}{b}{n}
\let\bold\mathbf
\DeclareSymbolFontAlphabet{\Bbb}{AMSb}
\newbox\Mathstrutbox@
\setbox\Mathstrutbox@\null
\def\Mathstrut@{\copy\Mathstrutbox@}
\addto@hook\every@size{\setbox\z@\hbox{$\m@th($}%
        \ht\Mathstrutbox@\ht\z@
        \dp\Mathstrutbox@\dp\z@}
\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.%
           \n@space
     $}}}
\addto@hook\every@size{\big@size\ht\Mathstrutbox@
  \advance\big@size\dp\Mathstrutbox@ \big@size 1.2\big@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@}
\DeclareFontEncodingDefaults{\relax}{\def\accentclass@{7}}
\DeclareFontEncoding{OML}{}{\noaccents@}
\DeclareFontEncoding{OMS}{}{\noaccents@}
\def\operator@font{\mathgroup\symoperators}
%% \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         \~}
\endinput
%% 
%% End of file `amsfonts.sty'.