/
newtxmath.sty
executable file
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/
newtxmath.sty
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\NeedsTeXFormat{LaTeX2e}[1997/06/01]
%
% Based on Young Ryu's txfonts.sty, v.3.2.1
% Text and math are now loaded in separate sty files---the text
% font family need not be txtext. The text font loaded when this package
% is processed is used for operator names, mathrm, mathit,
% and likewise for mathsf and mathtt.
% The original txfonts math fonts have been replaced by virtual fonts which
% render less tightly so that there are many fewer instances
% of glyph collisions.
% These modifications are by Michael Sharpe, msharpe at ucsd dot edu
\def\fileversion{1.241}
\def\filedate{2014/03/18}
\ProvidesPackage{newtxmath}
[\filedate\space v\fileversion]
\@ifundefined{newtxmathLoaded}{}{\endinput}
\message{`newtxmath' v\fileversion, \filedate\space Math macros based on txfonts (msharpe)}
\csname newtxmathLoaded\endcsname
\let\newtxmathLoaded\endinput
\RequirePackage{amsmath} % improves extendable delimiter handling
\RequirePackage{ifxetex,ifluatex,xkeyval}
\newif\ifxl@otf \xl@otffalse
\ifxetex
\xl@otftrue
\else\ifluatex
\xl@otftrue
\fi
\fi
\newcommand{\cmr@default}{cmr}
\input{binhex}
\let\ntxmath@scaled\@empty
\define@key{ntxmath}{scaled}[1.0]{\def\ntxmath@scaled{s*[#1]}}
\DeclareOption*{%
\begingroup
\edef\x{\endgroup
\noexpand\setkeys{ntxmath}{\CurrentOption}}%
\x}
\DeclareOption{varg}{\def\X@s@v@rg{}}
\newcount\tx@Isdigit
\newif\iftx@ams \newif\iftx@slantedG \newif\iftx@cmint \newif\iftx@braces
\newif\iftx@libertine \newif\iftx@varbb \newif\iftx@vvarbb \newif\iftx@symbolsC
\newif\iftx@gm \newif\iftx@bigdelims
\newif\iftx@liby \newif\iftx@tma % use Times math accents
\tx@symbolsCtrue
\newif\iftx@altnu
\newif\iftx@largelibfigs
\newif\iftx@minion \newif\iftx@libaltvw
\DeclareOption{timesmathacc}{\tx@tmatrue}
\DeclareOption{bigdelims}{\tx@bigdelimstrue}
\DeclareOption{varbb}{\tx@varbbtrue}
\DeclareOption{vvarbb}{\tx@vvarbbtrue}
\DeclareOption{libaltvw}{\tx@libaltvwtrue}
\DeclareOption{nosymbolsc}{\tx@symbolsCfalse}
\DeclareOption{libertine}{\tx@libertinetrue}
\DeclareOption{minion}{\tx@miniontrue}
\DeclareOption{garamondx}{\tx@gmtrue}
\DeclareOption{cmintegrals}{\tx@cminttrue}
\DeclareOption{cmbraces}{\tx@bracestrue}
\DeclareOption{noamssymbols}{\tx@amsfalse}
\DeclareOption{amssymbols}{\tx@amstrue}
\DeclareOption{uprightGreek}{\tx@slantedGfalse}
\DeclareOption{slantedGreek}{\tx@slantedGtrue}
\DeclareOption{altnu}{\tx@altnutrue}
\DeclareOption{largelibfigs}{\tx@largelibfigstrue}
\DeclareOption{liby}{\tx@libytrue}
\ExecuteOptions{%
amssymbols,uprightGreek}
\ProcessOptions*
%bigdelims cancels cmbraces
\iftx@bigdelims\tx@bracesfalse\fi
% No varg option with option libertine or option minion or garamond
\iftx@libertine\ifx\X@s@v@rg\undefined\else\let\X@s@v@rg\@undefined\fi\fi
\iftx@minion\ifx\X@s@v@rg\undefined\else\let\X@s@v@rg\@undefined\fi\fi
\iftx@gm\ifx\X@s@v@rg\undefined\else\let\X@s@v@rg\@undefined\fi\fi
% altnu, liby and largelibfigs valid only with libertine
\iftx@libertine\else\tx@altnufalse\tx@largelibfigsfalse\tx@libyfalse\fi
% Use existing text fonts for operators, mathrm, etc
\ifxl@otf
\iftx@libertine
\ifx\rmdefault\cmr@default
\renewcommand{\rmdefault}{minlibertine}% since can't load libertine twice
\fi
\fi
\fi
\edef\bold@wt{\ifx\iflibertine@otf\undefined b\else sb\fi}
\DeclareSymbolFont{operators}{\encodingdefault}{\rmdefault}{m}{n}
\SetSymbolFont{operators}{bold}{\encodingdefault}{\rmdefault}{\bold@wt}{n}
\def\operator@font{\mathgroup\symoperators}
\DeclareSymbolFontAlphabet{\mathrm}{operators}
\DeclareMathAlphabet{\mathsf}{\encodingdefault}{\sfdefault}{m}{n}
\DeclareMathAlphabet{\mathit}{\encodingdefault}{\rmdefault}{m}{it}
\DeclareMathAlphabet{\mathtt}{\encodingdefault}{\ttdefault}{m}{n}
\DeclareSymbolFontAlphabet{\mathrm}{operators}
\DeclareMathAlphabet{\mathbf}{\encodingdefault}{\rmdefault}{\bold@wt}{n}
\SetMathAlphabet{\mathit}{bold}{\encodingdefault}{\rmdefault}{\bold@wt}{it}
\SetMathAlphabet{\mathsf}{bold}{\encodingdefault}{\sfdefault}{b}{n}
\SetMathAlphabet{\mathtt}{bold}{\encodingdefault}{\ttdefault}{b}{n}
%%%%%%%%%%%%%%%
% Math Italic %
%%%%%%%%%%%%%%%
\iftx@libertine
\DeclareSymbolFont{letters}{OML}{nxlmi}{m}{it}
\SetSymbolFont{letters}{bold}{OML}{nxlmi}{b}{it}
\DeclareFontSubstitution{OML}{nxlmi}{m}{it}
\else
\iftx@minion
\DeclareSymbolFont{letters}{OML}{zmnmi}{m}{it}
\SetSymbolFont{letters}{bold}{OML}{zmnmi}{b}{it}
\DeclareFontSubstitution{OML}{zmnmi}{m}{it}
\else
\iftx@gm
\DeclareSymbolFont{letters}{OML}{zgmmi}{m}{it}
\SetSymbolFont{letters}{bold}{OML}{zgmmi}{b}{it}
\DeclareFontSubstitution{OML}{zgmmi}{m}{it}
\else
\DeclareSymbolFont{letters}{OML}{ntxmi}{m}{it}
\SetSymbolFont{letters}{bold}{OML}{ntxmi}{b}{it}
\DeclareFontSubstitution{OML}{ntxmi}{m}{it}
\fi
\fi
\fi
%%%%%%%%%%%%%%%%%
% Math Italic A %
%%%%%%%%%%%%%%%%%
% untxmia.fd makes switch in libertine case
\DeclareSymbolFont{lettersA}{U}{ntxmia}{m}{it}
\SetSymbolFont{lettersA}{bold}{U}{ntxmia}{b}{it}
\DeclareFontSubstitution{U}{ntxmia}{m}{it}
\DeclareSymbolFontAlphabet{\mathfrak}{lettersA}
%%%%%%%%%%%%%%%
% Math Symbol %
%%%%%%%%%%%%%%%
\DeclareSymbolFont{symbols}{OMS}{ntxsy}{m}{n}
\SetSymbolFont{symbols}{bold}{OMS}{ntxsy}{b}{n}
\DeclareFontSubstitution{OMS}{ntxsy}{m}{n}
\DeclareSymbolFontAlphabet{\symb@ls@lph@}{symbols}
\ifx\AmSfont\@undefined\else
\renewcommand{\AmSfont}{{%
\usefont{OMS}{ntxsy}{\if\@xp\@car\f@series\@nil bb\else m\fi}{n}}}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbols A (MSAM) %
%%%%%%%%%%%%%%%%%%%%%%%%%
\iftx@ams%
\DeclareSymbolFont{AMSa}{U}{ntxsya}{m}{n}
\SetSymbolFont{AMSa}{bold}{U}{ntxsya}{b}{n}
\DeclareFontSubstitution{U}{ntxsya}{m}{n}
%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbols B (MSBM) %
%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareSymbolFont{AMSb}{U}{ntxsyb}{m}{n}
\SetSymbolFont{AMSb}{bold}{U}{ntxsyb}{b}{n}
\DeclareFontSubstitution{U}{ntxsyb}{m}{n}
\DeclareSymbolFontAlphabet{\mathbb}{AMSb}
\fi
%%%%%%%%%%%%%%%%%%
% Math Symbols C %
%%%%%%%%%%%%%%%%%%
\iftx@symbolsC
\DeclareSymbolFont{symbolsC}{U}{ntxsyc}{m}{n}
\SetSymbolFont{symbolsC}{bold}{U}{ntxsyc}{b}{n}
\DeclareFontSubstitution{U}{ntxsyc}{m}{n}
\fi
%%%%%%%%%%%%%%%%%%
% Math Extension %
%%%%%%%%%%%%%%%%%%
% no OMX used
\DeclareFontEncoding{LMX}{}{}
\DeclareFontSubstitution{LMX}{ntxexx}{m}{n}
\DeclareFontFamily{LMX}{ntxexx}{}
\DeclareFontShape{LMX}{ntxexx}{m}{n}{<-> \ntxmath@scaled ntxexx}{}
\DeclareFontShape{LMX}{ntxexx}{b}{n}{<-> \ntxmath@scaled ntxbexx}{}
\DeclareFontShape{LMX}{ntxexx}{bx}{n}{<->ssub ntxexx/b/n}{}
\DeclareSymbolFont{largesymbols}{LMX}{ntxexx}{m}{n}
\SetSymbolFont{largesymbols}{bold}{LMX}{ntxexx}{b}{n}
\iftx@bigdelims
%default definitions of \big etc need some changes
%\renewcommand{\big}{\bBigg@\@ne}
\AtBeginDocument{\renewcommand{\Big}{\bBigg@{1.3}}
\renewcommand{\bigg}{\bBigg@{1.73}}
\renewcommand{\Bigg}{\bBigg@{2.16}}
}
\fi%
%%%%%%%%%%%%%%%%%%%%
% Math Extension A %
%%%%%%%%%%%%%%%%%%%%
\DeclareSymbolFont{largesymbolsTXA}{U}{ntxexa}{m}{n}
\SetSymbolFont{largesymbolsTXA}{bold}{U}{ntxexa}{b}{n}
\DeclareFontSubstitution{U}{ntxexa}{m}{n}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Common Macros
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\re@DeclareMathSymbol#1#2#3#4{%
\let#1=\undefined
\DeclareMathSymbol{#1}{#2}{#3}{#4}}
\def\re@DeclareMathDelimiter#1#2#3#4#5#6{%
\let#1=\undefined
\DeclareMathDelimiter{#1}{#2}{#3}{#4}{#5}{#6}}
\def\re@DeclareMathAccent#1#2#3#4{%
\let#1=\undefined
\DeclareMathAccent{#1}{#2}{#3}{#4}}
\def\DeclareMathSymbolCtr#1#2#3#4{%
\DeclareMathSymbol{#1}{#2}{#3}{#4}
\advance #4 by1}
\def\tx@isdigit#1{% #1 should be a single character
\tx@Isdigit=\z@ %
\count0=\number`#1\relax%
\ifnum\count0>47\relax%
\ifnum\count0<58\relax%
\tx@Isdigit=\@ne %
\fi%
\fi%
}
\def\tx@XXX#1#2\@nil{% #1=first character, #2=rest of string
\tx@isdigit{#1}%
\ifnum\tx@Isdigit>\z@ $#1$\else#1\fi%
\if\relax\detokenize{#2}\relax \else
\edef\tx@XXXcmd{\noexpand\tx@XXX #2\noexpand\@nil}\tx@XXXcmd \fi}
\def\equalht#1{\tx@XXX #1\@nil}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symols & Notations Definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\joinrel{\mathrel{\mkern-2.5mu}} %-3mu in plain TeX
%%%%%%%%%%%%%%%%%%%%%%
% Text Roman in Math % operators
%%%%%%%%%%%%%%%%%%%%%%
% LaTeX defaults are set to the following in the roman text font.
% Not all text fonts have these available, or not in the same slots.
%\DeclareMathSymbol{\Gamma}{\mathalpha}{operators}{0}
%\DeclareMathSymbol{\Delta}{\mathalpha}{operators}{1}
%\DeclareMathSymbol{\Theta}{\mathalpha}{operators}{2}
%\DeclareMathSymbol{\Lambda}{\mathalpha}{operators}{3}
%\DeclareMathSymbol{\Xi}{\mathalpha}{operators}{4}
%\DeclareMathSymbol{\Pi}{\mathalpha}{operators}{5}
%\DeclareMathSymbol{\Sigma}{\mathalpha}{operators}{6}
%\DeclareMathSymbol{\Upsilon}{\mathalpha}{operators}{7}
%\DeclareMathSymbol{\Phi}{\mathalpha}{operators}{8}
%\DeclareMathSymbol{\Psi}{\mathalpha}{operators}{9}
%\DeclareMathSymbol{\Omega}{\mathalpha}{operators}{10}
%"30-"39: 0-9
%\DeclareMathAccent{\grave}{\mathalpha}{operators}{18}
%\DeclareMathAccent{\acute}{\mathalpha}{operators}{19}
%\DeclareMathAccent{\check}{\mathalpha}{operators}{20}
%\DeclareMathAccent{\breve}{\mathalpha}{operators}{21}
%\DeclareMathAccent{\bar}{\mathalpha}{operators}{22}
%\DeclareMathAccent{\mathring}{\mathalpha}{operators}{23}
%\DeclareMathSymbol{\mathdollar}{\mathord}{operators}{36}
%\def\mathsterling{\mathit{\mathchar"7024}}
%Change the following two so we can adjust metrics in math mode
%\DeclareMathDelimiter{(}{\mathopen}{operators}{40}{largesymbols}{0}
%\DeclareMathDelimiter{)}{\mathclose}{operators}{41}{largesymbols}{1}
\iftx@bigdelims
\DeclareMathDelimiter{(}{\mathopen}{lettersA}{155}{largesymbols}{130}
\DeclareMathDelimiter{)}{\mathclose}{lettersA}{156}{largesymbols}{131}
\DeclareMathDelimiter{[}{\mathopen}{lettersA}{157}{largesymbols}{132}
\DeclareMathDelimiter{]}{\mathclose}{lettersA}{158}{largesymbols}{133}
\DeclareMathDelimiter{\lfloor}{\mathopen}{lettersA}{159}{largesymbols}{134}
\DeclareMathDelimiter{\rfloor}{\mathclose}{lettersA}{160}{largesymbols}{135}
\DeclareMathDelimiter{\lceil}{\mathopen}{lettersA}{161}{largesymbols}{136}
\DeclareMathDelimiter{\rceil}{\mathclose}{lettersA}{162}{largesymbols}{137}
\DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{163}{largesymbols}{138}
\DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{164}{largesymbols}{139}
\DeclareMathDelimiter{\langle}{\mathopen}{lettersA}{165}{largesymbols}{140}
%\DeclareMathDelimiter{<}{\mathopen}{letters}{60}{largesymbols}{140}
\DeclareMathDelimiter{\rangle}{\mathclose}{lettersA}{166}{largesymbols}{141}
%\DeclareMathDelimiter{>}{\mathclose}{letters}{62}{largesymbols}{141}
\DeclareMathSymbol{\mid}{\mathrel}{lettersA}{96}
\DeclareMathDelimiter{|}{\mathord}{lettersA}{96}{largesymbols}{128}
\DeclareMathDelimiter{\arrowvert}{\mathord}{lettersA}{167}{largesymbols}{60}
\DeclareMathDelimiter{\vert}{\mathord}{lettersA}{96}{largesymbols}{128}
%\DeclareMathSymbol{\parallel}{\mathrel}{lettersA}{129}
\DeclareMathDelimiter{\Arrowvert}{\mathord}{lettersA}{168}{largesymbols}{61}
\DeclareMathDelimiter{\Vert}{\mathord}{lettersA}{128}{largesymbols}{129}
\let\|=\Vert
\DeclareMathDelimiter{\updownarrow}{\mathrel}{lettersA}{167}{largesymbols}{63}
\DeclareMathDelimiter{\Updownarrow}{\mathrel}{lettersA}{167}{largesymbols}{119}
\DeclareMathDelimiter{\llbracket}{\mathopen}{lettersA}{251}{largesymbolsTXA}{18}
\DeclareMathDelimiter{\rrbracket}{\mathclose}{lettersA}{252}{largesymbolsTXA}{19}
\else
\iftx@braces
\DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{142}
\DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{143}
\fi
\iftx@minion\else
\iftx@libertine%
\DeclareMathDelimiter{(}{\mathopen}{lettersA}{123}{largesymbols}{0}
\DeclareMathDelimiter{)}{\mathclose}{lettersA}{124}{largesymbols}{1}
\else %Times
\DeclareMathDelimiter{(}{\mathopen}{lettersA}{125}{largesymbols}{0}
\DeclareMathDelimiter{)}{\mathclose}{lettersA}{126}{largesymbols}{1}
\fi
\fi
\fi
%\DeclareMathSymbol{+}{\mathbin}{operators}{43}
\DeclareMathSymbol{+}{\mathbin}{lettersA}{253}
%\DeclareMathDelimiter{/}{\mathord}{operators}{47}{largesymbols}{14}
%\DeclareMathSymbol{:}{\mathrel}{operators}{58}
%\DeclareMathSymbol{\colon}{\mathpunct}{operators}{58}
%\DeclareMathSymbol{;}{\mathpunct}{operators}{59}
\DeclareMathSymbol{=}{\mathrel}{lettersA}{61}
%\DeclareMathSymbol{?}{\mathclose}{operators}{63}
%change the following two for better sizing
%\DeclareMathDelimiter{[}{\mathopen}{operators}{91}{largesymbols}{2}
%\DeclareMathDelimiter{]}{\mathclose}{operators}{93}{largesymbols}{3}
%\DeclareMathAccent{\hat}{\mathalpha}{operators}{94}
%\DeclareMathAccent{\dot}{\mathalpha}{operators}{95}
%\DeclareMathAccent{\tilde}{\mathalpha}{operators}{126}
%\DeclareMathAccent{\ddot}{\mathalpha}{operators}{127}
\def\ly@one{LY1}
\def\t@one{T1}
\iftx@tma
\re@DeclareMathAccent{\grave}{\mathord}{lettersA}{254}
\re@DeclareMathAccent{\acute}{\mathord}{lettersA}{255}
\re@DeclareMathAccent{\check}{\mathord}{lettersA}{186}
\re@DeclareMathAccent{\breve}{\mathord}{lettersA}{187}
\re@DeclareMathAccent{\bar}{\mathord}{lettersA}{221}
\re@DeclareMathAccent{\mathring}{\mathord}{lettersA}{222}
\re@DeclareMathAccent{\hat}{\mathord}{lettersA}{223}
\re@DeclareMathAccent{\dot}{\mathord}{lettersA}{224}
\re@DeclareMathAccent{\tilde}{\mathord}{lettersA}{219}
\re@DeclareMathAccent{\ddot}{\mathord}{lettersA}{220}
\else
\ifx\encodingdefault\t@one%
\re@DeclareMathAccent{\grave}{\mathalpha}{operators}{0}
\re@DeclareMathAccent{\acute}{\mathalpha}{operators}{1}
\re@DeclareMathAccent{\check}{\mathalpha}{operators}{7}
\re@DeclareMathAccent{\breve}{\mathalpha}{operators}{8}
\re@DeclareMathAccent{\bar}{\mathalpha}{operators}{9}
\re@DeclareMathAccent{\mathring}{\mathalpha}{operators}{6}
\re@DeclareMathAccent{\hat}{\mathalpha}{operators}{2}
\re@DeclareMathAccent{\dot}{\mathalpha}{operators}{10}
\re@DeclareMathAccent{\tilde}{\mathalpha}{operators}{3}
\re@DeclareMathAccent{\ddot}{\mathalpha}{operators}{4}
\else\ifx\encodingdefault\ly@one
\re@DeclareMathAccent{\bar}{\mathalpha}{operators}{175}
\re@DeclareMathAccent{\hat}{\mathalpha}{operators}{94}
\re@DeclareMathAccent{\dot}{\mathalpha}{operators}{5}
\DeclareMathAccent{\tilde}{\mathalpha}{operators}{152}
\fi\fi
\fi
%
\iftx@slantedG
\re@DeclareMathSymbol{\Gamma}{\mathord}{letters}{0}
\re@DeclareMathSymbol{\Delta}{\mathord}{letters}{1}
\re@DeclareMathSymbol{\Theta}{\mathord}{letters}{2}
\re@DeclareMathSymbol{\Lambda}{\mathord}{letters}{3}
\re@DeclareMathSymbol{\Xi}{\mathord}{letters}{4}
\re@DeclareMathSymbol{\Pi}{\mathord}{letters}{5}
\re@DeclareMathSymbol{\Sigma}{\mathord}{letters}{6}
\re@DeclareMathSymbol{\Upsilon}{\mathord}{letters}{7}
\re@DeclareMathSymbol{\Phi}{\mathord}{letters}{8}
\re@DeclareMathSymbol{\Psi}{\mathord}{letters}{9}
\re@DeclareMathSymbol{\Omega}{\mathord}{letters}{10}
\else
\re@DeclareMathSymbol{\Gamma}{\mathord}{lettersA}{0}
\re@DeclareMathSymbol{\Delta}{\mathord}{lettersA}{1}
\re@DeclareMathSymbol{\Theta}{\mathord}{lettersA}{2}
\re@DeclareMathSymbol{\Lambda}{\mathord}{lettersA}{3}
\re@DeclareMathSymbol{\Xi}{\mathord}{lettersA}{4}
\re@DeclareMathSymbol{\Pi}{\mathord}{lettersA}{5}
\re@DeclareMathSymbol{\Sigma}{\mathord}{lettersA}{6}
\re@DeclareMathSymbol{\Upsilon}{\mathord}{lettersA}{7}
\re@DeclareMathSymbol{\Phi}{\mathord}{lettersA}{8}
\re@DeclareMathSymbol{\Psi}{\mathord}{lettersA}{9}
\re@DeclareMathSymbol{\Omega}{\mathord}{lettersA}{10}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbol (txsy) Definition % symbols
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\DeclareMathSymbol{-}{\mathbin}{symbols}{0}
%\DeclareMathSymbol{\cdotp}{\mathpunct}{symbols}{1}
%\DeclareMathSymbol{\cdot}{\mathbin}{symbols}{1}
%\DeclareMathSymbol{\times}{\mathbin}{symbols}{2}
%\DeclareMathSymbol{\ast}{\mathbin}{symbols}{3}
%\DeclareMathSymbol{*}{\mathbin}{symbols}{3} %
%\DeclareMathSymbol{\div}{\mathbin}{symbols}{4}
%\DeclareMathSymbol{\diamond}{\mathbin}{symbols}{5}
%\DeclareMathSymbol{\pm}{\mathbin}{symbols}{6}
%\DeclareMathSymbol{\mp}{\mathbin}{symbols}{7}
%\DeclareMathSymbol{\oplus}{\mathbin}{symbols}{8}
\let\circledplus\oplus
%\DeclareMathSymbol{\ominus}{\mathbin}{symbols}{9}
\let\circledminus\ominus
%\DeclareMathSymbol{\otimes}{\mathbin}{symbols}{10}
\let\circledtimes\otimes
%\DeclareMathSymbol{\oslash}{\mathbin}{symbols}{11}
\let\circledslash\oslash
%\DeclareMathSymbol{\odot}{\mathbin}{symbols}{12}
\let\circleddot\odot
%\DeclareMathSymbol{\bigcirc}{\mathbin}{symbols}{13}
%\DeclareMathSymbol{\circ}{\mathbin}{symbols}{14}
%\DeclareMathSymbol{\bullet}{\mathbin}{symbols}{15}
%\DeclareMathSymbol{\asymp}{\mathrel}{symbols}{16}
%\DeclareMathSymbol{\equiv}{\mathrel}{symbols}{17}
%\DeclareMathSymbol{\subseteq}{\mathrel}{symbols}{18}
%\DeclareMathSymbol{\supseteq}{\mathrel}{symbols}{19}
%\DeclareMathSymbol{\leq}{\mathrel}{symbols}{20}
% \let\le=\leq
%\DeclareMathSymbol{\geq}{\mathrel}{symbols}{21}
% \let\ge=\geq
%\DeclareMathSymbol{\preceq}{\mathrel}{symbols}{22}
%\DeclareMathSymbol{\succeq}{\mathrel}{symbols}{23}
%\DeclareMathSymbol{\sim}{\mathrel}{symbols}{24}
%\DeclareMathSymbol{\approx}{\mathrel}{symbols}{25}
%\DeclareMathSymbol{\subset}{\mathrel}{symbols}{26}
%\DeclareMathSymbol{\supset}{\mathrel}{symbols}{27}
%\DeclareMathSymbol{\ll}{\mathrel}{symbols}{28}
%\DeclareMathSymbol{\gg}{\mathrel}{symbols}{29}
%\DeclareMathSymbol{\prec}{\mathrel}{symbols}{30}
%\DeclareMathSymbol{\succ}{\mathrel}{symbols}{31}
%\DeclareMathSymbol{\leftarrow}{\mathrel}{symbols}{32}
% \let\gets=\leftarrow
%\DeclareMathSymbol{\rightarrow}{\mathrel}{symbols}{33}
% \let\to=\rightarrow
%\DeclareMathDelimiter{\uparrow}{\mathrel}{symbols}{34}{largesymbols}{120}
%\DeclareMathDelimiter{\downarrow}{\mathrel}{symbols}{35}{largesymbols}{121}
%\DeclareMathSymbol{\leftrightarrow}{\mathrel}{symbols}{36}
%\DeclareMathSymbol{\nearrow}{\mathrel}{symbols}{37}
%\DeclareMathSymbol{\searrow}{\mathrel}{symbols}{38}
%\DeclareMathSymbol{\simeq}{\mathrel}{symbols}{39}
%\DeclareMathSymbol{\Leftarrow}{\mathrel}{symbols}{40}
%\DeclareMathSymbol{\Rightarrow}{\mathrel}{symbols}{41}
%\DeclareMathDelimiter{\Uparrow}{\mathrel}{symbols}{42}{largesymbols}{126}
%\DeclareMathDelimiter{\Downarrow}{\mathrel}{symbols}{43}{largesymbols}{127}
%\DeclareMathSymbol{\Leftrightarrow}{\mathrel}{symbols}{44}
%\DeclareMathSymbol{\nwarrow}{\mathrel}{symbols}{45}
%\DeclareMathSymbol{\swarrow}{\mathrel}{symbols}{46}
%\DeclareMathSymbol{\propto}{\mathrel}{symbols}{47}
%\DeclareMathSymbol{\prime}{\mathord}{symbols}{48}
%\DeclareMathSymbol{\infty}{\mathord}{symbols}{49}
%\DeclareMathSymbol{\in}{\mathrel}{symbols}{50}
%\DeclareMathSymbol{\ni}{\mathrel}{symbols}{51}
% \let\owns=\ni
%\DeclareMathSymbol{\triangle}{\mathord}{symbols}{52}
%\DeclareMathSymbol{\bigtriangleup}{\mathbin}{symbols}{52}
%\DeclareMathSymbol{\bigtriangledown}{\mathbin}{symbols}{53}
%\DeclareMathSymbol{\not}{\mathrel}{symbols}{54}
%\DeclareMathSymbol{\mapstochar}{\mathrel}{symbols}{55}
% \def\mapsto{\mapstochar\rightarrow}
%\DeclareMathSymbol{\forall}{\mathord}{symbols}{56}
%\DeclareMathSymbol{\exists}{\mathord}{symbols}{57}
%\DeclareMathSymbol{\neg}{\mathord}{symbols}{58}
% \let\lnot=\neg
%\DeclareMathSymbol{\emptyset}{\mathord}{symbols}{59}
%\DeclareMathSymbol{\Re}{\mathord}{symbols}{60}
%\DeclareMathSymbol{\Im}{\mathord}{symbols}{61}
%\DeclareMathSymbol{\top}{\mathord}{symbols}{62}
%\DeclareMathSymbol{\bot}{\mathord}{symbols}{63}
%\DeclareMathSymbol{\perp}{\mathrel}{symbols}{63}
%\DeclareMathSymbol{\aleph}{\mathord}{symbols}{64}
% "41-"5A: \mathcal{A-Z}
%\DeclareMathSymbol{\cup}{\mathbin}{symbols}{91}
%\DeclareMathSymbol{\cap}{\mathbin}{symbols}{92}
%\DeclareMathSymbol{\uplus}{\mathbin}{symbols}{93}
%\DeclareMathSymbol{\wedge}{\mathbin}{symbols}{94}
% \let\land=\wedge
%\DeclareMathSymbol{\vee}{\mathbin}{symbols}{95}
% \let\lor=\vee
%\DeclareMathSymbol{\vdash}{\mathrel}{symbols}{96}
%\DeclareMathSymbol{\dashv}{\mathrel}{symbols}{97}
%\DeclareMathDelimiter{\lfloor}{\mathopen}{symbols}{98}{largesymbols}{4}
%\DeclareMathDelimiter{\rfloor}{\mathclose}{symbols}{99}{largesymbols}{5}
%\DeclareMathDelimiter{\lceil}{\mathopen}{symbols}{100}{largesymbols}{6}
%\DeclareMathDelimiter{\rceil}{\mathclose}{symbols}{101}{largesymbols}{7}
%\DeclareMathDelimiter{\lbrace}{\mathopen}{symbols}{102}{largesymbols}{8}
%\DeclareMathDelimiter{\rbrace}{\mathclose}{symbols}{103}{largesymbols}{9}
%\DeclareMathDelimiter{\langle}{\mathopen}{symbols}{104}{largesymbols}{10}
%\DeclareMathDelimiter{<}{\mathopen}{symbols}{104}{largesymbols}{10}
%\DeclareMathDelimiter{\rangle}{\mathclose}{symbols}{105}{largesymbols}{11}
%\DeclareMathDelimiter{>}{\mathclose}{symbols}{105}{largesymbols}{11}
%\DeclareMathSymbol{\mid}{\mathrel}{symbols}{106}
%\DeclareMathDelimiter{|}{\mathord}{symbols}{106}{largesymbols}{12}
%\DeclareMathDelimiter{\arrowvert}{\mathord}{symbols}{106}{largesymbols}{60}
%\DeclareMathDelimiter{\vert}{\mathord}{symbols}{106}{largesymbols}{12}
%\DeclareMathSymbol{\parallel}{\mathrel}{symbols}{107}
%\DeclareMathDelimiter{\Arrowvert}{\mathord}{symbols}{107}{largesymbols}{61}
%\DeclareMathDelimiter{\Vert}{\mathord}{symbols}{107}{largesymbols}{13}
% \let\|=\Vert
%\DeclareMathDelimiter{\updownarrow}{\mathrel}{symbols}{108}{largesymbols}{63}
%\DeclareMathDelimiter{\Updownarrow}{\mathrel}{symbols}{109}{largesymbols}{119}
%\DeclareMathSymbol{\setminus}{\mathbin}{symbols}{110}
%\DeclareMathDelimiter{\backslash}{\mathord}{symbols}{110}{largesymbols}{15}
%\expandafter\DeclareMathDelimiter\@backslashchar{\mathord}{symbols}{110}{largesymbols}{15}
%\DeclareMathSymbol{\wr}{\mathbin}{symbols}{111}
%\def\surd{{\mathchar"1270}}
%\DeclareMathRadical{\sqrtsign}{symbols}{112}{largesymbols}{112}
%\DeclareMathSymbol{\amalg}{\mathbin}{symbols}{113}
%\DeclareMathSymbol{\nabla}{\mathord}{symbols}{114}
%\DeclareMathSymbol{\smallint}{\mathop}{symbols}{115}
%\DeclareMathSymbol{\sqcup}{\mathbin}{symbols}{116}
%\DeclareMathSymbol{\sqcap}{\mathbin}{symbols}{117}
%\DeclareMathSymbol{\sqsubseteq}{\mathrel}{symbols}{118}
%\DeclareMathSymbol{\sqsupseteq}{\mathrel}{symbols}{119}
%\DeclareMathSymbol{\mathsection}{\mathord}{symbols}{120}
%\DeclareMathSymbol{\dagger}{\mathbin}{symbols}{121}
%\DeclareMathSymbol{\ddagger}{\mathbin}{symbols}{122}
%\DeclareMathSymbol{\mathparagraph}{\mathord}{symbols}{123}
%\DeclareMathSymbol{\clubsuit}{\mathord}{symbols}{124}
%\DeclareMathSymbol{\diamondsuit}{\mathord}{symbols}{125}
%\DeclareMathSymbol{\heartsuit}{\mathord}{symbols}{126}
%\DeclareMathSymbol{\spadesuit}{\mathord}{symbols}{127}
%\iftx@bigdelims
% \re@DeclareMathDelimiter{(}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{)}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{[}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{]}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
%
%\else
% \iftx@braces%
% \re@DeclareMathDelimiter{\lbrace}{\mathopen}{lettersA}{62}{largesymbols}{8}
% \re@DeclareMathDelimiter{\rbrace}{\mathclose}{lettersA}{63}{largesymbols}{9}
% \fi
%\fi
% Define \overgroup, \undergroup, like \overbrace, \underbrace
\DeclareMathSymbol{\groupld}{\mathord}{largesymbols}{160}
\DeclareMathSymbol{\grouprd}{\mathord}{largesymbols}{161}
\DeclareMathSymbol{\grouplu}{\mathord}{largesymbols}{162}
\DeclareMathSymbol{\groupru}{\mathord}{largesymbols}{163}
\DeclareMathSymbol{\grouplda}{\mathord}{largesymbols}{164}
\DeclareMathSymbol{\grouprda}{\mathord}{largesymbols}{165}
\DeclareMathSymbol{\grouplua}{\mathord}{largesymbols}{166}
\DeclareMathSymbol{\grouprua}{\mathord}{largesymbols}{167}
% Override default definitions of \widehat and \widetilde
\re@DeclareMathAccent{\widehat}{\mathalpha}{largesymbols}{98}
\re@DeclareMathAccent{\widetilde}{\mathalpha}{largesymbols}{101}
\def\overgroup#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern.4\p@}%
\downgroupfill\crcr\noalign{\kern1.5\p@\nointerlineskip}%
$\hfil\displaystyle{#1}\hfil$\crcr}}}\limits}
%
\def\undergroup#1{\mathop{\vtop{\ialign{##\crcr%
$\hfil\displaystyle{#1}\hfil$\crcr%
\noalign{\kern1.5\p@\nointerlineskip}%
\upgroupfill\crcr\noalign{\kern.5\p@}}}}\limits}
%
\def\downgroupfill{$\m@th%
\groupld\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\grouprd$}
%
\def\upgroupfill{$\m@th%
\grouplu\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\groupru$}
% same thing but with arrows
\def\overgroupra#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern.4\p@}%
\downgroupfillra\crcr\noalign{\kern1.5\p@\nointerlineskip}%
$\hfil\displaystyle{#1}\hfil$\crcr}}}\limits}
%
\def\undergroupra#1{\mathop{\vtop{\ialign{##\crcr%
$\hfil\displaystyle{#1}\hfil$\crcr%
\noalign{\kern1.5\p@\nointerlineskip}%
\upgroupfillra\crcr\noalign{\kern.5\p@}}}}\limits}
%
\def\overgroupla#1{\mathop{\vbox{\ialign{##\crcr\noalign{\kern.4\p@}%
\downgroupfillla\crcr\noalign{\kern1.5\p@\nointerlineskip}%
$\hfil\displaystyle{#1}\hfil$\crcr}}}\limits}
%
\def\undergroupla#1{\mathop{\vtop{\ialign{##\crcr%
$\hfil\displaystyle{#1}\hfil$\crcr%
\noalign{\kern1.5\p@\nointerlineskip}%
\upgroupfillla\crcr\noalign{\kern.5\p@}}}}\limits}
%
\def\downgroupfillra{$\m@th%
\groupld\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\grouprda$}
%
\def\upgroupfillra{$\m@th%
\grouplu\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\grouprua$}
%
\def\downgroupfillla{$\m@th%
\grouplda\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\grouprd$}
%
\def\upgroupfillla{$\m@th%
\grouplua\mkern-1mu\cleaders\hbox{$\mkern-.5mu\br@cext\mkern-.5mu$}\hfill\mkern-1mu\groupru$}
% Place a ring over an overgroup symbol, like yhmath \widering
\newcommand{\widering}[1]{\overset{\smash{\vbox to .2ex{%
\hbox{$\mathring{}$}}}}{\overgroup{#1}}}
% \widearc, \wideOarc
\DeclareMathAccent{\widearc}{\mathalpha}{largesymbols}{175}
\DeclareMathAccent{\wideOarc}{\mathalpha}{largesymbols}{180}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbol A Definitions % AMSa
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\iftx@ams
\re@DeclareMathSymbol{\boxdot}{\mathbin}{AMSa}{0}
\re@DeclareMathSymbol{\boxplus}{\mathbin}{AMSa}{1}
\re@DeclareMathSymbol{\boxtimes}{\mathbin}{AMSa}{2}
\re@DeclareMathSymbol{\square}{\mathord}{AMSa}{3}
\re@DeclareMathSymbol{\blacksquare}{\mathord}{AMSa}{4}
\re@DeclareMathSymbol{\centerdot}{\mathbin}{AMSa}{5}
\re@DeclareMathSymbol{\lozenge}{\mathord}{AMSa}{6}
\re@DeclareMathSymbol{\blacklozenge}{\mathord}{AMSa}{7}
\re@DeclareMathSymbol{\circlearrowright}{\mathrel}{AMSa}{8}
\re@DeclareMathSymbol{\circlearrowleft}{\mathrel}{AMSa}{9}
\re@DeclareMathSymbol{\rightleftharpoons}{\mathrel}{AMSa}{10}
\re@DeclareMathSymbol{\leftrightharpoons}{\mathrel}{AMSa}{11}
\re@DeclareMathSymbol{\boxminus}{\mathbin}{AMSa}{12}
\re@DeclareMathSymbol{\Vdash}{\mathrel}{AMSa}{13}
\re@DeclareMathSymbol{\Vvdash}{\mathrel}{AMSa}{14}
\re@DeclareMathSymbol{\vDash}{\mathrel}{AMSa}{15}
\re@DeclareMathSymbol{\twoheadrightarrow}{\mathrel}{AMSa}{16}
\re@DeclareMathSymbol{\twoheadleftarrow}{\mathrel}{AMSa}{17}
\re@DeclareMathSymbol{\leftleftarrows}{\mathrel}{AMSa}{18}
\re@DeclareMathSymbol{\rightrightarrows}{\mathrel}{AMSa}{19}
\re@DeclareMathSymbol{\upuparrows}{\mathrel}{AMSa}{20}
\re@DeclareMathSymbol{\downdownarrows}{\mathrel}{AMSa}{21}
\re@DeclareMathSymbol{\upharpoonright}{\mathrel}{AMSa}{22}
\let\restriction\upharpoonright
\re@DeclareMathSymbol{\downharpoonright}{\mathrel}{AMSa}{23}
\re@DeclareMathSymbol{\upharpoonleft}{\mathrel}{AMSa}{24}
\re@DeclareMathSymbol{\downharpoonleft}{\mathrel}{AMSa}{25}
\re@DeclareMathSymbol{\rightarrowtail}{\mathrel}{AMSa}{26}
\re@DeclareMathSymbol{\leftarrowtail}{\mathrel}{AMSa}{27}
\re@DeclareMathSymbol{\leftrightarrows}{\mathrel}{AMSa}{28}
\re@DeclareMathSymbol{\rightleftarrows}{\mathrel}{AMSa}{29}
\re@DeclareMathSymbol{\Lsh}{\mathrel}{AMSa}{30}
\re@DeclareMathSymbol{\Rsh}{\mathrel}{AMSa}{31}
\re@DeclareMathSymbol{\rightsquigarrow}{\mathrel}{AMSa}{32}
\re@DeclareMathSymbol{\leftrightsquigarrow}{\mathrel}{AMSa}{33}
\re@DeclareMathSymbol{\looparrowleft}{\mathrel}{AMSa}{34}
\re@DeclareMathSymbol{\looparrowright}{\mathrel}{AMSa}{35}
\re@DeclareMathSymbol{\circeq}{\mathrel}{AMSa}{36}
\re@DeclareMathSymbol{\succsim}{\mathrel}{AMSa}{37}
\re@DeclareMathSymbol{\gtrsim}{\mathrel}{AMSa}{38}
\re@DeclareMathSymbol{\gtrapprox}{\mathrel}{AMSa}{39}
\re@DeclareMathSymbol{\multimap}{\mathrel}{AMSa}{40}
\re@DeclareMathSymbol{\therefore}{\mathrel}{AMSa}{41}
\re@DeclareMathSymbol{\because}{\mathrel}{AMSa}{42}
\re@DeclareMathSymbol{\doteqdot}{\mathrel}{AMSa}{43}
\let\Doteq\doteqdot
\re@DeclareMathSymbol{\triangleq}{\mathrel}{AMSa}{44}
\re@DeclareMathSymbol{\precsim}{\mathrel}{AMSa}{45}
\re@DeclareMathSymbol{\lesssim}{\mathrel}{AMSa}{46}
\re@DeclareMathSymbol{\lessapprox}{\mathrel}{AMSa}{47}
\re@DeclareMathSymbol{\eqslantless}{\mathrel}{AMSa}{48}
\re@DeclareMathSymbol{\eqslantgtr}{\mathrel}{AMSa}{49}
\re@DeclareMathSymbol{\curlyeqprec}{\mathrel}{AMSa}{50}
\re@DeclareMathSymbol{\curlyeqsucc}{\mathrel}{AMSa}{51}
\re@DeclareMathSymbol{\preccurlyeq}{\mathrel}{AMSa}{52}
\re@DeclareMathSymbol{\leqq}{\mathrel}{AMSa}{53}
\re@DeclareMathSymbol{\leqslant}{\mathrel}{AMSa}{54}
\re@DeclareMathSymbol{\lessgtr}{\mathrel}{AMSa}{55}
\re@DeclareMathSymbol{\backprime}{\mathord}{AMSa}{56}
\re@DeclareMathSymbol{\risingdotseq}{\mathrel}{AMSa}{58}
\re@DeclareMathSymbol{\fallingdotseq}{\mathrel}{AMSa}{59}
\re@DeclareMathSymbol{\succcurlyeq}{\mathrel}{AMSa}{60}
\re@DeclareMathSymbol{\geqq}{\mathrel}{AMSa}{61}
\re@DeclareMathSymbol{\geqslant}{\mathrel}{AMSa}{62}
\re@DeclareMathSymbol{\gtrless}{\mathrel}{AMSa}{63}
\re@DeclareMathSymbol{\sqsubset}{\mathrel}{AMSa}{64}
\re@DeclareMathSymbol{\sqsupset}{\mathrel}{AMSa}{65}
\re@DeclareMathSymbol{\vartriangleright}{\mathrel}{AMSa}{66}
\re@DeclareMathSymbol{\vartriangleleft}{\mathrel}{AMSa}{67}
\re@DeclareMathSymbol{\trianglerighteq}{\mathrel}{AMSa}{68}
\re@DeclareMathSymbol{\trianglelefteq}{\mathrel}{AMSa}{69}
\re@DeclareMathSymbol{\bigstar}{\mathord}{AMSa}{70}
\re@DeclareMathSymbol{\between}{\mathrel}{AMSa}{71}
\re@DeclareMathSymbol{\blacktriangledown}{\mathord}{AMSa}{72}
\re@DeclareMathSymbol{\blacktriangleright}{\mathrel}{AMSa}{73}
\re@DeclareMathSymbol{\blacktriangleleft}{\mathrel}{AMSa}{74}
\re@DeclareMathSymbol{\vartriangle}{\mathrel}{AMSa}{77}
\re@DeclareMathSymbol{\blacktriangle}{\mathord}{AMSa}{78}
\re@DeclareMathSymbol{\triangledown}{\mathord}{AMSa}{79}
\re@DeclareMathSymbol{\eqcirc}{\mathrel}{AMSa}{80}
\re@DeclareMathSymbol{\lesseqgtr}{\mathrel}{AMSa}{81}
\re@DeclareMathSymbol{\gtreqless}{\mathrel}{AMSa}{82}
\re@DeclareMathSymbol{\lesseqqgtr}{\mathrel}{AMSa}{83}
\re@DeclareMathSymbol{\gtreqqless}{\mathrel}{AMSa}{84}
\re@DeclareMathSymbol{\Rrightarrow}{\mathrel}{AMSa}{86}
\re@DeclareMathSymbol{\Lleftarrow}{\mathrel}{AMSa}{87}
\re@DeclareMathSymbol{\veebar}{\mathbin}{AMSa}{89}
\re@DeclareMathSymbol{\barwedge}{\mathbin}{AMSa}{90}
\re@DeclareMathSymbol{\doublebarwedge}{\mathbin}{AMSa}{91}
\re@DeclareMathSymbol{\angle}{\mathord}{AMSa}{92}
\re@DeclareMathSymbol{\measuredangle}{\mathord}{AMSa}{93}
\re@DeclareMathSymbol{\sphericalangle}{\mathord}{AMSa}{94}
\re@DeclareMathSymbol{\varpropto}{\mathrel}{AMSa}{95}
\re@DeclareMathSymbol{\smallsmile}{\mathrel}{AMSa}{96}
\re@DeclareMathSymbol{\smallfrown}{\mathrel}{AMSa}{97}
\re@DeclareMathSymbol{\Subset}{\mathrel}{AMSa}{98}
\re@DeclareMathSymbol{\Supset}{\mathrel}{AMSa}{99}
\re@DeclareMathSymbol{\Cup}{\mathbin}{AMSa}{100}
\let\doublecup\Cup
\re@DeclareMathSymbol{\Cap}{\mathbin}{AMSa}{101}
\let\doublecap\Cap
\re@DeclareMathSymbol{\curlywedge}{\mathbin}{AMSa}{102}
\re@DeclareMathSymbol{\curlyvee}{\mathbin}{AMSa}{103}
\re@DeclareMathSymbol{\leftthreetimes}{\mathbin}{AMSa}{104}
\re@DeclareMathSymbol{\rightthreetimes}{\mathbin}{AMSa}{105}
\re@DeclareMathSymbol{\subseteqq}{\mathrel}{AMSa}{106}
\re@DeclareMathSymbol{\supseteqq}{\mathrel}{AMSa}{107}
\re@DeclareMathSymbol{\bumpeq}{\mathrel}{AMSa}{108}
\re@DeclareMathSymbol{\Bumpeq}{\mathrel}{AMSa}{109}
\re@DeclareMathSymbol{\lll}{\mathrel}{AMSa}{110}
\let\llless\lll
\re@DeclareMathSymbol{\ggg}{\mathrel}{AMSa}{111}
\let\gggtr\ggg
\re@DeclareMathDelimiter\ulcorner{\mathopen}{AMSa}{112}{AMSa}{112}
\re@DeclareMathDelimiter\urcorner{\mathclose}{AMSa}{113}{AMSa}{113}
\re@DeclareMathSymbol{\circledS}{\mathord}{AMSa}{115}
\re@DeclareMathSymbol{\pitchfork}{\mathrel}{AMSa}{116}
\re@DeclareMathSymbol{\dotplus}{\mathbin}{AMSa}{117}
\re@DeclareMathSymbol{\backsim}{\mathrel}{AMSa}{118}
\re@DeclareMathSymbol{\backsimeq}{\mathrel}{AMSa}{119}
\re@DeclareMathDelimiter\llcorner{\mathopen}{AMSa}{120}{AMSa}{120}
\re@DeclareMathDelimiter\lrcorner{\mathclose}{AMSa}{121}{AMSa}{121}
\re@DeclareMathSymbol{\complement}{\mathord}{AMSa}{123}
\re@DeclareMathSymbol{\intercal}{\mathbin}{AMSa}{124}
\re@DeclareMathSymbol{\circledcirc}{\mathbin}{AMSa}{125}
\re@DeclareMathSymbol{\circledast}{\mathbin}{AMSa}{126}
\re@DeclareMathSymbol{\circleddash}{\mathbin}{AMSa}{127}
\let\Box=\square % LaTeX symbol
\re@DeclareMathSymbol{\rhd}{\mathbin}{AMSa}{66} % LaTeX symbol
\re@DeclareMathSymbol{\lhd}{\mathbin}{AMSa}{67} % LaTeX symbol
\re@DeclareMathSymbol{\unrhd}{\mathbin}{AMSa}{68} % LaTeX symbol
\re@DeclareMathSymbol{\unlhd}{\mathbin}{AMSa}{69} % LaTeX symbol
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbol B Definitions % AMSb
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\re@DeclareMathSymbol{\lvertneqq}{\mathrel}{AMSb}{0}
\re@DeclareMathSymbol{\gvertneqq}{\mathrel}{AMSb}{1}
\re@DeclareMathSymbol{\nleq}{\mathrel}{AMSb}{2}
\re@DeclareMathSymbol{\ngeq}{\mathrel}{AMSb}{3}
\re@DeclareMathSymbol{\nless}{\mathrel}{AMSb}{4}
\re@DeclareMathSymbol{\ngtr}{\mathrel}{AMSb}{5}
\re@DeclareMathSymbol{\nprec}{\mathrel}{AMSb}{6}
\re@DeclareMathSymbol{\nsucc}{\mathrel}{AMSb}{7}
\re@DeclareMathSymbol{\lneqq}{\mathrel}{AMSb}{8}
\re@DeclareMathSymbol{\gneqq}{\mathrel}{AMSb}{9}
\re@DeclareMathSymbol{\nleqslant}{\mathrel}{AMSb}{10}
\re@DeclareMathSymbol{\ngeqslant}{\mathrel}{AMSb}{11}
\re@DeclareMathSymbol{\lneq}{\mathrel}{AMSb}{12}
\re@DeclareMathSymbol{\gneq}{\mathrel}{AMSb}{13}
\re@DeclareMathSymbol{\npreceq}{\mathrel}{AMSb}{14}
\re@DeclareMathSymbol{\nsucceq}{\mathrel}{AMSb}{15}
\re@DeclareMathSymbol{\precnsim}{\mathrel}{AMSb}{16}
\re@DeclareMathSymbol{\succnsim}{\mathrel}{AMSb}{17}
\re@DeclareMathSymbol{\lnsim}{\mathrel}{AMSb}{18}
\re@DeclareMathSymbol{\gnsim}{\mathrel}{AMSb}{19}
\re@DeclareMathSymbol{\nleqq}{\mathrel}{AMSb}{20}
\re@DeclareMathSymbol{\ngeqq}{\mathrel}{AMSb}{21}
\re@DeclareMathSymbol{\precneqq}{\mathrel}{AMSb}{22}
\re@DeclareMathSymbol{\succneqq}{\mathrel}{AMSb}{23}
\re@DeclareMathSymbol{\precnapprox}{\mathrel}{AMSb}{24}
\re@DeclareMathSymbol{\succnapprox}{\mathrel}{AMSb}{25}
\re@DeclareMathSymbol{\lnapprox}{\mathrel}{AMSb}{26}
\re@DeclareMathSymbol{\gnapprox}{\mathrel}{AMSb}{27}
\re@DeclareMathSymbol{\nsim}{\mathrel}{AMSb}{28}
\re@DeclareMathSymbol{\ncong}{\mathrel}{AMSb}{29}
\re@DeclareMathSymbol{\diagup}{\mathord}{AMSb}{30}
\re@DeclareMathSymbol{\diagdown}{\mathord}{AMSb}{31}
\re@DeclareMathSymbol{\varsubsetneq}{\mathrel}{AMSb}{32}
\re@DeclareMathSymbol{\varsupsetneq}{\mathrel}{AMSb}{33}
\re@DeclareMathSymbol{\nsubseteqq}{\mathrel}{AMSb}{34}
\re@DeclareMathSymbol{\nsupseteqq}{\mathrel}{AMSb}{35}
\re@DeclareMathSymbol{\subsetneqq}{\mathrel}{AMSb}{36}
\re@DeclareMathSymbol{\supsetneqq}{\mathrel}{AMSb}{37}
\re@DeclareMathSymbol{\varsubsetneqq}{\mathrel}{AMSb}{38}
\re@DeclareMathSymbol{\varsupsetneqq}{\mathrel}{AMSb}{39}
\re@DeclareMathSymbol{\subsetneq}{\mathrel}{AMSb}{40}
\re@DeclareMathSymbol{\supsetneq}{\mathrel}{AMSb}{41}
\re@DeclareMathSymbol{\nsubseteq}{\mathrel}{AMSb}{42}
\re@DeclareMathSymbol{\nsupseteq}{\mathrel}{AMSb}{43}
\re@DeclareMathSymbol{\nparallel}{\mathrel}{AMSb}{44}
\re@DeclareMathSymbol{\nmid}{\mathrel}{AMSb}{45}
\re@DeclareMathSymbol{\nshortmid}{\mathrel}{AMSb}{46}
\re@DeclareMathSymbol{\nshortparallel}{\mathrel}{AMSb}{47}
\re@DeclareMathSymbol{\nvdash}{\mathrel}{AMSb}{48}
\re@DeclareMathSymbol{\nVdash}{\mathrel}{AMSb}{49}
\re@DeclareMathSymbol{\nvDash}{\mathrel}{AMSb}{50}
\re@DeclareMathSymbol{\nVDash}{\mathrel}{AMSb}{51}
\re@DeclareMathSymbol{\ntrianglerighteq}{\mathrel}{AMSb}{52}
\re@DeclareMathSymbol{\ntrianglelefteq}{\mathrel}{AMSb}{53}
\re@DeclareMathSymbol{\ntriangleleft}{\mathrel}{AMSb}{54}
\re@DeclareMathSymbol{\ntriangleright}{\mathrel}{AMSb}{55}
\re@DeclareMathSymbol{\nleftarrow}{\mathrel}{AMSb}{56}
\re@DeclareMathSymbol{\nrightarrow}{\mathrel}{AMSb}{57}
\re@DeclareMathSymbol{\nLeftarrow}{\mathrel}{AMSb}{58}
\re@DeclareMathSymbol{\nRightarrow}{\mathrel}{AMSb}{59}
\re@DeclareMathSymbol{\nLeftrightarrow}{\mathrel}{AMSb}{60}
\re@DeclareMathSymbol{\nleftrightarrow}{\mathrel}{AMSb}{61}
\re@DeclareMathSymbol{\divideontimes}{\mathbin}{AMSb}{62}
%\re@DeclareMathSymbol{\varnothing}{\mathord}{AMSb}{63}
\re@DeclareMathSymbol{\nexists}{\mathord}{AMSb}{64}
\re@DeclareMathSymbol{\Finv}{\mathord}{AMSb}{96}
\re@DeclareMathSymbol{\Game}{\mathord}{AMSb}{97}
\re@DeclareMathSymbol{\mho}{\mathord}{AMSb}{102}
\re@DeclareMathSymbol{\eth}{\mathord}{AMSb}{103}
\re@DeclareMathSymbol{\eqsim}{\mathrel}{AMSb}{104}
\re@DeclareMathSymbol{\beth}{\mathord}{AMSb}{105}
\re@DeclareMathSymbol{\gimel}{\mathord}{AMSb}{106}
\re@DeclareMathSymbol{\daleth}{\mathord}{AMSb}{107}
\re@DeclareMathSymbol{\lessdot}{\mathbin}{AMSb}{108}
\re@DeclareMathSymbol{\gtrdot}{\mathbin}{AMSb}{109}
\re@DeclareMathSymbol{\ltimes}{\mathbin}{AMSb}{110}
\re@DeclareMathSymbol{\rtimes}{\mathbin}{AMSb}{111}
\re@DeclareMathSymbol{\shortmid}{\mathrel}{AMSb}{112}
\re@DeclareMathSymbol{\shortparallel}{\mathrel}{AMSb}{113}
\re@DeclareMathSymbol{\smallsetminus}{\mathbin}{AMSb}{114}
\re@DeclareMathSymbol{\thicksim}{\mathrel}{AMSb}{115}
\re@DeclareMathSymbol{\thickapprox}{\mathrel}{AMSb}{116}
\re@DeclareMathSymbol{\approxeq}{\mathrel}{AMSb}{117}
\re@DeclareMathSymbol{\precapprox}{\mathrel}{AMSb}{118}
\re@DeclareMathSymbol{\succapprox}{\mathrel}{AMSb}{119}
\re@DeclareMathSymbol{\curvearrowleft}{\mathrel}{AMSb}{120}
\re@DeclareMathSymbol{\curvearrowright}{\mathrel}{AMSb}{121}
\re@DeclareMathSymbol{\digamma}{\mathord}{AMSb}{122}
\re@DeclareMathSymbol{\varkappa}{\mathord}{AMSb}{123}
\re@DeclareMathSymbol{\Bbbk}{\mathord}{AMSb}{124}
\re@DeclareMathSymbol{\hslash}{\mathord}{AMSb}{125}
\re@DeclareMathSymbol{\hbar}{\mathord}{AMSb}{126}
\re@DeclareMathSymbol{\backepsilon}{\mathrel}{AMSb}{127}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math Symbol C Definitions % symbolsC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\iftx@symbolsC
\re@DeclareMathSymbol{\mappedfromchar}{\mathrel}{symbolsC}{0}
\def\mappedfrom{\leftarrow\mappedfromchar}
\let\mapsfrom\mappedfrom
\def\longmappedfrom{\longleftarrow\mappedfromchar}
\re@DeclareMathSymbol{\Mapstochar}{\mathrel}{symbolsC}{1}
\def\Mapsto{\Mapstochar\Rightarrow}
\def\Longmapsto{\Mapstochar\Longrightarrow}
\re@DeclareMathSymbol{\Mappedfromchar}{\mathrel}{symbolsC}{2}
\def\Mappedfrom{\Leftarrow\Mappedfromchar}
\let\Mapsfrom\Mappedfrom
\def\Longmappedfrom{\Longleftarrow\Mappedfromchar}
\re@DeclareMathSymbol{\mmapstochar}{\mathrel}{symbolsC}{3}
\def\mmapsto{\mmapstochar\rightarrow}
\def\longmmapsto{\mmapstochar\longrightarrow}
\re@DeclareMathSymbol{\mmappedfromchar}{\mathrel}{symbolsC}{4}
\def\mmappedfrom{\leftarrow\mmappedfromchar}
\def\longmmappedfrom{\longleftarrow\mmappedfromchar}
\re@DeclareMathSymbol{\Mmapstochar}{\mathrel}{symbolsC}{5}
\def\Mmapsto{\Mmapstochar\Rightarrow}
\def\Longmmapsto{\Mmapstochar\Longrightarrow}
\re@DeclareMathSymbol{\Mmappedfromchar}{\mathrel}{symbolsC}{6}
\def\Mmappedfrom{\Leftarrow\Mmappedfromchar}
\def\Longmmappedfrom{\Longleftarrow\Mmappedfromchar}
\re@DeclareMathSymbol{\medcirc}{\mathbin}{symbolsC}{7}
\re@DeclareMathSymbol{\medbullet}{\mathbin}{symbolsC}{8}
\re@DeclareMathSymbol{\varparallel}{\mathrel}{symbolsC}{9}
\re@DeclareMathSymbol{\varparallelinv}{\mathrel}{symbolsC}{10}
\re@DeclareMathSymbol{\nvarparallel}{\mathrel}{symbolsC}{11}
\re@DeclareMathSymbol{\nvarparallelinv}{\mathrel}{symbolsC}{12}
\re@DeclareMathSymbol{\colonapprox}{\mathrel}{symbolsC}{13}
\re@DeclareMathSymbol{\colonsim}{\mathrel}{symbolsC}{14}
\re@DeclareMathSymbol{\Colonapprox}{\mathrel}{symbolsC}{15}
\re@DeclareMathSymbol{\Colonsim}{\mathrel}{symbolsC}{16}
\re@DeclareMathSymbol{\doteq}{\mathrel}{symbolsC}{17}
\re@DeclareMathSymbol{\multimapinv}{\mathrel}{symbolsC}{18}
\re@DeclareMathSymbol{\multimapboth}{\mathrel}{symbolsC}{19}
\re@DeclareMathSymbol{\multimapdot}{\mathrel}{symbolsC}{20}
\re@DeclareMathSymbol{\multimapdotinv}{\mathrel}{symbolsC}{21}
\re@DeclareMathSymbol{\multimapdotboth}{\mathrel}{symbolsC}{22}
\re@DeclareMathSymbol{\multimapdotbothA}{\mathrel}{symbolsC}{23}
\re@DeclareMathSymbol{\multimapdotbothB}{\mathrel}{symbolsC}{24}
\re@DeclareMathSymbol{\VDash}{\mathrel}{symbolsC}{25}
\re@DeclareMathSymbol{\VvDash}{\mathrel}{symbolsC}{26}
\re@DeclareMathSymbol{\cong}{\mathrel}{symbolsC}{27}
\re@DeclareMathSymbol{\preceqq}{\mathrel}{symbolsC}{28}
\re@DeclareMathSymbol{\succeqq}{\mathrel}{symbolsC}{29}
\re@DeclareMathSymbol{\nprecsim}{\mathrel}{symbolsC}{30}
\re@DeclareMathSymbol{\nsuccsim}{\mathrel}{symbolsC}{31}
\re@DeclareMathSymbol{\nlesssim}{\mathrel}{symbolsC}{32}
\re@DeclareMathSymbol{\ngtrsim}{\mathrel}{symbolsC}{33}
\re@DeclareMathSymbol{\nlessapprox}{\mathrel}{symbolsC}{34}
\re@DeclareMathSymbol{\ngtrapprox}{\mathrel}{symbolsC}{35}
\re@DeclareMathSymbol{\npreccurlyeq}{\mathrel}{symbolsC}{36}
\re@DeclareMathSymbol{\nsucccurlyeq}{\mathrel}{symbolsC}{37}
\re@DeclareMathSymbol{\ngtrless}{\mathrel}{symbolsC}{38}
\re@DeclareMathSymbol{\nlessgtr}{\mathrel}{symbolsC}{39}
\re@DeclareMathSymbol{\nbumpeq}{\mathrel}{symbolsC}{40}
\re@DeclareMathSymbol{\nBumpeq}{\mathrel}{symbolsC}{41}
\re@DeclareMathSymbol{\nbacksim}{\mathrel}{symbolsC}{42}
\re@DeclareMathSymbol{\nbacksimeq}{\mathrel}{symbolsC}{43}
%\re@DeclareMathSymbol{\neq}{\mathrel}{symbolsC}{44}
% \let\ne=\neq
\re@DeclareMathSymbol{\nasymp}{\mathrel}{symbolsC}{45}
\re@DeclareMathSymbol{\nequiv}{\mathrel}{symbolsC}{46}
\re@DeclareMathSymbol{\nsim}{\mathrel}{symbolsC}{47}
\re@DeclareMathSymbol{\napprox}{\mathrel}{symbolsC}{48}
%\re@DeclareMathSymbol{\nsubset}{\mathrel}{symbolsC}{49}
%\re@DeclareMathSymbol{\nsupset}{\mathrel}{symbolsC}{50}
\re@DeclareMathSymbol{\nll}{\mathrel}{symbolsC}{51}
\re@DeclareMathSymbol{\ngg}{\mathrel}{symbolsC}{52}
\re@DeclareMathSymbol{\nthickapprox}{\mathrel}{symbolsC}{53}
\re@DeclareMathSymbol{\napproxeq}{\mathrel}{symbolsC}{54}
\re@DeclareMathSymbol{\nprecapprox}{\mathrel}{symbolsC}{55}
\re@DeclareMathSymbol{\nsuccapprox}{\mathrel}{symbolsC}{56}
\re@DeclareMathSymbol{\npreceqq}{\mathrel}{symbolsC}{57}
\re@DeclareMathSymbol{\nsucceqq}{\mathrel}{symbolsC}{58}
\re@DeclareMathSymbol{\nsimeq}{\mathrel}{symbolsC}{59}
%\re@DeclareMathSymbol{\notin}{\mathrel}{symbolsC}{60}
%\re@DeclareMathSymbol{\notni}{\mathrel}{symbolsC}{61}
% \let\notowns=\notni
\re@DeclareMathSymbol{\nSubset}{\mathrel}{symbolsC}{62}
\re@DeclareMathSymbol{\nSupset}{\mathrel}{symbolsC}{63}
\re@DeclareMathSymbol{\nsqsubseteq}{\mathrel}{symbolsC}{64}
\re@DeclareMathSymbol{\nsqsupseteq}{\mathrel}{symbolsC}{65}
\re@DeclareMathSymbol{\coloneqq}{\mathrel}{symbolsC}{66}
\re@DeclareMathSymbol{\eqqcolon}{\mathrel}{symbolsC}{67}
%\re@DeclareMathSymbol{\coloneq}{\mathrel}{symbolsC}{68}
%\re@DeclareMathSymbol{\eqcolon}{\mathrel}{symbolsC}{69}
\re@DeclareMathSymbol{\Coloneqq}{\mathrel}{symbolsC}{70}
\re@DeclareMathSymbol{\Eqqcolon}{\mathrel}{symbolsC}{71}
\re@DeclareMathSymbol{\Coloneq}{\mathrel}{symbolsC}{72}
\re@DeclareMathSymbol{\Eqcolon}{\mathrel}{symbolsC}{73}
\re@DeclareMathSymbol{\strictif}{\mathrel}{symbolsC}{74}
\re@DeclareMathSymbol{\strictfi}{\mathrel}{symbolsC}{75}
\re@DeclareMathSymbol{\strictiff}{\mathrel}{symbolsC}{76}
\re@DeclareMathSymbol{\invamp}{\mathbin}{symbolsC}{77}
\re@DeclareMathDelimiter{\lbag}{\mathopen}{symbolsC}{78}{largesymbolsTXA}{48}
\re@DeclareMathDelimiter{\rbag}{\mathclose}{symbolsC}{79}{largesymbolsTXA}{49}
\re@DeclareMathSymbol{\Lbag}{\mathopen}{symbolsC}{80}
\re@DeclareMathSymbol{\Rbag}{\mathclose}{symbolsC}{81}
\re@DeclareMathSymbol{\circledless}{\mathrel}{symbolsC}{82}
\re@DeclareMathSymbol{\circledgtr}{\mathrel}{symbolsC}{83}
\re@DeclareMathSymbol{\circledwedge}{\mathbin}{symbolsC}{84}
\re@DeclareMathSymbol{\circledvee}{\mathbin}{symbolsC}{85}
\re@DeclareMathSymbol{\circledbar}{\mathbin}{symbolsC}{86}
\re@DeclareMathSymbol{\circledbslash}{\mathbin}{symbolsC}{87}
\re@DeclareMathSymbol{\lJoin}{\mathrel}{symbolsC}{88}
\re@DeclareMathSymbol{\rJoin}{\mathrel}{symbolsC}{89}
\re@DeclareMathSymbol{\Join}{\mathrel}{symbolsC}{90}
\let\lrJoin=\Join
\re@DeclareMathSymbol{\openJoin}{\mathrel}{symbolsC}{91}
\re@DeclareMathSymbol{\lrtimes}{\mathrel}{symbolsC}{92}
% \let\bowtie\lrtimes
\re@DeclareMathSymbol{\opentimes}{\mathrel}{symbolsC}{93}
\re@DeclareMathSymbol{\Diamond}{\mathord}{symbolsC}{94}
\re@DeclareMathSymbol{\Diamondblack}{\mathord}{symbolsC}{95}
\re@DeclareMathSymbol{\nplus}{\mathbin}{symbolsC}{96}
\re@DeclareMathSymbol{\nsqsubset}{\mathrel}{symbolsC}{97}
\re@DeclareMathSymbol{\nsqsupset}{\mathrel}{symbolsC}{98}
\re@DeclareMathSymbol{\dashleftarrow}{\mathrel}{symbolsC}{99}
\re@DeclareMathSymbol{\dashrightarrow}{\mathrel}{symbolsC}{100}
\let\dasharrow\dashrightarrow
\re@DeclareMathSymbol{\dashleftrightarrow}{\mathrel}{symbolsC}{101}
\re@DeclareMathSymbol{\leftsquigarrow}{\mathrel}{symbolsC}{102}
\re@DeclareMathSymbol{\ntwoheadrightarrow}{\mathrel}{symbolsC}{103}
\re@DeclareMathSymbol{\ntwoheadleftarrow}{\mathrel}{symbolsC}{104}
\re@DeclareMathSymbol{\boxast}{\mathbin}{symbolsC}{105}
\re@DeclareMathSymbol{\boxbslash}{\mathbin}{symbolsC}{106}
\re@DeclareMathSymbol{\boxbar}{\mathbin}{symbolsC}{107}