%%
%% This is file `chairxmath.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% chairxmath.dtx  (with options: `chairxmath')
%% chairxmathFonts.dtx  (with options: `chairxmathFonts')
%% chairxmathDelimiters.dtx  (with options: `chairxmathDelimiters')
%% chairxmathDecoration.dtx  (with options: `chairxmathDecoration')
%% chairxmathGeneral.dtx  (with options: `chairxmathGeneral')
%% chairxmathAlgebra.dtx  (with options: `chairxmathAlgebra')
%% chairxmathAnalysis.dtx  (with options: `chairxmathAnalysis')
%% chairxmathCategory.dtx  (with options: `chairxmathCategory')
%% chairxmathDiffgeo.dtx  (with options: `chairxmathDiffgeo')
%% chairxmathLinalg.dtx  (with options: `chairxmathLinalg')
%% chairxmathStatistics.dtx  (with options: `chairxmathStatistics')
%% chairxmathTopology.dtx  (with options: `chairxmathTopology')
%% This is a generated file.
%% 
%% Copyright (C) 2018 by ChairX
%% 
%% This file may be distributed and/or modified under the
%% conditions of the LaTeX Project Public License, either
%% version 1.3 of this license or (at your option) any later
%% version.  The latest version of this license is in:
%% 
%% http://www.latex-project.org/lppl.txt
%% and version 1.3 or later is part of all distributions of
%% 
%% LaTeX version 2005/12/01 or later.
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{chairxmath}
[2021/07/29 v1.0.0 First major release]

\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{mathtools}
\DeclareSymbolFont{stmry}{U}{stmry}{m}{n}
\SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n}
\RequirePackage{xkeyval}
\RequirePackage{tensor}
\RequirePackage{suffix}
\newif\if@loadmath \@loadmathtrue
\if@loadmath
\DeclareMathAlphabet{\ch@airxmathbbm}{U}{bbm}{m}{n}
\SetMathAlphabet\ch@airxmathbbm{bold}{U}{bbm}{bx}{n}
\renewcommand{\mathbb}[1]{\ch@airxmathbbm{#1}}
\DeclareMathAlphabet{\mathscr}{U}{rsfso}{m}{n}
\DeclareSymbolFont{EulerScript}{U}{eus}{m}{n}
\SetSymbolFont{EulerScript}{bold}{U}{eus}{b}{n}
\DeclareSymbolFontAlphabet\mathcal{EulerScript}
\define@key[chairx]{fonts}{algebrafont}{
    \providecommand{\ch@irxalgebrafont}[1]{ }
    \renewcommand{\ch@irxalgebrafont}{#1}
}
\define@key[chairx]{fonts}{basisfont}{
\providecommand{\ch@irxbasisfont}[1]{ }
\renewcommand{\ch@irxbasisfont}{#1}
}
\define@key[chairx]{fonts}{categoryfont}{
    \providecommand{\ch@irxcategoryfont}[1]{ }
    \renewcommand{\ch@irxcategoryfont}{#1}
}
\define@key[chairx]{fonts}{categorynamefont}{
    \providecommand{\ch@irxcategorynamefont}[1]{ }
    \renewcommand{\ch@irxcategorynamefont}{#1}
}
\define@key[chairx]{fonts}{fieldfont}{
\providecommand{\ch@irxfieldfont}[1]{ }
\renewcommand{\ch@irxfieldfont}{#1}
}
\define@key[chairx]{fonts}{filterfont}{
\providecommand{\ch@irxfilterfont}[1]{ }
\renewcommand{\ch@irxfilterfont}{#1}
}
\define@key[chairx]{fonts}{functorfont}{
\providecommand{\ch@irxfunctorfont}[1]{ }
\renewcommand{\ch@irxfunctorfont}{#1}
}
\define@key[chairx]{fonts}{gerstenhaberfont}{
\providecommand{\ch@irxgerstenhaberfont}[1]{ }
\renewcommand{\ch@irxgerstenhaberfont}{#1}
}
\define@key[chairx]{fonts}{groupfont}{
\providecommand{\ch@irxgroupfont}[1]{ }
\renewcommand{\ch@irxgroupfont}{#1}
}
\define@key[chairx]{fonts}{groupoidfont}{
\providecommand{\ch@irxgroupoidfont}[1]{ }
\renewcommand{\ch@irxgroupoidfont}{#1}
}
\define@key[chairx]{fonts}{hilbertfont}{
\providecommand{\ch@irxhilbertfont}[1]{ }
\renewcommand{\ch@irxhilbertfont}{#1}
}
\define@key[chairx]{fonts}{liealgfont}{
\providecommand{\ch@irxliealgfont}[1]{ }
\renewcommand{\ch@irxliealgfont}{#1}
}
\define@key[chairx]{fonts}{modulefont}{
\providecommand{\ch@irxmodulefont}[1]{ }
\renewcommand{\ch@irxmodulefont}{#1}
}
\define@key[chairx]{fonts}{prehilbfont}{
\providecommand{\ch@irxprehilbfont}[1]{ }
\renewcommand{\ch@irxprehilbfont}{#1}
}
\define@key[chairx]{fonts}{operatorfont}{
    \providecommand{\ch@irxoperatorfont}[1]{ }
    \renewcommand{\ch@irxoperatorfont}{#1}
}
\define@key[chairx]{fonts}{ringfont}{
\providecommand{\ch@irxringfont}[1]{ }
\renewcommand{\ch@irxringfont}{#1}
}
\define@key[chairx]{fonts}{scriptfont}{
    \providecommand{\ch@irxscriptfont}[1]{ }
    \renewcommand{\ch@irxscriptfont}{#1}
}
\define@key[chairx]{fonts}{sheaffont}{
\providecommand{\ch@irxsheaffont}[1]{ }
\renewcommand{\ch@irxsheaffont}{#1}
}
\define@key[chairx]{fonts}{spacefont}{
    \providecommand{\ch@irxspacefont}[1]{ }
    \renewcommand{\ch@irxspacefont}{#1}
}
\define@key[chairx]{fonts}{topologyfont}{
\providecommand{\ch@irxtopologyfont}[1]{ }
\renewcommand{\ch@irxtopologyfont}{#1}
}
\newcommand{\chairxfonts}[1]{
  \setkeys[chairx]{fonts}{#1}
}
\chairxfonts{
    algebrafont = \mathscr,
    basisfont = \mathit,
    categoryfont = \mathfrak,
    categorynamefont = \mathsf,
    fieldfont = \mathbb,
    filterfont = \mathfrak,
    functorfont = \mathsf,
    groupfont = \mathrm,
    groupoidfont = \mathfrak,
    gerstenhaberfont = \mathfrak,
    hilbertfont = \mathfrak,
    liealgfont = \mathfrak,
    modulefont = \mathscr,
    prehilbfont = \mathcal,
    operatorfont = \mathrm,
    ringfont = \mathsf,
    scriptfont = \mathrm,
    sheaffont = \mathscr,
    spacefont = \mathscr,
    topologyfont = \mathscr
}
\newcommand{\ch@irxfont}[1]{\fontfamily{#1}\fontencoding{U}\fontseries{m}\fontshape{n}\selectfont}
\newcommand{\ch@irxsymbol}[2]{{\ch@irxfont{#1}\char#2}}
\newcommand\ch@irxmathsymbol[3][\mathord]{%
  #1{\ch@irxm@thsymbol{#2}{#3}}}
\def\ch@irxm@thsymbol#1#2{\mathchoice
  {\@ch@irxm@thsymbol{#1}{#2}\tf@size}
  {\@ch@irxm@thsymbol{#1}{#2}\tf@size}
  {\@ch@irxm@thsymbol{#1}{#2}\sf@size}
  {\@ch@irxm@thsymbol{#1}{#2}\ssf@size}}
\def\@ch@irxm@thsymbol#1#2#3{\mbox{\fontsize{#3}{#3}\ch@irxsymbol{#1}{#2}}}
\fi
\if@loadmath
\newcommand{\vast}{\bBigg@{4}}
\newcommand{\Vast}{\bBigg@{5}}
\newcommand{\vastl}{\mathopen\vast}
\newcommand{\vastm}{\mathrel\vast}
\newcommand{\vastr}{\mathclose\vast}
\newcommand{\Vastl}{\mathopen\Vast}
\newcommand{\Vastm}{\mathrel\Vast}
\newcommand{\Vastr}{\mathclose\Vast}
\fi
\if@loadmath
\let\originaltensor\tensor
\DeclareRobustCommand\decorate{\originaltensor}
\newcommand{\deco}[5]{\decorate*[^{#1}_{#2}]{#3}{^{#4}_{#5}}}
\newcommand{\script}[1]{\ch@irxscriptfont{#1}}
\fi
\if@loadmath
\newcommand{\I}{\mathrm{i}}
\newcommand{\E}{\mathrm{e}}
\newcommand{\D}{\mathop{}\!\mathrm{d}}
\newcommand{\cc}[1]{\overline{{#1}}}
\newcommand{\sign}{\operatorname{\ch@irxoperatorfont{sign}}}
\newcommand{\RE}{\operatorname{\ch@irxoperatorfont{Re}}}
\newcommand{\IM}{\operatorname{\ch@irxoperatorfont{Im}}}
\newcommand{\Unit}{\mathbb{1}}
\newcommand{\const}{\operatorname{\mathit{const}}}
\newcommand{\canonical}{\ch@irxscriptfont{can}}
\newcommand{\pt}{\ch@irxoperatorfont{pt}}
\newcommand{\at}[2][\big]{#1\vert_{#2}}
\newcommand{\Map}{\ch@irxoperatorfont{Map}}
\newcommand{\Bij}{\ch@irxoperatorfont{Bij}}
\newcommand{\argument}{\,\cdot\,}
\newcommand{\domain}{\operatorname{\ch@irxoperatorfont{dom}}}
\newcommand{\range}{\operatorname{\ch@irxoperatorfont{range}}}
\newcommand{\id}{\operatorname{\ch@irxoperatorfont{id}}}
\newcommand{\pr}{\operatorname{\ch@irxoperatorfont{pr}}}
\newcommand{\inv}{\operatorname{\ch@irxoperatorfont{inv}}}
\newcommand{\ev}{\operatorname{\ch@irxoperatorfont{ev}}}
\newcommand{\image}{\operatorname{\ch@irxoperatorfont{im}}}
\newcommand{\graph}{\operatorname{\ch@irxoperatorfont{graph}}}
\newcommand{\coimage}{\operatorname{\ch@irxoperatorfont{coim}}}
\newcommand{\coker}{\operatorname{\ch@irxoperatorfont{coker}}}
\newcommand{\operator}[1]{\operatorname{\ch@irxoperatorfont{#1}}}
\newcommand{\later}{\mathrel{\succcurlyeq}}
\newcommand{\earlier}{\mathrel{\preccurlyeq}}
\DeclareRobustCommand\big@p[2][1]{%
\mathop{\vphantom{\sum}\mathpalette\bigop@{{#1}{#2}}}\slimits@
}
\newcommand{\bigop@}[2]{\bigop@@#1#2}
\newcommand{\bigop@@}[3]{%
\vcenter{
\sbox\z@{$#1\sum$}
\hbox{\resizebox{\ifx#1\displaystyle#2\fi\dimexpr\ht\z@+\dp\z@}{!}{$\m@th#3$}}
}
}
\newcommand{\bigplus}{\DOTSB\big@p{+}}
\newcommand{\bigtimes}{\DOTSB\big@p{\times}}
\newcommand{\biprod}{\DOTSB\big@p{\mathrel{\prod\hspace{-0.4cm}\coprod}}}
\newcommand{\smiley}{\ch@irxmathsymbol[\mathord]{wasy}{44}}
\newcommand{\frownie}{\ch@irxmathsymbol[\mathord]{wasy}{47}}
\newcommand{\heart}{\heartsuit}
\fi
\if@loadmath
\newcommand{\field}[1]{\ch@irxfieldfont{#1}}
\newcommand{\ring}[1]{\ch@irxringfont{#1}}
\newcommand{\group}[1]{\ch@irxgroupfont{#1}}
\newcommand{\algebra}[1]{\ch@irxalgebrafont{#1}}
\newcommand{\module}[1]{\ch@irxmodulefont{#1}}
\newcommand{\liealg}[1]{\ch@irxliealgfont{#1}}
\newcommand{\MC}{{\scriptscriptstyle\ch@irxscriptfont{MC}}}
\newcommand{\gerstenhaber}[1] {\ch@irxgerstenhaberfont{#1}}
\newcommand{\Pol}{\ch@irxoperatorfont{Pol}}
\newcommand{\lmult}{\operatorname{\ch@irxoperatorfont{\ell}}}
\newcommand{\rmult}{\operatorname{\ch@irxoperatorfont{r}}}
\newcommand{\Lmult}{\operatorname{\ch@irxoperatorfont{L}}}
\newcommand{\Rmult}{\operatorname{\ch@irxoperatorfont{R}}}
\newcommand{\Center}{\mathscr{Z}}
\newcommand{\ad}{\operatorname{\ch@irxoperatorfont{ad}}}
\newcommand{\Ad}{\operatorname{\ch@irxoperatorfont{Ad}}}
\newcommand{\Conj}{\operatorname{\ch@irxoperatorfont{Conj}}}
\newcommand{\acts}{\mathbin{\triangleright}}
\newcommand{\racts}{\mathbin{\triangleleft}}
\newcommand{\Char}{\ch@irxoperatorfont{char}}
\newcommand{\modulo}{\operatorname{\ch@irxoperatorfont{mod}}}
\newcommand{\Clifford}{\operatorname{\ch@irxoperatorfont{Cl}}}
\newcommand{\cClifford}{\operatorname{\mathbb{C}\ch@irxoperatorfont{l}}}
\newcommand{\Der}{\operatorname{\ch@irxoperatorfont{Der}}}
\WithSuffix\newcommand\Der*{\decorate[^*]{\textrm{-}\Der}{}}
\newcommand{\InnDer}{\operatorname{\ch@irxoperatorfont{InnDer}}}
\WithSuffix\newcommand\InnDer*{\decorate[^*]{\textrm{-}\InnDer}{}}
\newcommand{\OutDer}{\operatorname{\ch@irxoperatorfont{OutDer}}}
\WithSuffix\newcommand\OutDer*{\decorate[^*]{\textrm{-}\OutDer}{}}
\newcommand{\InnAut}{\operatorname{\ch@irxoperatorfont{InnAut}}}
\WithSuffix\newcommand\InnAut*{\decorate[^*]{\textrm{-}\InnAut}{}}
\newcommand{\OutAut}{\operatorname{\ch@irxoperatorfont{OutAut}}}
\WithSuffix\newcommand\OutAut*{\decorate[^*]{\textrm{-}\OutAut}{}}
\newcommand{\formal}[1]{\ch@irxllbbracket #1\ch@irxrrbbracket}
\newcommand{\laurent}[1]{(\!(#1)\!)}
\newcommand{\sweedler}[1]{{\scriptscriptstyle(#1)}}
\newcommand{\algebras}{\categoryname{alg}}
\WithSuffix\newcommand\algebras*{\decorate[^*]{\textrm{-}\algebras}{}}
\newcommand{\Algebras}{\categoryname{Alg}}
\WithSuffix\newcommand\Algebras*{\decorate[^*]{\textrm{-}\Algebras}{}}
\newcommand{\reps}{\categoryname{rep}}
\WithSuffix\newcommand\reps*{\decorate[^*]{\textrm{-}\reps}{}}
\newcommand{\Reps}{\categoryname{Rep}}
\WithSuffix\newcommand\Reps*{\decorate[^*]{\textrm{-}\Reps}{}}
\newcommand{\PoissonAlg}{\categoryname{PoissonAlg}}
\WithSuffix\newcommand\PoissonAlg*{\decorate[^*]{\textrm{-}\PoissonAlg}{}}
\newcommand{\modules}{\categoryname{mod}}
\WithSuffix\newcommand\modules*{\decorate[^*]{\textrm{-}\modules}{}}
\newcommand{\Leftmodules}[1]{{#1}\textsf{-}\categoryname{mod}}
\newcommand{\Rightmodules}[2][]{\categoryname{mod}_{#1}\textsf{-}{#2}}
\newcommand{\Modules}{\categoryname{Mod}}
\WithSuffix\newcommand\Modules*{\decorate[^*]{\textrm{-}\Modules}{}}
\newcommand{\LeftModules}[1]{{#1}\textsf{-}\categoryname{Mod}}
\newcommand{\RightModules}[2][]{\categoryname{Mod}_{#1}\textsf{-}{#2}}
\newcommand{\Bimodules}{\categoryname{Bimod}}
\WithSuffix\newcommand\Bimodules*{\decorate[^*]{\textrm{-}\Bimodules}{}}
\newcommand{\Rings}{\categoryname{Ring}}
\newcommand{\Groups}{\categoryname{Group}}
\newcommand{\Ab}{\categoryname{Ab}}
\newcommand{\Lattices}{\categoryname{Lattice}}
\newcommand{\Sets}{\categoryname{Set}}
\newcommand{\Vect}{\categoryname{Vect}}
\newcommand{\LieAlgs}{\categoryname{LieAlg}}
\newcommand{\Posets}{\categoryname{Poset}}
\newcommand{\Directed}{\categoryname{Directed}}
\newcommand{\GSets}[1][{G}]{{#1}\textrm{-}\Sets}
\newcommand{\Groupoids}{\categoryname{Groupoid}}
\fi
\if@loadmath
\newcommand{\vol}{\ch@irxoperatorfont{vol}}
\newcommand{\complete}[1]{\widehat{#1}}
\newcommand{\Ball}{\ch@irxoperatorfont{B}}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\newcommand{\@supnormstar}[1]{\norm*{#1}_\infty}
\newcommand{\@supnormnostar}[2][]{\norm[#1]{#2}_\infty}
\newcommand{\supnorm}{\@ifstar\@supnormstar\@supnormnostar}
\newcommand{\expands}[1][2.5]{\mathrel{\scalebox{#1}[1.1]{$\sim$}}}
\newcommand{\std}{{\scriptscriptstyle{\ch@irxscriptfont{std}}}}
\newcommand{\Weyl}{{\scriptscriptstyle{\ch@irxscriptfont{Weyl}}}}
\newcommand{\Op}{\operatorname{Op}}
\newcommand{\Opstd}{\operatorname{Op}_\std}
\newcommand{\OpWeyl}{\operatorname{Op}_\Weyl}
\newcommand{\spacename}[1]{\ch@irxspacefont{#1}}
\newcommand{\Bounded}{\ch@irxspacefont{B}}
\newcommand{\Continuous}{\ch@irxspacefont{C}}
\newcommand{\Contbound}{\Continuous_{\mathrm{b}}}
\newcommand{\Fun}[1][k]{\ch@irxspacefont{C}^{#1}}
\newcommand{\Cinfty}{\Fun[\infty]}
\newcommand{\Comega}{\Fun[\omega]}
\newcommand{\Holomorphic}{\ch@irxspacefont{O}}
\newcommand{\AntiHolomorphic}{\cc{\Holomorphic}}
\newcommand{\Schwartz}{\ch@irxspacefont{S}}
\newcommand{\Riemann}{\ch@irxspacefont{R}}
\newcommand{\singsupp}{\operatorname{sing\,supp}}
\newcommand{\seminorm}[1]{\mathrm{#1}}
\newcommand{\ord}{\operatorname{ord}}
\newcommand{\conv}{\operatorname{conv}}
\newcommand{\extreme}{\operatorname{extreme}}
\newcommand{\hilbert}[1]{\ch@irxhilbertfont{#1}}
\newcommand{\prehilb}[1]{\ch@irxprehilbfont{#1}}
\newcommand{\Adjointable}[1][{}]{\mathfrak{B}_{\scriptscriptstyle{#1}}}
\newcommand{\Finite}[1][{}]{\mathfrak{F}_{\scriptscriptstyle{#1}}}
\newcommand{\Compact}[1][{}]{\mathfrak{K}_{\scriptscriptstyle{#1}}}
\newcommand{\opdomain}{\ch@irxhilbertfont{D}}
\newcommand{\spec}{\operatorname{\ch@irxoperatorfont{spec}}}
\newcommand{\closure}[1]{\overline{#1}}
\newcommand{\res}{\operatorname{\ch@irxoperatorfont{res}}}
\newcommand{\Res}{\operatorname{\ch@irxoperatorfont{Res}}}
\newcommand{\specrad}{\operatorname{\varrho}}
\newcommand{\slim}{\operatorname*{\ch@irxoperatorfont{s-lim}}}
\newcommand{\wlim}{\operatorname*{\ch@irxoperatorfont{w-lim}}}
\DeclarePairedDelimiter{\ketbr@}{\vert}{\vert}
\DeclarePairedDelimiter{\ket}{\vert}{\rangle}
\DeclarePairedDelimiter{\bra}{\langle}{\vert}
\newcommand{\braket}[3][]{\SP[#1]{#2 \,#1\vert\, #3}}
\newcommand{\ketbra}[3][]{\ketbr@[#1]{#2 #1\rangle #1\langle #3}}
\newcommand{\Spec}{\operatorname{\ch@irxoperatorfont{Spec}}}
\newcommand{\Rad}{\operatorname{\ch@irxoperatorfont{Rad}}}
\newcommand{\ind}{\operatorname{\ch@irxoperatorfont{ind}}}
\newcommand{\Measurable}{\ch@irxspacefont{M}}
\newcommand{\Meas}{\ch@irxoperatorfont{Meas}}
\newcommand{\BoundMeas}{\ch@irxspacefont{BM}}
\newcommand{\Lp}[1][{p}]{\mathrm{L}^{#1}}
\newcommand{\Lone}{\Lp[1]}
\newcommand{\Ltwo}{\Lp[2]}
\newcommand{\Linfty}{\Lp[\infty]}
\newcommand{\Intp}[1][{p}]{\ch@irxspacefont{L}^{#1}}
\newcommand{\Intone}{\Intp[1]}
\newcommand{\Inttwo}{\Intp[2]}
\newcommand{\Intinfty}{\Intp[\infty]}
\newcommand{\essrange}{\operatorname{\ch@irxoperatorfont{ess\,range}}}
\newcommand*{\esssup}{\operatorname*{\ch@irxoperatorfont{ess}\,\ch@irxoperatorfont{\sup}}}
\newcommand{\@esssupnormstar}[1]{\norm*{#1}_{\esssup}}
\newcommand{\@esssupnormnostar}[2][]{\norm[#1]{#2}_{\esssup}}
\newcommand{\esssupnorm}{\@ifstar\@esssupnormstar\@esssupnormnostar}
\newcommand{\ac}{\ch@irxscriptfont{ac}}
\newcommand{\sing}{\ch@irxscriptfont{sing}}
\newcommand{\indlim}{\operatorname*{{ind\,lim}}}
\renewcommand{\projlim}{\operatorname*{{proj\,lim}}}
\fi
\if@loadmath
\newcommand{\category}[1]{\ch@irxcategoryfont{#1}}
\newcommand{\categoryname}[1]{\ch@irxcategorynamefont{#1}}
\newcommand{\functor}[1]{\ch@irxfunctorfont{#1}}
\newcommand{\groupoid}[1]{\ch@irxgroupoidfont{#1}}
\newcommand{\source}{\ch@irxoperatorfont{source}}
\newcommand{\target}{\ch@irxoperatorfont{target}}
\newcommand{\unit}{\ch@irxoperatorfont{unit}}
\newcommand{\opp}{\ch@irxscriptfont{opp}}
\newcommand{\asso}{\ch@irxoperatorfont{asso}}
\newcommand{\Hom}{\operatorname{\ch@irxoperatorfont{Hom}}}
\newcommand{\End}{\operatorname{\ch@irxoperatorfont{End}}}
\newcommand{\Aut}{\operatorname{\ch@irxoperatorfont{Aut}}}
\WithSuffix\newcommand\Aut*{\decorate[^*]{\textrm{-}\Aut}{}}
\newcommand{\Iso}{\operatorname{\ch@irxoperatorfont{Iso}}}
\WithSuffix\newcommand\Iso*{\decorate[^*]{\textrm{-}\Iso}{}}
\newcommand{\Obj}{\operatorname{\ch@irxoperatorfont{Obj}}}
\newcommand{\Morph}{\operatorname{\ch@irxoperatorfont{Morph}}}
\newcommand{\colim}{\operatorname*{{colim}}}
\fi
\if@loadmath
\newcommand{\Lie}{\mathscr{L}}
\DeclarePairedDelimiter{\ch@irxbracket}{[}{]}
\DeclareMathDelimiter\ch@irxllbbracket{\mathopen}{stmry}{"4A}{stmry}{"71}
\DeclareMathDelimiter\ch@irxrrbbracket{\mathclose}{stmry}{"4B}{stmry}{"79}
\DeclarePairedDelimiter{\ch@irxbbracket}{\ch@irxllbbracket}{\ch@irxrrbbracket}
\newcommand{\@schoutenstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{S}}}
\newcommand{\@schoutennostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{S}}}
\newcommand{\Schouten}{\@ifstar\@schoutenstar\@schoutennostar}
\newcommand{\Forms}{\Omega}
\newcommand{\ZdR}{\ch@irxoperatorfont{Z}_{\scriptscriptstyle\mathrm{dR}}}
\newcommand{\BdR}{\ch@irxoperatorfont{B}_{\scriptscriptstyle\ch@irxscriptfont{dR}}}
\newcommand{\HdR}{\ch@irxoperatorfont{H}_{\scriptscriptstyle\ch@irxscriptfont{dR}}}
\newcommand{\Diffeo}{\operatorname{\ch@irxoperatorfont{Diffeo}}}
\newcommand{\Diffop}{\operatorname{\ch@irxoperatorfont{DiffOp}}}
\newcommand{\loc}{\ch@irxscriptfont{loc}}
\newcommand{\germ}{\operatorname{\ch@irxoperatorfont{germ}}}
\newcommand{\prol}{\ch@irxoperatorfont{prol}}
\newcommand{\@nrbracketstar}[1]{\ch@irxbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{NR}}}
\newcommand{\@nrbracketnostar}[2][]{\ch@irxbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{NR}}}
\newcommand{\NRbracket}{\@ifstar\@nrbracketstar\@nrbracketnostar}
\newcommand{\@fnbracketstar}[1]{\ch@irxbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{FN}}}
\newcommand{\@fnbracketnostar}[2][]{\ch@irxbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{FN}}}
\newcommand{\FNbracket}{\@ifstar\@fnbracketstar\@fnbracketnostar}
\newcommand{\Manifolds}{\categoryname{\categoryname{Manifold}}}
\newcommand{\lefttriv}{\ch@irxoperatorfont{left}}
\newcommand{\righttriv}{\ch@irxoperatorfont{right}}
\newcommand{\Gau}{\operatorname{\ch@irxoperatorfont{Gau}}}
\newcommand{\Conn}{\operatorname{\ch@irxoperatorfont{Conn}}}
\newcommand{\ratio}{\ch@irxoperatorfont{r}}
\newcommand{\Parallel}{\operatorname{\ch@irxoperatorfont{P}}}
\newcommand{\CE}{{\scriptscriptstyle{\ch@irxscriptfont{CE}}}}
\newcommand{\HCE}{\ch@irxoperatorfont{H}_\CE}
\newcommand{\fund}{\ch@irxoperatorfont{fund}}
\newcommand{\Universal}{\operatorname{\ch@irxoperatorfont{U}}}
\newcommand{\BCH}{\ch@irxscriptfont{\scriptscriptstyle{BCH}}}
\newcommand{\LieGroups}{\categoryname{\categoryname{LieGroup}}}
\newcommand{\Principal}{\categoryname{\categoryname{Principal}}}
\newcommand{\GPrincipal}[1][G]{#1\categoryname{\textrm{-}\categoryname{Principal}}}
\newcommand{\Fiber}{\categoryname{Fiber}}
\newcommand{\FFiber}[1][F]{#1\categoryname{\textrm{-}\categoryname{Fiber}}}
\newcommand{\Pin}{\group{Pin}}
\newcommand{\Spin}{\group{Spin}}

\newcommand{\nablaLC}{\nabla^{\scriptscriptstyle\ch@irxscriptfont{LC}}}
\newcommand{\Laplace}{\Delta}
\DeclareMathSymbol\dAlembert{\mathord}{AMSa}{"03}
\newcommand{\feynman}[1]{\ooalign{$#1$\cr\hidewidth$\raise0.19ex\hbox{/}$\hidewidth\cr}}

\newcommand{\Dirac}{\feynman{D}}
\newcommand{\rotation}{\operatorname{\ch@irxoperatorfont{rot}}}
\newcommand{\curl}{\operatorname{\ch@irxoperatorfont{curl}}}
\newcommand{\divergence}{\operatorname{\ch@irxoperatorfont{div}}}
\newcommand{\gradient}{\operatorname{\ch@irxoperatorfont{grad}}}
\newcommand{\Tor}{\operatorname{\ch@irxoperatorfont{Tor}}}
\newcommand{\Ric}{\operatorname{\ch@irxoperatorfont{Ric}}}
\newcommand{\scal}{\operatorname{\ch@irxoperatorfont{scal}}}
\newcommand{\Riem}{\operatorname{\ch@irxoperatorfont{Riem}}}
\newcommand{\Hessian}{\ch@irxoperatorfont{Hessian}}
\newcommand{\hodge}{\operatorname{\star}}
\newcommand{\Nijenhuis}{\operatorname{\ch@irxoperatorfont{Nij}}}
\newcommand{\del}{\mathop{}\!\partial}
\newcommand{\delbar}{\mathop{}\!\cc{\partial}}
\newcommand{\FS}{{\scriptscriptstyle{\ch@irxscriptfont{FS}}}}
\newcommand{\Lift}{{\scriptscriptstyle{\ch@irxscriptfont{Lift}}}}
\newcommand{\ver}{\ch@irxscriptfont{ver}}
\newcommand{\hor}{\ch@irxscriptfont{hor}}
\newcommand{\Ver}{\operatorname{\ch@irxoperatorfont{Ver}}}
\newcommand{\Hor}{\operatorname{\ch@irxoperatorfont{Hor}}}
\newcommand{\Sec}[1][k]{\Gamma^{#1}}
\newcommand{\Secinfty}{\Sec[\infty]}
\newcommand{\HolSec}{\Sec[]_{\ch@irxscriptfont{hol}}}
\newcommand{\SymD}{\mathop{}\!\ch@irxoperatorfont{D}}
\newcommand{\Densities}[1][n]{\abs{\Lambda^{#1}}}
\newcommand{\MeasurableSections}{\ch@irxspacefont{M}\Sec[]}
\newcommand{\IntpSections}[1][p]{\Intp[#1]\Sec[]}
\newcommand{\IntegrableSections}{\IntpSections[1]}
\newcommand{\Translation}{\ch@irxoperatorfont{T}}
\newcommand{\frames}[1]{\ch@irxoperatorfont{#1}}
\newcommand{\Frames}{\operatorname{\ch@irxoperatorfont{Frames}}}
\newcommand{\FDiff}{\ch@irxoperatorfont{F}}
\newcommand{\Sympl}{\operatorname{\ch@irxgroupfont{Sympl}}}
\newcommand{\Jacobiator}[1][\pi]{\operatorname{\ch@irxoperatorfont{Jac}}_{#1}}
\newcommand{\red}{\ch@irxscriptfont{red}}
\newcommand{\Hess}{\ch@irxoperatorfont{Hess}}
\newcommand{\KKS}{{\scriptscriptstyle\ch@irxscriptfont{KKS}}}
\newcommand{\@courantstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{C}}}
\newcommand{\@courantnostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{C}}}
\newcommand{\Courant}{\@ifstar\@courantstar\@courantnostar}
\newcommand{\@dorfmanstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{D}}}
\newcommand{\@dorfmannostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{D}}}
\newcommand{\Dorfman}{\@ifstar\@dorfmanstar\@dorfmannostar}
\newcommand{\Dir}{\operatorname{\ch@irxoperatorfont{Dir}}}
\newcommand{\Forward}{\mathcal{F}}
\newcommand{\Backward}{\mathcal{B}}
\newcommand{\Tangent}{\mathbb{T}}
\newcommand{\MWreduction}{\big/\!\!\big/}
\newcommand{\Mon}{\ch@irxoperatorfont{Mon}}
\newcommand{\Hol}{\ch@irxoperatorfont{Hol}}
\fi
\if@loadmath
\newcommand{\tr}{\operatorname{\ch@irxoperatorfont{tr}}}
\newcommand{\rank}{\operatorname{\ch@irxoperatorfont{rank}}}
\newcommand{\codim}{\operatorname{\ch@irxoperatorfont{codim}}}
\newcommand{\diag}{\operatorname{\ch@irxoperatorfont{diag}}}
\newcommand{\Trans}{{\ch@irxscriptfont{\scriptscriptstyle{T}}}}
\newcommand{\Mat}{\ch@irxoperatorfont{M}}
\newcommand{\SymMat}{\ch@irxoperatorfont{SymMat}}
\newcommand{\ann}{\ch@irxscriptfont{ann}}
\newcommand{\Span}[1][]{\operatorname{\ch@irxoperatorfont{span}_{#1}}}
\newcommand{\basis}[1]{\ch@irxbasisfont{#1}}
\renewcommand{\tensor}[1][{}]{\mathbin{\otimes_{\scriptscriptstyle{#1}}}}
\newcommand{\Tensor}{\ch@irxoperatorfont{T}}
\newcommand{\Anti}{\Lambda}
\newcommand{\Sym}{\ch@irxoperatorfont{S}}
\newcommand{\Symmetrizer}{\operatorname{\ch@irxoperatorfont{Sym}}}
\newcommand{\AntiSymmetrizer}{\operatorname{\ch@irxoperatorfont{Alt}}}
\newcommand{\ins}{\operatorname{\ch@irxoperatorfont{i}}}
\newcommand{\jns}{\operatorname{\ch@irxoperatorfont{j}}}
\newcommand{\insa}{\ins_{\ch@irxscriptfont{a}}}
\newcommand{\inss}{\ins_{\ch@irxscriptfont{s}}}
\newcommand{\degs}{\ch@irxoperatorfont{deg}_{\ch@irxscriptfont{s}}}
\newcommand{\dega}{\ch@irxoperatorfont{deg}_{\ch@irxscriptfont{a}}}
\DeclarePairedDelimiter{\SP} {\langle}{\rangle}
\newcommand{\littlepara}{{\scriptscriptstyle\parallel}}
\newcommand{\IP}[6][{}]{\decorate*[^{#2}_{#3}]{\SP[#1]{#4}}{^{#5}_{#6}}}
\fi
\if@loadmath
\newcommand{\EX}{\operatorname{\ch@irxoperatorfont{E}}}
\newcommand{\Var}{\operatorname{\ch@irxoperatorfont{Var}}}
\newcommand{\Cov}{\operatorname{\ch@irxoperatorfont{Cov}}}
\newcommand{\Cor}{\operatorname{\ch@irxoperatorfont{Cor}}}
\fi
\if@loadmath
\newcommand{\cl}{\ch@irxscriptfont{cl}}
\newcommand{\scl}{\ch@irxscriptfont{scl}}
\newcommand{\interior}{\circ}
\newcommand{\boundary}{\partial}
\newcommand{\supp}{\operatorname{\ch@irxoperatorfont{supp}}}
\newcommand{\dist}{\operatorname{\ch@irxoperatorfont{dist}}}
\newcommand{\topology}[1]{\ch@irxtopologyfont{#1}}
\newcommand{\filter}[1]{\ch@irxfilterfont{#1}}
\newcommand{\sheaf}[1]{\ch@irxsheaffont{#1}}
\newcommand{\Sections}{\operatorname{\ch@irxoperatorfont{Sections}}}
\newcommand{\HOM}{\operatorname{\ch@irxsheaffont{H}\!\mathit{om}}}
\DeclarePairedDelimiter{\etale}{\lvert}{\rvert}
\newcommand{\topological}{\categoryname{top}}
\newcommand{\Topological}{\categoryname{Top}}
\newcommand{\Sheaves}{\categoryname{Sheaves}}
\newcommand{\PreSheaves}{\categoryname{PreSheaves}}
\newcommand{\Etale}{\categoryname{Etale}}
\fi
\endinput
%%
%% End of file `chairxmath.sty'.
