Math_Symbols.sty

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Math Symbols
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\makeatletter


\newcommand{\newpar}{
  \nointerlineskip \vspace{\baselineskip}
  \hspace{\fill}\rule{0.35\linewidth}{.7pt}\hspace{\fill}
  \par\nointerlineskip \vspace{\baselineskip}
}

\newcommand{\und}{\underline}
\newcommand{\den}{\underline}
\newcommand{\te}{\text}
\newcommand{\bd}{\boldsymbol}
\newcommand{\df}{\boldsymbol}
\newcommand{\bv}{\boldsymbol}
\newcommand{\ma}{\mathbb}
\newcommand{\mb}{\mathbbm}
\newcommand{\mc}{\mathcal}
\newcommand{\mf}{\mathfrak}
\newcommand{\msc}{\mathscr}
\newcommand{\bvd}[1]{\dot{\boldsymbol{#1}}}
\newcommand{\bvdd}[1]{\ddot{\boldsymbol{#1}}}
\newcommand{\bvh}[1]{\hat{\boldsymbol{#1}}}
\newcommand{\sd}[1]{\hat{\boldsymbol{#1}}}
\newcommand{\sdf}[1]{\tilde{\boldsymbol{#1}}}
\newcommand{\bvt}[1]{\tilde{\boldsymbol{#1}}}




%%Stuff I don't understand
\stackMath

\newcommand\xxrightarrow[2][]{\mathrel{
  \setbox2=\hbox{\stackon{\scriptstyle#1}{\scriptstyle#2}}
  \stackunder[0pt]{
    \xrightarrow{\makebox[\dimexpr\wd2\relax]{$\scriptstyle#2$}}
  }{
   \scriptstyle#1\,
  }
}}

\newcommand\xxrightharpoonup[2][]{\mathrel{
  \setbox2=\hbox{\stackon{\scriptstyle#1}{\scriptstyle#2}}
  \stackunder[0pt]{
    \xrightharpoonup{\makebox[\dimexpr\wd2\relax]{$\scriptstyle#2$}}
  }{
   \scriptstyle#1\,
  }
}}

%%/Stuff I don't understand




%%subfactor stuff

\newcommand{\typeone}[1]{type $\mathrm{I}_{#1}$}
\newcommand{\typetwo}[1]{type $\mathrm{II}_{#1}$}
\newcommand{\typethree}{type $\mathrm{III}$}

\newcommand{\one}[1]{$\mathrm{I}_{#1}$}
\newcommand{\two}[1]{$\mathrm{II}_{#1}$}
\newcommand{\three}{$\mathrm{III}$}
%%/subfactor stuff




%Greek Letters
\newcommand{\A}{\alpha}
\newcommand{\B}{\beta}
\newcommand{\G}{\gamma}
\newcommand{\Ga}{\Gamma}
\newcommand{\de}{\delta}
\newcommand{\De}{\Delta}
\newcommand{\ep}{\epsilon}
\newcommand{\et}{\theta}
\newcommand{\Et}{\Theta}
\newcommand{\ka}{\kappa}
\newcommand{\da}{\lambda}
\newcommand{\Da}{\Lambda}
\newcommand{\rf}{\pi}
\newcommand{\Rf}{\Pi}
\newcommand{\si}{\sigma}
\newcommand{\Si}{\Sigma}
\newcommand{\ed}{\varphi}
\newcommand{\Ed}{\Phi}
\newcommand{\ws}{\psi}
\newcommand{\Ws}{\Psi}
\newcommand{\om}{\omega}
\newcommand{\Om}{\Omega}
%Greek Letters


%Category names
\newcommand{\Cat}[1]{\mathrm{\textbf{#1}}}

\let\Vec\relax
\newcommand{\Alg}{\Cat{Alt}}
\newcommand{\Fun}{\Cat{Fun}}
\newcommand{\Mod}{\Cat{Mod}}
\newcommand{\Hilb}{\Cat{Hilb}}
\newcommand{\Ring}{\Cat{Ring}}
\newcommand{\Smth}{\Cat{Smth}}
\newcommand{\Mon}{\Cat{Mon}}
\newcommand{\Set}{\Cat{Set}}
\newcommand{\Ab}{\Cat{Ab}}
\newcommand{\Vec}{\Cat{Vec}}
\newcommand{\Grp}{\Cat{Grp}}
\newcommand{\Top}{\Cat{Top}}
\newcommand{\hTop}{\Cat{hTop}}
\newcommand{\Ch}{\Cat{Ch}}
\newcommand{\homCh}{\Cat{homCh}}
\newcommand{\GrAbGrp}{\Cat{GrAbGrp}}
\newcommand{\CRing}{\Cat{CRing}}
\newcommand{\TvNA}{\Cat{TvNA}}
\newcommand{\TvNa}{\Cat{TvNa}}
\newcommand{\Rep}{\Cat{Rep}}

%Category names



%Typo Fixes

\newcommand{\codt}{\cdot}
\newcommand{\lodts}{\ldots}
\newcommand{\ldtos}{\ldots}
\newcommand{\codts}{\cdots}
\newcommand{\vodts}{\vdots}
\newcommand{\tua}{\tau}

%Typo Fixes









%Handy Symbols
\newcommand{\blank}{{-}}
\newcommand{\from}{\leftarrow}
\newcommand{\nat}[1]{\xRightarrow{#1}}
\newcommand{\op}{^{\te{op}}}
\newcommand{\mor}{\xrightarrow}
\newcommand{\rew}{\otimes}
\newcommand{\hrew}{\ba{\otimes}}
\newcommand{\sep}{\,\middle|\,}
\newcommand{\bijection}{\ar[r, rightharpoondown, shift right] \ar[r, leftarrow, leftharpoonup, shift left]}
\newcommand{\divisionsign}{\div}
\let\div\relax
\newcommand{\levi}{\varepsilon}
\newcommand{\ndots}[3]{{#2}_{1} #1 {#2}_{2} #1  \ldots #1 {{#2}_{#3}}}
%\newcommand{\undots}[3]{{#2}^{1} #1 {#2}^{2} #1  \ldots #1 {{#2}^{#3}}}
\newcommand{\infdots}[2]{{#2}_{1} #1 {#2}_{2} #1 \ldots}
%\newcommand{\oinfdots}[2]{{#2}_{0} #1 {#2}_{1} #1 \ldots}
\newcommand{\tg}{\hbar}
\newcommand{\del}{\partial}
\newcommand{\nab}{\bv \nabla}
\newcommand{\ap}{\approx}
\newcommand{\apr}{\doteq}
\newcommand{\nor}{\trianglelefteq}
\newcommand{\mo}{\mu_0}
\newcommand{\ef}{\epsilon_0}
\newcommand{\para}{\parallel}
\newcommand{\kcol}{\fa{1}{4 \rf \ef}}
\newcommand{\es}{\varnothing}
\newcommand{\subs}{\subseteq}
\newcommand{\sups}{\supseteq }
%\newcommand{\cut}{|}
\newcommand{\ba}{\overline}
\newcommand{\uba}{\underline}
\newcommand{\foral}{\ \ \forall}
\newcommand{\exist}{\ \ \exists}
%\newcommand{\ST}{\te{ such that }}
\newcommand{\tand}{\text{ and }}
\newcommand{\tfor}{\text{ for }}
\newcommand{\tas}{\text{ as }}
\newcommand{\tis}{\text{ is }}
\newcommand{\tif}{\text{ if }}
\newcommand{\twhere}{\text{ where }}
\newcommand{\teven}{\text{even}}
\newcommand{\todd}{\text{odd}}
\newcommand{\tin}{\text{ in }}
\newcommand{\twith}{\text{ with }}
\newcommand{\nth}{^{\text{th}}}
\newcommand{\back}{\setminus}
\newcommand{\symdif}{\mathbin{\Delta}}
\newcommand{\sequ}[2]{\ER {#1}_{#2} : {#2} \geq 1 \RE} %Real I Sequence macro
\newcommand{\ti}{\tilde}
\newcommand{\qtand}{\quad \text{and} \quad}
\newcommand{\toinfty}[1]{\xxrightarrow[#1 \to \infty]{}}
\newcommand{\toinftyweak}[1]{\xxrightharpoonup[#1 \to \infty]{}}
\newcommand{\toinftyweakstar}[1]{\xxrightharpoonup[#1 \to \infty]{*}}
\newcommand{\onetoinfty}[1]{_{{#1} = 1}^\infty}
\newcommand{\toweak}{\rightharpoonup}
\newcommand{\toau}{\xrightarrow{\te{AU}}}
\newcommand{\tomu}{\xrightarrow{\mu}}
\newcommand{\tozero}[1]{\xrightarrow{#1 \to 0}}
\newcommand{\normal}{\unlhd}
\newcommand{\bnormal}{\unrhd}
\newcommand{\notnormal}{\centernot{\unlhd}}
\def\dbar{{\mathchar'26\mkern-12mu d}}
\newcommand{\inc}{\hookrightarrow}
\newcommand{\htpy}{\approx}
\newcommand{\htp}[1]{\underset{{#1}}{\approx}}
\newcommand{\pathsim}{\underset{{\text{path}}}{\sim}}
\newcommand{\qeq}{\overset{?}{=}}
\newcommand{\act}{\curvearrowright}
\newcommand{\ec}{\eqqcolon}
\newcommand{\ce}{\coloneqq}
\newcommand{\restrict}{|}
\newcommand{\derzero}{\der{}{t} \bigg|_{t = 0}}
\newcommand{\ubrace}[2]{\smash{\underbrace{#1}_{#2}}\vphantom{#1}}
\newcommand{\obrace}[2]{\smash{\overbrace{#1}^{#2}}\vphantom{#1}}
\newcommand{\grad}{\nabla}
\newcommand{\AI}{\fint}
\newcommand{\toup}{\nearrow}
\newcommand{\todown}{\downarrow}
\newcommand{\quotient}[2]{{\left.\raisebox{.2em}{\ensuremath{#1}}\middle/\raisebox{-.2em}{\ensuremath{#2}}\right.}}
\newcommand{\csa}{{$\text{C}^*$-algebra}}
\renewcommand{\mod}{/}
\renewcommand{\l}{<}
\newcommand{\g}{>}
\let\bmod\relax


\newcommand{\bmod}[2]{{\raisebox{-.2em}{$#1$}\left\backslash\raisebox{.2em}{$#2$}\right.}}%backward quotient sign for right cosets


\newcommand{\bigmod}[2]{{\raisebox{.2em}{$#1$}\left/\raisebox{-.2em}{$#2$}\right.}}%big quotient sign


\newcommand{\dmod}[3]{{\raisebox{-.1em}{$#1$}\left\backslash\raisebox{.1em}{$#2$}\right/\raisebox{-.1em}{$#3$}}}%inline double quotient for double cosets.
\newcommand{\doublemod}[3]{{\raisebox{-.2em}{$#1$}\left\backslash\raisebox{.2em}{$#2$}\right/\raisebox{-.2em}{$#3$}}}%displayed double quotient for double cosets.
%Handy Symbols

%Script "r"
\def\rs{{\mbox{$\resizebox{.16in}{.08in}{\includegraphics{/home/zach/Dropbox/Public/LaTex/Pictures/Script-r/ScriptR}} \! \! \!$}}}
\def\brs{{\mbox{$\resizebox{.16in}{.08in}{\includegraphics{/home/zach/Dropbox/Public/LaTex/Pictures/Script-r/BoldR}}\! \! \!$}}}
\def\rshat{{\mbox{$\hat \brs$}}}
%Script "r"

%Delimiters
\newcommand{\E}{\left(}
\newcommand{\R}{\right)}
\newcommand{\DF}{\left[}
\newcommand{\FD}{\right]}
\newcommand{\ER}{\left\{}
\newcommand{\RE}{\right\}}
%\newcommand{\AW}{\left\langle} %Outdated
%\newcommand{\WA}{\right\rangle} %Outdated
\newcommand{\ET}{\left\langle}
\newcommand{\TE}{\right\rangle}
\newcommand{\MG}{\left|}
\newcommand{\GM}{\right|}
\newcommand{\NK}{\left\|}
\newcommand{\KN}{\right\|}
\newcommand{\SD}{\left\llbracket}
\newcommand{\DS}{\right\rrbracket}
\newcommand{\CL}{\left\lceil}
\newcommand{\LC}{\right\rceil}
\newcommand{\FL}{\left\lfloor}
\newcommand{\LF}{\right\rfloor}
%\newcommand{\MS}[1]{\left| #1 \right|^2}
%\newcommand{\magsquare}[1]{\MG #1 \GM^2} %Outdated
\newcommand{\IN}[2]{\left\langle #1 \middle| #2 \right\rangle}
\newcommand{\INP}[2]{\left( #1, #2 \right)}
\newcommand{\INO}[3]{\left\langle #2 \middle| #1 \middle| #3 \right\rangle}
% \newcommand{\ket}[1]{\left| #1 \right\rangle} % Conflicts with a better way. 
% \newcommand{\bra}[1]{\left\langle #1 \right|} % Same. 
\newcommand{\TB}{\left\vert\kern-0.25ex\left\vert\kern-0.25ex\left\vert}
\newcommand{\BT}{\right\vert\kern-0.25ex\right\vert\kern-0.25ex\right\vert}
%Delimiters

%Integrals, Sums, and Products
\newcommand{\infint}{\int\limits_{-\infty}^{\infty}}
\newcommand{\I}{\int}
%\newcommand{\ID}{\iint\limits}
%\newcommand{\IT}{\iiint\limits}
%\newcommand{\SF}{\iint \limits_{\mathcal S}}
%\newcommand{\VF}{\iiint \limits_{\mathcal V}}
%\newcommand{\spaceint}{\iiint \limits_{\substack{\text{All}\\\text{Space}}}}
%\newcommand{\SU}{\sum \limits}
%\newcommand{\PR}{\product \limits}
%Integrals, Sums, and Products

%Math Functions
\newcommand{\fa}{\frac}
\newcommand{\sq}{\sqrt}
\newcommand{\pd}[3][]{\frac{\partial^{#1} {#2}}{\partial {#3}{}^{#1}}}
\newcommand{\der}[3][]{\frac{d^{#1} #2}{d {#3}{}^{#1}}}
\newcommand{\fd}[3][]{\frac{\de^{#1} #2}{\de {#3}{}^{#1}}}
\newcommand {\concat}{
  \mathord{
    \mathchoice
    {\raisebox{1ex}{\scalebox{.7}{$\frown$}}}
    {\raisebox{1ex}{\scalebox{.7}{$\frown$}}}
    {\raisebox{.7ex}{\scalebox{.5}{$\frown$}}}
    {\raisebox{.7ex}{\scalebox{.5}{$\frown$}}}
  }
}
\newcommand{\pre}[1]{{#1}^{\te{pre}}}
%Math Modifiers

%MathOperators
\DeclareMathOperator{\Infl}{Infl}
\DeclareMathOperator{\Res}{Res}
\DeclareMathOperator{\Borel}{Borel}
\DeclareMathOperator{\reg}{reg}
\DeclareMathOperator{\Reg}{Reg}
\DeclareMathOperator{\rel}{rel}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\gr}{gr}
\DeclareMathOperator{\length}{length}
\let\id\relax
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\Stab}{Stab}
\DeclareMathOperator{\ann}{ann}
\DeclareMathOperator{\Obj}{Obj}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\ran}{ran}
\DeclareMathOperator{\real}{Re}
\DeclareMathOperator{\imag}{Im}
\let\Im\relax
\DeclareMathOperator{\Im}{Im}
\let\Re\relax
\DeclareMathOperator{\Re}{Re}
\DeclareMathOperator{\diam}{diam}
\DeclareMathOperator{\aut}{Aut} %Outdated
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\ch}{ch}
\DeclareMathOperator{\chra}{char}
\DeclareMathOperator{\gal}{Gal}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\inter}{int}
\DeclareMathOperator{\cl}{cl}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\dist}{dist}
\DeclareMathOperator{\spa}{Span}
\DeclareMathOperator{\Lin}{Lin}
\DeclareMathOperator{\nul}{null}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\dom}{dom}
\DeclareMathOperator{\cod}{cod}
\DeclareMathOperator{\epi}{epi}
\DeclareMathOperator{\Tor}{Tor}
\DeclareMathOperator{\Vol}{Vol}
\DeclareMathOperator{\Tr}{Tr}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\sech}{sech}
\DeclareMathOperator{\Vect}{Vect}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\vol}{vol}
\DeclareMathOperator{\Int}{Int}
\DeclareMathOperator{\div}{div}
\DeclareMathOperator{\Lip}{Lip}
\DeclareMathOperator{\ad}{ad}
\DeclareMathOperator{\range}{range}
\DeclareMathOperator{\obj}{obj}
\DeclareMathOperator{\arr}{arr}
\DeclareMathOperator{\meas}{meas}
\DeclareMathOperator{\cha}{char}
\DeclareMathOperator{\stab}{stab}
\DeclareMathOperator{\Syl}{Syl}
\DeclareMathOperator{\Free}{Free}
\DeclareMathOperator{\Id}{Id}
\DeclareMathOperator{\Area}{Area}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Und}{Und}
\DeclareMathOperator{\esssupWOOOO}{ess\,sup}
\newcommand{\esssup}{\esssupWOOOO\limits}
\DeclareMathOperator{\cov}{cov}
\DeclareMathOperator{\var}{var}
\DeclareMathOperator{\Ann}{Ann}
\DeclareMathOperator{\Fix}{Fix}
\DeclareMathOperator{\Gr}{Gr}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\orbit}{orbit}
\DeclareMathOperator{\co}{co}
\DeclareMathOperator{\conv}{conv}
\DeclareMathOperator{\Herm}{Herm}
\DeclareMathOperator{\Inner}{Inner}
\DeclareMathOperator{\Iso}{Iso}
\DeclareMathOperator{\BiLin}{BiLin}
\DeclareMathOperator{\Bilin}{Bilin}
\DeclareMathOperator{\spec}{sp}
\DeclareMathOperator{\Ob}{Ob}
\DeclareMathOperator{\Mor}{Mor}
\DeclareMathOperator{\Open}{Open}
\DeclareMathOperator{\colim}{colim}
\DeclareMathOperator{\coker}{coker}
\DeclareMathOperator{\Bal}{Bal}
\DeclareMathOperator{\Ext}{Ext}
\DeclareMathOperator{\Com}{Com}
\DeclareMathOperator{\Bim}{Bim}
\DeclareMathOperator{\tor}{tor}
\DeclareMathOperator{\Gal}{Gal}
\DeclareMathOperator{\Out}{Out}
\DeclareMathOperator{\Kar}{Kar}
\DeclareMathOperator{\Mat}{Mat}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\ind}{ind}
\DeclareMathOperator{\Irr}{Irr}
\DeclareMathOperator{\Conv}{Conv}
\DeclareMathOperator{\ev}{ev}
\DeclareMathOperator{\Der}{Der}
\DeclareMathOperator{\Map}{Map}
\DeclareMathOperator{\codim}{codim}
\DeclareMathOperator{\FreeMod}{FreeMod}
\DeclareMathOperator{\ins}{ins}
\DeclareMathOperator{\pconv}{PConv}
\DeclareMathOperator{\Lie}{Lie}
\DeclareMathOperator{\Skew}{Skew}
\DeclareMathOperator{\Alt}{Alt}
\DeclareMathOperator{\lub}{lub}
\DeclareMathOperator{\essrange}{essrange}
\DeclareMathOperator{\mate}{mate}
\DeclareMathOperator{\ext}{ext}
%MathOperators







\makeatother