115 lines
2.9 KiB
TeX
115 lines
2.9 KiB
TeX
\NeedsTeXFormat{LaTeX2e}
|
|
\ProvidesPackage{operators}[2021-04-27 - Operator Package]
|
|
%%%%%%%%%%%%%%%%%%mmmm
|
|
%Provides some commonly used Operators used in the write-ups of my lecture notes
|
|
|
|
\newif\ifenglish\englishtrue
|
|
\DeclareOption{german}{\englishfalse}
|
|
\DeclareOption{english}{\englishtrue}
|
|
\DeclareOption*{\PackageWarning{operators}{Unknown '\CurrentOption'}}
|
|
\ProcessOptions\relax
|
|
|
|
%Packages
|
|
\RequirePackage{amsmath}
|
|
|
|
|
|
%%%%%%%%%%% Operators
|
|
%Basic commands
|
|
\renewcommand\subset\subseteq
|
|
\renewcommand\supset\supseteq
|
|
\DeclareMathOperator{\id}{id}
|
|
\DeclareMathOperator{\im}{im}
|
|
\DeclareMathOperator{\Bild}{Bild}
|
|
\let\ggT\relax\DeclareMathOperator{\ggT}{\ifenglish gcd \else ggT\fi}
|
|
\let\kgV\relax\DeclareMathOperator{\kgV}{\ifenglish lcm \elese kgV\fi}
|
|
\DeclareMathOperator{\rhs}{RHS} %Right hand side
|
|
|
|
%Complex numbers
|
|
\DeclareMathOperator{\Impart}{Im}
|
|
\renewcommand\Im\Impart
|
|
\DeclareMathOperator{\Repart}{Re}
|
|
\renewcommand\Re\Repart
|
|
|
|
%Linear Algebra
|
|
\DeclareMathOperator{\Sym}{Sym}
|
|
\DeclareMathOperator{\supp}{supp}
|
|
\DeclareMathOperator{\sgn}{sgn}
|
|
\DeclareMathOperator{\coker}{coker}
|
|
\DeclareMathOperator{\rank}{rank}
|
|
\DeclareMathOperator{\Mat}{Mat}
|
|
|
|
%Algebra
|
|
\DeclareMathOperator{\Gal}{Gal}
|
|
\DeclareMathOperator{\Ext}{Ext}
|
|
\DeclareMathOperator{\Tor}{Tor}
|
|
\DeclareMathOperator{\Mspec}{MaxSpec}
|
|
\DeclareMathOperator{\Sh}{Sh}
|
|
\DeclareMathOperator{\Proj}{Proj}
|
|
\DeclareMathOperator{\QCoh}{QCoh}
|
|
\DeclareMathOperator{\MaxSpec}{MaxSpec}
|
|
\DeclareMathOperator{\Presh}{Pre-Sh}
|
|
\DeclareMathOperator{\Fun}{Fun}
|
|
\newcommand{\tensor}{\otimes}
|
|
|
|
%Category Theory
|
|
\DeclareMathOperator{\Ob}{Ob}
|
|
\newcommand{\cat}[1]{ \mathscr{#1} }
|
|
\DeclareMathOperator{\Hom}{Hom}
|
|
\DeclareMathOperator{\Mor}{Mor}
|
|
\DeclareMathOperator{\End}{End}
|
|
\DeclareMathOperator{\opposite}{opp}
|
|
\newcommand\opp{^{\opposite}}
|
|
|
|
%Analysis
|
|
\DeclareMathOperator{\dx}{dx}
|
|
\DeclareMathOperator{\dy}{dy}
|
|
\DeclareMathOperator{\dz}{dz}
|
|
\DeclareMathOperator{\dt}{dt}
|
|
|
|
%Sets
|
|
\DeclareMathOperator{\conv}{conv}
|
|
\DeclareMathOperator{\cone}{cone}
|
|
\DeclareMathOperator{\dist}{dist}
|
|
\DeclareMathOperator{\diam}{diam}
|
|
|
|
%%Stochastic (Algorithmische Mathematik II)
|
|
\DeclareMathOperator\Bin{Bin}
|
|
\DeclareMathOperator\Ber{Ber}
|
|
\DeclareMathOperator\Geo{Geo}
|
|
\DeclareMathOperator\Poi{Poi}
|
|
\DeclareMathOperator{\Var}{Var}
|
|
|
|
%Topology
|
|
\DeclareMathOperator\pr{pr}
|
|
\def\twedge{\vee}
|
|
\def\tsmash{\wedge}
|
|
|
|
%Categories
|
|
\newcommand\category[1]{\operatorname{\textbf{#1}}}
|
|
\newcommand\DeclareCategory[1]{\expandafter\def\csname #1\endcsname{\category{#1}}}
|
|
\DeclareCategory{Top}
|
|
\DeclareCategory{Set}
|
|
\DeclareCategory{CHaus}
|
|
\DeclareCategory{Grp}
|
|
\DeclareCategory{Ab}
|
|
\DeclareCategory{Vect}
|
|
\DeclareCategory{Fin}
|
|
\DeclareCategory{Ab}
|
|
\def\op{^{\textbf{op}}}
|
|
|
|
%Set theory
|
|
\DeclareMathOperator\card{card}
|
|
\DeclareMathOperator\Cd{Cd}
|
|
\DeclareMathOperator\Ord{Ord}
|
|
\DeclareMathOperator\otp{otp}
|
|
\DeclareMathOperator\Card{Card}
|
|
|
|
% Characteristic function
|
|
\newcommand*{\cfun}{\ensuremath{\mathbbm{1}}}
|
|
\newcommand*{\One}{\ensuremath{\mathbbm{1}}}
|
|
|
|
|
|
\DeclareMathOperator\lhs{LHS}
|
|
|
|
|
|
|