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