167 lines
5.4 KiB
TeX
167 lines
5.4 KiB
TeX
\NeedsTeXFormat{LaTeX2e}
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\ProvidesPackage{mkessler-operators}[2021-04-27 - Operator Package]
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%%%%%%%%%%%%%%%%%
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%Provides some commonly used Operators used in the write-ups of my lecture notes
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\newif\if@mkessler@operators@english\@mkessler@operators@englishtrue
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\DeclareOption{german}{\@mkessler@operators@englishfalse}
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\DeclareOption{english}{\@mkessler@operators@englishtrue}
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\DeclareOption*{\PackageWarning{mkessler-operators}{Unknown '\CurrentOption'}}
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\ProcessOptions\relax
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%%%%%Package dependencies
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\RequirePackage{amsmath}
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\RequirePackage{bbm}
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%%%%Different types of operator wrappers:
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% For simple math operators that are just to be printed as their name
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\newcommand\DeclareSimpleMathOperator[1]{
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\expandafter\providecommand\csname #1\endcsname{\operatorname{#1}}
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}
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%%%For distributions
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%Introduce synonym for \operatorname
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\newcommand\mkessler@operators@distribution[1]{\operatorname{#1}}
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%Easily declare new distributions
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\newcommand\DeclareDistribution[1]{\expandafter\def\csname #1\endcsname{\mkessler@operators@distribution{#1}}}
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%%%For categories
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%Introduce synonym for \operatorname
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\newcommand\mkessler@operators@category[1]{\operatorname{\textbf{#1}}}
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%Easily declare new categories
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\newcommand\DeclareCategory[1]{\expandafter\def\csname #1\endcsname{\mkessler@operators@category{#1}}}
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%%%%%%%%%%% Operators
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%Basic commands
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\DeclareSimpleMathOperator{id}
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\DeclareSimpleMathOperator{im}
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\DeclareSimpleMathOperator{Bild}
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\DeclareSimpleMathOperator{dom}
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\DeclareSimpleMathOperator{Span}
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\DeclareSimpleMathOperator{Aut}
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\DeclareMathOperator{\rhs}{RHS} %Right hand side of equation
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\DeclareMathOperator{\lhs}{LHS} %Left hand side of equation
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%%Provide \ggT \gcd \kgV \lcm for 'greatest common denominator' and 'least common multiple'
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% \ggT und \gcd, as well as \kgV and \lcm are synonyms and language-aware, so that
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% e.g. when the german language option is loaded, even
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% \lcm would print 'kgV'
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% The starred versions of the four commands will ignore the language option and print their
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% exact names (without the *, of course)
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\DeclareMathOperator{\@mkessler@operators@ggT}{ggT}
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\DeclareMathOperator{\@@mkessler@operators@ggT}{\if@mkessler@operators@english gcd\else ggT\fi}
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\def\ggT{\@ifstar\@mkessler@operators@ggT\@@mkessler@operators@ggT}
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\DeclareMathOperator{\@mkessler@operators@gcd}{gcd}
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\DeclareMathOperator{\@@mkessler@operators@gcd}{\if@mkessler@operators@english gcd\else ggT\fi}
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\def\gcd{\@ifstar\@mkessler@operators@gcd\@@mkessler@operators@gcd}
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\DeclareMathOperator{\@mkessler@operators@kgV}{kgV}
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\DeclareMathOperator{\@@mkessler@operators@kgV}{\if@mkessler@operators@english lcm\else kgV\fi}
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\def\kgV{\@ifstar\@mkessler@operators@kgV\@@mkessler@operators@kgV}
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\DeclareMathOperator{\@mkessler@operators@lcm}{lcm}
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\DeclareMathOperator{\@@mkessler@operators@lcm}{\if@mkessler@operators@english lcm\else kgV\fi}
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\def\lcm{\@ifstar\@mkessler@operators@lcm\@@mkessler@operators@lcm}
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%Complex numbers
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\DeclareMathOperator{\mkessler@impart}{Im}
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\renewcommand\Im\mkessler@impart
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\DeclareMathOperator{\mkessler@repart}{Re}
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\renewcommand\Re\mkessler@impart
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%Linear Algebra
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\DeclareSimpleMathOperator{Sym}
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\DeclareSimpleMathOperator{supp}
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\DeclareSimpleMathOperator{sgn}
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\DeclareSimpleMathOperator{coker}
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\DeclareSimpleMathOperator{rank}
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\DeclareSimpleMathOperator{Mat}
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\DeclareSimpleMathOperator{ev}
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%Algebra
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\DeclareSimpleMathOperator{Quot}
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\DeclareSimpleMathOperator{Gal}
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\DeclareSimpleMathOperator{Ext}
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\DeclareSimpleMathOperator{Tor}
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\DeclareSimpleMathOperator{MaxSpec}
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\DeclareSimpleMathOperator{Sh}
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\DeclareSimpleMathOperator{Proj}
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\DeclareSimpleMathOperator{QCoh}
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\DeclareSimpleMathOperator{MaxSpec}
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\DeclareSimpleMathOperator{Fun}
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\DeclareMathOperator{\PreSh}{Pre-Sh}
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\newcommand{\tensor}{\otimes} %Synonym for tensoring
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%Analysis
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\DeclareSimpleMathOperator{dx}
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\DeclareSimpleMathOperator{dy}
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\DeclareSimpleMathOperator{dz}
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\DeclareSimpleMathOperator{dt}
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%Sets
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\DeclareSimpleMathOperator{conv}
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\DeclareSimpleMathOperator{dist}
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\DeclareSimpleMathOperator{diam}
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%%Stochastic (Algorithmische Mathematik II)
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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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\DeclareDistribution{Var}
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\DeclareDistribution{Cov}
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%Topology
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\DeclareSimpleMathOperator{pr}
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\def\twedge{\vee} % Semantically correct macros for wedge product
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\def\tsmash{\wedge} % Semantically correct macro for smash product
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%Category Theory
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\DeclareSimpleMathOperator{Ob}
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\DeclareSimpleMathOperator{Hom}
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\DeclareSimpleMathOperator{Mor}
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\DeclareSimpleMathOperator{End}
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%Categories
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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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%Set theory
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\DeclareSimpleMathOperator{card}
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\DeclareSimpleMathOperator{Cd}
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\DeclareSimpleMathOperator{Ord}
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\DeclareSimpleMathOperator{otp}
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\DeclareSimpleMathOperator{Card}
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%%Galoiskohomologie
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\DeclareSimpleMathOperator{Br}
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\DeclareSimpleMathOperator{EXT}
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\DeclareSimpleMathOperator{Ind}
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\DeclareSimpleMathOperator{char}
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\DeclareSimpleMathOperator{res}
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\DeclareSimpleMathOperator{inf}
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\DeclareSimpleMathOperator{cov}
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\newcommand{\del}{\partial} % Semantically correct operator for boundary maps
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% Characteristic function
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\newcommand*{\cfun}{\ensuremath{\mathbbm{1}}}
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\newcommand*{\One}{\cfun}
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%Possibly destructive commands
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\renewcommand\subset\subseteq
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\renewcommand\supset\supseteq
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