280 lines
9.4 KiB
Text
280 lines
9.4 KiB
Text
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% Copyright © 2022 Maximilian Keßler
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%
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% Permission is hereby granted, free of charge, to any person obtaining a copy
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% of this software and associated documentation files (the “Software”), to deal
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% in the Software without restriction, including without limitation the rights
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% to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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% copies of the Software, and to permit persons to whom the Software is
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% furnished to do so, subject to the following conditions:
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% The above copyright notice and this permission notice shall be included in all
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% copies or substantial portions of the Software.
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%
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% THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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% AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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% OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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% SOFTWARE.
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%
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% This package has been generated by PyTeX, available at
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% https://github.com/kesslermaximilian/PyTeX
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% and built from source file 'mathop.pysty'.
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% It is STRONGLY DISCOURAGED to edit this source file directly, since local
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% changes will not be versioned by Git and overwritten by the next build. Always
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% edit the source file and build the package again.
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%
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% Build details:
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% PyTeX version: v1.0.0-18 (commit 126d420)
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% Source code version: v2.4.2 (commit 14c4939)
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%
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% This LaTeX package is free software and distributed under the MIT License. You
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% may use it freely for your purposes. The latest version of the package can be
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% obtained via GitHub under
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% https://github.com/kesslermaximilian/LatexPackages
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% For further information see the url above.
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% Reportings of bugs, suggestions and improvements are welcome, see the README
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% at the Git repository for further information.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\NeedsTeXFormat{LaTeX2e}
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\ProvidesPackage{mkessler-mathop}[2022/01/09 - Math Operator Package]
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%Provides some commonly used Operators used in the write-ups of my lecture notes
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\RequirePackage{xkeyval}
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\newif\ifmkessler@mathop@english\mkessler@mathop@englishtrue
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\DeclareOptionX{german}{\mkessler@mathop@englishfalse}
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\DeclareOptionX{ngerman}{\mkessler@mathop@englishfalse}
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\DeclareOptionX{english}{\mkessler@mathop@englishtrue}
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\DeclareOptionX*{\PackageWarning{mkessler-mathop}{Unknown '\CurrentOption'}}
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\ProcessOptionsX*\relax
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%%%%%Package dependencies
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\RequirePackage{amsmath}
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\RequirePackage{bbm}
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\RequirePackage{mathtools}
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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@mathop@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@mathop@distribution{#1}}}
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%%%For categories
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%Introduce synonym for \operatorname
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\newcommand\mkessler@mathop@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@mathop@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@mathop@ggT}{ggT}
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\DeclareMathOperator{\@@mkessler@mathop@ggT}{\if@mkessler@mathop@english gcd\else ggT\fi}
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\def\ggT{\@ifstar\@mkessler@mathop@ggT\@@mkessler@mathop@ggT}
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\DeclareMathOperator{\@mkessler@mathop@gcd}{gcd}
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\DeclareMathOperator{\@@mkessler@mathop@gcd}{\if@mkessler@mathop@english gcd\else ggT\fi}
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\def\gcd{\@ifstar\@mkessler@mathop@gcd\@@mkessler@mathop@gcd}
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\DeclareMathOperator{\@mkessler@mathop@kgV}{kgV}
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\DeclareMathOperator{\@@mkessler@mathop@kgV}{\if@mkessler@mathop@english lcm\else kgV\fi}
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\def\kgV{\@ifstar\@mkessler@mathop@kgV\@@mkessler@mathop@kgV}
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\DeclareMathOperator{\@mkessler@mathop@lcm}{lcm}
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\DeclareMathOperator{\@@mkessler@mathop@lcm}{\if@mkessler@mathop@english lcm\else kgV\fi}
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\def\lcm{\@ifstar\@mkessler@mathop@lcm\@@mkessler@mathop@lcm}
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%Complex numbers
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\DeclareMathOperator{\mkessler@mathop@impart}{Im}
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\renewcommand\Im\mkessler@mathop@impart
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\DeclareMathOperator{\mkessler@mathop@repart}{Re}
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\renewcommand\Re\mkessler@mathop@repart
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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{rk}
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\DeclareSimpleMathOperator{Mat}
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\DeclareSimpleMathOperator{ev}
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\DeclareSimpleMathOperator{tr}
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\DeclareSimpleMathOperator{GL}
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\DeclareSimpleMathOperator{PGL}
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%Algebra
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\DeclareSimpleMathOperator{Quot}
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\DeclareSimpleMathOperator{rad}
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\DeclareSimpleMathOperator{Spec}
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\DeclareSimpleMathOperator{Frac}
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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{Fun}
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\DeclareMathOperator{\Nil}{\mathcal{N}il}
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\DeclareMathOperator{\Ouv}{\mathcal{O}uv}
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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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\DeclareSimpleMathOperator{sing}
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\DeclareSimpleMathOperator{cell}
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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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\DeclareSimpleMathOperator{colim}
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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{Ring}
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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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\DeclareCategory{Mod}
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\DeclareCategory{AffVar}
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\DeclareCategory{Alg}
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\DeclareCategory{Field}
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\DeclareCategory{GrAb}
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\DeclareCategory{Sch}
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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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%% Algebraic geometry
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\DeclareSimpleMathOperator{eq}
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\DeclareSimpleMathOperator{Idem}
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\DeclareSimpleMathOperator{Supp}
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\DeclareSimpleMathOperator{Ann}
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\DeclareSimpleMathOperator{OC}
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\DeclareSimpleMathOperator{red}
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\DeclareSimpleMathOperator{can}
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\DeclareSimpleMathOperator{Pic}
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\newcommand\leftadjoint\vdash
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\newcommand\rightadjoint\dashv
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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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%Paired Delimiters
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\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
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\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
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%Norm and absolute value
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%Make them scaling by default and have \abs*{} as the non-scaling version of the command
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\DeclarePairedDelimiter\abs{\lvert}{\rvert}
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\let\oldabs\abs
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\def\abs{\@ifstar{\oldabs}{\oldabs*}}
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\DeclarePairedDelimiter\norm{\lVert}{\rVert}
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\let\oldnorm\norm
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\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
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\DeclareMathOperator{\amalgprod}{\star}
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\newcommand\op{\text{op}}
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\newcommand\opposite{^{\op}}
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\newcommand\ab{\text{ab}}
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\newcommand\abelianization{^{\ab}}
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%Taken from user egreg on
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% https://tex.stackexchange.com/a/22255
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\newcommand\frestriction[2]{{% we make the whole thing an ordinary symbol
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\left.\kern-\nulldelimiterspace % automatically resize the bar with \right
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#1 % the function
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\vphantom{\big|} % pretend it's a little taller at normal size
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\right|_{#2} % this is the delimiter
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}}
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\newcommand\directlimit{\varinjlim}
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\newcommand\inverselimit{\varprojlim}
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\DeclareMathOperator*{\freeproduct}{\raisebox{-0.5ex}{\scalebox{2}{$\ast$}}}
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