174 lines
5.5 KiB
Plaintext
174 lines
5.5 KiB
Plaintext
__HEADER__(Math Operator Package)
|
|
%Provides some commonly used Operators used in the write-ups of my lecture notes
|
|
|
|
__LANGUAGE_OPTIONS__
|
|
|
|
__END_OPTIONS__
|
|
|
|
%%%%%Package dependencies
|
|
\RequirePackage{amsmath}
|
|
\RequirePackage{bbm}
|
|
\RequirePackage{mathtools}
|
|
|
|
%%%%Different types of operator wrappers:
|
|
|
|
% For simple math operators that are just to be printed as their name
|
|
\newcommand\DeclareSimpleMathOperator[1]{
|
|
\expandafter\providecommand\csname #1\endcsname{\operatorname{#1}}
|
|
}
|
|
|
|
%%%For distributions
|
|
%Introduce synonym for \operatorname
|
|
\newcommand__PACKAGE_MACRO__(distribution)[1]{\operatorname{#1}}
|
|
%Easily declare new distributions
|
|
\newcommand\DeclareDistribution[1]{\expandafter\def\csname #1\endcsname{__PACKAGE_MACRO__(distribution){#1}}}
|
|
|
|
%%%For categories
|
|
%Introduce synonym for \operatorname
|
|
\newcommand__PACKAGE_MACRO__(category)[1]{\operatorname{\textbf{#1}}}
|
|
%Easily declare new categories
|
|
\newcommand\DeclareCategory[1]{\expandafter\def\csname #1\endcsname{__PACKAGE_MACRO__(category){#1}}}
|
|
|
|
|
|
%%%%%%%%%%% Operators
|
|
%Basic commands
|
|
\DeclareSimpleMathOperator{id}
|
|
\DeclareSimpleMathOperator{im}
|
|
\DeclareSimpleMathOperator{Bild}
|
|
\DeclareSimpleMathOperator{dom}
|
|
\DeclareSimpleMathOperator{Span}
|
|
\DeclareSimpleMathOperator{Aut}
|
|
\DeclareMathOperator{\rhs}{RHS} %Right hand side of equation
|
|
\DeclareMathOperator{\lhs}{LHS} %Left hand side of equation
|
|
|
|
%%Provide \ggT \gcd \kgV \lcm for 'greatest common denominator' and 'least common multiple'
|
|
% \ggT und \gcd, as well as \kgV and \lcm are synonyms and language-aware, so that
|
|
% e.g. when the german language option is loaded, even
|
|
% \lcm would print 'kgV'
|
|
% The starred versions of the four commands will ignore the language option and print their
|
|
% exact names (without the *, of course)
|
|
\DeclareMathOperator{\@__PACKAGE_PREFIX__ggT}{ggT}
|
|
\DeclareMathOperator{\@@__PACKAGE_PREFIX__ggT}{\if@__PACKAGE_PREFIX__english gcd\else ggT\fi}
|
|
\def\ggT{\@ifstar\@__PACKAGE_PREFIX__ggT\@@__PACKAGE_PREFIX__ggT}
|
|
|
|
\DeclareMathOperator{\@__PACKAGE_PREFIX__gcd}{gcd}
|
|
\DeclareMathOperator{\@@__PACKAGE_PREFIX__gcd}{\if@__PACKAGE_PREFIX__english gcd\else ggT\fi}
|
|
\def\gcd{\@ifstar\@__PACKAGE_PREFIX__gcd\@@__PACKAGE_PREFIX__gcd}
|
|
|
|
\DeclareMathOperator{\@__PACKAGE_PREFIX__kgV}{kgV}
|
|
\DeclareMathOperator{\@@__PACKAGE_PREFIX__kgV}{\if@__PACKAGE_PREFIX__english lcm\else kgV\fi}
|
|
\def\kgV{\@ifstar\@__PACKAGE_PREFIX__kgV\@@__PACKAGE_PREFIX__kgV}
|
|
|
|
\DeclareMathOperator{\@__PACKAGE_PREFIX__lcm}{lcm}
|
|
\DeclareMathOperator{\@@__PACKAGE_PREFIX__lcm}{\if@__PACKAGE_PREFIX__english lcm\else kgV\fi}
|
|
\def\lcm{\@ifstar\@__PACKAGE_PREFIX__lcm\@@__PACKAGE_PREFIX__lcm}
|
|
|
|
%Complex numbers
|
|
\DeclareMathOperator{__PACKAGE_MACRO__(impart)}{Im}
|
|
\renewcommand\Im__PACKAGE_MACRO__(impart)
|
|
\DeclareMathOperator{__PACKAGE_MACRO__(repart)}{Re}
|
|
\renewcommand\Re__PACKAGE_MACRO__(repart)
|
|
|
|
%Linear Algebra
|
|
\DeclareSimpleMathOperator{Sym}
|
|
\DeclareSimpleMathOperator{supp}
|
|
\DeclareSimpleMathOperator{sgn}
|
|
\DeclareSimpleMathOperator{coker}
|
|
\DeclareSimpleMathOperator{rank}
|
|
\DeclareSimpleMathOperator{Mat}
|
|
\DeclareSimpleMathOperator{ev}
|
|
|
|
%Algebra
|
|
\DeclareSimpleMathOperator{Quot}
|
|
\DeclareSimpleMathOperator{Gal}
|
|
\DeclareSimpleMathOperator{Ext}
|
|
\DeclareSimpleMathOperator{Tor}
|
|
\DeclareSimpleMathOperator{MaxSpec}
|
|
\DeclareSimpleMathOperator{Sh}
|
|
\DeclareSimpleMathOperator{Proj}
|
|
\DeclareSimpleMathOperator{QCoh}
|
|
\DeclareSimpleMathOperator{MaxSpec}
|
|
\DeclareSimpleMathOperator{Fun}
|
|
\DeclareMathOperator{\PreSh}{Pre-Sh}
|
|
\newcommand{\tensor}{\otimes} %Synonym for tensoring
|
|
|
|
%Analysis
|
|
\DeclareSimpleMathOperator{dx}
|
|
\DeclareSimpleMathOperator{dy}
|
|
\DeclareSimpleMathOperator{dz}
|
|
\DeclareSimpleMathOperator{dt}
|
|
|
|
%Sets
|
|
\DeclareSimpleMathOperator{conv}
|
|
\DeclareSimpleMathOperator{dist}
|
|
\DeclareSimpleMathOperator{diam}
|
|
|
|
%%Stochastic (Algorithmische Mathematik II)
|
|
\DeclareDistribution{Bin}
|
|
\DeclareDistribution{Ber}
|
|
\DeclareDistribution{Geo}
|
|
\DeclareDistribution{Poi}
|
|
\DeclareDistribution{Unif}
|
|
\DeclareDistribution{Var}
|
|
\DeclareDistribution{Cov}
|
|
|
|
%Topology
|
|
\DeclareSimpleMathOperator{pr}
|
|
\def\twedge{\vee} % Semantically correct macros for wedge product
|
|
\def\tsmash{\wedge} % Semantically correct macro for smash product
|
|
|
|
%Category Theory
|
|
\DeclareSimpleMathOperator{Ob}
|
|
\DeclareSimpleMathOperator{Hom}
|
|
\DeclareSimpleMathOperator{Mor}
|
|
\DeclareSimpleMathOperator{End}
|
|
\DeclareSimpleMathOperator{colim}
|
|
|
|
%Categories
|
|
\DeclareCategory{Top}
|
|
\DeclareCategory{hTop}
|
|
\DeclareCategory{Set}
|
|
\DeclareCategory{CHaus}
|
|
\DeclareCategory{Grp}
|
|
\DeclareCategory{Ab}
|
|
\DeclareCategory{CRing}
|
|
\DeclareCategory{Vect}
|
|
\DeclareCategory{Fin}
|
|
\DeclareCategory{Ab}
|
|
\DeclareCategory{Cat}
|
|
|
|
%Set theory
|
|
\DeclareSimpleMathOperator{card}
|
|
\DeclareSimpleMathOperator{Cd}
|
|
\DeclareSimpleMathOperator{Ord}
|
|
\DeclareSimpleMathOperator{otp}
|
|
\DeclareSimpleMathOperator{Card}
|
|
|
|
%%Galoiskohomologie
|
|
\DeclareSimpleMathOperator{Br}
|
|
\DeclareSimpleMathOperator{EXT}
|
|
\DeclareSimpleMathOperator{Ind}
|
|
\DeclareSimpleMathOperator{char}
|
|
\DeclareSimpleMathOperator{res}
|
|
\DeclareSimpleMathOperator{inf}
|
|
\DeclareSimpleMathOperator{cov}
|
|
\newcommand{\del}{\partial} % Semantically correct operator for boundary maps
|
|
|
|
% Characteristic function
|
|
\newcommand*{\cfun}{\ensuremath{\mathbbm{1}}}
|
|
\newcommand*{\One}{\cfun}
|
|
|
|
%Paired Delimiters
|
|
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
|
|
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
|
|
|
|
%Norm and absolute value
|
|
%Make them scaling by default and have \abs*{} as the non-scaling version of the command
|
|
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
|
|
\let\oldabs\abs
|
|
\def\abs{\@ifstar{\oldabs}{\oldabs*}}
|
|
|
|
\DeclarePairedDelimiter\norm{\lVert}{\rVert}
|
|
\let\oldnorm\norm
|
|
\def\norm{\@ifstar{\oldnorm}{\oldnorm*}}
|