TUD_MATH_BA/Erasmus/Applied statistics/mathoperators.sty

\ProvidesPackage{mathoperators}

\RequirePackage{xparse}
\RequirePackage{xkeyval}
\RequirePackage{xstring}

%\OptFractionAppearence - differenciate between multiple appearences of fraction
%	- 0: simple slash: a/b 												(option slash)(default)
%	- 1: fraction by slash, raised nominator, lowered denominator		(option lowerraise)
\let\OptFractionAppearence\z@
\DeclareOptionX{fractionappearence}{%
	\IfStrEq{#1}{slash}{}{%
		\IfStrEq{#1}{lowerraise}{%
			\let\OptFractionAppearence\@ne
		}{}%further options can be inserted here
	}
}

\DeclareOptionX*{\PackageWarning{mathoperator}{Unknown option >\CurrentOption<}}
\ProcessOptionsX

%Provides some common math related commands and operators
\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{amsfonts}
\RequirePackage{scalerel,stackengine}
\RequirePackage{calc}

%transpose
\newcommand\transpose[1]{\ensuremath{#1^\mathsf{T}}}
%new macro for "equals" ^=
\newcommand\equalhat{\mathrel{\stackon[1.5pt]{=}{\stretchto{%
				\scalerel*[\widthof{=}]{\wedge}{\rule{1ex}{3ex}}}{0.5ex}}}}

%fraction with backslash
\newcommand\bsfrac[2]{%
	\scalebox{-1}[1]{\nicefrac{\scalebox{-1}[1]{$#1$}}{\scalebox{-1}[1]{$#2$}}}%
}

\DeclareRobustCommand{\properideal}{\mathrel{\text{$\m@th\proper@ideal$}}}
\newcommand{\proper@ideal}{%
  \ooalign{$\lneq$\cr\raise.22ex\hbox{$\lhd$}\cr}%
}

\DeclareRobustCommand{\properidealright}{\mathrel{\text{$\m@th\proper@idealright$}}}
\newcommand{\proper@idealright}{%
	\ooalign{$\gneq$\cr\raise.22ex\hbox{$\rhd$}\cr}%
}

%General newcommands!
\newcommand{\comp}{\mathbb{C}} % complex set C
\newcommand{\real}{\mathbb{R}} % real set R
\newcommand{\whole}{\mathbb{Z}} % whole number Symbol
\newcommand{\natur}{\mathbb{N}} % natural number Symbol
\newcommand{\ratio}{\mathbb{Q}} % rational number symbol
\newcommand{\field}{\mathbb{K}} % general field for the others above!
\newcommand{\diff}{\mathrm{d}} % differential d
\newcommand{\s}{\,\,}     % space after the function in the intergral
\newcommand{\cont}{\mathcal{C}} % Contour C
\newcommand{\fuk}{f(z) \s\diff z} % f(z) dz
\newcommand{\diffz}{\s\diff z}
\newcommand{\subint}{\int\limits} % lower boundaries for the integral
\newcommand{\poly}{\mathcal{P}} % special P - polygon
\newcommand{\defi}{\mathcal{D}} % D for the domain of a function
\newcommand{\cover}{\mathcal{U}} % cover for a set
\newcommand{\setsys}{\mathcal{M}} % set system M
\newcommand{\setnys}{\mathcal{N}} % set system N
\newcommand{\zetafunk}{f(\zeta)\s\diff \zeta} %f(zeta) d zeta
\newcommand{\ztfunk}{f(\zeta)} % f(zeta)
\newcommand{\bocirc}{S_r(z)}
\newcommand{\prop}{\,|\,}
\newcommand*{\QEDA}{\hfill\ensuremath{\blacksquare}} %tombstone
\newcommand{\emptybra}{\{\varnothing\}} % empty set with set-bracket
\newcommand{\realpos}{\real_{>0}}
\newcommand{\realposr}{\real_{\geq0}}
\newcommand{\naturpos}{\natur_{>0}}
\newcommand{\Imag}{\operatorname{Im}} % Imaginary symbol
\newcommand{\Realz}{\operatorname{Re}} % Real symbol
\newcommand{\norm}{\Vert \cdot \Vert}
\newcommand{\metric}{\vert \cdot \vert}
\newcommand{\foralln}{\forall n} %all n
\newcommand{\forallnset}{\forall n \in \natur} %all n € |N
\newcommand{\forallnz}{\forall n \geq _0} % all n >= n_0
\newcommand{\conjz}{\overline{z}} % conjugated z
\newcommand{\tildz}{\tilde{z}} % different z
\newcommand{\lproofar}{"`$ \Leftarrow $"'} % "`<="'
\newcommand{\rproofar}{"`$ \Rightarrow $"'} % "`=>"'
\newcommand{\beha}{\Rightarrow \text{ Behauptung}}
\newcommand{\powerset}{\mathcal{P}}
\newcommand{\person}[1]{\textsc{#1}}
\newcommand{\highlight}[1]{\emph{#1}}
\newcommand{\realz}{\mathfrak{Re}}
\newcommand{\imagz}{\mathfrak{Im}}
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\phi}{\varphi}
\newcommand{\lebesque}{\textsc{Lebesgue}}
\renewcommand{\Re}{\mathfrak{Re}}
\renewcommand{\Im}{\mathfrak{Im}}
\renewcommand*{\arraystretch}{1.4}
\newcommand{\bigcupdot}{\bigcup \hspace{-0.35cm} \cdot}
\newcommand{\BIGboxplus}{\mathop{\mathchoice{\raise-0.35em\hbox{\huge $\boxplus$}}{\raise-0.15em\hbox{\Large $\boxplus$}}{\hbox{\large $\boxplus$}}{\boxplus}}}
\newcommand{\eps}{\textit{eps }}

\newcommand{\skalar}[2]{\left\langle #1,#2\right\rangle}
\newcommand{\qraum}[2]{\sfrac{#1}{#2}}
\newcommand{\lnkset}[2]{%Menge der Linksnebenklassen
	\ifcase\OptFractionAppearence\relax%
		\ifmmode%
			#1\slash #2%
		\else%
			$#1\slash #2$%
		\fi%
	\or%
		\nicefrac{#1}{#2}%
	\else%
		\PackageWarning{mathoperator}{Unkown value for option >fractionAppearence<: \meaning\OptFractionAppearence}%
	\fi%
}
\newcommand{\rnkset}[2]{%
	\ifcase\OptFractionAppearence\relax%
		\ifmmode%
			#1\backslash#2%
		\else%
			$#1\backslash#2$%
		\fi%
	\or%
		\bsfrac{#1}{#2}% Menge der Rechtsnebenklassen
	\else%
		\PackageWarning{mathoperator}{Unkown value for option >fractionAppearence<: \meaning\OptFractionAppearence}%
	\fi%
}

% Math Operators
\DeclareMathOperator{\inn}{int} % Set of inner points
\DeclareMathOperator{\ext}{ext} % Set of outer points
\DeclareMathOperator{\cl}{cl} % Closure
\DeclareMathOperator{\grad}{grad}
\DeclareMathOperator{\D}{d}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\graph}{graph}
\DeclareMathOperator{\Int}{int}
\DeclareMathOperator{\Ext}{ext}
\DeclareMathOperator{\diam}{diam}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\cond}{cond}
\DeclareMathOperator{\rd}{rd}
\undef\div
\DeclareMathOperator{\div}{div}
\DeclareMathOperator{\rot}{rot}

\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Aff}{Aff}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Abb}{Abb}
\DeclareMathOperator{\Bil}{Bil}
\DeclareMathOperator{\Eig}{Eig}
\DeclareMathOperator{\Mat}{Mat}
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\ZR}{ZR}
\DeclareMathOperator{\SR}{SR}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\Span}{span}
\DeclareMathOperator{\Image}{Im}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\Hau}{Hau}
\DeclareMathOperator{\pr}{pr}
\DeclareMathOperator{\Orth}{O}
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\Uni}{U}
\DeclareMathOperator{\SU}{SU}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\ggT}{ggT}
\DeclareMathOperator{\kgV}{kgV}
\DeclareMathOperator{\rang}{rang}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\Z}{Z}
\DeclareMathOperator{\UG}{UG}
\DeclareMathOperator{\Fix}{Fix}
\DeclareMathOperator{\Stab}{Stab}
\DeclareMathOperator{\Syl}{Syl}
\DeclareMathOperator{\Typ}{Typ}
\DeclareMathOperator{\LC}{LC}
\DeclareMathOperator{\Quot}{Quot}
\DeclareMathOperator{\SE}{SE}
\DeclareMathOperator{\PDF}{PDF}

\endinput