%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Packages
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[hidelinks]{hyperref}
\usepackage{todonotes}

\mathtoolsset{showonlyrefs}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Operators
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareMathOperator{\dt}{d}
\DeclareMathOperator{\diverg}{div}
\DeclareMathOperator{\grad}{grad}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sym}{sym}
\DeclareMathOperator{\skw}{skw}
\DeclareMathOperator{\cov}{Cov}
\DeclareMathOperator{\var}{Var}

\newcommand{\C}{\mathbf{C}}
\newcommand{\E}{\mathbf{E}}

\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\PP}{\mathbb{P}}

\newcommand{\pdN}{\mathcal{N}}

\theoremstyle{plain}
\newtheorem{satz}{Satz}

\theoremstyle{definition}
\newtheorem{definition}{Definition}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\vx}{\underline{x}}
\newcommand{\vy}{\underline{y}}
\newcommand{\vz}{\underline{z}}
\newcommand{\vmu}{\underline{\mu}}

\newcommand{\rrx}{\bm{x}}
\newcommand{\rry}{\bm{y}}
\newcommand{\rrz}{\bm{z}}

\newcommand{\rvx}{\bm{\vx}}
\newcommand{\rvy}{\bm{\vy}}
\newcommand{\rvz}{\bm{\vz}}

\newcommand{\evx}{\hat{\vx}}
\newcommand{\evy}{\hat{\vy}}
\newcommand{\evz}{\hat{\vz}}

\renewcommand{\eps}{\ensuremath{\varepsilon}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Commands
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\vec}[1]{\underline{#1}}
\newcommand{\dx}[1][x]{\,\dt\!#1}

\newcommand{\func}[2]{ #1 ( #2 )}
\newcommand{\funcb}[2]{ #1 [ #2 ]}

\newcommand{\brr}[1]{\left( #1 \right)}
\newcommand{\bre}[1]{\left[ #1 \right]}
\newcommand{\brg}[1]{\left{ #1 \right}}

\newcommand{\bis}[2]{= #1,\ldots\,, #2}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Text
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\konst}{\textit{konst.}}
\newcommand{\const}{\textit{const.}}
\newcommand{\for}{\text{for }}