mymath.sty

\ProvidesPackage{mymath}

\usepackage{mathtools}
\usepackage{amsfonts}
\usepackage{MnSymbol}

\usepackage{xifthen}

% ---- Quantifiers ----
\newcommand{\Forall}[1]{\ensuremath{\forall #1 \:}}
\newcommand{\Exists}[1]{\ensuremath{\exists #1 \colon \:}}

% ---- Number sets ----
\newcommand{\Natural}{\mathbb{N}}
\newcommand{\Integers}{\mathbb{Z}}
\newcommand{\Rational}{\mathbb{Q}}
\newcommand{\Real}{\mathbb{R}}

\newcommand{\To}{\Rightarrow}

% ---- Order of element in group ----
\DeclareMathOperator{\ord}{ord}

% ---- Field characteristic ----
\DeclareMathOperator{\fchar}{char}

% ---- Matrices set on filed #1 with #2 rows and #3 columns ----
\newcommand{\Matrices}[3][]{M_{#2 \times #3}\ifthenelse{\isempty{#1}}{}{(#1)}}

% ---- Matrix rank ----
\DeclareMathOperator{\rk}{rk}

% ---- Linear map kernel and image ----
\DeclareMathOperator{\Ker}{Ker}
\DeclareMathOperator{\Img}{Im}

% ---- Sign operator ----
\DeclareMathOperator{\sgn}{sgn}

\renewcommand\qedsymbol{$\blacksquare$}