mymath.sty

\ProvidesPackage{mymath}

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

\usepackage{xifthen}

\RequirePackage{xparse}

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

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

\newcommand{\ot}{\leftarrow}
\newcommand{\otto}{\leftrightarrow}
\newcommand{\To}{\Rightarrow}
\newcommand{\oT}{\Leftarrow}
\newcommand{\oTTo}{\Leftrightarrow}

\newcommand{\Set}[1]{\{ #1 \}}
\DeclareMathOperator{\Expectation}{\mathbb{E}}
\DeclareMathOperator{\Reg}{Reg}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\GCD}{GCD}

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

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

% ---- Matrices set on filed #1 with #2 rows and #3 columns ----
\NewDocumentCommand{\Matrices}{o m m}{%
  M_{#2 \times #3}\IfNoValueF{#1}{(#1)}}

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

% ---- Factor ----
\NewDocumentCommand{\Factor}{o m o}{%
  \IfNoValueTF{#1}{}{#1 \backslash} #2 \IfNoValueTF{#3}{}{/ {\textstyle #3}}
}

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

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

\newcommand{\inang}[1]{\langle #1 \rangle}

\renewcommand\qedsymbol{$\blacksquare$}

\NewDocumentCommand{\NSG}{}{\triangleleft}
\NewDocumentCommand{\NGS}{}{\triangleright}
\DeclareMathOperator{\St}{St}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Inn}{Inn}
\DeclareMathOperator{\tr}{tr}

\NewDocumentCommand{\GenGroup}{m o}{\langle #1 
\IfNoValueF{#2}{\mid #2} \rangle}
\NewDocumentCommand{\GenNGroup}{m}{\langle #1 \rangle_\text{норм}}
\NewDocumentCommand{\GenFGroup}{m}{\langle #1 \rangle_\text{своб}}

\NewDocumentCommand{\Cycle}{m}{\arraycolsep=1.5pt (\begin{matrix} #1 \end{matrix})}

\NewDocumentCommand{\Centre}{m}{Z(#1)}

% ---- Russian symbols ----
\RenewDocumentCommand{\epsilon}{}{\varepsilon}
\RenewDocumentCommand{\phi}{}{\varphi}
\RenewDocumentCommand{\kappa}{}{\varkappa}

\RenewDocumentCommand{\emptyset}{}{\varnothing}

\RenewDocumentCommand{\le}{}{\leqslant}
\RenewDocumentCommand{\ge}{}{\geqslant}