\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{Math_Notations}

% For matrixes and vectors
\newcommand{\vect}[1]{{\underline{#1}}}
\newcommand{\mat}[1]{{\underline{\underline{#1}}}}
\newcommand{\Tr}[1]{{{#1}^t}}

% Bold letters 
\newcommand{\bdA}{{\boldsymbol{A}}}
\newcommand{\bdB}{{\boldsymbol{B}}}
\newcommand{\bdC}{{\boldsymbol{C}}}
\newcommand{\bdD}{{\boldsymbol{D}}}
\newcommand{\bdE}{{\boldsymbol{E}}}
\newcommand{\bdF}{{\boldsymbol{F}}}
\newcommand{\bdG}{{\boldsymbol{G}}}
\newcommand{\bdH}{{\boldsymbol{H}}}
\newcommand{\bdI}{{\boldsymbol{I}}}
\newcommand{\bdJ}{{\boldsymbol{J}}}
\newcommand{\bdK}{{\boldsymbol{K}}}
\newcommand{\bdL}{{\boldsymbol{L}}}
\newcommand{\bdM}{{\boldsymbol{M}}}
\newcommand{\bdN}{{\boldsymbol{N}}}
\newcommand{\bdO}{{\boldsymbol{O}}}
\newcommand{\bdP}{{\boldsymbol{P}}}
\newcommand{\bdQ}{{\boldsymbol{Q}}}
\newcommand{\bdR}{{\boldsymbol{R}}}
\newcommand{\bdS}{{\boldsymbol{S}}}
\newcommand{\bdT}{{\boldsymbol{T}}}
\newcommand{\bdU}{{\boldsymbol{U}}}
\newcommand{\bdV}{{\boldsymbol{V}}}
\newcommand{\bdW}{{\boldsymbol{W}}}
\newcommand{\bdX}{{\boldsymbol{X}}}
\newcommand{\bdY}{{\boldsymbol{Y}}}
\newcommand{\bdZ}{{\boldsymbol{Z}}}
\newcommand{\bda}{{\boldsymbol{a}}}
\newcommand{\bdb}{{\boldsymbol{b}}}
\newcommand{\bdc}{{\boldsymbol{c}}}
\newcommand{\bdd}{{\boldsymbol{d}}}
\newcommand{\bde}{{\boldsymbol{e}}}
\newcommand{\bdf}{{\boldsymbol{f}}}
\newcommand{\bdg}{{\boldsymbol{g}}}
\newcommand{\bdh}{{\boldsymbol{h}}}
\newcommand{\bdi}{{\boldsymbol{i}}}
\newcommand{\bdj}{{\boldsymbol{j}}}
\newcommand{\bdk}{{\boldsymbol{k}}}
\newcommand{\bdl}{{\boldsymbol{l}}}
\newcommand{\bdm}{{\boldsymbol{m}}}
\newcommand{\bdn}{{\boldsymbol{n}}}
\newcommand{\bdo}{{\boldsymbol{o}}}
\newcommand{\bdp}{{\boldsymbol{p}}}
\newcommand{\bdq}{{\boldsymbol{q}}}
\newcommand{\bdr}{{\boldsymbol{r}}}
\newcommand{\bds}{{\boldsymbol{s}}}
\newcommand{\bdt}{{\boldsymbol{t}}}
\newcommand{\bdu}{{\boldsymbol{u}}}
\newcommand{\bdv}{{\boldsymbol{v}}}
\newcommand{\bdw}{{\boldsymbol{w}}}
\newcommand{\bdx}{{\boldsymbol{x}}}
\newcommand{\bdy}{{\boldsymbol{y}}}
\newcommand{\bdz}{{\boldsymbol{z}}}

% special caracters
\newcommand{\ca}{{\mathcal A}}
\newcommand{\cb}{{\mathcal B}}
\newcommand{\cc}{{\mathcal C}}
\newcommand{\cd}{{\mathcal D}}
\newcommand{\ce}{{\mathcal E}}
\newcommand{\cf}{{\mathcal F}}
\newcommand{\cg}{{\mathcal G}}
\newcommand{\ch}{{\mathcal H}}
\newcommand{\ck}{{\mathcal K}}
\newcommand{\cl}{{\mathcal L}}
\newcommand{\cn}{{\mathcal N}}
\newcommand{\cm}{{\mathcal M}}
\newcommand{\cp}{{\mathcal P}}
\newcommand{\cs}{{\mathcal S}}
\newcommand{\cu}{{\mathcal U}}
\newcommand{\cw}{{\mathcal W}}
\newcommand{\cx}{{\mathcal X}}
\newcommand{\C}{{\mathbb C}}
\newcommand{\E}{{\mathbb E}}
\newcommand{\N}{{\mathbb N}}
\renewcommand{\P}{{\mathbb P}}
\newcommand{\Q}{{\mathbb Q}}
\newcommand{\R}{{\mathbb R}}
\newcommand{\Z}{{\mathbb Z}}
\newcommand{\D}{{\mathrm{d}}}

% short commands
\newcommand{\un}[1]{\underline{#1}}
\newcommand{\dpl}[1]{\displaystyle{#1}}
\newcommand{\ux}{\underline{x}}
\newcommand{\uX}{\underline{X}}
\newcommand{\uy}{\underline{y}}
\newcommand{\uY}{\underline{Y}}
\newcommand{\uz}{\underline{z}}
\newcommand{\uZ}{\underline{Z}}
\newcommand{\muX}{\underline{\mu}_{\:X}}
\newcommand{\Var}[1]{{\rm Var}\left[ #1 \right]}
\newcommand{\Cov}[1]{{\rm Cov}\left[ #1 \right]}
\newcommand{\Esp}[1]{{\mathbb E}\left[ #1 \right]}
\newcommand{\Prob}[1]{{\mathbb P}\left( #1 \right)}
\newcommand{\pdf}{f_{\un{X}}(\un{x})}
\newcommand{\ech}{\left\{ x_1, \, \dots\,, x_N  \right\}}
\newcommand{\matcov} {\mathbf C}
\newcommand{\matcor} {\mathbf R}
\newcommand{\fcar}[2] {{\mathbf 1}_{#1}(#2)}