\ProvidesPackage{MHD}

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%%%%% Package %%%%
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\usepackage[utf8]{inputenc}  	% LaTeX, comprends les accents !
\usepackage[T1]{fontenc}     	% Police contenant les caractères français
\usepackage{geometry}        	% Definir les marges
\usepackage[english]{babel} 		% Placez ici une liste de langues, la dernière étant la langue principale
\usepackage{enumerate}
\usepackage{amsmath}          	% pour faire des maths
\usepackage{amssymb}				% pour faire + de maths
\usepackage{amsthm}
\usepackage{mathrsfs}
\usepackage{eucal}
\usepackage{enumitem}

\usepackage{graphicx}			    % \usepackage{hyperref}
\usepackage{subfigure}				% pour faire des figures
%\usepackage{caption}
\usepackage{placeins}			    % idem
\usepackage{float}					    % idem
\usepackage{wrapfig}				    % idem
%\usepackage[usenames,dvipsnames]{color} % permet de mettre plus de couleurs
\usepackage{xcolor}

\usepackage{sidecap}
\usepackage{epstopdf}
\usepackage{braket}
\usepackage{natbib}
\usepackage{multicol}

\usepackage{lipsum}
\usepackage{hyperref}
\usepackage{cleveref}
\usepackage{mathdots}

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%%%% Theorem  %%%%
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%sign operator
\def\sgn{\mathop{\rm sign}\nolimits}
%Landau's big O 
\newcommand{\Bo}{\ensuremath{\mathcal{O}}}
\newcommand{\so}{\ensuremath{\mathfrak{o}}}
%Sign related operator
\newcommand{\Pl}{\ensuremath{\mathcal{P}}}
\newcommand{\Mn}{\ensuremath{\mathcal{M}}}

\theoremstyle{plain}
\newtheorem{theo}{Theorem}[section]
\newtheorem{lem}[theo]{Lemma}
\newtheorem{coro}[theo]{Corollary}

%\newtheorem{coro}{Corollary}[theo]

\theoremstyle{definition}
\newtheorem{defi}[theo]{Definition}

\theoremstyle{remark}
\newtheorem*{nota}{Note}

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%%% Scalar product %%
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\newcommand{\scalpr}[2]{\ensuremath{ \left ( #1 \, , \; #2 \right ) } }

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%%%%%%% Lax %%%%%%
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%%%%%%%%%%%%%%%%

\newcommand{\st}[1]{\ensuremath{#1\text{-st} }}
\newcommand{\cist}[2]{\ensuremath{#1\text{-cist} \left[#2\right]}}
\newcommand{\cv}[3]{\ensuremath{CV^{#1}_{#2} \left[#3\right]}}
\newcommand{\feq}{\ensuremath{\mathfrak{eq}}}

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%%%%%% Matrix %%%%%
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%%%%%%%%%%%%%%%%

%\newcommand*{\transp}[2][-3mu]{\ensuremath{\mskip 
%1mu\prescript{\smash{\mathrm t\mkern#1}}{}{\mathstrut#2}}}%
\newcommand*{\transp}[1]{\ensuremath{ 
\smash{{}^\mathrm{t} \! {#1} }}}
\newcommand{\id}{\ensuremath{ \mathit{Id} }}

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%%%%%% Color %%%%%
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%%%%%%%%%%%%%%%%

\newcommand{\cred}[1]{\textcolor{red}{#1}}
\definecolor{CamBlue}{rgb}{0,0.5,0.9}
\newcommand{\cblue}[1]{\textcolor{CamBlue}{#1}}
\definecolor{CamOrange}{rgb}{1,0.5,0}
\newcommand{\corang}[1]{\textcolor{CamOrange}{#1}}
\definecolor{CamGreen}{rgb}{0,0.7,0.6}
\newcommand{\cgreen}[1]{\textcolor{CamGreen}{#1}}
\definecolor{CamYellow}{rgb}{0.7,0.6,0.2}
\newcommand{\cyello}[1]{\textcolor{CamYellow}{#1}}
\definecolor{CamViole}{rgb}{0.6,0,0.5}
\newcommand{\cviole}[1]{\textcolor{CamViole}{#1}}

%%%%%%%%%%%%%%%%
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%%%% Short cut  %%%%
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%%%%%%%%%%%%%%%%

\newcommand{\specialcell}[2][c]{%
  \begin{tabular}[#1]{@{}c@{}}#2\end{tabular}}

\newcommand*{\Cdot}{\raisebox{-0.25ex}{\scalebox{1.75}{$\cdot$}}}

\newcommand{\one}{\ensuremath{1\!\!1}}

\newcommand{\lb}{\ensuremath{\text{lb}}}

\newcommand{\figcm}{3.55cm}
\newcommand{\tabsz}{\footnotesize}

\newcommand{\avec}{\mathbf{\gamma}}
\newcommand{\ddif}{\mathrm{\; d}}
\newcommand{\unit}{$1\!\!1$ }
\newcommand{\dfun}{\mathscr{D}}
\newcommand{\vvec}{\mathbf{v}}
\newcommand{\uvec}{\mathbf{u}}
\newcommand{\rvec}{\mathbf{r}}
\newcommand{\kvec}{\mathbf{k}}
\newcommand{\xvec}{\mathbf{X}}
\newcommand{\strs}{\underline{\underline{\epsilon}}}
\newcommand{\strn}{\underline{\underline{\tau}}}
\newcommand{\dbd}{\overline{\overline{:}}}

\newcommand{\fou}{\mathscr{F}}
\newcommand{\fouin}{\mathscr{F}^{-1}}

%%%%%% Short vector
%\newcommand{\vct}[1]{\ensuremath{\underline{#1}}}
\newcommand{\vct}[1]{\ensuremath{\mathBF{#1}}}

\newcommand{\bu}{\vct{b}}
\newcommand{\vu}{\vct{v}}
\newcommand{\ku}{\vct{k}}
\newcommand{\ru}{\vct{r}}

\newcommand{\RR}{\vct{R}}
\newcommand{\R}{\vct{r}}
\newcommand{\U}{\vct{u}}
\newcommand{\uabc}{\vct{U}}
\newcommand{\V}{\vct{V}}
\newcommand{\W}{\vct{W}}
\newcommand{\OM}{\vct{\omega}}
\newcommand{\UP}{\vct{\Upsilon}}
\newcommand{\PSI}{\vct{\psi}}
\newcommand{\A}{\vct{A}}
\newcommand{\B}{\vct{B}}
\newcommand{\J}{\vct{J}}
\newcommand{\E}{\vct{E}}
\newcommand{\F}{\vct{F}}
\newcommand{\f}{\vct{f}}
\newcommand{\G}{\vct{G}}
\newcommand{\e}{\vct{e}}
\newcommand{\lL}{\vct{l}}
\newcommand{\LL}{\vct{L}}
\newcommand{\N}{\vct{n}}
\newcommand{\0}{\vct{0}}
\newcommand{\SIG}{\vct{\sigma}}
\newcommand{\minus}{\ensuremath{\scalebox{0.5}[0.75]{\( - \)}}}
\newcommand{\plus}{\ensuremath{\scalebox{0.5}[0.75]{\( + \)}}}
\newcommand{\MINUS}{\ensuremath{\quad - \quad}}
\newcommand{\PLUS}{\ensuremath{\quad + \quad}}

%%%%%% Norm and differential operator
\newcommand{\X}{\! \times \!}
\newcommand{\norm}[1]{\ensuremath{\left\lVert#1\right\rVert}}
\renewcommand{\i}{\ensuremath{\mathrm{i}}}
\newcommand{\vect}[1]{\ensuremath{\mathbf{#1}}}
\newcommand{\hel}[2]{\ensuremath{ \left < #1 \right. \vert  \left. #2 \right > }}
\newcommand{\kronecker}[2]{\ensuremath{\delta_{\negmedspace #1#2}}}
\DeclareMathOperator{\lap}{L_2}
\DeclareMathOperator{\dif}{d}

%%%%%% Spatial-temporal operator
\newcommand{\dt}{\ensuremath{\partial_t}}
\newcommand{\Dt}{\ensuremath{D_t}}
\newcommand{\Ct}{\ensuremath{C_t}}
\newcommand{\Pt}{\ensuremath{P_t}}

%%%%%% Vecorial calculus	
\newcommand{\Div}[1]{\vct{\nabla} \cdot \left(#1\right)}
\newcommand{\Rot}[1]{\vct{\nabla} \! \times \! \left(#1\right)}
\newcommand{\diV}{\vct{\nabla} \cdot }
\newcommand{\roT}{\vct{\nabla} \!\times\! }
\newcommand{\grad}{\vct{\nabla}}
\newcommand{\gradd}{\vct{\nabla}_d}
\newcommand{\diVo}{\vct{\nabla}_{\!\! O} \cdot }
\newcommand{\roTo}{\vct{\nabla}_{\!\! O} \!\times\!}
\newcommand{\grado}{\vct{\nabla}_{\!\! O}}
\newcommand{\diVp}{\vct{\nabla}_{\!\! P} \cdot }
\newcommand{\roTp}{\vct{\nabla}_{\!\! P} \!\times\!}
\newcommand{\gradp}{\vct{\nabla}_{\!\! P}}
\newcommand{\laplacien}{\ensuremath{\vct{\nabla}^2}}
\newcommand{\Laplace}{\ensuremath{\mathop{}\!\mathbin\bigtriangleup}}

\newcommand{\ptial}[2]{\ensuremath{\left[\partial_{#1}\right]_{\! #2}}}

\newcommand{\av}[1]{\ensuremath{\langle #1 \rangle}}
\newcommand{\utot}{\ensuremath{u^{tot}}}
\newcommand{\Itot}{\ensuremath{\vect{I}^{tot}}}
\newcommand{\Iq}{\ensuremath{\vect{I}^{q}}}
\newcommand{\IS}{\ensuremath{\vect{I}^{S}}}
\newcommand{\ISt}{\ensuremath{\vect{I}^{St}}}
\newcommand{\Inu}{\ensuremath{\vect{I}^{\nu}}}
\newcommand{\Ek}{\ensuremath{E^k}}
\newcommand{\EI}{\ensuremath{E^I}}
\newcommand{\EH}{\ensuremath{E^H}}
\newcommand{\Qnu}{\ensuremath{Q^\nu}}

%%%%%% Dilaplacian
\newcommand{\dilap}{\vct{\Delta \!\!\! \Delta}}
\newcommand{\al}{\vct{\alpha}}

%%%%%% Phy stat
\newcommand{\zcan}{\mathscr{Z}}
\newcommand{\zcano}{\mathscr{Z}_{0}}
\newcommand{\zcani}{\mathscr{Z}_{1}}
\newcommand{\zcanii}{\mathscr{Z}_{2}}

\newcommand{\zcanab}{\mathscr{Z}_{AB}}
\newcommand{\zcanc}{\mathscr{Z}_{C}}
\newcommand{\zcande}{\mathscr{Z}_{DE}}

%%%%% Raph
\newcommand{\gG}{\vct{g}}
\newcommand{\ez}{\vct{e}_\text{z}}
\newcommand{\Tzero}{\ensuremath{T_0}}
\newcommand{\rhozero}{\ensuremath{\rho_0}}
\newcommand{\Ra}{\ensuremath{\mathrm{Ra}}}
\newcommand{\Prandtl}{\ensuremath{\mathrm{Pr} \,}}

%%%%%% MACRO
\newcommand{\ign}[1]{\ensuremath{ s \left ( #1 \right)}}
%\newcommand{\ign}[1]{\ensuremath{ s _ {#1} }}

%%%%% Complexity
%\newcommand{\Ld}[1]{\ensuremath{\overset{#1}{L}}}
\newcommand{\Ld}[1]{\ensuremath{L^{#1}{}}}

%%%%% Variables used for scheme ABC
\newcommand{\sme}[2]{\ensuremath{ {#1} _{\mbox{\tiny $#2$}} \!{} }}
\newcommand{\smea}[2]{\ensuremath{ {#1}^a_{\mbox{\tiny $#2$}} \!{} }}
%\newcommand{\sme}[2]{\ensuremath{ \left . #1 \right \vert_{\mbox{\tiny $#2$}} \!{} }}
%\newcommand{\sme}[2]{\ensuremath{{}^{\mbox{\tiny $#2$ }}\!\! #1}}

\newcommand{\xicN}{\sme{\xi}{\cgreen{\mathscr{N}}}}
\newcommand{\xicA}{\sme{\xi}{\cred{\mathscr{A}}}}
\newcommand{\xicB}{\sme{\xi}{\cblue{\mathscr{B}}}}
\newcommand{\xicC}{\sme{\xi}{\cyello{\mathscr{C}}}}

\newcommand{\xiN}{\sme{\xi}{\mathscr{N}}}
\newcommand{\xiA}{\sme{\xi}{\mathscr{A}}}
\newcommand{\xiB}{\sme{\xi}{\mathscr{B}}}
\newcommand{\xiC}{\sme{\xi}{\mathscr{C}}}

\newcommand{\PhiN}{\sme{\Phi}{\mathscr{N}}}
\newcommand{\PhiA}{\sme{\Phi}{\mathscr{A}}}
\newcommand{\PhiB}{\sme{\Phi}{\mathscr{B}}}
\newcommand{\PhiC}{\sme{\Phi}{\mathscr{C}}}
\newcommand{\PhiF}{\sme{\Phi}{\mathscr{F}}}

\newcommand{\PHIA}{\sme{\Phi}{\mathscr{A}}}
\newcommand{\PHIB}{\sme{\Phi}{\mathscr{B}}}
\newcommand{\PHIC}{\sme{\Phi}{\mathscr{C}}}
\newcommand{\PHID}{\sme{\Phi}{\mathscr{D}}}

\newcommand{\SA}{\sme{S}{\mathscr{A}}}
\newcommand{\SB}{\sme{S}{\mathscr{B}}}
\newcommand{\SC}{\sme{S}{\mathscr{C}}}
\newcommand{\SD}{\sme{S}{\mathscr{D}}}

\newcommand{\cN}{\sme{c}{\mathscr{N}}}
\newcommand{\cA}{\sme{c}{\mathscr{A}}}
\newcommand{\cB}{\sme{c}{\mathscr{B}}}
\newcommand{\cC}{\sme{c}{\mathscr{C}}}
\newcommand{\cD}{\sme{c}{\mathscr{D}}}

\newcommand{\caN}{\smea{c}{\mathscr{N}}}
\newcommand{\caA}{\smea{c}{\mathscr{A}}}
\newcommand{\caB}{\smea{c}{\mathscr{B}}}
\newcommand{\caC}{\smea{c}{\mathscr{C}}}
\newcommand{\caD}{\smea{c}{\mathscr{D}}}

\newcommand{\cMA}{\sme{c_{\max}}{\mathscr{A}}}
\newcommand{\cMB}{\sme{c_{\max}}{\mathscr{B}}}

\newcommand{\CN}{\sme{c}{\mathscr{N}}}
\newcommand{\CA}{\sme{c}{\mathscr{A}}}
\newcommand{\CB}{\sme{c}{\mathscr{B}}}
\newcommand{\CC}{\sme{c}{\mathscr{C}}}
\newcommand{\CD}{\sme{c}{\mathscr{D}}}

\newcommand{\dN}{\sme{d}{\mathscr{N}}}
\newcommand{\dA}{\sme{d}{\mathscr{A}}}
\newcommand{\dB}{\sme{d}{\mathscr{B}}}
\newcommand{\dC}{\sme{d}{\mathscr{C}}}
\newcommand{\dD}{\sme{d}{\mathscr{D}}}

\newcommand{\ups}{\ensuremath{\underline{\upsilon}}}
\newcommand{\upsN}{\sme{\underline{\upsilon}}{\mathscr{N}}}
\newcommand{\upsA}{\sme{\underline{\upsilon}}{\mathscr{A}}}
\newcommand{\upsB}{\sme{\underline{\upsilon}}{\mathscr{B}}}
\newcommand{\upsC}{\sme{\underline{\upsilon}}{\mathscr{C}}}

\newcommand{\ALX}{\ensuremath{\mathscr{A}}}
\newcommand{\BEC}{\ensuremath{\mathscr{B}}}
\newcommand{\CAM}{\ensuremath{\mathscr{C}}}
\newcommand{\FIC}{\ensuremath{\mathscr{F}}}
\newcommand{\NSL}{\ensuremath{\mathscr{N}}}
\newcommand{\RMT}{\ensuremath{\mathscr{R}}}
\newcommand{\ULM}{\CAM}

\newcommand{\MSL}{\ensuremath{\mathscr{M}}}
\newcommand{\ICM}{\ensuremath{\mathscr{I}}}
\newcommand{\JCM}{\ensuremath{\mathscr{J}}}
\newcommand{\KCM}{\ensuremath{\mathscr{K}}}
