$
\newcommand{\parallele}{\sslash}
\newcommand{\para}{\sslash}
\newcommand{\er}{\textsuperscript{er}\ }
\newcommand{\eme}{\textsuperscript{ème}\ }
\newcommand{\ere}{\textsuperscript{ère}\ }
\newcommand{\snd}{\textsuperscript{nd}\ }
\newcommand{\snde}{\textsuperscript{nde}\ }
\newcommand{\iem}{\textsuperscript{ième}\ }
\newcommand{\x}{\times}
\newcommand{\ie}{\leqslant}
\newcommand{\se}{\geqslant}
\newcommand{\qqquad}{\quad\qquad}
\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\D}{\mathbb D}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}
\newcommand{\F}{\mathbb F}
\newcommand{\K}{\mathbb K}
\newcommand{\U}{\mathbb U}
%\newcommand{\Code}[1]{ {\verb+#1+} }
\newcommand{\Code}[1]{{\ttfamily #1}}
%\newcommand{\partent}{\mathsf{ent}}
\newcommand{\E}{\mathsf{E}}
%\newcommand{\alea}{\verb?alea?}
\newcommand{\partent}{\text{\Code{ent}} }
\newcommand{\alea}{\text{\Code{alea}} }
\newcommand{\epsi}{\varepsilon} % epsilonn
\newcommand{\f}{\othervarphi} % fonction phi
\newcommand{\g}{\gamma}
\newcommand{\al}{\alpha}
\newcommand{\de}{\delta}
\newcommand{\De}{\Delta}
\newcommand{\Ga}{\Gamma}
\newcommand{\La}{\Lambda}
\newcommand{\la}{\lambda}
\renewcommand{\o}{\otheromega}
\newcommand{\si}{\sigma}
\newcommand{\Ta}{\Theta}
\newcommand{\teta}{\theta}
\renewcommand{\O}{\Omega}
\newcommand{\prive}{\setminus}%{\backslash}
\newcommand{\union}{\cup}
\newcommand{\inter}{\cap}
\newcommand{\vide}{\varnothing}
\newcommand{\card}{\mathop{\rm card}\nolimits}
\newcommand{\paire}[2]{\{#1\, ;\, #2\}}
\newcommand{\Paire}[2]{\left\{#1\, ;\, #2\right\}}
\newcommand{\enstrois}[3]{\{#1\, ;\, #2\, ;\, #3\}}
\newcommand{\Enstrois}[3]{\left\{#1\, ;\, #2\, ;\, #3\right\}}
\newcommand{\ensquatre}[4]{\{#1\, ;\, #2\, ;\, #3\, ;\, #4\}}
\newcommand{\Ensquatre}[4]{\left\{#1\, ;\, #2\, ;\, #3\, ;\, #4\right\}}
\newcommand{\triplet}[3]{(#1\, ;\, #2\, ;\, #3)}
\newcommand{\quadruplet}[4]{(#1\, ;\, #2\, ;\, #3\, ; #4)}
\newcommand{\nuplet}[2]{(#1\, ;\,\ldots\, ;\, #2)}
\newcommand{\Nuplet}[2]{\left(#1\, ;\,\ldots\, ;\, #2\right)}
\newcommand{\ensemble}[2]{\{#1\, ;\,\ldots\, ;\, #2\}}
\newcommand{\interieur}[1]{\ring{#1}}
\newcommand{\ens}[1]{\left\{\,#1\,\right\}}
\newcommand{\tq}{ \ \ \textrm{t.q} \ \ }
\newcommand{\tqc}{ \textrm{t.q} }
\newcommand{\Frac}[2]{\frac{\disp #1}{\disp #2}}
\newcommand{\tvi}[2]{\vrule height #1 depth #2 width 0pt}
\newcommand{\rond}{\circ}
\newcommand{\ps}{\cdot}
\newcommand{\ovra}[3]{\mkern #1mu\overrightarrow{\mkern -#1mu #2\mkern -#3mu}\mkern #3mu}
\newcommand{\ovla}[3]{\mkern #1mu\overleftarrow{\mkern -#1mu #2\mkern -#3mu}\mkern #3mu}
% La definition d'origine encadrait son corps de deux delimiteurs de formule.
% Ces delimiteurs coupaient le bloc de macros en morceaux : MathJax cherche
% simplement le prochain delimiteur sans tenir compte des accolades, si bien
% que les macros situees plus bas n'etaient plus definies du tout.
% La version ci-dessous rend le meme service, sans delimiteur imbrique.
% ATTENTION : ne jamais ecrire de delimiteur de formule dans ce fichier,
% pas meme a l'interieur d'un commentaire : MathJax les lit quand meme.
\newcommand{\delim}[3]{#2}
\renewcommand{\(}{\left( }
\renewcommand{\)}{\right) }
\newcommand{\oc}{\left[}
\newcommand{\fc}{\right]}
\newcommand{\norme}[1]{\| #1 \|}
\newcommand{\normebis}[1]{\delim{2pt}{\|}{9pt}\! #1\delim{2pt}{\|}{9pt}}
\newcommand{\normetriple}[1]{\left |\kern -.07em\left\| #1\right |\kern -.07em\right\|}
\newcommand{\valabs}[1]{\delim{2pt}{|}{9pt}#1\delim{2pt}{|}{9pt}}
\newcommand{\Abs}[1]{\left \lvert#1\right \rvert}
\newcommand{\dist}[2]{\textrm{d}(#1\textrm{;\,} #2)}
\newcommand{\limit}[2]{\displaystyle\lim_{#1} #2}
\newcommand{\limitx}[3]{\displaystyle\lim_{#1\to #2} #3}
\newcommand{\limitxinf}[3]{\displaystyle\lim_{#1\build{\to}_{<}^{} #2} #3}
\newcommand{\limitxsup}[3]{\displaystyle\lim_{#1\build{\to}_{>}^{} #2} #3}
\newcommand{\tend}[2]{\displaystyle\build\longrightarrow_{#1\rightarrow #2}^{}}
\newcommand{\ds}{\displaystyle}
\newcommand{\fonc}[4]{#1\ :\begin{array}{rll} #2 &\to \\ x& \mapsto \end{array}}
\newcommand{\Fonc}[5]{#1\ :\begin{array}{rll} #2 &\to \\ #4& \mapsto \end{array}}
\newcommand{\limd}[2][x]{\ds\lim_{{#1\to #2}\atop{#1>#2}} }
\newcommand{\limcd}[1]{\ds\lim_{#1^+} }
\newcommand{\limg}[2][x]{\ds\lim_{{#1\to #2}\atop{#1<#2}} }
\newcommand{\limcg}[1]{\ds\lim_{#1^-} }
\newcommand{\limc}[1]{\ds\lim_{#1} }
\newcommand{\lin}{\ds\lim_{n\to +\infty}}
\newcommand{\Lim}[2][x]{\displaystyle{\lim_{#1 \to #2}}}
\newcommand{\Li}[2]{\left.\begin{array}{lcr} #1\\ #2 \end{array}\right\}}
\newcommand{\somme}[3][i]{\sum\limits_{\substack{#1=#2}}^{#3}}
\newcommand{\Tendvers}[2][h]{\underset{#1\rightarrow #2}{\longrightarrow}}
\newcommand{\un}{{(u_n)}_{n\in\N}\ } % suite un {(t_{n})}_{n\in\N}
\newcommand{\unstar}{{(u_n)}_{n\in\N^{\ast}}\ } % suite un
\newcommand{\vn}{{(v_n)}_{n\in\N}\ } %suite vn
\newcommand{\wn}{{(w_n)}_{n\in\N}\ } %suite wn
\newcommand{\tn}{{(t_n)}_{n\in\N}\ } %suite tn
\newcommand{\sn}{{(s_n)}_{n\in\N}\ } %suite tn
\newcommand{\rn}{{(r_n)}_{n\in\N}\ } %suite tn
\newcommand{\xn}{{(x_n)}_{n\in\N}\ } %suite tn
\newcommand{\yn}{{(y_n)}_{n\in\N}\ } %suite tn
\newcommand{\zn}{{(z_n)}_{n\in\N}\ } %suite tn
\newcommand{\an}{{(a_n)}_{n\in\N}\ } %suite tn
\newcommand{\bn}{{(b_n)}_{n\in\N}\ } %suite tn
\newcommand{\cn}{{(c_n)}_{n\in\N}\ } %suite tn
\newcommand{\dn}{{(d_n)}_{n\in\N}\ } %suite tn
\newcommand{\en}{{(e_n)}_{n\in\N}\ } %suite tn
\newcommand{\enstar}{{(e_n)}_{n\in\N^{\ast}}\ } % suite un
%
%
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Equivalent
\newcommand{\equivalent}[1]{\build\sim_{#1}^{}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% o et O
\renewcommand{\o}[2]{\build o_{#1\to #2}^{}}
\renewcommand{\O}[2]{\build O_{#1\to #2}^{}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Displaystyle
\newcommand{\disp}{\displaystyle}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signes d'equivalence et d'implication
\newcommand{\equivaut}{\Longleftrightarrow}
\newcommand{\equi}{\Leftrightarrow}
\newcommand{\implique}{\Longrightarrow}
\newcommand{\impli}{\Rightarrow}
\newcommand{\ssi}{\textrm{ \ ssi \ }}
\newcommand{\idest}{\quad \textrm{i.e} \quad}
\newcommand{\cad}{\quad \textrm{c-à-d} \quad}
%
\newcommand{\ssic}{\textrm{ssi} }
\newcommand{\idestc}{\textrm{i.e} }
\newcommand{\cadc}{\textrm{c-à-d}}
\newcommand{\maxi}{ \textrm{max}}
\newcommand{\sgn}{\textrm{sgn}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signe associe
\newcommand{\associe}{\longmapsto}
\newcommand{\asso}{\mapsto}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Angles
\renewcommand{\angle}[1]{\widehat{#1}}
\newcommand{\anglevec}[2]{(\vec #1\, ,\,\vec #2)}
\newcommand{\Anglevec}[2]{(\V{#1}\, ,\,\V{#2})}
\newcommand{\anglecouple}[2]{\left( #1\, ,\, #2 \right) }
%\newcommand{\anglevecteur0}[3][black]{(\widehat{\vec{#2}\, , \, \textcolor{#1}{\vec{#3}}})}
%\newcommand{\anglevecteur}[4][black]{\anglevecteur0{#2}{ \textcolor{#1}{#3} }{#4} }
\newcommand{\anglevecteur}[2]{(\widehat{\vec{#1}\, , \, \vec{#2}} ) }
%\newcommand{\anglevecteurcouleur}[4]{(\textcolor{#1}{\vec{#3}}\, , \, \textcolor{#2}{\vec{#4}}) }
\newcommand{\Anglevecteur}[2]{\(\widehat{\V{#1},\V{#2}}\)}
\newcommand{\rad}{ \,\,\textrm{rad} }
\newcommand{\mes}{\textrm{mes} }
\newcommand{\°}{\degres}
\newcommand{°}{\degres}
\newcommand{\Mes}[1]{\mes\,\widehat{#1}}
\newcommand{\mesvec}[2]{\textrm{mes}\(\vec{#1} \, , \, \vec{#2}\)}
\newcommand{\mesvecteur}[2]{\textrm{mes}\anglevecteur{#1}{#2}}
\newcommand{\mesVec}[2]{\textrm{mes}\(\V{#1} \, , \, \V{#2}\)}
\newcommand{\mesarc}[1]{\textrm{mes}\(\widehat{#1}\)}
\newcommand{\mesarco}[1]{\textrm{mes}\(\arcoriente{#1}\)}
\newcommand{\ao}[2]{\left(#1\, , \, #2\right)}
%\newcommand{\Mes}[1]{%
% \ensuremath{%
% \mathrm{mes}
% \DecalV{\widehat{#1}}
% }}
%\DeclareTextSymbol{\degree}{T1}{6}
%\DeclareTextSymbol{\degre}{OT1}{23}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vecteurs
%\newcommand{\vecteur}[1]{\ovra 0{#1}0}
\newcommand{\prodscal}[2]{<#1,#2>}
\newcommand{\prodvec}[2]{#1\wedge #2}
\newcommand{\vectoriel}[2]{\prodvec{\vec #1}{\vec #2}}
\newcommand{\Vectoriel}[2]{\prodvec{\vecteur{#1}}{\vecteur{#2}}}
\newcommand{\prodmixte}[3]{\big[#1, #2, #3\big]}
\newcommand{\mixte}[3]{\prodmixte{\vec #1}{\vec #2}{\vec #3}}
\newcommand{\Mixte}[3]{\prodmixte{\vecteur{#1}}{\vecteur{#2}}{\vecteur{#3}}}
\newcommand{\V}[1]{\ovra 0{#1}0}
%
\newcommand{\test}[2]{#1^2-#2^2}
%
%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Repères (O,i), (O,i,j), (O,u,v), (O,I,J) et quelconques
\newcommand{\Oi}{(O\, ;\,\vec\imath\,)}
\newcommand{\Oj}{(O\, ;\,\vec\jmath\,)}
\newcommand{\Oij}{(O\, ;\,\vec\imath\, ;\vec\jmath\,)}
\newcommand{\Aij}{(A\, ;\,\vec\imath\, ;\vec\jmath\,)}
\newcommand{\Omegaij}{(\Omega\, ;\,\vec\imath\, ;\vec\jmath\,)}
\newcommand{\Ai}{(A\, ;\,\vec\imath\,)}
\newcommand{\Aj}{(A\, ;\,\vec\jmath\,)}
\newcommand{\Ojk}{(O\, ;\,\vec\jmath\, ;\vec k\,)}
\newcommand{\Oik}{(O\, ;\,\vec\imath\, ;\vec k\,)}
\newcommand{\Ouv}{(O\, ;\,\vec u\, ;\vec v\,)}
\renewcommand{\ij}{(\vec\imath\, ;\vec\jmath\,)}
\newcommand{\ijk}{(\vec\imath\, ;\vec\jmath\, ;\vec k\,)}
\newcommand{\Oijk}{\big(O\, ;\,\vec\imath\, ;\vec\jmath\, ;\vec k\,\big)}
\newcommand{\oijk}{\big(o\, ;\,\vec\imath\, ;\vec\jmath\, ;\vec k\,\big)}
\newcommand{\OIJ}{(O\,;\, I\,;\, J\,)}
\newcommand{\repere}[3]{\big(#1\, ;\,\vecteur{#2} ;\vecteur{#3}\big)}
\newcommand{\reperesp}[4]{\big(#1\, ;\,\vecteur{#2} ;\vecteur{#3} ;\vecteur{#4}\big)}
%
\newcommand{\reperepol}[2]{\big(#1\, ;\,\vecteur{#2}\big)}
\newcommand{\reperesf}[3]{\big(#1\, ;\,#2 ; #3 \big)}
%
%Redéfinition de \longrightarrow
% Ligne d'origine desactivee, retiree ici : elle contenait des delimiteurs de
% formule que MathJax lisait malgre le commentaire, ce qui coupait le bloc.
% \newcommand\longrightarrow{\mathrel{\raise .02em\hbox{\relbar}}\joinrel\rightarrow}
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Aire d'une surface
\newcommand{\aire}[1]{%
\ensuremath{\mathscr{A}_{#1}}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Volume d'un volume
\newcommand{\volume}[1]{%
\ensuremath{\mathscr{V}_{#1}}}
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% un ; avec un peu d'espace autour
\newcommand{\pv}{\ensuremath{\: ; \,}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intervalles
\newcommand{\interoo}[2]{]#1\, ;\, #2[}
\newcommand{\Interoo}[2]{\left]#1\, ;\, #2\right[}
\newcommand{\interof}[2]{]#1\, ;\, #2]}
\newcommand{\Interof}[2]{\left]#1\, ;\, #2\right]}
\newcommand{\interfo}[2]{[#1\, ;\, #2[}
\newcommand{\Interfo}[2]{\left[#1\, ;\, #2\right[}
\newcommand{\interff}[2]{[#1\, ;\, #2]}
\newcommand{\Interff}[2]{\left[#1\, ;\, #2\right]}
%
\newcommand{\of}[2]{\left] \,#1 \, ; \, #2 \,\right] }
\newcommand{\fo}[2]{\left[ \,#1 \, ; \, #2 \,\right[ }
\newcommand{\oo}[2]{\left] \,#1 \, ; \, #2 \,\right[ }
\newcommand{\ff}[2]{\left[ \,#1 \, ; \, #2 \,\right] }
%
%\newcommand\interentiers #1#2{[\! [#1\, ;\, #2]\! ]}
\newcommand{\interentiers}[2]{\llbracket #1\, ;\, #2\rrbracket}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% autres intervalles
\newcommand{\Intff}[2]{\ensuremath{\left[#1\pv #2\right]}}
\newcommand{\Intfo}[2]{\ensuremath{\left[#1\pv #2\right[}}
\newcommand{\Intof}[2]{\ensuremath{\left]#1\pv #2\right]}}
\newcommand{\Intoo}[2]{\ensuremath{\left]#1\pv #2\right[}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées
%\newcommand{\coord}[2]{(#1\, ;\, #2)}
\newcommand{\bigcoord}[2]{\big(#1\, ;\, #2\big)}
\newcommand{\coord}[2]{\left(#1\, ;\, #2\right)}
\newcommand{\Coord}[2]{\left(#1\, ;\, #2\right)}
\newcommand{\coordesp}[3]{(#1\, ;\, #2\, ;\, #3)}
\newcommand{\bigcoordesp}[3]{\big(#1\, ;\, #2\, ;\, #3\big)}
\newcommand{\Coordesp}[3]{\left(#1\, ;\, #2\, ;\, #3\right)}
\newcommand{\coordpol}[2]{\left[#1\, ;\, #2\right]}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées verticales dans le plan
\newcommand{\coordp}[2]{%
\begin{pmatrix}
#1 \\ #2
\end{pmatrix}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées verticales dans l'espace
\newcommand{\coordpp}[3]{%
\scalebox{.7}{%
\begin{pmatrix}
#1 \\ #2 \\ #3
\end{pmatrix}}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Congruences
\newcommand{\congru}{\equiv}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Modulo 2pi ou autre
\newcommand{\Mod}[1][2\pi]{\enspace{(#1)}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Quel que soit
\newcommand{\qqsoit}{\forall\,}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Différentielles
\renewcommand{\d}{\textrm d}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intégrale
\newcommand{\integ}[4]{\int_{#1}^{#2} #3\,\d #4}
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intégration par parties
% Les delimiteurs de formule qui encadraient cette definition ont ete retires :
% on est deja en mode mathematique, et ils coupaient le bloc de macros en deux.
\newcommand{\intpp}[4]{%
\left\{%
\begin{matrix}
#1 & #3 \\
\stackrel{}{#2} & \stackrel{}{#4} \\
\end{matrix}
\right.}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Somme majuscule
\newcommand{\Sum}{\displaystyle{\sum}}
%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Barycentres
\newcommand{\bary}{\mathop{\rm Bar}\nolimits}
\newcommand{\baryd}[4]{\(#1\, ;\, #2\)\ \textrm{et}\ \(#3\, ;\, #4 \)}
\newcommand{\baryt}[6]{(#1\, ;\, #2),\ (#3\, ;\, #4)\ \textrm{et}\ (#5\, ;\, #6)}
\newcommand{\baryq}[8]{(#1\, ;\, #2),\ (#3\, ;\, #4),\ (#5\, ;\, #6)\ \textrm{et}\ (#7\, ;\, #8)}
\newcommand{\Baryd}[4]{\bary \left\lbrace \(#1\, ;\, #2 \)\, ;\, \(#3\, ;\, #4 \) \right\rbrace }
\newcommand{\Baryt}[6]{\bary \left\lbrace \(#1\, ;\, #2\)\, ;\, \(#3\, ;\, #4 \)\, ;\, \(#5\, ;\, #6 \) \right\rbrace }
\newcommand{\Baryn}[6]{\bary \left\lbrace \(#1\, ;\, #2\)\, ;\, \(#3\, ;\, #4 \)\, ;\,\ldots\, ;\, \(#5\, ;\, #6\) \right\rbrace }
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signe inclusion
\newcommand{\inclus}{\subset}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonctions
\newcommand{\fonction}[5]{
\begin{eqnarray*}
#1 & \!\!\!\!\! : & \!\!\!\!\! #2\longrightarrow #3\\
& & \!\!\!\!\! #4\longmapsto #5
\end{eqnarray*}
}
\newcommand{\fonctionligne}[5]{#1:#2\longrightarrow #3,\ #4\longmapsto #5}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Unités de longueur en rm
\newcommand{\cm}{\mathop{\rm cm}\nolimits}
\newcommand{\mm}{\mathop{\rm mm}\nolimits}
\newcommand{\dm}{\mathop{\rm dm}\nolimits}
\newcommand{\m}{\mathop{\rm m}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction logarithme intégral [Plt137]
\newcommand{\li}{\mathop{\rm li}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction exponentielle
\newcommand{\e}{\mathop{\rm e}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction cotangente
\newcommand{\cotan}{\mathop{\rm cotan}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonctions hyperboliques
\newcommand{\ch}{\mathop{\rm ch}\nolimits}
\newcommand{\sh}{\mathop{\rm sh}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Parties entière, réelle, imaginaire, nombre i
\newcommand{\ent}{\mathop{\rm E}\nolimits}
\newcommand{\Int}{\mathop{\rm Int}\nolimits}
\renewcommand{\Re}{\mathop{\rm Re}\nolimits}
\renewcommand{\Im}{\mathop{\rm Im}\nolimits}
\renewcommand{\i}{\textrm{i}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Comatrice
\newcommand{\com}{\mathop{\rm com}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Trace
\newcommand{\tr}{\mathop{\rm tr}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Transposée
\newcommand{\transposee}[1]{{\vphantom{#1}}^t\negmedspace #1}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Noyau
\newcommand{\Ker}{\mathop{\rm Ker}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PGCD, PPCM
\newcommand{\PGCD}{\mathop{\rm PGCD}\nolimits}
\newcommand{\PPCM}{\mathop{\rm PPCM}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Matrices
\newcommand{\Mn}{\mathcal M_n}
\newcommand{\matrice}[4]{
\left(
\begin{array}{cc}
#1 & #2 \\
#3 & #4
\end{array}
\right)}
\newcommand{\vect}[2]{
\left(\negmedspace
\begin{array}{c}
#1\\
#2
\end{array}\negmedspace
\right)}
\newcommand{\Matrice}[9]{
\left(
\begin{array}{ccc}
#1 & #2 & #3\\
#4 & #5 & #6\\
#7 & #8 & #9
\end{array}
\right)}
\newcommand{\Vect}[3]{
\left(\negmedspace
\begin{array}{c}
#1\\
#2\\
#3
\end{array}\negmedspace
\right)}
\newcommand{\Ideux}{\matrice{1}{0}{0}{1}}
\newcommand{\Itrois}{\Matrice{1}{0}{0}{0}{1}{0}{0}{0}{1}}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Determinants
\newcommand{\determinant}[4]{
\left|
\begin{array}{cc}
#1 & #3 \\
#2 & #4
\end{array}
\right|}
\newcommand{\Determinant}[9]{
\left|
\begin{array}{ccc}
#1 & #2 & #3\\
#4 & #5 & #6\\
#7 & #8 & #9
\end{array}
\right|}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Systemes
\newcommand{\sysu}[1]{
\left\lbrace
\begin{array}{l}
#1\\
\end{array}
\right.}
\newcommand{\sys}[2]{
\left\lbrace
\begin{array}{l}
\negthickspace\negthickspace #1\\
\negthickspace\negthickspace #2\\
\end{array}
\right.\negthickspace\negthickspace}
\newcommand{\sysd}[2]{
%\left\lbrace
\left\{
\begin{array}{l}
#1\\
#2
\end{array}
\right.}
%%%%%%%%%%%%%%%%%%%%%%%%
%\left\{\begin{array}{l c l}
%v_{0} &=& 1\\
%v_{n + 1}&=& \dfrac{9}{6 - v_{n}}
%\end{array}\right.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\syst}[3]{
\left\lbrace
\begin{array}{l}
#1\\
#2\\
#3\\
\end{array}
\right.}
\newcommand{\sysq}[4]{
\left\lbrace
\begin{array}{l}
#1\\
#2\\
#3\\
#4\\
\end{array}
\right.}
\newcommand{\sysc}[5]{
\left\lbrace
\begin{array}{l}
#1\\
#2\\
#3\\
#4\\
#5\\
\end{array}
\right.}
\newcommand{\sisi}[4]{
\left\lbrace
\begin{array}{rm{0.2cm}l}
#1 & & \text{#2}\\
#3 & & \text{#4}
\end{array}
\right.}
%
%\newcommand{\accod}[4]{\begin{cases} #1 & #2 \\ #3 & #4 \end{cases} }
%
\newcommand{\accot}[6]{\begin{cases} #1 & #2 \\ #3 & #4 \\ #5 & #6 \end{cases} }
%%
%\newcommand{\accod}[2]{ \left\{
% \begin{split}
% #1 \\
% #2
% \end{split}
% \right. }
%
\newcommand{\accott}[3]{
\begin{equation}
\left\{
\begin{split}
#1 \\
#2 \\
#3
\end{split}
\right.
\end{equation} }
\newcommand{\Syst}[2]{\left\{\begin{array}{ccccc} #1\\ #2 \end{array}\right.}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Covariance
\newcommand{\cov}{\mathop{\rm cov}\nolimits}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Symboles entre droites
%\newcommand{\paral}{\sslash}
\newcommand{\paral}{\mathop{/\!\! /}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% jours heures minutes secondes
\newcommand{\jour}{\ \textrm{j} \ }
\newcommand{\heure}{\ \textrm{h} \ }
\newcommand{\minute}{\ \textrm{min} \ }
\newcommand{\seconde}{\ \textrm{s} \ }
\newcommand{\algobox}{\texttt{AlgoBox}}
\newcommand{\xcas}{\texttt{Xcas}}
\newcommand{\excel}{\texttt{Excel}\ }
\newcommand{\calc}{\texttt{Calc}}
\newcommand{\geogebra}{\texttt{GeoGebra}}
\newcommand{\python}{\texttt{Python}\ }
\newcommand{\ou}{ \quad \text{ ou } \quad }
\newcommand{\et}{ \quad \text{ et } \quad }
\newcommand{\btr}{\ensuremath{\blacktriangleright\ }}
\newcommand{\wtr}{\ensuremath{\triangleright\ }}
\newcommand{\bp}{\ensuremath{\bullet\ }}
%%%%%%%%%%%%%%%%%%%%% B(n;p) - Loi binomiale %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\bnp}[2][n]{\ensuremath{\mathscr B\(#1 \pv #2 \)}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Adaptations pour MathJax
%
% Ces quelques macros reposaient sur des primitives de mise en boite de TeX
% (\vbox, \vrule, \raise\hbox) qui n'ont pas d'equivalent en HTML. On leur
% redonne ici un sens, avec les delimiteurs extensibles de MathJax qui font
% exactement le meme travail.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\delim}[3]{#2}
\renewcommand{\tvi}[2]{}
\renewcommand{\normebis}[1]{\left\| #1 \right\|}
\renewcommand{\valabs}[1]{\left| #1 \right|}
\renewcommand{\Code}[1]{\texttt{#1}}
\renewcommand{\partent}{\texttt{ent}}
\renewcommand{\alea}{\texttt{alea}}
\renewcommand{\interieur}[1]{\mathring{#1}}
$
Aller au contenu
Mathématiques au lycée & au collège
Tous les documents de la classe, au même endroit.
Les supports exploités en classe — illustrations du cours, fiches d'exercices, devoirs
à la maison et devoirs surveillés — ainsi que leurs corrigés.
S'y ajoutent des ressources complémentaires : exercices corrigés, rappels des années
précédentes, diaporamas de correction et vidéos.
Pour ceux qui doutent de l'utilité des mathématiques :
L'explosion des mathématiques, les métiers
avec des maths et quelques autres lectures.
9documents
4chapitres
1niveaux
