$ \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} \newcommand{\delim}[3]{\raise #1\hbox{$\left #2\vbox to #3{}\right.$}} \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 %\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 \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\(#1 \pv #2 \)}} $
