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diff --git a/macros/latex/contrib/profcollege/latex/PfCResoudreEquation.tex b/macros/latex/contrib/profcollege/latex/PfCResoudreEquation.tex new file mode 100644 index 0000000000..ae3896a98e --- /dev/null +++ b/macros/latex/contrib/profcollege/latex/PfCResoudreEquation.tex @@ -0,0 +1,286 @@ +%%% +% Equations +%%% +\setKVdefault[ClesEquation]{Ecart=0.5,Fleches=false,FlecheDiv=false,Laurent=false,Decomposition=false,Terme=false,Composition=false,Symbole=false,Decimal=false,Entier=false,Lettre=x,Solution=false,LettreSol=true,Bloc=false,Simplification=false,CouleurTerme=black,CouleurCompo=black,CouleurSous=red,CouleurSymbole=orange,Verification=false,Nombre=0,Egalite=false,Produit=false,Facteurs=false,Carre=false,Exact=false,Pose=false,Equivalence=false} + +\newcommand\rightcomment[4]{% + \begin{tikzpicture}[remember picture,overlay] + \draw[Cfleches,-stealth] + ($({pic cs:#3}|-{pic cs:#1})+(\useKV[ClesEquation]{Ecart},0)$) + .. controls +(0.2,-0.05) and +(0.2,0.1) .. + node[right,align=left]{#4} + ($({pic cs:#3}|-{pic cs:#2})+(\useKV[ClesEquation]{Ecart},0.1)$); + \end{tikzpicture}% +}% + +\newcommand\leftcomment[4]{% + \begin{tikzpicture}[remember picture,overlay] + \draw[Cfleches,-stealth] + ($({pic cs:#3}|-{pic cs:#1})-(\useKV[ClesEquation]{Ecart},0)$) + .. controls +(-0.2,-0.05) and +(-0.2,0.1) .. + node[left,align=right]{#4} + ($({pic cs:#3}|-{pic cs:#2})-(\useKV[ClesEquation]{Ecart},-0.1)$); + \end{tikzpicture}% +}% + +\newcommand\Rightcomment[4]{% + \begin{tikzpicture}[remember picture,overlay] + \draw[Cfleches,-stealth] + ($({pic cs:#3}|-{pic cs:#1})+(\useKV[ClesEquation]{Ecart},0)$) + .. controls +(0.2,-0.05) and +(0.2,0.1) .. + node[right,align=left]{#4} + ($({pic cs:#3}|-{pic cs:#2})+(\useKV[ClesEquation]{Ecart},0.1)$); + \end{tikzpicture}% +}% +\newcommand\Leftcomment[4]{% + \begin{tikzpicture}[remember picture,overlay] + \draw[Cfleches,-stealth] + ($({pic cs:#3}|-{pic cs:#1})-(\useKV[ClesEquation]{Ecart},0)$) + .. controls +(-0.2,-0.05) and +(-0.2,0.1) .. + node[left,align=right]{#4} + ($({pic cs:#3}|-{pic cs:#2})-(\useKV[ClesEquation]{Ecart},-0.1)$); + \end{tikzpicture}% +}% + +% Pour "oublier" les tikzmarks. En cas de plusieurs utilisations de la macro \ResolEquation +\newcounter{Nbequa} +\setcounter{Nbequa}{0} + +%CT +\newdimen\fdashwidth \fdashwidth = 0.8pt % \'epaisseur traits +\newdimen\fdashlength \fdashlength = 0.5mm % longueur des pointill\'es et s\'eparation entre pointill\'es +\newdimen\fdashsep \fdashsep = 3pt % s\'eparateur entre contenu et traits + +\def\fdash#1{% + \leavevmode\begingroup% + \setbox0\hbox{#1}% + \def\hdash{\vrule height\fdashwidth width\fdashlength\relax}% + \def\vdash{\hrule height\fdashlength width\fdashwidth\relax}% + \def\dashblank{\kern\fdashlength}% + \ifdim\fdashsep>0pt + \setbox0\hbox{\vrule width0pt height\dimexpr\ht0+\fdashsep depth\dimexpr\dp0+\fdashsep\kern\fdashsep\unhbox0 \kern\fdashsep}% + \fi + \edef\hdash{\hbox to\the\wd0{\noexpand\color{Csymbole}\hdash\kern.5\fdashlength\xleaders\hbox{\hdash\dashblank}\hfil\hdash}}% + \edef\vdash{\vbox to\the\dimexpr\ht0+\dp0+2\fdashwidth{\noexpand\color{Csymbole}\vdash\kern.5\fdashlength\xleaders\vbox{\vdash\dashblank}\vfil\vdash}}% + \hbox{% + \vdash + \vtop{\vbox{\offinterlineskip\hdash\hbox{\unhbox0 }\hdash}}% + \vdash}% + \endgroup +} +% fin CT +\def\Fdash#1{\raisebox{-2\fdashsep+\fdashwidth}{\fdash{#1}}} + +%Une simplification de a/b est possible ou non ? +\newboolean{Simplification} + +\newcommand\SSimpliTest[2]{% + % Test d'une simplification possible ou pas de #1/#2 + \newcount\numerateur\newcount\denominateur\newcount\valabsnum\newcount\valabsdeno% + \numerateur=\number#1 + \denominateur=\number#2 + \ifnum\number#1<0 + \valabsnum=\numexpr0-\number#1 + \else + \valabsnum=\number#1 + \fi + \ifnum\number#2<0 + \valabsdeno=\numexpr0-\number#2 + \else + \valabsdeno=\number#2 + \fi + \ifnum\the\valabsnum=0 + \setboolean{Simplification}{true} + \else + \PGCD{\the\valabsnum}{\the\valabsdeno} + \ifnum\pgcd>1 + \setboolean{Simplification}{true} + \else + \ifnum\the\numerateur<0 + \ifnum\the\denominateur<0 + \setboolean{Simplification}{true} + \else + \ifnum\valabsdeno=1\relax + \setboolean{Simplification}{true} + \else + \setboolean{Simplification}{false} + \fi + \fi + \else + \ifnum\valabsdeno=1\relax + \setboolean{Simplification}{true} + \else + \setboolean{Simplification}{false} + \fi + \fi + \fi + \fi +} + +\definecolor{Cfleches}{RGB}{100,100,100}% + +\newcommand\AffichageEqua[4]{% + \def\LETTRE{\useKV[ClesEquation]{Lettre}}% + \ensuremath{% + % partie du x + \xintifboolexpr{#1==0}{}{\xintifboolexpr{#1==1}{}{\xintifboolexpr{#1==-1}{-}{\num{#1}}}\LETTRE}% + % partie du nombre + \xintifboolexpr{#2==0}{\xintifboolexpr{#1==0}{0}{}}{\xintifboolexpr{#2>0}{\xintifboolexpr{#1==0}{}{+}\num{#2}}{\num{#2}}}% + % egal + = + % partie du x + \xintifboolexpr{#3==0}{}{\xintifboolexpr{#3==1}{}{\xintifboolexpr{#3==-1}{-}{\num{#3}}}\LETTRE}% + % partie du nombre + \xintifboolexpr{#4==0}{% + \xintifboolexpr{#3==0}{0}{} + }{% + \xintifboolexpr{#4>0}{\xintifboolexpr{#3==0}{}{+}\num{#4}}{\num{#4}}% + } + }% +}% + +\newcommand\EcrireSolutionEquation[4]{% + L'équation \AffichageEqua{#1}{#2}{#3}{#4} a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$. +}% + +\input{PfCEquationSoustraction2}% +\input{PfCEquationTerme1}% +\input{PfCEquationComposition2}% +\input{PfCEquationPose1}% +\input{PfCEquationSymbole1}% +\input{PfCEquationLaurent1} + +\newcommand\ResolEquation[5][]{% + \useKVdefault[ClesEquation]% + \setKV[ClesEquation]{#1}% + \colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}% + \colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}% + \colorlet{Csymbole}{\useKV[ClesEquation]{CouleurSymbole}}% + \colorlet{Cdecomp}{\useKV[ClesEquation]{CouleurSous}}% + \ifboolKV[ClesEquation]{Carre}{% + \ResolEquationCarre[#1]{#2}% + }{% + \ifboolKV[ClesEquation]{Produit}{% + \ResolEquationProduit[#1]{#2}{#3}{#4}{#5}% + }{% + \ifboolKV[ClesEquation]{Verification}{% + \Verification[#1]{#2}{#3}{#4}{#5}% + }{% + \ifboolKV[ClesEquation]{Symbole}{% + \ResolEquationSymbole[#1]{#2}{#3}{#4}{#5}% + }{% + \ifboolKV[ClesEquation]{Laurent}{% + \ResolEquationLaurent[#1]{#2}{#3}{#4}{#5}% + }{% + \ifboolKV[ClesEquation]{Terme}{% + \ResolEquationTerme[#1]{#2}{#3}{#4}{#5}% + }{\ifboolKV[ClesEquation]{Composition}{% + \ResolEquationComposition[#1]{#2}{#3}{#4}{#5}% + }{\ifboolKV[ClesEquation]{Pose}{% + \ResolEquationL[#1]{#2}{#3}{#4}{#5}% + }{% + \ResolEquationSoustraction[#1]{#2}{#3}{#4}{#5}% + }% + }% + }% + }% + }% + }% + }% + }% +}% + +\newcommand\ResolEquationCarre[2][]{% + \setKV[ClesEquation]{#1}% + \xintifboolexpr{#2<0}{% + Comme $\num{#2}$ est n\'egatif, alors l'\'equation $\useKV[ClesEquation]{Lettre}^2=\num{#2}$ n'a aucune solution.% + }{\xintifboolexpr{#2==0}{% + L'\'equation $\useKV[ClesEquation]{Lettre}^2=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.% + }{% + Comme \num{#2} est positif, alors l'\'equation $\useKV[ClesEquation]{Lettre}^2=\num{#2}$ a deux solutions :% + \begin{align*} + \useKV[ClesEquation]{Lettre}&=\sqrt{\num{#2}}&&\text{et}&\useKV[ClesEquation]{Lettre}&=-\sqrt{\num{#2}}%\\ + \ifboolKV[ClesEquation]{Exact}{\\% + \useKV[ClesEquation]{Lettre}&=\num{\fpeval{sqrt(#2)}}&&\text{et}&\useKV[ClesEquation]{Lettre}&=-\num{\fpeval{sqrt(#2)}}}{}% + \end{align*} + }% + }% +}% + +\newcommand\ResolEquationProduit[5][]{% + \setKV[ClesEquation]{#1}% + \ifboolKV[ClesEquation]{Equivalence}{}{C'est un produit nul donc \ifboolKV[ClesEquation]{Facteurs}{l'un au + moins des facteurs est nul}{} :}% + \ifboolKV[ClesEquation]{Equivalence}{% + \[\Distri{#2}{#3}{#4}{#5}=0\] + \begin{align*}% + &\makebox[0pt]{$\Longleftrightarrow$}&\xintifboolexpr{#3==0}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}&=0&\quad&\makebox[0pt]{ou}\quad&\xintifboolexpr{#5==0}{\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}{\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}&=0\\ + &\makebox[0pt]{$\Longleftrightarrow$}&\xintifboolexpr{#3==0}{\xdef\Coeffa{1}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{#2==1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}}&&&\xintifboolexpr{#5==0}{\xdef\Coeffc{1}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{#4==1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffc{#4}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{\Coeffc==1}{}{\num{\Coeffc}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffd}}%\\ + \xintifboolexpr{\Coeffa==1 'and' \Coeffc==1}{}{\\%\ifnum\cmtd>1 + &\makebox[0pt]{$\Longleftrightarrow$}&\xintifboolexpr{\Coeffa==1}{&}{\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}}\xintifboolexpr{\Coeffc==1}{}{&&&\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffd}}{\num{\Coeffc}}} + % accolade%\\ + %%%% + \ifboolKV[ClesEquation]{Entier}{% + \xdef\TSimp{}% + \SSimpliTest{\Coeffb}{\Coeffa}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#3==0}{\xdef\TSimp{0}}{\xdef\TSimp{1}}}{\xdef\TSimp{0}} + \SSimpliTest{\Coeffd}{\Coeffc}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#5==0}{}{\xdef\TSimp{\fpeval{\TSimp+1}}}}{} + \xintifboolexpr{\TSimp==0}{}{\\ + \ifboolKV[ClesEquation]{Simplification}{% + &\makebox[0pt]{$\Longleftrightarrow$}&\SSimpliTest{\Coeffb}{\Coeffa}\xintifboolexpr{\Coeffa==1}{&}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{&}%\\ + } + }{} + &&&\ifboolKV[ClesEquation]{Simplification}{% + \SSimpliTest{\Coeffd}{\Coeffc}% + \xintifboolexpr{\Coeffc==1}{}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffd}{\Coeffc}}{}%\\ + } + }{} + } + }{} + } + \end{align*} + }{% + \begin{align*} + \xintifboolexpr{#3==0}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}&=0&&\text{ou}&\xintifboolexpr{#5==0}{\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}{\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}&=0\\ + \xintifboolexpr{#3==0}{\xdef\Coeffa{1}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{#2==1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}}&&&\xintifboolexpr{#5==0}{\xdef\Coeffc{1}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{#4==1}{&}{\useKV[ClesEquation]{Lettre}&=0}}{\xdef\Coeffc{#4}\xdef\Coeffd{\fpeval{0-#5}}\xintifboolexpr{\Coeffc==1}{}{\num{\Coeffc}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffd}}%\\ + \xintifboolexpr{\Coeffa==1 'and' \Coeffc==1}{}{\\%\ifnum\cmtd>1 + \xintifboolexpr{\Coeffa==1}{&}{\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}}\xintifboolexpr{\Coeffc==1}{}{&&&\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffd}}{\num{\Coeffc}}} + %accolade%\\ + %%%% + \ifboolKV[ClesEquation]{Entier}{% + \xdef\TSimp{} + \SSimpliTest{\Coeffb}{\Coeffa}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#3==0}{\xdef\TSimp{0}}{\xdef\TSimp{1}}}{\xdef\TSimp{0}} + \SSimpliTest{\Coeffd}{\Coeffc}\ifthenelse{\boolean{Simplification}}{\xintifboolexpr{#5==0}{}{\xdef\TSimp{\fpeval{\TSimp+1}}}}{} + \xintifboolexpr{\TSimp==0}{}{\\ + \ifboolKV[ClesEquation]{Simplification}{% + \SSimpliTest{\Coeffb}{\Coeffa} + \xintifboolexpr{\Coeffa==1}{&}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{&}%\\ + } + }{} + &&&\ifboolKV[ClesEquation]{Simplification}{% + \SSimpliTest{\Coeffd}{\Coeffc}% + \xintifboolexpr{\Coeffc==1}{}{\ifthenelse{\boolean{Simplification}}{\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffd}{\Coeffc}}{}%\\ + } + }{} + } + }{} + } + \end{align*} + }% + \ifboolKV[ClesEquation]{Solution}{L'\'equation $\xintifboolexpr{#3==0}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}{(\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}})}\xintifboolexpr{#5==0}{\times\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}{(\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}})}=0$ a deux solutions : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$ et \opdiv*{\Coeffd}{\Coeffc}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffd}{\Coeffc}}{\frac{\num{\Coeffd}}{\num{\Coeffc}}}\fi$. + }{}% +} + +\newcommand\Verification[5][]{% + \setKV[ClesEquation]{#1}% + \xdef\ValeurTest{\useKV[ClesEquation]{Nombre}}% + Testons la valeur $\useKV[ClesEquation]{Lettre}=\num{\ValeurTest}$ :% + \begin{align*} + \xintifboolexpr{#2==0}{\num{#3}}{\num{#2}\times\xintifboolexpr{\ValeurTest<0}{(\num{\ValeurTest})}{\num{\ValeurTest}}\xintifboolexpr{#3==0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{\num{#3}}}}&&\xintifboolexpr{#4==0}{\num{#5}}{\num{#4}\times\xintifboolexpr{\ValeurTest<0}{(\num{\ValeurTest})}{\num{\ValeurTest}}\xintifboolexpr{#5==0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{\num{#5}}}}\\ + \xintifboolexpr{#2==0}{}{\num{\fpeval{#2*\useKV[ClesEquation]{Nombre}}}\xintifboolexpr{#3==0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{\num{#3}}}}&&\xintifboolexpr{#4==0}{}{\num{\fpeval{#4*\useKV[ClesEquation]{Nombre}}}\xintifboolexpr{#5==0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{\num{#5}}}}\\ + \xintifboolexpr{#2==0}{}{\num{\fpeval{#2*\useKV[ClesEquation]{Nombre}+#3}}}&&\xintifboolexpr{#4==0}{}{\num{\fpeval{#4*\useKV[ClesEquation]{Nombre}+#5}}} + \end{align*} + \xdef\Testa{\fpeval{#2*\useKV[ClesEquation]{Nombre}+#3}}\xdef\Testb{\fpeval{#4*\useKV[ClesEquation]{Nombre}+#5}}% + \ifboolKV[ClesEquation]{Egalite}{% + Comme \xintifboolexpr{\Testa==\Testb}{$\num{\Testa}=\num{\Testb}$}{$\num{\Testa}\not=\num{\Testb}$}, alors l'\'egalit\'e $\xintifboolexpr{#2==0}{\num{#3}}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3==0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}}=\xintifboolexpr{#4==0}{\num{#5}}{\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5==0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}}$ \xintifboolexpr{\Testa==\Testb}{ est v\'erifi\'ee }{ n'est pas v\'erifi\'ee } pour $\useKV[ClesEquation]{Lettre}=\num{\useKV[ClesEquation]{Nombre}}$.% + }{\xintifboolexpr{\Testa==\Testb}{Comme $\num{\Testa}=\num{\Testb}$, alors $\useKV[ClesEquation]{Lettre}=\num{\useKV[ClesEquation]{Nombre}}$ est bien }{Comme $\num{\Testa}\not=\num{\Testb}$, alors $\useKV[ClesEquation]{Lettre}=\num{\useKV[ClesEquation]{Nombre}}$ n'est pas }une solution de l'\'equation $\xintifboolexpr{#2==0}{\num{#3}}{\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3==0}{}{\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}}=\xintifboolexpr{#4==0}{\num{#5}}{\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5==0}{}{\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}}$.}% +}%
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