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authorNorbert Preining <norbert@preining.info>2021-01-18 03:03:11 +0000
committerNorbert Preining <norbert@preining.info>2021-01-18 03:03:11 +0000
commit62b141a25b6f63cb4cc626d1a005ecf67c19e5cd (patch)
treeb7d0b0cdf0cae01fab47cd7deb6f19d4dc04ff1e /macros/latex/contrib/profcollege/latex/EquationLaurent1.tex
parent8591b56496b93eed20f638ee1ce46b11c3f7be58 (diff)
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+% Licence : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaBaseLaurent}[5][]{%type ax=d ou b=cx
+ \useKVdefault[ClesEquation]%
+ \setKV[ClesEquation]{#1}%
+ \ifx\bla#2\bla%on teste si le paramètre #2 est vide:
+ % si oui, on est dans le cas b=cx. Eh bien on échange :)
+ % Mais attention si les deux paramètres a et c sont vides...
+ \EquaBase[#1]{#4}{}{}{#3}
+ \else
+ % si non, on est dans le cas ax=d
+ \xintifboolexpr{#2=0}{%
+ \xintifboolexpr{#5=0}{%
+ L'équation $0\useKV[ClesEquation]{ELettre}=0$ a une infinité de solution.}{L'équation $0\useKV[ClesEquation]{Lettre}=\num{#5}$ n'a aucune solution.}%
+ }{%\else
+ \xintifboolexpr{#5=0}{L'équation $\num{#2}\useKV[ClesEquation]{Lettre}=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.}{%\else
+ \begin{align*}%
+ \xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{#2}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{#2}}}}&=\xintifboolexpr{#2=1}{\num{#5}}{\color{Cdecomp}\frac{\color{black}\num{#5}}{\num{#2}}}
+ \xintifboolexpr{#2=1}{}{\\\useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}}%\\
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{#5}{#2}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\
+ }{}
+ }{}
+ \end{align*}
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}=\num{#5}}{\num{#2}\useKV[ClesEquation]{Lettre}=\num{#5}}$ a une unique solution : $\displaystyle\useKV[ClesEquation]{Lettre}=\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.%
+ }{}
+ }
+ }
+ \fi
+}
+
+\newcommand{\EquaDeuxLaurent}[5][]{%type ax+b=d ou b=cx+d$
+ \useKVdefault[ClesEquation]%
+ \setKV[ClesEquation]{#1}%
+ \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide
+ \EquaDeuxLaurent[#1]{#4}{#5}{#2}{#3}
+ \else%cas ax+b=d
+ \xintifboolexpr{#2=0}{%
+ \xintifboolexpr{#3=#5}{%b=d
+ L'équation $\num{#3}=\num{#5}$ a une infinité de solution.}%
+ {%b<>d
+ L'équation $\num{#3}=\num{#5}$ n'a aucune solution.%
+ }%
+ }{%ELSE
+ \xintifboolexpr{#3=0}{%ax+b=d
+ \EquaBaseLaurent[#1]{#2}{}{}{#5}%
+ }{%ax+b=d$ Ici
+ \begin{align*}
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=\num{#5}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+ \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}%\\
+ \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \end{align*}
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\num{#5}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+ }{}
+ }
+ }
+}
+
+\newcommand{\EquaTroisLaurent}[5][]{%ax+b=cx ou ax=cx+d
+ \useKVdefault[ClesEquation]%
+ \setKV[ClesEquation]{#1}%
+ \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5
+ \ifx\bla#5\bla%
+ %% paramètre oublié
+ \else
+ \EquaTroisLaurent[#1]{#4}{#5}{#2}{}%
+ \fi
+ \else
+ \xintifboolexpr{#2=0}{%b=cx
+ \EquaBaseLaurent[#1]{#4}{}{}{#3}
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0
+ \EquaDeuxLaurent[#1]{#2}{#3}{}{0}
+ }{%ax+b=cx
+ \xintifboolexpr{#2=#4}{%
+ \xintifboolexpr{#3=0}{%ax=ax
+ L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solution.}%
+ {%ax+b=ax
+ L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.%
+ }%
+ }{%% Cas délicat
+ \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c
+ \begin{align*}
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}\\
+ \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{0-#3}}%\\
+ \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \end{align*}
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}
+ }{%ax+b=cx avec a<c % Autre cas délicat
+ \begin{align*}%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\\
+ \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{0-#3}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=0\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+ \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \end{align*}
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}%
+ }%
+ }%
+ }%
+ }%
+ \fi
+}%
+
+\newcommand{\ResolEquationLaurent}[5][]{%
+ \useKVdefault[ClesEquation]%
+ \setKV[ClesEquation]{#1}%
+ \xintifboolexpr{#2=0}{%
+ \xintifboolexpr{#4=0}{%
+ \xintifboolexpr{#3=#5}{%b=d
+ L'équation $\num{#3}=\num{#5}$ a une infinité de solution.}%
+ {%b<>d
+ L'équation $\num{#3}=\num{#5}$ n'a aucune solution.%
+ }%
+ }%
+ {%0x+b=cx+d
+ \EquaDeuxLaurent[#1]{#4}{#5}{}{#3}%
+ }%
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0x+d
+ \EquaDeuxLaurent[#1]{#2}{#3}{}{#5}%
+ }
+ {%ax+b=cx+d
+ \xintifboolexpr{#3=0}{%
+ \xintifboolexpr{#5=0}{%ax=cx
+ \EquaTroisLaurent[#1]{#2}{0}{#4}{}%
+ }%
+ {%ax=cx+d
+ \EquaTroisLaurent[#1]{#4}{#5}{#2}{}%
+ }%
+ }%
+ {\xintifboolexpr{#5=0}{%ax+b=cx
+ \EquaTroisLaurent[#1]{#2}{#3}{#4}{}%
+ }%
+ {%ax+b=cx+d -- ici
+ \xintifboolexpr{#2=#4}{%
+ \xintifboolexpr{#3=#5}{%b=d
+ L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solution.}%
+ {%b<>d
+ L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.%
+ }%
+ }{%% Cas délicat
+ \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c
+ \begin{align*}
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{-\num{\fpeval{0-#3}}\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}}}\stackText}\\
+ \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{#5-#3}}%\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{\Coeffb>0}{+\num{\Coeffb}}{-\num{\fpeval{0-\Coeffb}}}\\
+ \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \end{align*}
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ }{}
+ }{%ax+b=cx+d avec a<c % Autre cas délicat
+ \begin{align*}%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}} {}}\stackText}%
+ &=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\xintifboolexpr{#3>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#3} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#3}} {}}\stackText}
+ \\
+ \xdef\Coeffa{\fpeval{#2-#4}}\xdef\Coeffb{\fpeval{#5-#3}}%\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{\stackMath\Longstack{\tiny\color{Cdecomp}-\num{#4}\useKV[ClesEquation]{Lettre} {}}\stackText}{\stackMath\Longstack{\tiny\color{Cdecomp}+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre} {}}\stackText}\xintifboolexpr{\Coeffb>0}{+\num{\Coeffb}}{-\num{\fpeval{0-\Coeffb}}}\\
+ \xintifboolexpr{\Coeffa=1}{\useKV[ClesEquation]{Lettre}}{\color{Cdecomp}\frac{\cancel{\color{black}\num{\Coeffa}}\color{black}\useKV[ClesEquation]{Lettre}}{\cancel{\num{\Coeffa}}}}&=\xintifboolexpr{\Coeffa=1}{\num{\Coeffb}}{\color{Cdecomp}\frac{\color{black}\num{\Coeffb}}{\num{\Coeffa}}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \end{align*}
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\useKV[ClesEquation]{Lettre}=\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ }{}%
+ }%
+ }%
+ }%
+ }%
+ }%
+ }%
+}% \ No newline at end of file