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author | Karl Berry <karl@freefriends.org> | 2021-04-27 12:58:55 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2021-04-27 12:58:55 +0000 |
commit | 1f3f8f2f09e41e60169435266645008a4407f650 (patch) | |
tree | b131f951fe6574654294681e968e6691072c6f46 /Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex | |
parent | 56887973b56bae72759bb0b0bf0d2e378810946b (diff) |
profcollege runtime
git-svn-id: svn://tug.org/texlive/trunk@58995 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex')
-rw-r--r-- | Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex | 226 |
1 files changed, 226 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex b/Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex new file mode 100644 index 00000000000..8bce1eb7c80 --- /dev/null +++ b/Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex @@ -0,0 +1,226 @@ +% 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 solutions.}{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 : $\displaystyle\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.% + }{} + } + } + \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 solutions.}% + {%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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$. + }{} + } + } +} + +\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 solutions.}% + {%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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{} + }{%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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}% + }% + }% + }% + }% + \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 solutions.}% + {%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 solutions.}% + {%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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{} + }{%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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{}% + }% + }% + }% + }% + }% + }% +}%
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