% Licence : Released under the LaTeX Project Public License v1.3c % or later, see http://www.latex-project.org/lppl.txtf \newcommand\EquaBaseSymbole[5][]{%type ax=d ou b=cx \useKVdefault[ClesEquation]% \setKV[ClesEquation]{#1}% \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false} \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... \ifx\bla#4\bla %% il manque un paramètre \else \EquaBaseSymbole[#1]{#4}{}{}{#3} \fi \else % si non, on est dans le cas ax=d \xintifboolexpr{#2==0}{% \xintifboolexpr{#5==0}{% L'équation $0\times\useKV[ClesEquation]{Lettre}=0$ a une infinité de solutions.}{L'équation $0\times\useKV[ClesEquation]{Lettre}=\num{#5}$ n'a aucune solution.}% }{%\else \xintifboolexpr{#5==0}{L'équation $\num{#2}\times\useKV[ClesEquation]{Lettre}=0$ a une unique solution : $\useKV[ClesEquation]{Lettre}=0$.}{%\else \begin{align*}% \xintifboolexpr{#2==1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}&=\num{#5}\\ \useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}%\\ %% decimal \ifboolKV[ClesEquation]{Decimal}{% \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{#5/#2}}% }{}% % %%% \ifboolKV[ClesEquation]{Entier}{% \SSimpliTest{#5}{#2}% \ifboolKV[ClesEquation]{Simplification}{% \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\ }{} }{} \end{align*} } } \fi } \newcommand\EquaDeuxSymbole[5][]{%type ax+b=d ou b=cx+d$ \useKVdefault[ClesEquation]% \setKV[ClesEquation]{#1}% \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false} \ifx\bla#2\bla%On échange en faisant attention à ne pas boucler : c doit être non vide \EquaDeuxSymbole[#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 \EquaBaseSymbole[#1]{#2}{}{}{#5}% }{%ax+b=d$ Ici \begin{align*} \xintifboolexpr{#2==1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\ \ifboolKV[ClesEquation]{Bloc}{\Fdash{$\xintifboolexpr{#2==1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}$}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\}{}% \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa==1}{\useKV[ClesEquation]{Lettre}}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}&=\num{\Coeffb}%\\ \xintifboolexpr{\Coeffa==1}{% }{%\ifnum\cmtd>1 \\ \useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\ %% decimal \ifboolKV[ClesEquation]{Decimal}{% \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\Coeffa}}% }{}% %%% \ifboolKV[ClesEquation]{Entier}{% \SSimpliTest{\Coeffb}{\Coeffa}% \ifboolKV[ClesEquation]{Simplification}{% \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ }{} }{} } \end{align*} } } \fi } \newcommand\EquaTroisSymbole[5][]{%ax+b=cx ou ax=cx+d \useKVdefault[ClesEquation]% \setKV[ClesEquation]{#1}% \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false} \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5 \ifx\bla#5\bla% %% paramètre oublié \else \EquaTroisSymbole[#1]{#4}{#5}{#2}{}% \fi \else \xintifboolexpr{#2==0}{%b=cx \EquaBaseSymbole[#1]{#4}{}{}{#3} }{% \xintifboolexpr{#4==0}{%ax+b=0 \EquaDeuxSymbole[#1]{#2}{#3}{}{0} }{%ax+b=cx \xintifboolexpr{#2==#4}{% \xintifboolexpr{#3==0}{%ax=ax L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}=\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}$ a une infinité de solutions.}% {%ax+b=ax L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.% }% }{%% Cas délicat \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c \begin{align*} \multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\\ \mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#4-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#2-#4}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\\ \xdef\Coeffa{\fpeval{#2-#4}}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\ \ifboolKV[ClesEquation]{Bloc}{\Fdash{\mathcolor{Csymbole}{$\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}$}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\}{} \xdef\Coeffb{\fpeval{0-#3}}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}%\\ \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1 \\\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\ %% decimal \ifboolKV[ClesEquation]{Decimal}{% \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\Coeffa}}% }{}% %%% \ifboolKV[ClesEquation]{Entier}{% \SSimpliTest{\Coeffb}{\Coeffa}% \ifboolKV[ClesEquation]{Simplification}{% \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ }{} }{} } \end{align*} }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\\ \mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#2-1}}{+\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#2-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#4-#2}}{+\useKV[ClesEquation]{Lettre}}\\ \xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{\Coeffa-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}% \\ \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1 \\\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\ %% decimal \ifboolKV[ClesEquation]{Decimal}{% \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}% }{}% %%% \ifboolKV[ClesEquation]{Entier}{% \SSimpliTest{\Coeffb}{\Coeffa}% \ifboolKV[ClesEquation]{Simplification}{% \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ }{} }{} } \end{align*} }% }% }% }% \fi }% \newcommand\ResolEquationSymbole[5][]{% \useKVdefault[ClesEquation]% \setKV[ClesEquation]{#1}% \setKV[ClesEquation]{Fleches=false,FlecheDiv=false,Terme=false,Decomposition=false} \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$ \EquaDeuxSymbole[#1]{#4}{#5}{#2}{#3}% }% }{% \xintifboolexpr{#4==0}{%ax+b=0x+d \EquaDeuxSymbole[#1]{#2}{#3}{}{#5}% } {%ax+b=cx+d$ \xintifboolexpr{#3==0}{% \xintifboolexpr{#5==0}{%ax=cx \EquaTroisSymbole[#1]{#2}{0}{#4}{}% }% {%ax=cx+d \EquaTroisSymbole[#1]{#4}{#5}{#2}{}% }% }% {\xintifboolexpr{#5==0}{%ax+b=cx \EquaTroisSymbole[#1]{#2}{#3}{#4}{}% }% {%ax+b=cx+d -- ici \xintifboolexpr{#2==#4}{% \xintifboolexpr{#3==#5}{%b=d L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une infinité de solutions.}% {%b<>d L'équation $\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ n'a aucune solution.% }% }{ %% Cas délicat \xintifboolexpr{#2>#4}{%ax+b=cx+d avec a>c \begin{align*} \multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ \mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#4-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#2-#4}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ \xdef\Coeffa{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\ \ifboolKV[ClesEquation]{Bloc}{% \Fdash{$\mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}}$}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\ }{}% \xdef\Coeffb{\fpeval{#5-#3}}\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}&=\num{\Coeffb}%\\ \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1 \\\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\ %% decimal \ifboolKV[ClesEquation]{Decimal}{% \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\Coeffa}}% }{}% %%% \ifboolKV[ClesEquation]{Entier}{% \SSimpliTest{\Coeffb}{\Coeffa}% \ifboolKV[ClesEquation]{Simplification}{% \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\ }{} }{} } \end{align*} }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\multido{\i=1+1}{\fpeval{#4-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ \mathcolor{Csymbole}{\multido{\i=1+1}{\fpeval{#2-1}}{\useKV[ClesEquation]{Lettre}+}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{#2-1}}{+\useKV[ClesEquation]{Lettre}}}\multido{\i=1+1}{\fpeval{#4-#2}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ \xdef\Coeffa{\fpeval{#4-#2}}\num{#3}&=\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ \ifboolKV[ClesEquation]{Bloc}{% \num{#3}&=\Fdash{$\mathcolor{Csymbole}{\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}}$}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\ }{}% \xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\useKV[ClesEquation]{Lettre}\multido{\i=1+1}{\fpeval{\Coeffa-1}}{+\useKV[ClesEquation]{Lettre}}%\\ \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1 \\\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\ %% decimal \ifboolKV[ClesEquation]{Decimal}{% \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}% }{}% %%% \ifboolKV[ClesEquation]{Entier}{% \SSimpliTest{\Coeffb}{\Coeffa}% \ifboolKV[ClesEquation]{Simplification}{% \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ }{} }{} } \end{align*} }% }% }% }% }% }% }%