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diff --git a/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex b/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex new file mode 100644 index 00000000000..3cc345c5242 --- /dev/null +++ b/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex @@ -0,0 +1,225 @@ +% 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}}%\\ + \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}}%\\ + \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}}%\\ + \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 a<c % Autre cas délicat + \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{#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}%\\ + \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}}\tikzmark{H-\theNbequa}%\\ + \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 a<c % Autre cas délicat + \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}{\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}%\\ + \ifboolKV[ClesEquation]{Entier}{% + \SSimpliTest{\Coeffb}{\Coeffa}% + \ifboolKV[ClesEquation]{Simplification}{% + \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\ + }{} + }{} + } + \end{align*} + }% + }% + }% + }% + }% + }% +}% + + |