texlive[58995] Master: profcollege runtime
commits+karl at tug.org
commits+karl at tug.org
Tue Apr 27 14:58:55 CEST 2021
Revision: 58995
http://tug.org/svn/texlive?view=revision&revision=58995
Author: karl
Date: 2021-04-27 14:58:55 +0200 (Tue, 27 Apr 2021)
Log Message:
-----------
profcollege runtime
Modified Paths:
--------------
trunk/Master/tlpkg/libexec/ctan2tds
Added Paths:
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trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationComposition2.tex
trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex
trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationPose1.tex
trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSoustraction2.tex
trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSymbole1.tex
trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationTerme1.tex
Removed Paths:
-------------
trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationComposition2.tex
trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationLaurent1.tex
trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationPose1.tex
trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSoustraction2.tex
trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex
trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationTerme1.tex
Deleted: trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationComposition2.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationComposition2.tex 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationComposition2.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -1,275 +0,0 @@
-% Licence : Released under the LaTeX Project Public License v1.3c
-% or later, see http://www.latex-project.org/lppl.txtf
-\newcommand{\EquaDeuxComposition}[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
- \EquaDeuxComposition[#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
- \EquaBase[#1]{#2}{}{}{#5}%
- }{%ax+b=d$ Ici
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
- \begin{align*}
- \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{%
- }{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{%ICI ?
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
- }{}
- }
- }
- \fi
-}
-
-\newcommand{\EquaTroisComposition}[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
- \EquaTroisComposition[#1]{#4}{#5}{#2}{}%
- \fi
- \else
- \xintifboolexpr{#2=0}{%b=cx
- \EquaBase[#1]{#4}{}{}{#3}
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0
- \EquaDeuxComposition[#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
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
- \begin{align*}
- \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\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}\tikzmark{E-\theNbequa}\\
- \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{0}\tikzmark{F-\theNbequa}\\
- \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{0-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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+d avec a<c % Autre cas délicat
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
- \begin{align*}%
- \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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{\ResolEquationComposition}[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$
- \EquaDeuxComposition[#1]{#4}{#5}{#2}{#3}%
- }%
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0x+d
- \EquaDeuxComposition[#1]{#2}{#3}{}{#5}%
- }
- {%ax+b=cx+d$
- \xintifboolexpr{#3=0}{%
- \xintifboolexpr{#5=0}{%ax=cx
- \EquaTroisComposition[#1]{#2}{0}{#4}{}%
- }%
- {%ax=cx+d
- \EquaTroisComposition[#1]{#4}{#5}{#2}{}%
- }%
- }%
- {\xintifboolexpr{#5=0}{%ax+b=cx
- \EquaTroisComposition[#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
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
- \begin{align*}
- \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\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}}}\tikzmark{E-\theNbequa}\\
- \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\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}}}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{F-\theNbequa}\\
- \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}%
- \begin{align*}%
- \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\
- \mathcolor{Ccompo}{\num{\fpeval{#3-#5}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
- }{}%
- }%
- }%
- }%
- }%
- }%
- }%
-}%
\ No newline at end of file
Deleted: trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationLaurent1.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationLaurent1.tex 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationLaurent1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -1,226 +0,0 @@
-% 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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
- }{}%
- }%
- }%
- }%
- }%
- }%
- }%
-}%
\ No newline at end of file
Deleted: trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationPose1.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationPose1.tex 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationPose1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -1,246 +0,0 @@
-% Licence : Released under the LaTeX Project Public License v1.3c
-% or later, see http://www.latex-project.org/lppl.txtf
-\newcommand{\EquaBaseL}[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...
- \EquaBaseL[#1]{#4}{}{}{#3}
- \else
- % si non, on est dans le cas ax=d
- \xintifboolexpr{#2=0}{%
- \xintifboolexpr{#5=0}{%
- L'équation $0\useKV[ClesEquation]{Lettre}=0$ 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}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\\
- \xintifboolexpr{#2=1}{}{%
- \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\phantom{\useKV[ClesEquation]{Lettre}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\\}
- \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}}{}%\\
- }{}
- }{}
- %\ifboolKV[ClesEquation]{Fleches}{%
- %\stepcounter{Nbequa}}%
- %{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}
- %}
- \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{\EquaDeuxL}[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
- \EquaDeuxL[#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
- \EquaBaseL[#1]{#2}{}{}{#5}%
- }{%ax+b=d$ Ici
- \begin{align*}
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\
- \phantom{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&\phantom{\mathrel{=}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
- \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\Coeffb}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \xintifboolexpr{\Coeffa=1}{%
- }{%\ifnum\cmtd>1
- \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\\
- \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{%
- \\\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
- }{}
- }
- }
- \fi
-}
-
-\newcommand{\EquaTroisL}[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
- \EquaTroisL[#1]{#4}{#5}{#2}{}%
- \fi
- \else
- \xintifboolexpr{#2=0}{%b=cx
- \EquaBaseL[#1]{#4}{}{}{#3}
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0
- \EquaDeuxL[#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}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\
- \mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
- \xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
- \phantom{\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}&\phantom{\mathrel{=}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}\\
- \xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\Coeffb}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \xintifboolexpr{\Coeffa=1}{%
- }{%\ifnum\cmtd>1
- \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
- \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\%
- \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\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+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{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\
- \mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
- \xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \xintifboolexpr{\Coeffa=1}{%
- }{%\ifnum\cmtd>1
- \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
- \frac{\num{\Coeffb}}{\num{\Coeffa}}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\%
- \SSimplifie{\Coeffb}{\Coeffa}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
- }{}
- }{}
- }{}
- \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{\ResolEquationL}[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$
- \EquaDeuxL[#1]{#4}{#5}{}{#3}%
- }%
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0x+d
- \EquaDeuxL[#1]{#2}{#3}{}{#5}%
- }
- {%ax+b=cx+d$
- \xintifboolexpr{#3=0}{%
- \xintifboolexpr{#5=0}{%ax=cx
- \EquaTroisL[#1]{#2}{0}{#4}{}%
- }%
- {%ax=cx+d
- \EquaTroisL[#1]{#4}{#5}{#2}{}%
- }%
- }%
- {\xintifboolexpr{#5=0}{%ax+b=cx
- \EquaTroisL[#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}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{\phantom{{}={}}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
- \xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{\phantom{{}+{}}\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}&\phantom{{}={}\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}\\
- \xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{\Coeffb>0}{\phantom{{}+{}}\num{\Coeffb}}{{}-{}\num{\fpeval{0-\Coeffb}}}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
- \phantom{\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{\Coeffb>0}{{}+{}}{}}\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\%
- \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{\Coeffb>0}{{}+{}}{}}\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{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\xintifboolexpr{#4<0}{\phantom{={}}}{}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
- \xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{{}-{}\num{#5}}{{}+{}\num{\fpeval{0-#5}}}}&\phantom{{}={}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\
- \xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}&\xintifboolexpr{\Coeffa<0}{\phantom{{}={}}}{\phantom{=}}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
- \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*}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
- }{}%
- }%
- }%
- }%
- }%
- }%
- }%
-}%
Deleted: trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSoustraction2.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSoustraction2.tex 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSoustraction2.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -1,345 +0,0 @@
-% Licence : Released under the LaTeX Project Public License v1.3c
-% or later, see http://www.latex-project.org/lppl.txtf
-\newcommand{\EquaBase}[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*}%
- \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\tikzmark{C-\theNbequa}\\
- \tikzmark{B-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}\tikzmark{D-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
- \rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
- }{%
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \Leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
- \Rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
- }{}%
- }%%
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{#5}{#2}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\
- }{}
- }{}
- \ifboolKV[ClesEquation]{Fleches}{%
- \stepcounter{Nbequa}}%
- {\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}
- }
- \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{\EquaDeuxSoustraction}[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
- \EquaDeuxSoustraction[#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
- \EquaBase[#1]{#2}{}{}{#5}%
- }{%ax+b=d$ Ici
- \begin{align*}
- \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
- }{}%
- \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}
- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{%
- }{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{%ICI ?
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
- }{}
- }
- }
- \fi
-}
-
-\newcommand{\EquaTroisSoustraction}[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
- \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}%
- \fi
- \else
- \xintifboolexpr{#2=0}{%b=cx
- \EquaBase[#1]{#4}{}{}{#3}
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0
- \EquaDeuxSoustraction[#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*}
- \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
- }{}
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=0\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\
- }{}%
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- %eric
- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}
- % eric
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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+d avec a<c % Autre cas délicat
- \begin{align*}%
- \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
- }{}
- \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- }{}
- % eric
- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{}
- % eric
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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{\ResolEquationSoustraction}[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$
- \EquaDeuxSoustraction[#1]{#4}{#5}{}{#3}%
- }%
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0x+d
- \EquaDeuxSoustraction[#1]{#2}{#3}{}{#5}%
- }
- {%ax+b=cx+d$
- \xintifboolexpr{#3=0}{%
- \xintifboolexpr{#5=0}{%ax=cx
- \EquaTroisSoustraction[#1]{#2}{0}{#4}{}%
- }%
- {%ax=cx+d
- \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}%
- }%
- }%
- {\xintifboolexpr{#5=0}{%ax+b=cx
- \EquaTroisSoustraction[#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*}
- \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- }{}
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{F-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
- }{}%
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- % eric
- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}
- % eric
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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*}%
- \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- }{}
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\
- \ifboolKV[ClesEquation]{Decomposition}{%
- \num{#3}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\
- }{}%
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\
- % eric
- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{}
- % eric
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
- }{}%
- }%
- }%
- }%
- }%
- }%
- }%
-}%
-
-
Deleted: trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationSymbole1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -1,225 +0,0 @@
-% 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*}
- }%
- }%
- }%
- }%
- }%
- }%
-}%
-
-
Deleted: trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationTerme1.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationTerme1.tex 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/texmf-dist/doc/latex/profcollege/PfCEquationTerme1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -1,276 +0,0 @@
-% Licence : Released under the LaTeX Project Public License v1.3c
-% or later, see http://www.latex-project.org/lppl.txtf
-\newcommand{\EquaDeuxTerme}[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
- \EquaDeuxTerme[#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
- \EquaBase[#1]{#2}{}{}{#5}%
- }{%ax+b=d$ Ici
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
- \begin{align*}
- \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}&=\num{#5}\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{%
- }{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{%ICI ?
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
- }{}
- }
- }
- \fi
-}
-
-\newcommand{\EquaTroisTerme}[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
- \EquaTroisTerme[#1]{#4}{#5}{#2}{}%
- \fi
- \else
- \xintifboolexpr{#2=0}{%b=cx
- \EquaBase[#1]{#4}{}{}{#3}
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0
- \EquaDeuxTerme[#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
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
- \begin{align*}
- \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\
- \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=0\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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+d avec a<c % Autre cas délicat
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
- \begin{align*}%
- \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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{\ResolEquationTerme}[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$
- \EquaDeuxTerme[#1]{#4}{#5}{#2}{#3}%
- }%
- }{%
- \xintifboolexpr{#4=0}{%ax+b=0x+d
- \EquaDeuxTerme[#1]{#2}{#3}{}{#5}%
- }
- {%ax+b=cx+d$
- \xintifboolexpr{#3=0}{%
- \xintifboolexpr{#5=0}{%ax=cx
- \EquaTroisTerme[#1]{#2}{0}{#4}{}%
- }%
- {%ax=cx+d
- \EquaTroisTerme[#1]{#4}{#5}{#2}{}%
- }%
- }%
- {\xintifboolexpr{#5=0}{%ax+b=cx
- \EquaTroisTerme[#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
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
- \begin{align*}
- \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#5>0}{\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{F-\theNbequa}\tikzmark{F-\theNbequa}\\
- \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{#5}\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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
- \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
- \begin{align*}%
- \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
- \xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\
- \num{#3}\mathcolor{Cterme}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\\
- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\
- \xintifboolexpr{\Coeffa=1}{}{\\}
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
- }{}
- \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
- \ifboolKV[ClesEquation]{Fleches}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{
- \ifboolKV[ClesEquation]{FlecheDiv}{%
- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
- }{}
- }
- \ifboolKV[ClesEquation]{Entier}{%
- \SSimpliTest{\Coeffb}{\Coeffa}%
- \ifboolKV[ClesEquation]{Simplification}{%
- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
- }{}
- }{}
- }
- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
- \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
- }{}%
- }%
- }%
- }%
- }%
- }%
- }%
-}%
-
-
Added: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationComposition2.tex
===================================================================
--- trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationComposition2.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationComposition2.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -0,0 +1,275 @@
+% Licence : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaDeuxComposition}[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
+ \EquaDeuxComposition[#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
+ \EquaBase[#1]{#2}{}{}{#5}%
+ }{%ax+b=d$ Ici
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{%ICI ?
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+ }{}
+ }
+ }
+ \fi
+}
+
+\newcommand{\EquaTroisComposition}[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
+ \EquaTroisComposition[#1]{#4}{#5}{#2}{}%
+ \fi
+ \else
+ \xintifboolexpr{#2=0}{%b=cx
+ \EquaBase[#1]{#4}{}{}{#3}
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0
+ \EquaDeuxComposition[#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
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\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}\tikzmark{E-\theNbequa}\\
+ \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{0}\tikzmark{F-\theNbequa}\\
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{0-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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+d avec a<c % Autre cas délicat
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
+ \begin{align*}%
+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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{\ResolEquationComposition}[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$
+ \EquaDeuxComposition[#1]{#4}{#5}{#2}{#3}%
+ }%
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0x+d
+ \EquaDeuxComposition[#1]{#2}{#3}{}{#5}%
+ }
+ {%ax+b=cx+d$
+ \xintifboolexpr{#3=0}{%
+ \xintifboolexpr{#5=0}{%ax=cx
+ \EquaTroisComposition[#1]{#2}{0}{#4}{}%
+ }%
+ {%ax=cx+d
+ \EquaTroisComposition[#1]{#4}{#5}{#2}{}%
+ }%
+ }%
+ {\xintifboolexpr{#5=0}{%ax+b=cx
+ \EquaTroisComposition[#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
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\mathcolor{Ccompo}{\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}}}\tikzmark{E-\theNbequa}\\
+ \mathcolor{Ccompo}{\num{\fpeval{#2-#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#4>0}{+\num{#4}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#4}}\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}}}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{#5}}\tikzmark{F-\theNbequa}\\
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#5-#3}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Ccompo}{\useKV[ClesEquation]{CouleurCompo}}}{}%
+ \begin{align*}%
+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\mathcolor{Ccompo}{\num{\fpeval{#4-#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#2>0}{+\num{#2}\useKV[ClesEquation]{Lettre}}{-\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\
+ \mathcolor{Ccompo}{\num{\fpeval{#3-#5}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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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Added: svn:eol-style
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+native
\ No newline at end of property
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===================================================================
--- trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationLaurent1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ }{}%
+ }%
+ }%
+ }%
+ }%
+ }%
+ }%
+}%
\ No newline at end of file
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Added: svn:eol-style
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+native
\ No newline at end of property
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===================================================================
--- trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationPose1.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationPose1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -0,0 +1,246 @@
+% Licence : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaBaseL}[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...
+ \EquaBaseL[#1]{#4}{}{}{#3}
+ \else
+ % si non, on est dans le cas ax=d
+ \xintifboolexpr{#2=0}{%
+ \xintifboolexpr{#5=0}{%
+ L'équation $0\useKV[ClesEquation]{Lettre}=0$ 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}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\\
+ \xintifboolexpr{#2=1}{}{%
+ \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\phantom{\useKV[ClesEquation]{Lettre}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\\}
+ \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}}{}%\\
+ }{}
+ }{}
+ %\ifboolKV[ClesEquation]{Fleches}{%
+ %\stepcounter{Nbequa}}%
+ %{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}
+ %}
+ \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{\EquaDeuxL}[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
+ \EquaDeuxL[#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
+ \EquaBaseL[#1]{#2}{}{}{#5}%
+ }{%ax+b=d$ Ici
+ \begin{align*}
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\\
+ \phantom{\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&\phantom{\mathrel{=}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+ \xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\Coeffb}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}}\\
+ \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{%
+ \\\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+ }{}
+ }
+ }
+ \fi
+}
+
+\newcommand{\EquaTroisL}[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
+ \EquaTroisL[#1]{#4}{#5}{#2}{}%
+ \fi
+ \else
+ \xintifboolexpr{#2=0}{%b=cx
+ \EquaBaseL[#1]{#4}{}{}{#3}
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0
+ \EquaDeuxL[#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}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\
+ \mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
+ \xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
+ \phantom{\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}&\phantom{\mathrel{=}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}\\
+ \xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\Coeffb}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+ \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\%
+ \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\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+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{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\\
+ \mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+ \xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}&\phantom{=}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+ \frac{\num{\Coeffb}}{\num{\Coeffa}}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\%
+ \SSimplifie{\Coeffb}{\Coeffa}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+ }{}
+ }{}
+ }{}
+ \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{\ResolEquationL}[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$
+ \EquaDeuxL[#1]{#4}{#5}{}{#3}%
+ }%
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0x+d
+ \EquaDeuxL[#1]{#2}{#3}{}{#5}%
+ }
+ {%ax+b=cx+d$
+ \xintifboolexpr{#3=0}{%
+ \xintifboolexpr{#5=0}{%ax=cx
+ \EquaTroisL[#1]{#2}{0}{#4}{}%
+ }%
+ {%ax=cx+d
+ \EquaTroisL[#1]{#4}{#5}{#2}{}%
+ }%
+ }%
+ {\xintifboolexpr{#5=0}{%ax+b=cx
+ \EquaTroisL[#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}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{{}-{}\num{#4}\useKV[ClesEquation]{Lettre}}{\phantom{{}={}}+{}\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
+ \xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{#5>0}{\phantom{{}+{}}\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}&\phantom{{}={}\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{{}-{}\num{#3}}{{}+{}\num{\fpeval{0-#3}}}}\\
+ \xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\xintifboolexpr{\Coeffb>0}{\phantom{{}+{}}\num{\Coeffb}}{{}-{}\num{\fpeval{0-\Coeffb}}}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\phantom{\useKV[ClesEquation]{Lettre}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\phantom{{}={}}\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+ \phantom{\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{\Coeffb>0}{{}+{}}{}}\frac{\num{\Coeffb}}{\num{\Coeffa}}%\\
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\%
+ \useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\phantom{\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{\Coeffb>0}{{}+{}}{}}\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{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&\xintifboolexpr{#4<0}{\phantom{={}}}{}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{{}-{}\num{#2}\useKV[ClesEquation]{Lettre}}{{}+{}\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+ \xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{{}-{}\num{#5}}{{}+{}\num{\fpeval{0-#5}}}}&\phantom{{}={}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\
+ \xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}&\xintifboolexpr{\Coeffa<0}{\phantom{{}={}}}{\phantom{=}}\mathcolor{Cdecomp}{\mathrel{\div}\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}}\\
+ \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*}
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ }{}%
+ }%
+ }%
+ }%
+ }%
+ }%
+ }%
+}%
Property changes on: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationPose1.tex
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Added: svn:eol-style
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+native
\ No newline at end of property
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===================================================================
--- trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSoustraction2.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSoustraction2.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -0,0 +1,345 @@
+% Licence : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaBase}[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*}%
+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{\useKV[ClesEquation]{Lettre}}{\num{#2}\useKV[ClesEquation]{Lettre}}&=\num{#5}\tikzmark{C-\theNbequa}\\
+ \tikzmark{B-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{#5}}{\num{#2}}\tikzmark{D-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
+ \rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
+ }{%
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \Leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
+ \Rightcomment{C-\theNbequa}{D-\theNbequa}{D-\theNbequa}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
+ }{}%
+ }%%
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{#5}{#2}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\
+ }{}
+ }{}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \stepcounter{Nbequa}}%
+ {\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}
+ }
+ \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{\EquaDeuxSoustraction}[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
+ \EquaDeuxSoustraction[#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
+ \EquaBase[#1]{#2}{}{}{#5}%
+ }{%ax+b=d$ Ici
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+ }{}%
+ \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}
+ \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{%ICI ?
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+ }{}
+ }
+ }
+ \fi
+}
+
+\newcommand{\EquaTroisSoustraction}[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
+ \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}%
+ \fi
+ \else
+ \xintifboolexpr{#2=0}{%b=cx
+ \EquaBase[#1]{#4}{}{}{#3}
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0
+ \EquaDeuxSoustraction[#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*}
+ \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\
+ }{}
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=0\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\
+ }{}%
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ %eric
+ \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}
+ % eric
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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+d avec a<c % Autre cas délicat
+ \begin{align*}%
+ \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+ }{}
+ \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ }{}
+ % eric
+ \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{}
+ % eric
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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{\ResolEquationSoustraction}[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$
+ \EquaDeuxSoustraction[#1]{#4}{#5}{}{#3}%
+ }%
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0x+d
+ \EquaDeuxSoustraction[#1]{#2}{#3}{}{#5}%
+ }
+ {%ax+b=cx+d$
+ \xintifboolexpr{#3=0}{%
+ \xintifboolexpr{#5=0}{%ax=cx
+ \EquaTroisSoustraction[#1]{#2}{0}{#4}{}%
+ }%
+ {%ax=cx+d
+ \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}%
+ }%
+ }%
+ {\xintifboolexpr{#5=0}{%ax+b=cx
+ \EquaTroisSoustraction[#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*}
+ \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ }{}
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{F-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+ }{}%
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ % eric
+ \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}
+ % eric
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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*}%
+ \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ }{}
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\
+ \ifboolKV[ClesEquation]{Decomposition}{%
+ \num{#3}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\mathcolor{Cdecomp}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}\\
+ }{}%
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\
+ % eric
+ \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa=1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{}
+ % eric
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ }{}%
+ }%
+ }%
+ }%
+ }%
+ }%
+ }%
+}%
+
+
Property changes on: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSoustraction2.tex
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSymbole1.tex
===================================================================
--- trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSymbole1.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSymbole1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -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*}
+ }%
+ }%
+ }%
+ }%
+ }%
+ }%
+}%
+
+
Property changes on: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationSymbole1.tex
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationTerme1.tex
===================================================================
--- trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationTerme1.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationTerme1.tex 2021-04-27 12:58:55 UTC (rev 58995)
@@ -0,0 +1,276 @@
+% Licence : Released under the LaTeX Project Public License v1.3c
+% or later, see http://www.latex-project.org/lppl.txtf
+\newcommand{\EquaDeuxTerme}[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
+ \EquaDeuxTerme[#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
+ \EquaBase[#1]{#2}{}{}{#5}%
+ }{%ax+b=d$ Ici
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}&=\num{#5}\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{%
+ }{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{%ICI ?
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+ }{}
+ }
+ }
+ \fi
+}
+
+\newcommand{\EquaTroisTerme}[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
+ \EquaTroisTerme[#1]{#4}{#5}{#2}{}%
+ \fi
+ \else
+ \xintifboolexpr{#2=0}{%b=cx
+ \EquaBase[#1]{#4}{}{}{#3}
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0
+ \EquaDeuxTerme[#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
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=0\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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+d avec a<c % Autre cas délicat
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+ \begin{align*}%
+ \tikzmark{A-\theNbequa}\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}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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{\ResolEquationTerme}[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$
+ \EquaDeuxTerme[#1]{#4}{#5}{#2}{#3}%
+ }%
+ }{%
+ \xintifboolexpr{#4=0}{%ax+b=0x+d
+ \EquaDeuxTerme[#1]{#2}{#3}{}{#5}%
+ }
+ {%ax+b=cx+d$
+ \xintifboolexpr{#3=0}{%
+ \xintifboolexpr{#5=0}{%ax=cx
+ \EquaTroisTerme[#1]{#2}{0}{#4}{}%
+ }%
+ {%ax=cx+d
+ \EquaTroisTerme[#1]{#4}{#5}{#2}{}%
+ }%
+ }%
+ {\xintifboolexpr{#5=0}{%ax+b=cx
+ \EquaTroisTerme[#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
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+ \begin{align*}
+ \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#2=1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#5>0}{\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{F-\theNbequa}\tikzmark{F-\theNbequa}\\
+ \xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{#5}\mathcolor{Cterme}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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
+ \ifboolKV[ClesEquation]{Decomposition}{\colorlet{Cterme}{\useKV[ClesEquation]{CouleurTerme}}}{}
+ \begin{align*}%
+ \tikzmark{A-\theNbequa}\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}}}\tikzmark{E-\theNbequa}\\
+ \xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4=1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cterme}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\\
+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{F-\theNbequa}\\
+ \num{#3}\mathcolor{Cterme}{\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\\
+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{#3-#5}}\num{\Coeffb}&=\xintifboolexpr{\Coeffa=1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{G-\theNbequa}%\\
+ \xintifboolexpr{\Coeffa=1}{}{\\}
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#5>0}{-\num{#5}}{+\num{\fpeval{0-#5}}}$}%
+ }{}
+ \xintifboolexpr{\Coeffa=1}{}{%\ifnum\cmtd>1
+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\
+ \ifboolKV[ClesEquation]{Fleches}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{
+ \ifboolKV[ClesEquation]{FlecheDiv}{%
+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Entier}{%
+ \SSimpliTest{\Coeffb}{\Coeffa}%
+ \ifboolKV[ClesEquation]{Simplification}{%
+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\
+ }{}
+ }{}
+ }
+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ }{}%
+ }%
+ }%
+ }%
+ }%
+ }%
+ }%
+}%
+
+
Property changes on: trunk/Master/texmf-dist/tex/latex/profcollege/PfCEquationTerme1.tex
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Modified: trunk/Master/tlpkg/libexec/ctan2tds
===================================================================
--- trunk/Master/tlpkg/libexec/ctan2tds 2021-04-26 23:48:27 UTC (rev 58994)
+++ trunk/Master/tlpkg/libexec/ctan2tds 2021-04-27 12:58:55 UTC (rev 58995)
@@ -2113,7 +2113,7 @@
'pdfx', '\.(def|dfu|icc|xmp)$|(glyph|Profiles).*tex|pdfx\.sty|ICC_LIC',
'pdfxup', '(template\.tex|\.xup)$',
'petri-nets', 'pnets\.tex|pntext\.tex|\.sty|pndraw\.tex|pnversion\.tex|\.sty|pndraw\.tex',
- 'profcollege', 'PfC-.*\.tex|' . $standardtex,
+ 'profcollege', 'PfC.*\.tex|' . $standardtex,
'pgf-blur', 'tikzlibraryshadows.blur.code.tex',
'pgf-spectra', 'spectra.data.*tex|' . $standardtex,
'pgfmolbio', 'pgfmolbio\..*\.|' . $standardtex, # .lua+.tex submodules
More information about the tex-live-commits
mailing list.