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authorNorbert Preining <norbert@preining.info>2021-06-06 03:02:43 +0000
committerNorbert Preining <norbert@preining.info>2021-06-06 03:02:43 +0000
commit4338972cc175be565a3441c4ae8a6aa0dfcbe9f9 (patch)
tree9ec52a5d0d9c8a00b1a6801cc82248c0c008465d /macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex
parent4e703bdd2f304028698cd4ab92b0dda0b95a95a8 (diff)
CTAN sync 202106060302
Diffstat (limited to 'macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex')
-rw-r--r--macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex152
1 files changed, 86 insertions, 66 deletions
diff --git a/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex b/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex
index 1137140d28..8bc7bb339f 100644
--- a/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex
+++ b/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex
@@ -9,28 +9,28 @@
\EquaBaseL[#1]{#4}{}{}{#3}
\else
% si non, on est dans le cas ax=d
- \xintifboolexpr{#2=0}{%
- \xintifboolexpr{#5=0}{%
+ \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
+ \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}{}{%
+ \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]{Decimal}{%
+ \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{#5/#2}}%
+ }{}%
+% %%%
\ifboolKV[ClesEquation]{Entier}{%
\SSimpliTest{#5}{#2}%
\ifboolKV[ClesEquation]{Simplification}{%
\ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{#5}{#2}}{}%\\
}{}
}{}
- %\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 : $\displaystyle\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.%
+ \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{\useKV[ClesEquation]{Lettre}=\num{#5}}{\num{#2}\useKV[ClesEquation]{Lettre}=\num{#5}}$ a une unique solution : $\displaystyle\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.%
}{}
}
}
@@ -43,26 +43,30 @@
\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
+ \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
+ \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}{%
+ \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]{Decimal}{%
+ \\\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\fpeval{\Coeffb/\Coeffa}}%
+ }{}%
+% %%%
\ifboolKV[ClesEquation]{Entier}{%
\SSimpliTest{\Coeffb}{\Coeffa}%
\ifboolKV[ClesEquation]{Simplification}{%
@@ -72,7 +76,7 @@
}{}
}{}
\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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.
}{}
}
}
@@ -89,32 +93,36 @@
\EquaTroisL[#1]{#4}{#5}{#2}{}%
\fi
\else
- \xintifboolexpr{#2=0}{%b=cx
+ \xintifboolexpr{#2==0}{%b=cx
\EquaBaseL[#1]{#4}{}{}{#3}
}{%
- \xintifboolexpr{#4=0}{%ax+b=0
+ \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.}%
+ \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.%
+ 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}\\
+ \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}{%
+ \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]{Decimal}{%
+ \\\useKV[ClesEquation]{Lettre}\phantom{\xintifboolexpr{#3>0}{{}+{}\num{#3}}{{}-{}\num{\fpeval{0-#3}}}}&=\num{\fpeval{\Coeffb/\Coeffa}}%
+ }{}%
+% %%%
\ifboolKV[ClesEquation]{Entier}{%
\SSimpliTest{\Coeffb}{\Coeffa}%
\ifboolKV[ClesEquation]{Simplification}{%
@@ -124,18 +132,22 @@
}{}
}{}
\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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}
+ \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}\\
+ \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}{%
+ \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]{Decimal}{%
+ \\\num{\fpeval{\Coeffb/\Coeffa}}&=\phantom{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}%
+ }{}%
+% %%%
\ifboolKV[ClesEquation]{Entier}{%
\SSimpliTest{\Coeffb}{\Coeffa}%
\ifboolKV[ClesEquation]{Simplification}{%
@@ -145,7 +157,7 @@
}{}
}{}
\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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}%
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}%
}%
}%
}%
@@ -157,9 +169,9 @@
\newcommand{\ResolEquationL}[5][]{%
\useKVdefault[ClesEquation]%
\setKV[ClesEquation]{#1}%
- \xintifboolexpr{#2=0}{%
- \xintifboolexpr{#4=0}{%
- \xintifboolexpr{#3=#5}{%b=d
+ \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.%
@@ -169,65 +181,73 @@
\EquaDeuxL[#1]{#4}{#5}{}{#3}%
}%
}{%
- \xintifboolexpr{#4=0}{%ax+b=0x+d
+ \xintifboolexpr{#4==0}{%ax+b=0x+d
\EquaDeuxL[#1]{#2}{#3}{}{#5}%
}
{%ax+b=cx+d$
- \xintifboolexpr{#3=0}{%
- \xintifboolexpr{#5=0}{%ax=cx
+ \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
+ {\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.}%
+ \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.%
+ 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}}}\\
+ \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}}%\\
+ \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]{Decimal}{%
+ \\\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}{{}+{}}{}}\num{\fpeval{\Coeffb/\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}%\\
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ \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}}}\\
+ \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
+ \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]{Decimal}{%
+ \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}%
+ }{}%
+% %%%
\ifboolKV[ClesEquation]{Entier}{%
\SSimpliTest{\Coeffb}{\Coeffa}%
\ifboolKV[ClesEquation]{Simplification}{%
@@ -235,7 +255,7 @@
}{}
}{}
\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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
+ \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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%
}{}%
}%
}%