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author | Norbert Preining <norbert@preining.info> | 2021-04-24 03:01:03 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2021-04-24 03:01:03 +0000 |
commit | 00abda4c22e1a32ae68e103e9bf15497afac9983 (patch) | |
tree | bd3cb2522708fd11846e9caabef6e05bfadc5b96 /macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex | |
parent | 24c5753beaf378d35553785f02c3110a1c0fe293 (diff) |
CTAN sync 202104240301
Diffstat (limited to 'macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex')
-rw-r--r-- | macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex | 246 |
1 files changed, 246 insertions, 0 deletions
diff --git a/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex b/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex new file mode 100644 index 0000000000..1137140d28 --- /dev/null +++ b/macros/latex/contrib/profcollege/latex/PfCEquationPose1.tex @@ -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}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.% + }{}% + }% + }% + }% + }% + }% + }% +}% |