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+\setKVdefault[Facto]{Aide=false,AideMul=false,Couleur=Crimson,NomExpression=A,Lettre=x,Details,Formel=false,VariableSup=false,ParenthesesFin=false,Finale=false}
+\defKV[Facto]{Litteral=\setKV[Facto]{Details=false}}
+\defKV[Facto]{AutreVariable=\setKV[Facto]{VariableSup}}
+\defKV[Facto]{Resultat=\setKV[Facto]{Finale}}
+
+\NewDocumentCommand\PfCEcrireFacteur{mm}{%
+ \StrCount{#1}{+}[\PfCCountArgTroisPlus]%
+ \StrCount{#1}{-}[\PfCCountArgTroisMoins]%
+ \xdef\PfCCountArgTrois{\fpeval{\PfCCountArgTroisPlus+\PfCCountArgTroisMoins}}%
+ \ensuremath{%
+ \IfDecimal{#1}{%
+ \ifboolKV[Facto]{Aide}{%
+ \phantom{(}\print{#2}\phantom{)}%
+ }{%
+ \print{#2}%
+ }%
+ }{%
+ \xintifboolexpr{\PfCCountArgTrois==0}{%
+ \ifboolKV[Facto]{Aide}{%
+ \phantom{(}\print{#2}\phantom{)}%
+ }{%
+ \print{#2}%
+ }%
+ }{
+ (\print{#2})%
+ }
+ }%
+ }%
+}%
+
+\NewDocumentCommand\Factorisation{sommm}{%
+ \directlua{dofile('poly_render_fix.lua')}
+ \useKVdefault[Facto]%
+ \setKV[Facto]{#2}%
+ \colorlet{Csymbole}{\useKV[Facto]{Couleur}}%
+ \IfBooleanTF{#1}{%
+ \xdef\PfCFactoSymbole{-}%
+ }{%
+ \xdef\PfCFactoSymbole{+}%
+ }%
+ \xdef\PfCFactoNE{\useKV[Facto]{NomExpression}}%
+ \ifx\bla#5\bla%
+ % Cas a^2-b^2
+ \begin{CAS}
+ % La variable
+ vars('\useKV[Facto]{Lettre}')
+ % Les facteurs
+ Ka=#3
+ Kb=#4
+ Kc=(#3)^2
+ Kd=(#4)^2
+ Ke=(#3)-(#4)
+ Kf=(#3)+(#4)
+ % Les dérivées pour savoir si ce sont des facteurs littéraux ou pas.
+ PfCDDn=DD(Ka,\useKV[Facto]{Lettre}):autosimplify()
+ PfCDDm=DD(Kb,\useKV[Facto]{Lettre}):autosimplify()
+ PfCDDo=DD(Ke,\useKV[Facto]{Lettre}):autosimplify()
+ PfCDDp=DD(Kf,\useKV[Facto]{Lettre}):autosimplify()
+ % opposé
+ Ko=topoly(-Kb)
+ %
+ \end{CAS}
+ \setsepchar{,}\ignoreemptyitems
+ \readlist\ListeElementDeriveeA{\fetch{PfCDDn}}
+ \readlist\ListeElementDeriveeB{\fetch{PfCDDm}}
+ \readlist\ListeElementDeriveeE{\fetch{PfCDDo}}
+ \readlist\ListeElementDeriveeF{\fetch{PfCDDp}}
+ \reademptyitems
+ \xdef\TestCASA{\ListeElementDeriveeA[1]}
+ \xdef\TestCASB{\ListeElementDeriveeB[1]}
+ \ifboolKV[Facto]{Details}{%Version monome mais pas deux nombres
+ \begin{align*}
+ \PfCFactoNE&=\print{Kc:expand()}-\print{Kd:expand()}\\
+ \PfCFactoNE&=\ifboolKV[Facto]{Aide}{\xintifboolexpr{\TestCASA>1}{(\,}{}{\underbrace{\Fdash{$\print{Ka}$}}_{A}}\xintifboolexpr{\TestCASA>1}{\,)}{}^{\,2}-\xintifboolexpr{\TestCASB>1}{(\,}{}{\underbrace{\Fdash{$\print{Kb}$}}_{B}}\xintifboolexpr{\TestCASB>1}{\,)}{}^{\,2}}{\IfDecimal{#3}{\print{Ka}^2}{\print{Kc}}-\IfDecimal{#4}{\print{Kb}^2}{\print{Kd}}}\\
+ \PfCFactoNE&=(\print{Ke})\times(\print{Kf})%
+ \ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=(\print{Ke})(\print{Kf})}{}%
+ \end{align*}
+ }{%Avec au moins un des facteurs polynomes
+ \begin{align*}
+ \ifboolKV[Facto]{Aide}{\IfDecimal{#3}{\PfCFactoNE&=\print{Kc}-\print{Kd}}{\IfDecimal{#4}{\PfCFactoNE&=\print{Kc}-\print{Kd}}{\PfCFactoNE&={\underbrace{\Fdash{$(\print{Ka})$}}_{A}}^{\,2}-{\underbrace{\Fdash{$(\print{Kb})$}}_{B}}^{\,2}}}}{\PfCFactoNE&=\print{Kc}-\print{Kd}}\\
+ \IfDecimal{#3}{\PfCFactoNE\uppercase{&}=\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$\phantom{(}\print{Ka}\phantom{)}$}}_{A}}^{\,2}}{\print{Ka}^2}-\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$(\print{Kb})$}}_{B}}^{\,2}}{\print{Kd}}\\}{\IfDecimal{#4}{\PfCFactoNE\uppercase{&}=\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$(\print{Ka})$}}_{A}}^{\,2}}{\print{Kc}}-\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$\phantom{(}\print{Kb}\phantom{)}$}}_{B}}^{\,2}}{\print{Kb}^2}\\}{}}
+ \PfCFactoNE&=\left[\IfDecimal{#3}{\print{Ka}}{(\print{Ka})}-\IfDecimal{#4}{\print{Kb}}{(\print{Kb})}\right]\times\left[\IfDecimal{#3}{\print{Ka}}{(\print{Ka})}+\IfDecimal{#4}{\print{Kb}}{(\print{Kb})}\right]\\
+ \PfCFactoNE&=\left[\print{Ka}\xintifboolexpr{\TestCASB<0}{+}{}\print{Ko}\right]\times\left[\print{Ka}\StrChar{#4}{1}[\PfCTestCaracUn]\StrCompare{\PfCTestCaracUn}{-}[\PfCTestCaracRetour]\xintifboolexpr{\PfCTestCaracRetour==0}{}{+}\print{Kb}\right]\\
+ \PfCFactoNE&=\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Ke:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}\times\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Kf:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}%
+ \ifboolKV[Facto]{Finale}{\\\PfCFactoNE&=\useKV[Facto]{Resultat}}{\ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Ke:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Kf:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}}{}}%
+ \end{align*}
+ }
+ \else%k*a+-k*b=k(a+-b)
+ \begin{CAS}
+ % La variable
+ vars('\useKV[Facto]{Lettre}'\ifboolKV[Facto]{VariableSup}{%
+ ,'\useKV[Facto]{AutreVariable}'
+ }{})
+ % Les facteurs
+ Kk=#3
+ Ka=#4
+ Kb=#5
+ Kka=Kk*Ka
+ Kkb=Kk*Kb
+ % Les dérivées pour savoir si ce sont des facteurs littéraux ou pas.
+ PfCDDn=DD(Ka,\useKV[Facto]{Lettre}):autosimplify()
+ PfCDDm=DD(Kb,\useKV[Facto]{Lettre}):autosimplify()
+ % opposé
+ Ko=topoly(-Kb)
+ Ke=(#4)\PfCFactoSymbole(#5)
+ \end{CAS}
+ \setsepchar{,}\ignoreemptyitems
+ \readlist\ListeElementDeriveeA{\fetch{PfCDDn}}
+ \readlist\ListeElementDeriveeB{\fetch{PfCDDm}}
+ \reademptyitems
+ \xdef\TestCAS{\ListeElementDeriveeA[1]}
+ \xdef\TestCASB{\ListeElementDeriveeB[1]}
+ \ifboolKV[Facto]{Details}{%Version monome mais pas des nombres
+ \begin{align*}
+ \PfCFactoNE&=\print{Kka:expand()}\PfCFactoSymbole\print{Kkb:expand()}\\
+ \PfCFactoNE&=\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{Kk}\phantom{)}$}}_{k}}{\print{Kk}}\times\xintifboolexpr{\TestCAS<0}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$(\print{Ka}$}}_{a}}{(\print{Ka})}}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{Ka}\phantom{)}$}}_{a}}{\print{Ka}}}\PfCFactoSymbole\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{Kk}\phantom{)}$}}_{k}}{\print{Kk}}\times\xintifboolexpr{\TestCASB<0}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$(\print{Kb}$}}_{b}}{(\print{Kb})}}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{Kb}\phantom{)}$}}_{b}}{\print{Kb}}}\\
+ \PfCFactoNE&=\print{Kk}\times(\print{Ka\PfCFactoSymbole Kb})%
+ \ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=\print{Kk}(\print{Ka\PfCFactoSymbole Kb})}{}%
+ \end{align*}
+ }{%Avec au moins un des facteurs polynomes
+ \StrCompare{\PfCFactoSymbole}{-}[\PfCRetiensSigneFacteurDeux]
+ \begin{align*}
+ \ifboolKV[Facto]{Aide}{\PfCFactoNE&=\setKV[Facto]{Aide=false}\PfCEcrireFacteur{#3}{Kk}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#4}{Ka}\PfCFactoSymbole\PfCEcrireFacteur{#3}{Kk}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#5}{Kb}\\\setKV[Facto]{Aide}}{}%
+ \PfCFactoNE&=\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{\PfCEcrireFacteur{#3}{Kk}}}_{k}\times\underbrace{\Fdash{\PfCEcrireFacteur{#4}{Ka}}}_{a}\PfCFactoSymbole\underbrace{\Fdash{\PfCEcrireFacteur{#3}{Kk}}}_{k}\times\underbrace{\Fdash{\PfCEcrireFacteur{#5}{Kb}}}_{b}}{\PfCEcrireFacteur{#3}{Kk}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#4}{Ka}\PfCFactoSymbole\PfCEcrireFacteur{#3}{Kk}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#5}{Kb}}\setKV[Facto]{Aide=false}\\
+ \PfCFactoNE&=\setKV[Facto]{Aide=false}\PfCEcrireFacteur{#3}{Kk}\times\left[\PfCEcrireFacteur{#4}{Ka}\PfCFactoSymbole\PfCEcrireFacteur{#5}{Kb}\right]\\
+ \PfCFactoNE&=\setKV[Facto]{Aide=false}\PfCEcrireFacteur{#3}{Kk}\times\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Ka}\xintifboolexpr{\PfCRetiensSigneFacteurDeux==1}{\xintifboolexpr{\TestCASB<0}{}{+}\print{Kb}}{\xintifboolexpr{\TestCASB<0}{+}{}\print{Ko}}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}\\
+ \PfCFactoNE&=\setKV[Facto]{Aide=false}\PfCEcrireFacteur{#3}{Kk}\times\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Ke:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}%
+ \ifboolKV[Facto]{Finale}{\\\PfCFactoNE&=\useKV[Facto]{Resultat}}{\ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=\setKV[Facto]{Aide=false}\PfCEcrireFacteur{#3}{Kk}\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{Ke:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}}{}}%
+ \end{align*}
+ }
+ \fi
+}%
+
+\NewDocumentCommand\Factorisationold{sommm}{%
+ \directlua{dofile('poly_render_fix.lua')}
+ \useKVdefault[Facto]%
+ \setKV[Facto]{#2}%
+ \colorlet{Csymbole}{\useKV[Facto]{Couleur}}%
+ \IfBooleanTF{#1}{%
+ \xdef\PfCFactoSymbole{-}%
+ }{%
+ \xdef\PfCFactoSymbole{+}%
+ }%
+ \xdef\PfCFactoNE{\useKV[Facto]{NomExpression}}%
+ \ifx\bla#5\bla%
+ % Cas a^2-b^2
+ \begin{CAS}
+ % La variable
+ vars('\useKV[Facto]{Lettre}')
+ % Les facteurs
+ a=#3
+ b=#4
+ % Les dérivées pour savoir si ce sont des facteurs littéraux ou pas.
+ PfCDDn=DD(a,\useKV[Facto]{Lettre}):autosimplify()
+ PfCDDm=DD(b,\useKV[Facto]{Lettre}):autosimplify()
+ % opposé
+ o=topoly(-b)
+ %
+ c=(#3)^2
+ d=(#4)^2
+ e=(#3)-(#4)
+ f=(#3)+(#4)
+ \end{CAS}
+ \setsepchar{,}\ignoreemptyitems
+ \readlist\ListeElementDeriveeA{\fetch{PfCDDn}}
+ \readlist\ListeElementDeriveeB{\fetch{PfCDDm}}
+ \reademptyitems
+ \xdef\TestCASA{\ListeElementDeriveeA[1]}
+ \xdef\TestCASB{\ListeElementDeriveeB[1]}
+ \ifboolKV[Facto]{Details}{%Version monome mais pas deux nombres
+ \begin{align*}
+ \PfCFactoNE&=\print{c:expand()}-\print{d:expand()}\\
+ \PfCFactoNE&=\ifboolKV[Facto]{Aide}{\xintifboolexpr{\TestCASA>1}{(\,}{}{\underbrace{\Fdash{$\print{a}$}}_{A}}\xintifboolexpr{\TestCASA>1}{\,)}{}^{\,2}-\xintifboolexpr{\TestCASB>1}{(\,}{}{\underbrace{\Fdash{$\print{b}$}}_{B}}\xintifboolexpr{\TestCASB>1}{\,)}{}^{\,2}}{\print{c}-\print{d}}\\
+ \PfCFactoNE&=(\print{e})\times(\print{f})%
+ \ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=(\print{e})(\print{f})}{}%
+ \end{align*}
+ }{%Avec au moins un des facteurs polynomes
+ Ici
+ \begin{align*}
+ \ifboolKV[Facto]{Aide}{\IfDecimal{#3}{\PfCFactoNE&=\print{c}-\print{d}}{\IfDecimal{#4}{\PfCFactoNE&=\print{c}-\print{d}}{\PfCFactoNE&={\underbrace{\Fdash{$(\print{a})$}}_{A}}^{\,2}-{\underbrace{\Fdash{$(\print{b})$}}_{B}}^{\,2}}}}{\PfCFactoNE&=\print{c}-\print{d}}\\
+ \IfDecimal{#3}{\PfCFactoNE\uppercase{&}=\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$\phantom{(}\print{a}\phantom{)}$}}_{A}}^{\,2}}{\print{a}^2}-\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$(\print{b})$}}_{B}}^{\,2}}{\print{d}}\\}{\IfDecimal{#4}{\PfCFactoNE\uppercase{&}=\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$(\print{a})$}}_{A}}^{\,2}}{\print{c}}-\ifboolKV[Facto]{Aide}{{\underbrace{\Fdash{$\phantom{(}\print{b}\phantom{)}$}}_{B}}^{\,2}}{\print{b}^2}\\}{}}
+ \PfCFactoNE&=\left[\IfDecimal{#3}{\print{a}}{(\print{a})}-\IfDecimal{#4}{\print{b}}{(\print{b})}\right]\times\left[\IfDecimal{#3}{\print{a}}{(\print{a})}+\IfDecimal{#4}{\print{b}}{(\print{b})}\right]\\
+ \PfCFactoNE&=\left[\print{a}\xintifboolexpr{\TestCASB<0}{+}{}\print{o}\right]\times\left[\print{a}%
+ \xintifboolexpr{\TestCASB<0}{\StrChar{\print{b}}{1}[\PfCTestCaracUn]\StrCompare*{\PfCTestCaracUn}{-}[\PfCTestCaracRetour]\xintifboolexpr{\PfCTestCaracRetour==0}{}{+}}{+}\print{b}\right]\\
+ \PfCFactoNE&=\left[\print{e:expand():topolynomial()}\right]\times\left[\print{f:expand():topolynomial()}\right]%
+ \ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=\left[\print{e:expand():topolynomial()}\right]\left[\print{f:expand():topolynomial()}\right]}{}%
+ \end{align*}
+ }
+ \else%k*a+-k*b=k(a+-b)
+ \begin{CAS}
+ % La variable
+ vars('\useKV[Facto]{Lettre}'\ifboolKV[Facto]{VariableSup}{%
+ ,'\useKV[Facto]{AutreVariable}'
+ }{})
+ % Les facteurs
+ k=#3
+ a=#4
+ b=#5
+ ka=k*a
+ kb=k*b
+ % Les dérivées pour savoir si ce sont des facteurs littéraux ou pas.
+ PfCDDn=DD(a,\useKV[Facto]{Lettre}):autosimplify()
+ PfCDDm=DD(b,\useKV[Facto]{Lettre}):autosimplify()
+ % opposé
+ o=topoly(-b)
+ e=(#4)\PfCFactoSymbole(#5)
+ \end{CAS}
+ \setsepchar{,}\ignoreemptyitems
+ \readlist\ListeElementDeriveeA{\fetch{PfCDDn}}
+ \readlist\ListeElementDeriveeB{\fetch{PfCDDm}}
+ \reademptyitems
+ \xdef\TestCAS{\ListeElementDeriveeA[1]}
+ \xdef\TestCASB{\ListeElementDeriveeB[1]}
+ \ifboolKV[Facto]{Details}{%Version monome mais pas des nombres
+ \begin{align*}
+ \PfCFactoNE&=\print{ka:expand()}\PfCFactoSymbole\print{kb:expand()}\\
+ \PfCFactoNE&=\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{k}\phantom{)}$}}_{k}}{\print{k}}\times\xintifboolexpr{\TestCAS<0}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$(\print{a}$}}_{a}}{(\print{a})}}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{a}\phantom{)}$}}_{a}}{\print{a}}}\PfCFactoSymbole\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{k}\phantom{)}$}}_{k}}{\print{k}}\times\xintifboolexpr{\TestCASB<0}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$(\print{b}$}}_{b}}{(\print{b})}}{\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{$\phantom{(}\print{b}\phantom{)}$}}_{b}}{\print{b}}}\\
+ \PfCFactoNE&=\print{k}\times(\print{a\PfCFactoSymbole b})%
+ \ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=\print{k}(\print{a\PfCFactoSymbole b})}{}%
+ \end{align*}
+ }{%Avec au moins un des facteurs polynomes
+ \StrCompare{\PfCFactoSymbole}{-}[\PfCRetiensSigneFacteurDeux]
+ \begin{align*}
+ \ifboolKV[Facto]{Aide}{\PfCFactoNE&=\setKV[Facto]{Aide=false}\PfCEcrireFacteur{#3}{k}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#4}{a}\PfCFactoSymbole\PfCEcrireFacteur{#3}{k}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#5}{b}\\\setKV[Facto]{Aide}}{}%
+ \PfCFactoNE&=\ifboolKV[Facto]{Aide}{\underbrace{\Fdash{\PfCEcrireFacteur{#3}{k}}}_{k}\times\underbrace{\Fdash{\PfCEcrireFacteur{#4}{a}}}_{a}\PfCFactoSymbole\underbrace{\Fdash{\PfCEcrireFacteur{#3}{k}}}_{k}\times\underbrace{\Fdash{\PfCEcrireFacteur{#5}{b}}}_{b}}{\PfCEcrireFacteur{#3}{k}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#4}{a}\PfCFactoSymbole\PfCEcrireFacteur{#3}{k}\ifboolKV[Facto]{AideMul}{\times}{}\PfCEcrireFacteur{#5}{b}}\\
+ \PfCFactoNE&=\PfCEcrireFacteur{#3}{k}\times\left[\PfCEcrireFacteur{#4}{a}\PfCFactoSymbole\PfCEcrireFacteur{#5}{b}\right]\\
+ \PfCFactoNE&=\PfCEcrireFacteur{#3}{k}\times\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{a}\xintifboolexpr{\PfCRetiensSigneFacteurDeux==1}{\xintifboolexpr{\TestCASB<0}{}{+}\print{b}}{\xintifboolexpr{\TestCASB<0}{+}{}\print{o}}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}\\
+ \PfCFactoNE&=\PfCEcrireFacteur{#3}{k}\times\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{e:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}%
+ \ifboolKV[Facto]{Formel}{\\\PfCFactoNE&=\PfCEcrireFacteur{#3}{k}\ifboolKV[Facto]{ParenthesesFin}{\left(}{\left[}\print{e:expand():topolynomial()}\ifboolKV[Facto]{ParenthesesFin}{\right)}{\right]}}{}%
+ \end{align*}
+ }
+ \fi
+}%
+
+
+