% 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}{0}{0}{#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*}%
        \ifemptyKV[ClesEquation]{Ajouts}{}{%
        \xintFor* ##1 in{\xintSeq{1}{\ListeEquaAjoutlen}}\do{%
        \ListeEquaAjout[##1,1]&=\ListeEquaAjout[##1,2]\\
        }%
        }%
        \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}{$\div\xintifboolexpr{#2<0}{(\num{#2})}{\num{#2}}$}%
        }{}%
        }%%
        %% decimal
        \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*}
      \xdef\Coeffb{#5}%
      \xdef\Coeffa{#2}%
      \ifboolKV[ClesEquation]{Solution}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}%
    }%
  }%
  \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}{0}{0}{#5}%
      }{%ax+b=d$
        \begin{align*}
          \ifemptyKV[ClesEquation]{Ajouts}{}{%
              \xintFor* ##1 in{\xintSeq{1}{\ListeEquaAjoutlen}}\do{%
                \ListeEquaAjout[##1,1]&=\ListeEquaAjout[##1,2]\\
              }%
            }%
          \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}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%
          }{}%
          }%
          }%
          %%decimal
        \ifboolKV[ClesEquation]{Decimal}{%
        \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\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}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}%
      }%
    }%
  \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}{0}%
    \fi%
  \else%
  \xintifboolexpr{#2==0}{%b=cx
    \EquaBase[#1]{#4}{0}{0}{#3}
  }{%
    \xintifboolexpr{#4==0}{%ax+b=0
      \EquaDeuxSoustraction[#1]{#2}{#3}{0}{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*}
            \ifemptyKV[ClesEquation]{Ajouts}{}{%
              \xintFor* ##1 in{\xintSeq{1}{\ListeEquaAjoutlen}}\do{%
                \ListeEquaAjout[##1,1]&=\ListeEquaAjout[##1,2]\\
              }%
            }%
            \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}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%                 
            }{}
            }
            %% decimal
            \ifboolKV[ClesEquation]{Decimal}{%
            \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\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*}
        }{%ax+b=cx avec a<c              % Autre cas délicat
          \begin{align*}%
            \ifemptyKV[ClesEquation]{Ajouts}{}{%
              \xintFor* ##1 in{\xintSeq{1}{\ListeEquaAjoutlen}}\do{%
                \ListeEquaAjout[##1,1]&=\ListeEquaAjout[##1,2]\\
              }%
            }%
            \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}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}
            }{}%\\
            \ifboolKV[ClesEquation]{Decomposition}{\xintifboolexpr{\Coeffa==1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\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}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%                 
            }{}
            }
            %% decimal
            \ifboolKV[ClesEquation]{Decimal}{%
            \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\
            }{}%
            %
            \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}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}%
    }%
  }%
  \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}{0}{#3}%
    }%
  }{%
    \xintifboolexpr{#4==0}{%ax+b=0x+d
      \EquaDeuxSoustraction[#1]{#2}{#3}{0}{#5}%
    }
    {%ax+b=cx+d$
      \xintifboolexpr{#3==0}{%
        \xintifboolexpr{#5==0}{%ax=cx
          \EquaTroisSoustraction[#1]{#2}{0}{#4}{0}%
        }%
        {%ax=cx+d
          \EquaTroisSoustraction[#1]{#4}{#5}{#2}{0}%
        }%
      }%
      {\xintifboolexpr{#5==0}{%ax+b=cx
          \EquaTroisSoustraction[#1]{#2}{#3}{#4}{0}%
        }%
        {%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*}
                \ifemptyKV[ClesEquation]{Ajouts}{}{%
                \xintFor* ##1 in{\xintSeq{1}{\ListeEquaAjoutlen}}\do{%
                \ListeEquaAjout[##1,1]&=\ListeEquaAjout[##1,2]\\
                }%
                }%
                \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}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%                 
                }{}
                }
                %% decimal
                \ifboolKV[ClesEquation]{Decimal}{%
                \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\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*}
            }{%ax+b=cx+d avec a<c              % Autre cas délicat
              \begin{align*}%
                \ifemptyKV[ClesEquation]{Ajouts}{}{%
                \xintFor* ##1 in{\xintSeq{1}{\ListeEquaAjoutlen}}\do{%
                \ListeEquaAjout[##1,1]&=\ListeEquaAjout[##1,2]\\
                }%
                }%
                \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}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%                 
                }{}
                }
                %% decimal
                \ifboolKV[ClesEquation]{Decimal}{%
                \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}%
                                                }{}%
                                                %                                        %%% 
                \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}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}%
          }%
        }%
      }%
    }%
  }%
}%


