%%%
% Tables Addition-Multiplication
%%%
\setKVdefault[Tables]{Addition=false,Soustraction=false,Multiplication,Seul=false,Debut=0,Fin=10,Couleur=white,Inverse=false}

% pour m\'emoire
\newcommand\TableMultiplicationComplete{%
  \xdef\NbColTabMul{\fpeval{\useKV[Tables]{Fin}+1-\useKV[Tables]{Debut}}}%
  \begin{tabular}{|>{\columncolor{gray!15}\centering\arraybackslash}p{1.5em}|*{\NbColTabMul}{>{\centering\arraybackslash}p{1.5em}|}}%
    \hline
    $\times$\xintFor* ##1 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
    &\cellcolor{gray!15}\fpeval{##1}
      }
    \\
    \hline
    \xintFor* ##1 in {\xintSeq {0}{10}}\do{%
    ##1\xintFor* ##2 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
    &\fpeval{##2*##1}
      }
    \\
    \hline
    }
  \end{tabular}%
}
%%%%

\newcommand\TableMultiplicationCompleteColore{%
  \xdef\NbColTabMul{\fpeval{\useKV[Tables]{Fin}+1-\useKV[Tables]{Debut}}}%
  \begin{tabular}{|>{\columncolor{gray!15}\centering}p{15pt}|*{\NbColTabMul}{>{\centering\arraybackslash}p{15pt}|}}%
    \hline
    $\times$\xintFor* ##1 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
    &\cellcolor{gray!15}\fpeval{##1}%
      }
    \\
    \hline
    \xintFor* ##1 in {\xintSeq {0}{10}}\do{%
    ##1\xintFor* ##2 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
    &\xintifboolexpr{##2<##1}{\cellcolor{\useKV[Tables]{Couleur}!\fpeval{##1*10}}}{\xintifboolexpr{##2>##1}{\cellcolor{\useKV[Tables]{Couleur}!\fpeval{##2*10}}}{}}\fpeval{##2*##1}%
      }%
    \\
    \hline
    }%
  \end{tabular}%
}%

\newcommand\TableAdditionComplete{%
  \xdef\NbColTabMul{\fpeval{\useKV[Tables]{Fin}+1-\useKV[Tables]{Debut}}}%
  \begin{tabular}{|>{\columncolor{gray!15}\centering}p{15pt}|*{\NbColTabMul}{>{\centering\arraybackslash}p{15pt}|}}%
    \hline
    $+$\xintFor* ##1 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
    &\cellcolor{gray!15}\fpeval{##1}
      }
    \\
    \hline
    \xintFor* ##1 in {\xintSeq {0}{10}}\do{%
    ##1\xintFor* ##2 in {\xintSeq {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{%
    &\fpeval{##2+##1}
      }
    \\
    \hline
    }
  \end{tabular}%
}

\newcommand\TableMultiplicationSeule[1]{%
  \ensuremath{%
    \begin{array}{ccccc}%
      \xintFor* ##1 in {\xintSeq
      {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{
      ##1&\times&#1&=&\fpeval{##1*#1}\\
      }
    \end{array}
  }%
}%

\newcommand\TableAdditionSeule[1]{%
  \ensuremath{%
    \begin{array}{ccccc}
      \xintFor* ##1 in {\xintSeq
      {\useKV[Tables]{Debut}}{\useKV[Tables]{Fin}}}\do{
      ##1&+&#1&=&\fpeval{##1+#1}\\
      }
    \end{array}
  }%
}%

\newcommand\TableSoustractionSeule[1]{%
  \ensuremath{%
    \begin{array}{ccccc}
      \xintFor* ##1 in {\xintSeq
      {\fpeval{#1+\useKV[Tables]{Debut}}}{\fpeval{#1+\useKV[Tables]{Fin}}}}\do{
      ##1&-&#1&=&\fpeval{##1-#1}\\
      }
    \end{array}
  }%
}%

\NewDocumentCommand\PfCTableInverse{om}{%
  % #1 paramètres
  % #2 dizaine concernée
  \useKVdefault[Tables]%
  \setKV[Tables]{#1}%
  \ifnum#2=0\relax%
    \xdef\TIDepart{2}%
  \else%
    \xdef\TIDepart{\fpeval{#2*10}}%
  \fi%
  \xdef\TIFin{\fpeval{#2*10+9}}%
  % On sauvegarde les nombres non premiers de la dizaine
  \xdef\PfCRetiensNonPremiersInv{}%
  \xintFor* ##1 in{\xintSeq{\TIDepart}{\TIFin}}\do{%
    \TestPremier{##1}%
    \ifboolKV[ClesEra]{Premier}{}{%
      \xdef\PfCRetiensNonPremiersInv{\PfCRetiensNonPremiersInv##1,}%
    }%
  }%
  \setsepchar{,}\ignoreemptyitems%
  \readlist*\ListeNombresRetenus{\PfCRetiensNonPremiersInv}%
  \reademptyitems%
  \xdef\PfCRetiensIntermediaire{}%
  \xintFor* ##1 in{\xintSeq{1}{\ListeNombresRetenuslen}}\do{%
    \xdef\PfCRetiensIntermediaire{\PfCRetiensIntermediaire,\ListeNombresRetenus[##1]}%
    \xintFor* ##2 in{\xintSeq{2}{\fpeval{floor(sqrt(\ListeNombresRetenus[##1]))}}}\do{%
      \modulo{\ListeNombresRetenus[##1]}{##2}%
      \ifnum\remainder=0\relax%
        \xdef\PfCRetiensIntermediaire{\PfCRetiensIntermediaire/##2}%
      \fi%
    }%
  }%
  \setsepchar[*]{,*/}\ignoreemptyitems%
  \readlist*\ListeNombresRetenusInd{\PfCRetiensIntermediaire}%
  \reademptyitems%
  \ensuremath{%
    \begin{array}[t]{ccrcl}%
      \xintFor* ##1 in{\xintSeq{1}{\ListeNombresRetenusIndlen}}\do{%
      \xintifForFirst{}{\\}%
      \xintFor* ##2 in{\xintSeq{2}{\listlen\ListeNombresRetenusInd[##1]}}\do{%
      \num{\ListeNombresRetenusInd[##1,1]}\uppercase{&}=\uppercase{&}\num{\ListeNombresRetenusInd[##1,##2]}\uppercase{&}\times\uppercase{&}\quotient{\ListeNombresRetenusInd[##1,1]}{\ListeNombresRetenusInd[##1,##2]}\num{\the\intquotient}\\%
      }
      }
    \end{array}%
  }%
}%

\newcommand\Tables[2][]{%
  \useKVdefault[Tables]%
  \setKV[Tables]{#1}%
  \ifboolKV[Tables]{Seul}{%
    \ifboolKV[Tables]{Inverse}{%
        \PfCTableInverse[#1]{#2}%
    }{%
      \ifboolKV[Tables]{Soustraction}{%
        \TableSoustractionSeule{#2}%
      }{%
        \ifboolKV[Tables]{Addition}{%
          \TableAdditionSeule{#2}%
        }{%
          \TableMultiplicationSeule{#2}%
        }%
      }%
    }%
  }{%
    \ifboolKV[Tables]{Soustraction}{%
      La clé Soustraction n'est pas disponible ici.%
    }{%
      \ifboolKV[Tables]{Addition}{%
        \TableAdditionComplete%
      }{%
        \TableMultiplicationCompleteColore%
      }%
    }%
  }%
}%