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\setKVdefault[CalculsFractions]{Couleur=Crimson}
\NewDocumentCommand\tofrac{m}{%
\IfDecimal{#1}{#1}{%
\StrBefore{#1}{/}[\PfCnum]%
\StrBehind{#1}{/}[\PfCden]%
\frac{\PfCnum}{\PfCden}%
}%
}%
\NewDocumentCommand\AddFraction{soommo}{%
\useKVdefault[CalculsFractions]%
\setKV[CalculsFractions]{#2}%
\IfBooleanTF{#1}{%
\xdef\PfCFractionOp{-}%
}{%
\xdef\PfCFractionOp{+}%
}%
\IfDecimal{#4}{%
\xdef\PfCNumA{#4}%
\xdef\PfCNumB{1}%
}{%
\StrCut{#4}{/}\PfCNumA\PfCNumB%
}%
\IfDecimal{#5}{%
\xdef\PfCNumC{#5}%
\xdef\PfCNumD{1}%
}{%
\StrCut{#5}{/}\PfCNumC\PfCNumD%
}
\xdef\PfCAddFoo{\PfCNumA/\PfCNumB,\PfCNumC/\PfCNumD}%
\setsepchar[*]{,*/}\ignoreemptyitems%
\readlist*\ListeFractions{\PfCAddFoo}%
\reademptyitems
\setsepchar{,}%
% Partie calculs
\PGCD{\ListeFractions[1,2]}{\ListeFractions[2,2]}%
\xdef\PfCPremierMul{\fpeval{\ListeFractions[2,2]/\the\pgcd}}%
\xdef\PfCDeuxiemeMul{\fpeval{\ListeFractions[1,2]/\the\pgcd}}%
\xdef\PfCAddNumFin{\fpeval{(\ListeFractions[1,1])*(\PfCPremierMul)\PfCFractionOp(\ListeFractions[2,1])*(\PfCDeuxiemeMul)}}%
\xdef\PfCAddDenoFin{\fpeval{(\ListeFractions[1,2])*(\PfCPremierMul)}}%
\PGCD{\fpeval{abs(\PfCAddNumFin)}}{\fpeval{abs(\PfCAddDenoFin)}}\xdef\PfCAddPgcd{\the\pgcd}%
\xdef\PfCAddNumSimp{\fpeval{\PfCAddNumFin/\PfCAddPgcd}}%
\xdef\PfCAddDenoSimp{\fpeval{\PfCAddDenoFin/\PfCAddPgcd}}%
\xdef\PfCAddSumSimp{\PfCAddNumSimp/\PfCAddDenoSimp}%
\IfValueT{#6}{\xdef#6{\PfCAddSumSimp}}%
% Partie affichage
\ensuremath{%
\IfValueTF{#3}{%
\ifnum#3=4\relax%
\tofrac{\PfCAddSumSimp}%
\else%
\ifnum#3=3\relax%
\SSimpliTest{\fpeval{abs(\PfCAddNumFin)}}{\fpeval{abs(\PfCAddDenoFin)}}\ifthenelse{\boolean{Simplification}}{\tofrac{\PfCAddNumFin/\PfCAddDenoFin}}{\tofrac{\PfCAddSumSimp}}%
\else%
\ifnum#3=1\relax%
\ifnum\PfCPremierMul>1\relax%
\frac{\ListeFractions[1,1]_{\times\num{\PfCPremierMul}}}{\ListeFractions[1,2]_{\times\num{\PfCPremierMul}}}
\else%
\tofrac{#4}%
\fi%
\PfCFractionOp%
\ifnum\PfCDeuxiemeMul>1\relax%
\frac{\ListeFractions[2,1]_{\times\num{\PfCDeuxiemeMul}}}{\ListeFractions[2,2]_{\times\num{\PfCDeuxiemeMul}}}%
\else%
\tofrac{#5}%
\fi%
\else%
\ifnum#3=2\relax%
\frac{\num{\fpeval{\ListeFractions[1,1]*\PfCPremierMul}}}{\num{\fpeval{\ListeFractions[1,2]*\PfCPremierMul}}}\PfCFractionOp\frac{\num{\fpeval{\ListeFractions[2,1]*\PfCDeuxiemeMul}}}{\num{\fpeval{\ListeFractions[2,2]*\PfCDeuxiemeMul}}}%
\fi%
\fi%
\fi%
\fi%
}{\tofrac{#4}\PfCFractionOp\tofrac{#5}
}%
}%
}%
\NewDocumentCommand\SousFraction{oomm}{%
\AddFraction*[#1][#2]{#3}{#4}%
}%
\NewDocumentCommand\MulFraction{oommo}{%
\useKVdefault[CalculsFractions]%
\setKV[CalculsFractions]{#1}%
\IfDecimal{#3}{%
\xdef\PfCNumA{#3}%
\xdef\PfCNumB{1}%
}{%
\StrCut{#3}{/}{\PfCNumA}{\PfCNumB}%
}%
\IfDecimal{#4}{%
\xdef\PfCNumC{#4}%
\xdef\PfCNumD{1}%
}{%
\StrCut{#4}{/}{\PfCNumC}{\PfCNumD}%
}%
\xdef\PfCMulFoo{\PfCNumA/\PfCNumB,\PfCNumC/\PfCNumD}%
\setsepchar[*]{,*/}\ignoreemptyitems%
\readlist*\ListeFractions{\PfCMulFoo}%
\reademptyitems
\setsepchar{,}%
% Calculs
\xdef\PfCMulNumFin{\fpeval{(\ListeFractions[1,1])*(\ListeFractions[2,1])}}
\xdef\PfCMulDenoFin{\fpeval{\ListeFractions[1,2]*\ListeFractions[2,2]}}
\PGCD{\fpeval{abs(\PfCMulNumFin)}}{\fpeval{abs(\PfCMulDenoFin)}}\xdef\PfCMulPgcd{\pgcd}%
\xdef\PfCMulNumSimp{\fpeval{\PfCMulNumFin/\PfCMulPgcd}}%
\xdef\PfCMulDenoSimp{\fpeval{\PfCMulDenoFin/\PfCMulPgcd}}%
\xdef\PfCMulPdtSimp{\PfCMulNumSimp/\PfCMulDenoSimp}%
\IfValueT{#5}{\xdef#5{\PfCMulPdtSimp}}%
\ensuremath{%
\IfValueTF{#2}{%
\ifnum#2=3\relax
\tofrac{\PfCMulPdtSimp}%
\else
\ifnum#2=2\relax%
\SSimpliTest{\PfCMulNumFin}{\PfCMulDenoFin}\ifthenelse{\boolean{Simplification}}{\frac{\ifnum\PfCMulNumFin<0\relax-\fi\Decomposition[Longue]{\fpeval{abs(\PfCMulNumFin)}}}{\ifnum\PfCMulDenoFin<0\relax-\fi\Decomposition[Longue]{\fpeval{abs(\PfCMulDenoFin)}}}}{\tofrac{\PfCMulPdtSimp}}%
\else%
\ifnum#2=1\relax%
\frac{\ListeFractions[1,1]\times\ifnum\ListeFractions[2,1]<0\relax(\fi\ListeFractions[2,1]\ifnum\ListeFractions[2,1]<0\relax)\fi}{\ListeFractions[1,2]\times\ifnum\ListeFractions[2,2]<0\relax(\fi\ListeFractions[2,2]\ifnum\ListeFractions[2,2]<0\relax)\fi}
\fi
\fi
\fi
}{\tofrac{#3}\times\tofrac{#4}
}
}%
}%
\NewDocumentCommand\DivFraction{oommo}{%
\useKVdefault[CalculsFractions]%
\setKV[CalculsFractions]{#1}%
\IfDecimal{#3}{%
\xdef\PfCNumA{#3}%
\xdef\PfCNumB{1}%
}{%
\StrCut{#3}{/}{\PfCNumA}{\PfCNumB}%
}%
\IfDecimal{#4}{%
\xdef\PfCNumC{#4}%
\xdef\PfCNumD{1}%
}{%
\StrCut{#4}{/}{\PfCNumC}{\PfCNumD}%
}%
\xdef\PfCDivFoo{\PfCNumA/\PfCNumB,\PfCNumC/\PfCNumD}%
\setsepchar[*]{,*/}\ignoreemptyitems%
\readlist*\ListeFractions{\PfCDivFoo}%
\reademptyitems%
\setsepchar{,}%
% Calculs
\xdef\PfCDivNumFin{\fpeval{(\ListeFractions[1,1])*(\ListeFractions[2,2])}}%
\xdef\PfCDivDenoFin{\fpeval{\ListeFractions[1,2]*\ListeFractions[2,1]}}%
\PGCD{\fpeval{abs(\PfCDivNumFin)}}{\fpeval{abs(\PfCDivDenoFin)}}\xdef\PfCDivPgcd{\pgcd}%
\xdef\PfCDivNumSimp{\fpeval{\PfCDivNumFin/\PfCDivPgcd}}%
\xdef\PfCDivDenoSimp{\fpeval{\PfCDivDenoFin/\PfCDivPgcd}}%
\xdef\PfCDivPdtSimp{\PfCDivNumSimp/\PfCDivDenoSimp}%
\IfValueT{#5}{\xdef#5{\PfCDivPdtSimp}}%
\ensuremath{%
\IfValueTF{#2}{%
\ifnum#2=4\relax
\tofrac{\PfCDivPdtSimp}%
\else\ifnum#2=3\relax
\MulFraction[][\fpeval{#2-1}]{\ListeFractions[1,1]/\ListeFractions[1,2]}{\ListeFractions[2,2]/\ListeFractions[2,1]}%
\else
\ifnum#2=2\relax%
\MulFraction[][\fpeval{#2-1}]{\ListeFractions[1,1]/\ListeFractions[1,2]}{\ListeFractions[2,2]/\ListeFractions[2,1]}%
\else%
\ifnum#2=1\relax%
\tofrac{\ListeFractions[1,1]/\ListeFractions[1,2]}\times\tofrac{\ListeFractions[2,2]/\ListeFractions[2,1]}
\fi
\fi
\fi
\fi
}{\tofrac{#3}\div\tofrac{#4}
}
}%
}%
|
