diff options
Diffstat (limited to 'Master/texmf-dist/tex/latex')
4 files changed, 680 insertions, 38 deletions
diff --git a/Master/texmf-dist/tex/latex/proflycee/ProfLycee.sty b/Master/texmf-dist/tex/latex/proflycee/ProfLycee.sty index 6d2d836957a..d1c9f5a0867 100644 --- a/Master/texmf-dist/tex/latex/proflycee/ProfLycee.sty +++ b/Master/texmf-dist/tex/latex/proflycee/ProfLycee.sty @@ -3,7 +3,8 @@ % or later, see http://www.latex-project.org/lppl.txtf \NeedsTeXFormat{LaTeX2e} -\ProvidesPackage{ProfLycee}[2023/12/06 3.01a Aide pour l'utilisation de LaTeX en lycee] +\ProvidesPackage{ProfLycee}[2024/01/02 3.01b Aide pour l'utilisation de LaTeX en lycee] +% 3.01b Ajout de la division euclidienne + correction du bugs mineurs % 3.01a Ajout des courbes ECC/FCC + paramètres par interpolation % 3.00g Amélioration de la marge Gauche dans le PseudoCode % 3.00f Conversion d'une écriture décimale périodique en fraction (avec rédaction éventuelle) @@ -187,6 +188,8 @@ \input{proflycee-tools-aleatoire.tex} %%------Suites \input{proflycee-tools-suites.tex} +%%------Complexes +\input{proflycee-tools-complexes.tex} %%------Géométrie \input{proflycee-tools-geom.tex} %%------Récréations diverses diff --git a/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-analyse.tex b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-analyse.tex index 00f6f0206aa..90672aaf1d5 100644 --- a/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-analyse.tex +++ b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-analyse.tex @@ -2,6 +2,8 @@ % Copyright 2023 Cédric Pierquet % Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txt +%Correction d'un bug sur la raacine carrée... le cas où ça fait 1 ! + %%------SimplFrac nouvelle version \NewDocumentCommand\ConversionFraction{ s O{} m }{% %*=moins sur le numérateur @@ -295,43 +297,49 @@ %%------SIMPLIFRACINES \DeclareDocumentCommand\SimplificationRacine{ m }{% argument mandataire {calcul ou fraction} \xdef\calculargument{\xintIrr{\xinteval{#1}}}% - \IfEndWith{\calculargument}{/1}% - {%si c'est un entier ! - \xdef\calculargument{\xintiieval{#1}}% - \xdef\ExtractRacStop{\xintiFloor{\xintfloateval{sqrt(\calculargument)}}}% - \xintFor* ##1 in {\xintSeq{1}{\ExtractRacStop}}\do{% - \xintifboolexpr{ \xintiiRem{\calculargument}{\xintiieval{##1*##1}} == 0}%si le carré divise - {\xdef\ExtractRacID{##1}}% - {}% - }% - \xdef\ExtracReste{\xintiieval{\calculargument/(\ExtractRacID*\ExtractRacID)}}% - \ensuremath{\xintifboolexpr{\ExtractRacID == 1 && \ExtracReste == 1}% - {1}% - { \xintifboolexpr{\ExtractRacID == 1}{}{\num{\xintiieval{\ExtractRacID}}}% - \xintifboolexpr{\ExtracReste == 1}{}{\sqrt{\num{\ExtracReste}}} }}% -% }% - }% - {%on va mettre sous forme a\sqrt(d)/b := buggue avec des millièmes... - \StrBefore{\calculargument}{/}[\numerateur]%on extrait le numérateur - \StrBehind{\calculargument}{/}[\denominateur]%on extrait le dénominateur - \xdef\ExtractRacNNum{\xintiieval{\numerateur*\denominateur}}% - \xdef\ExtractRacStop{\xintiFloor{\xintfloateval{sqrt(\ExtractRacNNum)}}}% - \xintFor* ##1 in {\xintSeq{1}{\ExtractRacStop}}\do{% - \xintifboolexpr{ \xintiiRem{\ExtractRacNNum}{\xintiieval{##1*##1}} == 0}%si le carré divise - {\xdef\ExtractRacID{##1}}% - {} + \xintifboolexpr{\calculargument == 1}% + {% + \ensuremath{1}% }% - \xdef\ExtractRacGCD{\xintiiGCD{\ExtractRacID}{\denominateur}}% - \xdef\RacNumSimpl{\xintiieval{\ExtractRacID/\ExtractRacGCD}}%simpl num - \xdef\RacDenomSimpl{\xintiieval{\denominateur/\ExtractRacGCD}}% - \xdef\RacRacSimpl{\xintiieval{\ExtractRacNNum/(\ExtractRacID*\ExtractRacID)}}% - \ensuremath{\frac{% - \xintifboolexpr{\RacNumSimpl == 1 && \RacRacSimpl == 1}% - {1}% - { \xintifboolexpr{\RacNumSimpl == 1}{}{\RacNumSimpl} \xintifboolexpr{\RacRacSimpl == 1}{}{\sqrt{\num{\RacRacSimpl}}} }% + {% + \IfEndWith{\calculargument}{/1}% + {%si c'est un entier ! + \xdef\calculargument{\xintiieval{#1}}% + \xdef\ExtractRacStop{\xintiFloor{\xintfloateval{sqrt(\calculargument)}}}% + \xintFor* ##1 in {\xintSeq{1}{\ExtractRacStop}}\do{% + \xintifboolexpr{ \xintiiRem{\calculargument}{\xintiieval{##1*##1}} == 0}%si le carré divise + {\xdef\ExtractRacID{##1}}% + {}% + }% + \xdef\ExtracReste{\xintiieval{\calculargument/(\ExtractRacID*\ExtractRacID)}}% + \ensuremath{\xintifboolexpr{\ExtractRacID == 1 && \ExtracReste == 1}% + {1}% + { \xintifboolexpr{\ExtractRacID == 1}{}{\num{\xintiieval{\ExtractRacID}}}% + \xintifboolexpr{\ExtracReste == 1}{}{\sqrt{\num{\ExtracReste}}} }}% + % }% + }% + {%on va mettre sous forme a\sqrt(d)/b := buggue avec des millièmes... + \StrBefore{\calculargument}{/}[\numerateur]%on extrait le numérateur + \StrBehind{\calculargument}{/}[\denominateur]%on extrait le dénominateur + \xdef\ExtractRacNNum{\xintiieval{\numerateur*\denominateur}}% + \xdef\ExtractRacStop{\xintiFloor{\xintfloateval{sqrt(\ExtractRacNNum)}}}% + \xintFor* ##1 in {\xintSeq{1}{\ExtractRacStop}}\do{% + \xintifboolexpr{ \xintiiRem{\ExtractRacNNum}{\xintiieval{##1*##1}} == 0}%si le carré divise + {\xdef\ExtractRacID{##1}}% + {} }% - { \RacDenomSimpl }}% - }% + \xdef\ExtractRacGCD{\xintiiGCD{\ExtractRacID}{\denominateur}}% + \xdef\RacNumSimpl{\xintiieval{\ExtractRacID/\ExtractRacGCD}}%simpl num + \xdef\RacDenomSimpl{\xintiieval{\denominateur/\ExtractRacGCD}}% + \xdef\RacRacSimpl{\xintiieval{\ExtractRacNNum/(\ExtractRacID*\ExtractRacID)}}% + \ensuremath{\frac{% + \xintifboolexpr{\RacNumSimpl == 1 && \RacRacSimpl == 1}% + {1}% + { \xintifboolexpr{\RacNumSimpl == 1}{}{\RacNumSimpl} \xintifboolexpr{\RacRacSimpl == 1}{}{\sqrt{\num{\RacRacSimpl}}} }% + }% + { \RacDenomSimpl }}% + }% + }% } %%------DICHOTOMIE @@ -631,6 +639,8 @@ %clés \restoreKV[FracPeriod]% revenir au valeurs par défaut \setKV[FracPeriod]{#1}% lit les arguments optionnels + %vmode ? + \ifvmode\leavevmode\fi% %les variables utiles \IfEndWith{#2}{.}% {% diff --git a/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-arithm.tex b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-arithm.tex index cabba276fb0..9b2d9eb6530 100644 --- a/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-arithm.tex +++ b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-arithm.tex @@ -502,11 +502,11 @@ \xintFor* ##1 in {\xintSeq{2}{\argcal}}\do{% \xintifboolexpr{ \xintiiRem{\argcal}{##1} == 0 }% {% - \xdef\tmplistdiv{\tmplistdiv /\num{##1}} + \xdef\tmplistdiv{\tmplistdiv /\num{##1}}% }% {}% }% - \ensuremath{\ifboolKV[listdiv]{AffNom}{\IfBooleanTF{#1}{\mathscr{D}}{\mathcal{D}}_{\num{\argcal}}=}{}\EcritureEnsemble[\strut]{\tmplistdiv}} + \ensuremath{\ifboolKV[listdiv]{AffNom}{\IfBooleanTF{#1}{\mathscr{D}}{\mathcal{D}}_{\num{\argcal}}=}{}\EcritureEnsemble[\strut]{\tmplistdiv}}% } %arbre diviseurs @@ -913,4 +913,24 @@ }% } +%====DIV EUCL (OK) +\setKVdefault[diveucl]{% + Quotient=true,% + Reste=true,% + Vide=false,% + Pointilles=\ldots +} +\NewDocumentCommand\DivEucl{ s O{} m m }{% + \restoreKV[diveucl]% + \setKV[diveucl]{#2}% + \ifboolKV[diveucl]{Vide}% + {% + \setKV[diveucl]{Quotient=false,Reste=false}% + }% + {}% + \xdef\tmp@quotient{\xintiiQuo{#3}{#4}}\xdef\tmp@reste{\xintiiRem{#3}{#4}}% + \ensuremath{\num{#3}=\num{#4}\times\ifboolKV[diveucl]{Quotient}{\xintifboolexpr{\tmp@quotient < 0}{(\num{\tmp@quotient})}{\num{\tmp@quotient}}}{\useKV[diveucl]{Pointilles}}+\ifboolKV[diveucl]{Reste}{\num{\tmp@reste}}{\useKV[diveucl]{Pointilles}}}% + \IfBooleanT{#1}{~avec $0 \leqslant \num{\xintiiRem{#3}{#4}} < \xintifboolexpr{#4 < 0}{\lvert\num{#4}\rvert}{\num{#4}}$}% +} + \endinput
\ No newline at end of file diff --git a/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-complexes.tex b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-complexes.tex new file mode 100644 index 00000000000..ca64c0ac400 --- /dev/null +++ b/Master/texmf-dist/tex/latex/proflycee/proflycee-tools-complexes.tex @@ -0,0 +1,609 @@ +% proflycee-tools-complexes.tex +% Copyright 2023 Cédric Pierquet +% Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txt + +\NewDocumentCommand\PartieReelle{ D<>{} m O{\PartReRes} }{% + \StrSubstitute{#2}{I}{0}[#3]% + \IfEq{#1}{n}% + {\ensuremath{\num{\xinteval{#3}}}}{}% + \IfEq{#1}{f}% + {\ensuremath{\ConversionFraction{#3}}}{}% + \IfEq{#1}{df}% + {\ensuremath{\ConversionFraction[d]{#3}}}{}% +} +\NewDocumentCommand\PartieImaginaire{ D<>{} m O{\PartImRes} }{% + \StrSubstitute{#2}{I}{0}[\TmpPartReCplxA]% + \StrSubstitute{(#2)-(\TmpPartReCplxA)}{I}{1}[#3]% + \IfEq{#1}{n}% + {\ensuremath{\num{\xinteval{#3}}}}{}% + \IfEq{#1}{f}% + {\ensuremath{\ConversionFraction{#3}}}{}% + \IfEq{#1}{df}% + {\ensuremath{\ConversionFraction[d]{#3}}}{}% +} + +\NewDocumentCommand\AffComplexe{ O{} }{% + \ensuremath{% + \xintifboolexpr{\xinttmpreCalc == 0 'and' \xinttmpimCalc == 0}{0}{}% + \xintifboolexpr{\xinttmpreCalc == 0 'and' \xinttmpimCalc == 1}{\i}{}% + \xintifboolexpr{\xinttmpreCalc == 0 'and' \xinttmpimCalc == -1}{-\i}{}% + \xintifboolexpr{\xinttmpreCalc == 0 'and' abs(\xinttmpimCalc) != 1 'and' \xinttmpimCalc != 0}{\ConversionFraction[#1]{\tmpimCalc}\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc < 0 'and' \xinttmpimCalc != -1}{\ConversionFraction[#1]{\tmpreCalc}-\ConversionFraction[#1]{-(\tmpimCalc)}\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc == -1}{\ConversionFraction[#1]{\tmpreCalc}-\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc == 1}{\ConversionFraction[#1]{\tmpreCalc}+\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc > 0 'and' \xinttmpimCalc != 1}{\ConversionFraction[#1]{\tmpreCalc}+\ConversionFraction[#1]{\tmpimCalc}\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc == 0}{\ConversionFraction[#1]{\tmpreCalc}}{}% + }% +} + +\NewDocumentCommand\Complexe{ O{} m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieImaginaire{#2}[\tmpimA]% + \xdef\xinttmpreCalc{\xinteval{\tmpreA}}% + \xdef\xinttmpimCalc{\xinteval{\tmpimA}}% + \ensuremath{% + \xintifboolexpr{\xinttmpreCalc == 0 'and' \xinttmpimCalc == 0}{0}{}% + \xintifboolexpr{\xinttmpreCalc == 0 'and' \xinttmpimCalc == 1}{\i}{}% + \xintifboolexpr{\xinttmpreCalc == 0 'and' \xinttmpimCalc == -1}{-\i}{}% + \xintifboolexpr{\xinttmpreCalc == 0 'and' abs(\xinttmpimCalc) != 1 'and' \xinttmpimCalc != 0}{\ConversionFraction[#1]{\tmpimA}\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc < 0 'and' \xinttmpimCalc != -1}{\ConversionFraction[#1]{\tmpreA}-\ConversionFraction[#1]{-(\tmpimA)}\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc == -1}{\ConversionFraction[#1]{\tmpreA}-\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc == 1}{\ConversionFraction[#1]{\tmpreA}+\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc > 0 'and' \xinttmpimCalc != 1}{\ConversionFraction[#1]{\tmpreA}+\ConversionFraction[#1]{\tmpimA}\i}{}% + \xintifboolexpr{\xinttmpreCalc != 0 'and' \xinttmpimCalc == 0}{\ConversionFraction[#1]{\tmpreA}}{}% + }% +} + +\NewDocumentCommand\SommeComplexes{ O{} m m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieReelle{#3}[\tmpreB]% + \PartieImaginaire{#2}[\tmpimA]% + \PartieImaginaire{#3}[\tmpimB]% + \xdef\tmpreCalc{(\tmpreA)+(\tmpreB)}% + \xdef\xinttmpreCalc{\xinteval{(\tmpreA)+(\tmpreB)}}% + \xdef\tmpimCalc{(\tmpimA)+(\tmpimB)}% + \xdef\xinttmpimCalc{\xinteval{(\tmpimA)+(\tmpimB)}}% + %\xinttmpreCalc\text{ et }\xinttmpimCalc. + \AffComplexe[#1]% +} + +\NewDocumentCommand\ProduitComplexes{ O{} m m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieReelle{#3}[\tmpreB]% + \PartieImaginaire{#2}[\tmpimA]% + \PartieImaginaire{#3}[\tmpimB]% + \xdef\tmpreCalc{(\tmpreA)*(\tmpreB)-(\tmpimA)*(\tmpimB)}% + \xdef\xinttmpreCalc{\xinteval{\tmpreCalc}}% + \xdef\tmpimCalc{(\tmpreA)*(\tmpimB)+(\tmpimA)*(\tmpreB)}% + \xdef\xinttmpimCalc{\xinteval{\tmpimCalc}}% + %\xinttmpreCalc\text{ et }\xinttmpimCalc. + \AffComplexe[#1]% +} + +\NewDocumentCommand\QuotientComplexes{ O{} m m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieReelle{#3}[\tmpreB]% + \PartieImaginaire{#2}[\tmpimA]% + \PartieImaginaire{#3}[\tmpimB]% + \xdef\tmpreCalc{((\tmpreA)*(\tmpreB)+(\tmpimA)*(\tmpimB))/((\tmpreB)*(\tmpreB)+(\tmpimB)*(\tmpimB))}% + \xdef\xinttmpreCalc{\xinteval{\tmpreCalc}}% + \xdef\tmpimCalc{(-(\tmpreA)*(\tmpimB)+(\tmpimA)*(\tmpreB))/((\tmpreB)*(\tmpreB)+(\tmpimB)*(\tmpimB))}% + \xdef\xinttmpimCalc{\xinteval{\tmpimCalc}}% + %\xinttmpreCalc\text{ et }\xinttmpimCalc. + \AffComplexe[#1]% +} + +\NewDocumentCommand\CarreComplexe{ O{} m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieImaginaire{#2}[\tmpimA]% + \xdef\tmpreCalc{(\tmpreA)*(\tmpreA)-(\tmpimA)*(\tmpimA)}% + \xdef\xinttmpreCalc{\xinteval{\tmpreCalc}}% + \xdef\tmpimCalc{2*(\tmpreA)*(\tmpimA)}% + \xdef\xinttmpimCalc{\xinteval{\tmpimCalc}}% + %\xinttmpreCalc\text{ et }\xinttmpimCalc. + \AffComplexe[#1]% +} + +\NewDocumentCommand\CubeComplexe{ O{} m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieImaginaire{#2}[\tmpimA]% + \xdef\tmpreCalc{(\tmpreA)*(\tmpreA)*(\tmpreA)-3*(\tmpreA)*(\tmpimA)*(\tmpimA)}% + \xdef\xinttmpreCalc{\xinteval{\tmpreCalc}}% + \xdef\tmpimCalc{3*(\tmpreA)*(\tmpreA)*(\tmpimA)-(\tmpimA)*(\tmpimA)*(\tmpimA)}% + \xdef\xinttmpimCalc{\xinteval{\tmpimCalc}}% + %\xinttmpreCalc\text{ et }\xinttmpimCalc. + \AffComplexe[#1]% +} + +\NewDocumentCommand\ModuleComplexe{ m }{% + \PartieReelle{#1}[\tmpreA]% + \PartieImaginaire{#1}[\tmpimA]% + \IfSubStr{\tmpreA}{sqrt}% + {% + \StrDel{\tmpreA}{sqrt}[\tmpretmpA]% + }% + {% + \xdef\tmpretmpA{\tmpreA}% + }% + \IfSubStr{\tmpimA}{sqrt}% + {% + \StrDel{\tmpimA}{sqrt}[\tmpimtmpA]% + }% + {% + \xdef\tmpimtmpA{\tmpimA}% + }% + \IfSubStr{\tmpreA}{sqrt}% + {% + \IfSubStr{\tmpimA}{sqrt}% + {% + \xdef\tmpCarreModule{abs(\tmpretmpA)+abs(\tmpimtmpA)}% + }% + {% + \xdef\tmpCarreModule{abs(\tmpretmpA)+(\tmpimtmpA)*(\tmpimtmpA)}% + }% + }% + {% + \xdef\tmpCarreModule{(\tmpretmpA)*(\tmpretmpA)+(\tmpimtmpA)*(\tmpimtmpA)}% + }% + \ensuremath{\SimplificationRacine{\tmpCarreModule}}% +} + +\NewDocumentCommand\ArgumentComplexe{ O{} m }{% + \PartieReelle{#2}[\tmpreA]% + \PartieImaginaire{#2}[\tmpimA]% + \xdef\tmpCarreModule{(\tmpreA)*(\tmpreA)+(\tmpimA)*(\tmpimA)}% + \xdef\tmpModUnRe{(\tmpreA)/(sqrt(\tmpCarreModule))}% + \xdef\tmpModUnIm{(\tmpimA)/(sqrt(\tmpCarreModule))}% + \ensuremath{% + \xintifboolexpr{\tmpModUnRe == 1 'and' \tmpModUnIm == 0}{0}{}% + \xintifboolexpr{\tmpModUnRe == -1 'and' \tmpModUnIm == 0}{\pi}{}% + \xintifboolexpr{\tmpModUnRe == 0.5 'and' \tmpModUnIm > 0}{\IfEq{#1}{d}{\dfrac{\pi}{3}}{\frac{\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe == 0.5 'and' \tmpModUnIm < 0}{\IfEq{#1}{d}{\dfrac{-\pi}{3}}{\frac{-\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe == -0.5 'and' \tmpModUnIm > 0}{\IfEq{#1}{d}{\dfrac{2\pi}{3}}{\frac{2\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe == -0.5 'and' \tmpModUnIm < 0}{\IfEq{#1}{d}{\dfrac{-2\pi}{3}}{\frac{-2\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe > 0 'and' \tmpModUnIm == 0.5}{\IfEq{#1}{d}{\dfrac{\pi}{6}}{\frac{\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe < 0 'and' \tmpModUnIm == 0.5}{\IfEq{#1}{d}{\dfrac{5\pi}{6}}{\frac{5\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe > 0 'and' \tmpModUnIm == -0.5}{\IfEq{#1}{d}{\dfrac{-\pi}{6}}{\frac{-\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe < 0 'and' \tmpModUnIm == -0.5}{\IfEq{#1}{d}{\dfrac{-5\pi}{6}}{\frac{-5\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe == \tmpModUnIm 'and' \tmpModUnRe > 0}{\IfEq{#1}{d}{\dfrac{\pi}{4}}{\frac{\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == \tmpModUnIm 'and' \tmpModUnRe < 0}{\IfEq{#1}{d}{\dfrac{-3\pi}{4}}{\frac{-3\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == -\tmpModUnIm 'and' \tmpModUnRe > 0}{\IfEq{#1}{d}{\dfrac{-\pi}{4}}{\frac{-\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == -\tmpModUnIm 'and' \tmpModUnRe < 0}{\IfEq{#1}{d}{\dfrac{3\pi}{4}}{\frac{3\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == 0 'and' \tmpModUnIm == 1}{\IfEq{#1}{d}{\dfrac{\pi}{2}}{\frac{\pi}{2}}}{}% + \xintifboolexpr{\tmpModUnRe == 0 'and' \tmpModUnIm == -1}{\IfEq{#1}{d}{\dfrac{-\pi}{2}}{\frac{-\pi}{2}}}{}% + }% +} + +\NewDocumentCommand\FormeExpoComplexe{ m }{% + \PartieReelle{#1}[\tmpreA]% + \PartieImaginaire{#1}[\tmpimA]% + \IfSubStr{\tmpreA}{sqrt}% + {% + \StrDel{\tmpreA}{sqrt}[\tmpretmpA]% + }% + {% + \xdef\tmpretmpA{\tmpreA}% + }% + \IfSubStr{\tmpimA}{sqrt}% + {% + \StrDel{\tmpimA}{sqrt}[\tmpimtmpA]% + }% + {% + \xdef\tmpimtmpA{\tmpimA}% + }% + \IfSubStr{\tmpreA}{sqrt}% + {% + \IfSubStr{\tmpimA}{sqrt}% + {% + \xdef\tmpCarreModule{abs(\tmpretmpA)+abs(\tmpimtmpA)}% + }% + {% + \xdef\tmpCarreModule{abs(\tmpretmpA)+(\tmpimtmpA)*(\tmpimtmpA)}% + }% + }% + {% + \xdef\tmpCarreModule{(\tmpretmpA)*(\tmpretmpA)+(\tmpimtmpA)*(\tmpimtmpA)}% + }% + \xdef\tmpModUnRe{(\tmpreA)/(sqrt(\tmpCarreModule))}% + \xdef\tmpModUnIm{(\tmpimA)/(sqrt(\tmpCarreModule))}% + \ensuremath{% + \xintifboolexpr{\tmpCarreModule == 1}{}{\SimplificationRacine{\tmpCarreModule}}% + \e^{% + \xintifboolexpr{\tmpModUnRe == 1 'and' \tmpModUnIm == 0}{0}{}% + \xintifboolexpr{\tmpModUnRe == -1 'and' \tmpModUnIm == 0}{\i\pi}{}% + \xintifboolexpr{\tmpModUnRe == 0.5 'and' \tmpModUnIm > 0}{\IfEq{#1}{d}{\dfrac{\i\pi}{3}}{\frac{\i\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe == 0.5 'and' \tmpModUnIm < 0}{\IfEq{#1}{d}{\dfrac{-\i\pi}{3}}{\frac{-\i\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe == -0.5 'and' \tmpModUnIm > 0}{\IfEq{#1}{d}{\dfrac{2\i\pi}{3}}{\frac{2\i\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe == -0.5 'and' \tmpModUnIm < 0}{\IfEq{#1}{d}{\dfrac{-2\i\pi}{3}}{\frac{-2\i\pi}{3}}}{}% + \xintifboolexpr{\tmpModUnRe > 0 'and' \tmpModUnIm == 0.5}{\IfEq{#1}{d}{\dfrac{\i\pi}{6}}{\frac{\i\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe < 0 'and' \tmpModUnIm == 0.5}{\IfEq{#1}{d}{\dfrac{5\i\pi}{6}}{\frac{5\i\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe > 0 'and' \tmpModUnIm == -0.5}{\IfEq{#1}{d}{\dfrac{-\i\pi}{6}}{\frac{-\i\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe < 0 'and' \tmpModUnIm == -0.5}{\IfEq{#1}{d}{\dfrac{-5\i\pi}{6}}{\frac{-5\i\pi}{6}}}{}% + \xintifboolexpr{\tmpModUnRe == \tmpModUnIm 'and' \tmpModUnRe > 0}{\IfEq{#1}{d}{\dfrac{\i\pi}{4}}{\frac{\i\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == \tmpModUnIm 'and' \tmpModUnRe < 0}{\IfEq{#1}{d}{\dfrac{-3\i\pi}{4}}{\frac{-3\i\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == -\tmpModUnIm 'and' \tmpModUnRe > 0}{\IfEq{#1}{d}{\dfrac{-\i\pi}{4}}{\frac{-\i\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == -\tmpModUnIm 'and' \tmpModUnRe < 0}{\IfEq{#1}{d}{\dfrac{3\i\pi}{4}}{\frac{3\i\pi}{4}}}{}% + \xintifboolexpr{\tmpModUnRe == 0 'and' \tmpModUnIm == 1}{\IfEq{#1}{d}{\dfrac{\i\pi}{2}}{\frac{\i\pi}{2}}}{}% + \xintifboolexpr{\tmpModUnRe == 0 'and' \tmpModUnIm == -1}{\IfEq{#1}{d}{\dfrac{-\i\pi}{2}}{\frac{-\i\pi}{2}}}{}% + }% + }% +} + +%====commandes alternatives +\NewDocumentCommand\ExtractionCoeffExprRacines{ m O{\tmpCoeffA} O{\tmpCoeffB} O{\tmpCoeffC} O{\tmpCoeffD} }{%a*rac(b)+c*rac(d) + \IfSubStr{#1}{+} + {% + \StrCut{#1}{+}{\exprtestG}{\exprtestD}% + \IfSubStr{\exprtestG}{*sqrt}% + {% + \StrBefore{\exprtestG}{*}[#2]% + \StrBetween{\exprtestG}{sqrt(}{)}[#3]% + }% + {% + \xdef#2{\exprtestG}\xdef#3{1}% + }% + \IfSubStr{\exprtestD}{*sqrt}% + {% + \StrBefore{\exprtestD}{*}[#4]% + \StrBetween{\exprtestD}{sqrt(}{)}[#5]% + }% + {% + \xdef#4{\exprtestD}\xdef#5{1}% + }% + }% + {% + %si 2 moins... + \StrCount{#1}{-}[\tmpNbmoins]% + \xintifboolexpr{\tmpNbmoins == 2}% + {% + \StrCut[2]{#1}{-}{\exprtestG}{\exprtestD}% + }% + {% + \StrCut{#1}{-}{\exprtestG}{\exprtestD}% + }% + \IfSubStr{\exprtestG}{*sqrt}% + {% + \StrBefore{\exprtestG}{*}[#2]% + \StrBetween{\exprtestG}{sqrt(}{)}[#3]% + }% + {% + \xdef#2{\exprtestG}\xdef#3{1}% + }% + \IfSubStr{\exprtestD}{*sqrt}% + {% + \StrBefore{\exprtestD}{*}[#4]% + \xdef#4{-#4}% + \StrBetween{\exprtestD}{sqrt(}{)}[#5]% + }% + {% + \xdef#4{-#4}\xdef#5{1}% + }% + }% +} + +\NewDocumentCommand\SimplifCarreExprRacine{ O{} m }{% + \ExtractionCoeffExprRacines{#2}% + \xintifboolexpr{\tmpCoeffA > 0 'and' \tmpCoeffC > 0}% + {% + \ensuremath{% + \ConversionFraction[#1]{(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffB)+(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffD)}+% + \IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{4*(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffB)*(\tmpCoeffD)}% + }% + }% + {}% + \xintifboolexpr{\tmpCoeffA > 0 'and' \tmpCoeffC < 0}% + {% + \ensuremath{% + \ConversionFraction[#1]{(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffB)+(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffD)}-% + \IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{4*(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffB)*(\tmpCoeffD)}% + }% + }% + {}% + \xintifboolexpr{\tmpCoeffA < 0 'and' \tmpCoeffC > 0}% + {% + \ensuremath{% + \ConversionFraction[#1]{(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffB)+(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffD)}-% + \IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{4*(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffB)*(\tmpCoeffD)}% + }% + }% + {}% + \xintifboolexpr{\tmpCoeffA < 0 'and' \tmpCoeffC < 0}% + {% + \ensuremath{% + \ConversionFraction[#1]{(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffB)+(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffD)}+% + \IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{4*(\tmpCoeffA)*(\tmpCoeffA)*(\tmpCoeffC)*(\tmpCoeffC)*(\tmpCoeffB)*(\tmpCoeffD)}% + }% + }% + {}% +} + +\NewDocumentCommand\CalculModuleCplx{ O{} m m }{% + \ExtractionCoeffExprRacines{#2}[\Crea][\Creb][\Crec][\Cred]% + \ExtractionCoeffExprRacines{#3}[\Cima][\Cimb][\Cimc][\Cimd]% + \xdef\TmpCoeffsDebut{(\Crea)*(\Crea)*(\Creb)+(\Crec)*(\Crec)*(\Cred)+(\Cima)*(\Cima)*(\Cimb)+(\Cimc)*(\Cimc)*(\Cimd)}% + \xdef\TmpCoeffsRacineA{4*(\Crea)*(\Crea)*(\Crec)*(\Crec)*(\Creb)*(\Cred)}% + \xdef\TmpCoeffsRacineB{4*(\Cima)*(\Cima)*(\Cimc)*(\Cimc)*(\Cimb)*(\Cimd)}% + %\xinteval{\TmpCoeffsDebut}/\xinteval{\TmpCoeffsRacineA}/\xinteval{\TmpCoeffsRacineB}/\xinteval{(\Crea)*(\Crec)}/\xinteval{(\Cima)*(\Cimc)}= + \xintifboolexpr{\TmpCoeffsRacineA == 0 'and' \TmpCoeffsRacineB == 0}% + {% + \ensuremath{\IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{\TmpCoeffsDebut}}% + }% + {}% + \xintifboolexpr{\TmpCoeffsRacineA == 0 'and' \TmpCoeffsRacineB != 0}% + {% + \ensuremath{\IfEq{#1}{d}{\displaystyle}{}\sqrt{\SimplificationRacine{(\TmpCoeffsDebut)*(\TmpCoeffsDebut)}\xintifboolexpr{(\Cima)*(\Cimc) < 0}{-}{+}\SimplificationRacine{\TmpCoeffsRacineB}}}% + }% + {}% + \xintifboolexpr{\TmpCoeffsRacineA != 0 'and' \TmpCoeffsRacineB == 0}% + {% + \ensuremath{\IfEq{#1}{d}{\displaystyle}{}\sqrt{\SimplificationRacine{(\TmpCoeffsDebut)*(\TmpCoeffsDebut)}\xintifboolexpr{(\Crea)*(\Crec) < 0}{-}{+}\SimplificationRacine{\TmpCoeffsRacineA}}}% + }% + {}% + \xintifboolexpr{\TmpCoeffsRacineA != 0 'and' \TmpCoeffsRacineB != 0 'and' (\Crea)*(\Crec) < 0 'and' (\Cima)*(\Cimc) > 0 'and' \TmpCoeffsRacineA == \TmpCoeffsRacineB}% + {% + \ensuremath{\IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{\TmpCoeffsDebut}}% + }% + {}% + \xintifboolexpr{\TmpCoeffsRacineA != 0 'and' \TmpCoeffsRacineB != 0 'and' (\Crea)*(\Crec) > 0 'and' (\Cima)*(\Cimc) < 0 'and' \TmpCoeffsRacineA == \TmpCoeffsRacineB}% + {% + \ensuremath{\IfEq{#1}{d}{\displaystyle}{}\SimplificationRacine{\TmpCoeffsDebut}}% + }% + {}% + \xintifboolexpr{\TmpCoeffsRacineA != \TmpCoeffsRacineB}% + {% + \ensuremath{\IfEq{#1}{d}{\displaystyle}{}\sqrt{\SimplificationRacine{(\TmpCoeffsDebut)*(\TmpCoeffsDebut)}\xintifboolexpr{(\Crea)*(\Crec) < 0}{-}{+}\SimplificationRacine{\TmpCoeffsRacineA}\xintifboolexpr{(\Cima)*(\Cimc) < 0}{-}{+}\SimplificationRacine{\TmpCoeffsRacineB}}}% + }% + {}% +} + +\NewDocumentCommand\TestArgumentComplexe{ O{} m m m }{% + \xintifboolexpr{\TmpArg == #2 'or' \TmpArg == #3}{\ensuremath{\IfEq{#1}{d}{\displaystyle}{}#4}}{}% +} + +\NewDocumentCommand\CalculArgumentCplx{ s O{} m m }{% + \xdef\TmpArg{\xintfloateval{trunc(Argd(#3,#4),1)}}%\TmpArg% + \IfBooleanTF{#1}% + {% + %les pi/2 + \TestArgumentComplexe[#2]{0}{0.0}{0}% + \TestArgumentComplexe[#2]{90}{90.0}{\frac{\pi}{2}}% + \TestArgumentComplexe[#2]{-90}{-90.0}{\frac{3\pi}{2}}% + \TestArgumentComplexe[#2]{180}{180.0}{\pi}% + %les pi/3 + \TestArgumentComplexe[#2]{60}{60.0}{\frac{\pi}{3}}% + \TestArgumentComplexe[#2]{120}{120.0}{\frac{2\pi}{3}}% + \TestArgumentComplexe[#2]{-60}{-60.0}{\frac{5\pi}{3}}% + \TestArgumentComplexe[#2]{-120}{-120.0}{\frac{4\pi}{3}}% + %les pi/4 + \TestArgumentComplexe[#2]{45}{45.0}{\frac{\pi}{4}}% + \TestArgumentComplexe[#2]{135}{135.0}{\frac{3\pi}{4}}% + \TestArgumentComplexe[#2]{-45}{-45.0}{\frac{7\pi}{4}}% + \TestArgumentComplexe[#2]{-135}{-135.0}{\frac{5\pi}{4}}% + %les pi/5 + \TestArgumentComplexe[#2]{36}{36.0}{\frac{\pi}{5}}% + \TestArgumentComplexe[#2]{72}{72.0}{\frac{2\pi}{5}}% + \TestArgumentComplexe[#2]{108}{108.0}{\frac{3\pi}{5}}% + \TestArgumentComplexe[#2]{144}{144.0}{\frac{4\pi}{5}}% + \TestArgumentComplexe[#2]{-36}{-36.0}{\frac{9\pi}{5}}% + \TestArgumentComplexe[#2]{-72}{-72.0}{\frac{8\pi}{5}}% + \TestArgumentComplexe[#2]{-108}{-108.0}{\frac{7\pi}{5}}% + \TestArgumentComplexe[#2]{-144}{-144.0}{\frac{6\pi}{5}}% + %les pi/6 + \TestArgumentComplexe[#2]{30}{30.0}{\frac{\pi}{6}}% + \TestArgumentComplexe[#2]{150}{150.0}{\frac{5\pi}{6}}% + \TestArgumentComplexe[#2]{-30}{-30.0}{\frac{11\pi}{6}}% + \TestArgumentComplexe[#2]{-150}{-150.0}{\frac{7\pi}{6}}% + %les pi/8 + \TestArgumentComplexe[#2]{22.5}{22.5}{\frac{\pi}{8}}% + \TestArgumentComplexe[#2]{67.5}{67.5}{\frac{3\pi}{8}}% + \TestArgumentComplexe[#2]{112.5}{112.5}{\frac{5\pi}{8}}% + \TestArgumentComplexe[#2]{157.5}{157.5}{\frac{7\pi}{8}}% + \TestArgumentComplexe[#2]{-22.5}{-22.5}{\frac{15\pi}{8}}% + \TestArgumentComplexe[#2]{-67.5}{-67.5}{\frac{13\pi}{8}}% + \TestArgumentComplexe[#2]{-112.5}{-112.5}{\frac{11\pi}{8}}% + \TestArgumentComplexe[#2]{-157.5}{-157.5}{\frac{9\pi}{8}}% + %les pi/12 + \TestArgumentComplexe[#2]{15}{15.0}{\frac{\pi}{12}}% + \TestArgumentComplexe[#2]{75}{75.0}{\frac{5\pi}{12}}% + \TestArgumentComplexe[#2]{105}{105.0}{\frac{7\pi}{12}}% + \TestArgumentComplexe[#2]{165}{165.0}{\frac{11\pi}{12}}% + \TestArgumentComplexe[#2]{-15}{-15.0}{\frac{23\pi}{12}}% + \TestArgumentComplexe[#2]{-75}{-75.0}{\frac{19\pi}{12}}% + \TestArgumentComplexe[#2]{-105}{-105.0}{\frac{17\pi}{12}}% + \TestArgumentComplexe[#2]{-165}{-165.0}{\frac{13\pi}{12}}% + %les pi/10 + \TestArgumentComplexe[#2]{18}{18.0}{\frac{\pi}{10}}% + \TestArgumentComplexe[#2]{54}{54.0}{\frac{3\pi}{10}}% + \TestArgumentComplexe[#2]{126}{126.0}{\frac{7\pi}{10}}% + \TestArgumentComplexe[#2]{162}{162.0}{\frac{9\pi}{10}}% + \TestArgumentComplexe[#2]{-18}{-18.0}{\frac{19\pi}{10}}% + \TestArgumentComplexe[#2]{-54}{-54.0}{\frac{17\pi}{10}}% + \TestArgumentComplexe[#2]{-126}{-126.0}{\frac{13\pi}{10}}% + \TestArgumentComplexe[#2]{-162}{-162.0}{\frac{11\pi}{10}}% + }% + {% + %les pi/2 + \TestArgumentComplexe[#2]{0}{0.0}{0}% + \TestArgumentComplexe[#2]{90}{90.0}{\frac{\pi}{2}}% + \TestArgumentComplexe[#2]{-90}{-90.0}{\frac{-\pi}{2}}% + \TestArgumentComplexe[#2]{180}{180.0}{\pi}% + %les pi/3 + \TestArgumentComplexe[#2]{60}{60.0}{\frac{\pi}{3}}% + \TestArgumentComplexe[#2]{120}{120.0}{\frac{2\pi}{3}}% + \TestArgumentComplexe[#2]{-60}{-60.0}{\frac{-\pi}{3}}% + \TestArgumentComplexe[#2]{-120}{-120.0}{\frac{-2\pi}{3}}% + %les pi/4 + \TestArgumentComplexe[#2]{45}{45.0}{\frac{\pi}{4}}% + \TestArgumentComplexe[#2]{135}{135.0}{\frac{3\pi}{4}}% + \TestArgumentComplexe[#2]{-45}{-45.0}{\frac{-\pi}{4}}% + \TestArgumentComplexe[#2]{-135}{-135.0}{\frac{-3\pi}{4}}% + %les pi/5 + \TestArgumentComplexe[#2]{36}{36.0}{\frac{\pi}{5}}% + \TestArgumentComplexe[#2]{72}{72.0}{\frac{2\pi}{5}}% + \TestArgumentComplexe[#2]{108}{108.0}{\frac{3\pi}{5}}% + \TestArgumentComplexe[#2]{144}{144.0}{\frac{4\pi}{5}}% + \TestArgumentComplexe[#2]{-36}{-36.0}{\frac{-\pi}{5}}% + \TestArgumentComplexe[#2]{-72}{-72.0}{\frac{-2\pi}{5}}% + \TestArgumentComplexe[#2]{-108}{-108.0}{\frac{-3\pi}{5}}% + \TestArgumentComplexe[#2]{-144}{-144.0}{\frac{-4\pi}{5}}% + %les pi/6 + \TestArgumentComplexe[#2]{30}{30.0}{\frac{\pi}{6}}% + \TestArgumentComplexe[#2]{150}{150.0}{\frac{5\pi}{6}}% + \TestArgumentComplexe[#2]{-30}{-30.0}{\frac{-\pi}{6}}% + \TestArgumentComplexe[#2]{-150}{-150.0}{\frac{-5\pi}{6}}% + %les pi/8 + \TestArgumentComplexe[#2]{22.5}{22.5}{\frac{\pi}{8}}% + \TestArgumentComplexe[#2]{67.5}{67.5}{\frac{3\pi}{8}}% + \TestArgumentComplexe[#2]{112.5}{112.5}{\frac{5\pi}{8}}% + \TestArgumentComplexe[#2]{157.5}{157.5}{\frac{7\pi}{8}}% + \TestArgumentComplexe[#2]{-22.5}{-22.5}{\frac{-\pi}{8}}% + \TestArgumentComplexe[#2]{-67.5}{-67.5}{\frac{-3\pi}{8}}% + \TestArgumentComplexe[#2]{-112.5}{-112.5}{\frac{-5\pi}{8}}% + \TestArgumentComplexe[#2]{-157.5}{-157.5}{\frac{-7\pi}{8}}% + %les pi/12 + \TestArgumentComplexe[#2]{15}{15.0}{\frac{\pi}{12}}% + \TestArgumentComplexe[#2]{75}{75.0}{\frac{5\pi}{12}}% + \TestArgumentComplexe[#2]{105}{105.0}{\frac{7\pi}{12}}% + \TestArgumentComplexe[#2]{165}{165.0}{\frac{11\pi}{12}}% + \TestArgumentComplexe[#2]{-15}{-15.0}{\frac{-\pi}{12}}% + \TestArgumentComplexe[#2]{-75}{-75.0}{\frac{-5\pi}{12}}% + \TestArgumentComplexe[#2]{-105}{-105.0}{\frac{-7\pi}{12}}% + \TestArgumentComplexe[#2]{-165}{-165.0}{\frac{-11\pi}{12}}% + %les pi/10 + \TestArgumentComplexe[#2]{18}{18.0}{\frac{\pi}{10}}% + \TestArgumentComplexe[#2]{54}{54.0}{\frac{3\pi}{10}}% + \TestArgumentComplexe[#2]{126}{126.0}{\frac{7\pi}{10}}% + \TestArgumentComplexe[#2]{162}{162.0}{\frac{9\pi}{10}}% + \TestArgumentComplexe[#2]{-18}{-18.0}{\frac{-\pi}{10}}% + \TestArgumentComplexe[#2]{-54}{-54.0}{\frac{-3\pi}{10}}% + \TestArgumentComplexe[#2]{-126}{-126.0}{\frac{-7\pi}{10}}% + \TestArgumentComplexe[#2]{-162}{-162.0}{\frac{-9\pi}{10}}% + }% +} + +\NewDocumentCommand\CalculFormeExpoCplx{ s O{} m m }{% + \xdef\TmpArg{\xintfloateval{trunc(Argd(#3,#4),1)}}%\TmpArg% + \ensuremath{% + \xintifboolexpr{(#3)**2+(#4)**2 == 1 'and' \TmpArg == 0}{1}{}% + \xintifboolexpr{(#3)**2+(#4)**2 == 1 'and' \TmpArg != 0}{}{\CalculModuleCplx[#2]{#3}{#4}}% + \IfBooleanTF{#1}% + {% + %les pi/2 + \TestArgumentComplexe[#2]{0}{0.0}{}% + \TestArgumentComplexe[#2]{90}{90.0}{\e^{\frac{\i\pi}{2}}}% + \TestArgumentComplexe[#2]{-90}{-90.0}{\e^{\frac{3\i\pi}{2}}}% + \TestArgumentComplexe[#2]{180}{180.0}{\e^{\i\pi}}% + %les pi/3 + \TestArgumentComplexe[#2]{60}{60.0}{\e^{\frac{\i\pi}{3}}}% + \TestArgumentComplexe[#2]{120}{120.0}{\e^{\frac{2\i\pi}{3}}}% + \TestArgumentComplexe[#2]{-60}{-60.0}{\e^{\frac{5\i\pi}{3}}}% + \TestArgumentComplexe[#2]{-120}{-120.0}{\e^{\frac{4\i\pi}{3}}}% + %les pi/4 + \TestArgumentComplexe[#2]{45}{45.0}{\e^{\frac{\i\pi}{4}}}% + \TestArgumentComplexe[#2]{135}{135.0}{\e^{\frac{3\i\pi}{4}}}% + \TestArgumentComplexe[#2]{-45}{-45.0}{\e^{\frac{7\i\pi}{4}}}% + \TestArgumentComplexe[#2]{-135}{-135.0}{\e^{\frac{5\i\pi}{4}}}% + %les pi/5 + \TestArgumentComplexe[#2]{36}{36.0}{\e^{\frac{\i\pi}{5}}}% + \TestArgumentComplexe[#2]{72}{72.0}{\e^{\frac{2\i\pi}{5}}}% + \TestArgumentComplexe[#2]{108}{108.0}{\e^{\frac{3\i\pi}{5}}}% + \TestArgumentComplexe[#2]{144}{144.0}{\e^{\frac{4\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-36}{-36.0}{\e^{\frac{9\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-72}{-72.0}{\e^{\frac{8\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-108}{-108.0}{\e^{\frac{7\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-144}{-144.0}{\e^{\frac{6\i\pi}{5}}}% + %les pi/6 + \TestArgumentComplexe[#2]{30}{30.0}{\e^{\frac{\i\pi}{6}}}% + \TestArgumentComplexe[#2]{150}{150.0}{\e^{\frac{5\i\pi}{6}}}% + \TestArgumentComplexe[#2]{-30}{-30.0}{\e^{\frac{11\i\pi}{6}}}% + \TestArgumentComplexe[#2]{-150}{-150.0}{\e^{\frac{7\i\pi}{6}}}% + %les pi/8 + \TestArgumentComplexe[#2]{22.5}{22.5}{\e^{\frac{\i\pi}{8}}}% + \TestArgumentComplexe[#2]{67.5}{67.5}{\e^{\frac{3\i\pi}{8}}}% + \TestArgumentComplexe[#2]{112.5}{112.5}{\e^{\frac{5\i\pi}{8}}}% + \TestArgumentComplexe[#2]{157.5}{157.5}{\e^{\frac{7\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-22.5}{-22.5}{\e^{\frac{15\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-67.5}{-67.5}{\e^{\frac{13\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-112.5}{-112.5}{\e^{\frac{11\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-157.5}{-157.5}{\e^{\frac{9\i\pi}{8}}}% + %les pi/12 + \TestArgumentComplexe[#2]{15}{15.0}{\e^{\frac{\i\pi}{12}}}% + \TestArgumentComplexe[#2]{75}{75.0}{\e^{\frac{5\i\pi}{12}}}% + \TestArgumentComplexe[#2]{105}{105.0}{\e^{\frac{7\i\pi}{12}}}% + \TestArgumentComplexe[#2]{165}{165.0}{\e^{\frac{11\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-15}{-15.0}{\e^{\frac{23\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-75}{-75.0}{\e^{\frac{19\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-105}{-105.0}{\e^{\frac{17\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-165}{-165.0}{\e^{\frac{13\i\pi}{12}}}% + %les pi/10 + \TestArgumentComplexe[#2]{18}{18.0}{\e^{\frac{\i\pi}{10}}}% + \TestArgumentComplexe[#2]{54}{54.0}{\e^{\frac{3\i\pi}{10}}}% + \TestArgumentComplexe[#2]{126}{126.0}{\e^{\frac{7\i\pi}{10}}}% + \TestArgumentComplexe[#2]{162}{162.0}{\e^{\frac{9\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-18}{-18.0}{\e^{\frac{19\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-54}{-54.0}{\e^{\frac{17\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-126}{-126.0}{\e^{\frac{13\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-162}{-162.0}{\e^{\frac{11\i\pi}{10}}}% + }% + {% + %les pi/2 + \TestArgumentComplexe[#2]{0}{0.0}{}% + \TestArgumentComplexe[#2]{90}{90.0}{\e^{\frac{\i\pi}{2}}}% + \TestArgumentComplexe[#2]{-90}{-90.0}{\e^{\frac{-\i\pi}{2}}}% + \TestArgumentComplexe[#2]{180}{180.0}{\e^{\i\pi}}% + %les pi/3 + \TestArgumentComplexe[#2]{60}{60.0}{\e^{\frac{\i\pi}{3}}}% + \TestArgumentComplexe[#2]{120}{120.0}{\e^{\frac{2\i\pi}{3}}}% + \TestArgumentComplexe[#2]{-60}{-60.0}{\e^{\frac{-\i\pi}{3}}}% + \TestArgumentComplexe[#2]{-120}{-120.0}{\e^{\frac{-2\i\pi}{3}}}% + %les pi/4 + \TestArgumentComplexe[#2]{45}{45.0}{\e^{\frac{\i\pi}{4}}}% + \TestArgumentComplexe[#2]{135}{135.0}{\e^{\frac{3\i\pi}{4}}}% + \TestArgumentComplexe[#2]{-45}{-45.0}{\e^{\frac{-\i\pi}{4}}}% + \TestArgumentComplexe[#2]{-135}{-135.0}{\e^{\frac{-3\i\pi}{4}}}% + %les pi/5 + \TestArgumentComplexe[#2]{36}{36.0}{\e^{\frac{\i\pi}{5}}}% + \TestArgumentComplexe[#2]{72}{72.0}{\e^{\frac{2\i\pi}{5}}}% + \TestArgumentComplexe[#2]{108}{108.0}{\e^{\frac{3\i\pi}{5}}}% + \TestArgumentComplexe[#2]{144}{144.0}{\e^{\frac{4\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-36}{-36.0}{\e^{\frac{-\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-72}{-72.0}{\e^{\frac{-2\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-108}{-108.0}{\e^{\frac{-3\i\pi}{5}}}% + \TestArgumentComplexe[#2]{-144}{-144.0}{\e^{\frac{-4\i\pi}{5}}}% + %les pi/6 + \TestArgumentComplexe[#2]{30}{30.0}{\e^{\frac{\i\pi}{6}}}% + \TestArgumentComplexe[#2]{150}{150.0}{\e^{\frac{5\i\pi}{6}}}% + \TestArgumentComplexe[#2]{-30}{-30.0}{\e^{\frac{-\i\pi}{6}}}% + \TestArgumentComplexe[#2]{-150}{-150.0}{\e^{\frac{-5\i\pi}{6}}}% + %les pi/8 + \TestArgumentComplexe[#2]{22.5}{22.5}{\e^{\frac{\i\pi}{8}}}% + \TestArgumentComplexe[#2]{67.5}{67.5}{\e^{\frac{3\i\pi}{8}}}% + \TestArgumentComplexe[#2]{112.5}{112.5}{\e^{\frac{5\i\pi}{8}}}% + \TestArgumentComplexe[#2]{157.5}{157.5}{\e^{\frac{7\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-22.5}{-22.5}{\e^{\frac{-\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-67.5}{-67.5}{\e^{\frac{-3\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-112.5}{-112.5}{\e^{\frac{-5\i\pi}{8}}}% + \TestArgumentComplexe[#2]{-157.5}{-157.5}{\e^{\frac{-7\i\pi}{8}}}% + %les pi/12 + \TestArgumentComplexe[#2]{15}{15.0}{\e^{\frac{\i\pi}{12}}}% + \TestArgumentComplexe[#2]{75}{75.0}{\e^{\frac{5\i\pi}{12}}}% + \TestArgumentComplexe[#2]{105}{105.0}{\e^{\frac{7\i\pi}{12}}}% + \TestArgumentComplexe[#2]{165}{165.0}{\e^{\frac{11\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-15}{-15.0}{\e^{\frac{-\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-75}{-75.0}{\e^{\frac{-5\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-105}{-105.0}{\e^{\frac{-7\i\pi}{12}}}% + \TestArgumentComplexe[#2]{-165}{-165.0}{\e^{\frac{-11\i\pi}{12}}}% + %les pi/10 + \TestArgumentComplexe[#2]{18}{18.0}{\e^{\frac{\i\pi}{10}}}% + \TestArgumentComplexe[#2]{54}{54.0}{\e^{\frac{3\i\pi}{10}}}% + \TestArgumentComplexe[#2]{126}{126.0}{\e^{\frac{7\i\pi}{10}}}% + \TestArgumentComplexe[#2]{162}{162.0}{\e^{\frac{9\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-18}{-18.0}{\e^{\frac{-\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-54}{-54.0}{\e^{\frac{-3\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-126}{-126.0}{\e^{\frac{-7\i\pi}{10}}}% + \TestArgumentComplexe[#2]{-162}{-162.0}{\e^{\frac{-9\i\pi}{10}}}% + }% + }% +} + +\endinput
\ No newline at end of file |