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-rw-r--r--Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.pdfbin1444492 -> 1450770 bytes
-rw-r--r--Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.tex4
-rw-r--r--Master/texmf-dist/doc/latex/proflycee/ProfLycee-docctan.zipbin1642767 -> 1652549 bytes
-rw-r--r--Master/texmf-dist/tex/latex/proflycee/ProfLycee.sty5
-rw-r--r--Master/texmf-dist/tex/latex/proflycee/proflycee-tools-analyse.tex80
-rw-r--r--Master/texmf-dist/tex/latex/proflycee/proflycee-tools-arithm.tex24
-rw-r--r--Master/texmf-dist/tex/latex/proflycee/proflycee-tools-complexes.tex609
7 files changed, 682 insertions, 40 deletions
diff --git a/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.pdf b/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.pdf
index 21a32e22f85..7928e78fefe 100644
--- a/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.pdf
+++ b/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.tex b/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.tex
index 0dfda9ed87a..806a31ab3ba 100644
--- a/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.tex
+++ b/Master/texmf-dist/doc/latex/proflycee/ProfLycee-doc.tex
@@ -5,8 +5,8 @@
% arara: lualatex: {shell: yes, synctex: no, interaction: batchmode} if found('log', '(undefined references|Please rerun|Rerun to get)')
\documentclass[a4paper,french,11pt]{article}
-\def\PLversion{3.01a}
-\def\PLdate{6 décembre 2023}
+\def\PLversion{3.01b}
+\def\PLdate{2 janvier 2024}
\usepackage{amsfonts}
\usepackage{ProfLycee}
\useproflyclib{piton,minted,pythontex,ecritures}
diff --git a/Master/texmf-dist/doc/latex/proflycee/ProfLycee-docctan.zip b/Master/texmf-dist/doc/latex/proflycee/ProfLycee-docctan.zip
index 0b837379db1..f1a104f2dac 100644
--- a/Master/texmf-dist/doc/latex/proflycee/ProfLycee-docctan.zip
+++ b/Master/texmf-dist/doc/latex/proflycee/ProfLycee-docctan.zip
Binary files differ
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