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+% proflycee-tools-probas.tex
+% Copyright 2023 Cédric Pierquet
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+
+%%------LOISPROBAS
+%calculs "simples"
+\newcommand\CalcBinomP[3]{%npk
+ \xintFloatToDecimal{\xintfloateval{binomial(#1,#3)*#2^#3*(1-#2)^(#1-#3)}}
+}
+\newcommand\CalcBinomC[4]{%npab
+ \def\BorneInf{#3}\def\BorneSup{#4}
+ \ifthenelse{\equal{#3}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#4}{*}}%
+ {\def\BorneSup{#1}}
+ {}
+ \xintFloatToDecimal{\xintfloateval{add(binomial(#1,i)*#2^i*(1-#2)^(#1-i), i=\BorneInf..\BorneSup)}}
+}
+\newcommand\CalcGeomP[2]{%pk
+ \xintFloatToDecimal{\xintfloateval{(1-#1)^(#2-1)*(#1)}}
+}
+\newcommand\CalcGeomC[3]{%pab
+ \def\BorneInf{#2}\def\BorneSup{#3}
+ \ifthenelse{\equal{#2}{*}}%
+ {\def\BorneInf{1}}
+ {}
+ \ifthenelse{\equal{#3}{*}}%
+ {\def\BorneSup{\fpeval{trunc(1/#1*10,0)}}}
+ {}
+ \xintFloatToDecimal{\xintfloateval{add((1-#1)^(i-1)*(#1), i=\BorneInf..\BorneSup)}}
+}
+\newcommand\CalcHypergeomP[4]{%Nnmk
+ \xintFloatToDecimal{\xintfloateval{binomial(#3,#4)*binomial(#1-#3,#2-#4)/binomial(#1,#2)}}
+}
+\newcommand\CalcHypergeomC[5]{%Nnmab
+ \def\BorneInf{#4}\def\BorneSup{#5}
+ \ifthenelse{\equal{#4}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#5}{*}}%
+ {\def\BorneSup{#1}}
+ {}
+ \xintFloatToDecimal{\xintfloateval{add(binomial(#3,i)*binomial(#1-#3,#2-i)/binomial(#1,#2), i=\BorneInf..\BorneSup)}}
+}
+\newcommand\CalcPoissP[2]{%lk
+ \xintFloatToDecimal{\xintfloateval{exp(-#1)*#1^#2/factorial(#2)}}
+}
+\newcommand\CalcPoissC[3]{%lab
+ \def\BorneInf{#2}\def\BorneSup{#3}
+ \ifthenelse{\equal{#2}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#3}{*}}%
+ {\def\BorneSup{10*#1}}
+ {}
+ \xintFloatToDecimal{\xintfloateval{add(exp(-#1)*#1^i/factorial(i), i=\BorneInf..\BorneSup)}}
+}
+%utiles idée de https://tex.stackexchange.com/questions/355574/im-searching-for-a-table-with-cdf-of-standard-normal-distribution
+\xintdeffloatvar a_1,a_2,a_3,a_4,a_5,a_6 :=
+0.0705230784,0.0422820123,0.0092705272,0.0001520143,0.0002765672,0.0000430638;
+\xintdeffloatvar rac2inv := sqrt(2)/2 ;
+\xintdeffloatfunc erfc(x) := % uniquement pour x positif
+((((((a_6*x+a_5)*x+a_4)*x+a_3)*x+a_2)*x+a_1)*x+1)**-16 ; % fin de définition de erfc(x)
+\xintdeffloatfunc Phi(z) := (z>=0)?{1 - 0.5 * erfc(rac2inv * z)}{0.5 * erfc(-rac2inv * z)};
+
+\newcommand\CalcNormC[4]{%msab
+ %def des bornes de l'intervalle suivant l'absence de a ou de b...
+ \def\BorneInf{#3}\def\BorneSup{#4}
+ \ifthenelse{\equal{#3}{*}}%
+ {\def\BorneInf{#4-10*#2}}
+ {}
+ \ifthenelse{\equal{#4}{*}}%
+ {\def\BorneSup{#3+10*#2}}
+ {}
+ \xintFloatToDecimal{\xintfloateval{Phi((\BorneSup-#1)/#2)-Phi((\BorneInf-#1)/#2)}}
+}
+%calculs "simples" fiabilite
+\newcommand\CalcExpoC[3]{%lab
+ \def\BorneInf{#2}\def\BorneSup{#3}
+ \ifthenelse{\equal{#2}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#3}{*}}%
+ {\def\BorneSup{100/#1}}
+ {}
+ \xintFloatToDecimal{\xintfloateval{exp(-#1*\BorneInf)-exp(-#1*\BorneSup)}}
+}
+
+%calculs formatés
+\NewDocumentCommand{\BinomP}{ s O{3} m m m }{%*=sci,2=prec,3=n,4=p,5=k
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(binomial(#3,#5)*#4^#5*(1-#4)^(#3-#5),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(binomial(#3,#5)*#4^#5*(1-#4)^(#3-#5),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\BinomC}{ s O{3} m m m m }{%*=sci,2=prec,3=n,4=p,5=a,6=b
+ \def\BorneInf{#5}\def\BorneSup{#6}
+ \ifthenelse{\equal{#5}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#6}{*}}%
+ {\def\BorneSup{#3}}
+ {}
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#3,i)*#4^i*(1-#4)^(#3-i), i=\BorneInf..\BorneSup),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#3,i)*#4^i*(1-#4)^(#3-i), i=\BorneInf..\BorneSup),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\GeomP}{ s O{3} m m }{%*=sci,2=prec,3=p,4=k
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round((1-#3)^(#4-1)*(#3),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round((1-#3)^(#4-1)*(#3),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\GeomC}{ s O{3} m m m }{%*=sci,2=prec,3=p,4=a,5=b
+ \def\BorneInf{#4}\def\BorneSup{#5}
+ \ifthenelse{\equal{#4}{*}}%
+ {\def\BorneInf{1}}
+ {}
+ \ifthenelse{\equal{#5}{*}}%
+ {\def\BorneSup{\fpeval{trunc(1/#3*10,0)}}}
+ {}
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add((1-#3)^(i-1)*(#3), i=\BorneInf..\BorneSup),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add((1-#3)^(i-1)*(#3), i=\BorneInf..\BorneSup),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\HypergeomP}{ s O{3} m m m m }{%*=sci,2=prec,3=N,4=n,5=m,6=k
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(binomial(#5,#6)*binomial(#3-#5,#4-#6)/binomial(#3,#4),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(binomial(#5,#6)*binomial(#3-#5,#4-#6)/binomial(#3,#4),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\HypergeomC}{ s O{3} m m m m m }{%*=sci,2=prec,3=N,4=n,5=m,6=a,7=b
+ \def\BorneInf{#6}\def\BorneSup{#7}
+ \ifthenelse{\equal{#6}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#7}{*}}%
+ {\def\BorneSup{#3}}
+ {}
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#5,i)*binomial(#3-#5,#4-i)/binomial(#3,#4), i=\BorneInf..\BorneSup),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(binomial(#5,i)*binomial(#3-#5,#4-i)/binomial(#3,#4), i=\BorneInf..\BorneSup),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\PoissonP}{ s O{3} m m }{%*=sci,2=prec,3=lbda,4=k
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3)*#3^#4/factorial(#4),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3)*#3^#4/factorial(#4),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\PoissonC}{ s O{3} m m m }{%*=ing,2=prec,3=lbda,4=a,5=b
+ \def\BorneInf{#4}\def\BorneSup{#5}
+ \ifthenelse{\equal{#4}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#5}{*}}%
+ {\def\BorneSup{10*#3}}
+ {}
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(add(exp(-#3)*#3^i/factorial(i), i=\BorneInf..\BorneSup),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(add(exp(-#3)*#3^i/factorial(i), i=\BorneInf..\BorneSup),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\NormaleC}{ s O{3} m m m m }{%
+ %*=ing,2=prec,3=mu,4=sigma,5=a,6=b
+ %def des bornes de l'intervalle suivant l'absence de a ou de b...
+ \def\BorneInf{#5}\def\BorneSup{#6}
+ \ifthenelse{\equal{#5}{*}}%
+ {\def\BorneInf{#6-10*#4}}
+ {}
+ \ifthenelse{\equal{#6}{*}}%
+ {\def\BorneSup{#5+10*#4}}
+ {}
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(Phi((\BorneSup-#3)/#4)-Phi((\BorneInf-#3)/#4),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintfloateval{round(Phi((\BorneSup-#3)/#4)-Phi((\BorneInf-#3)/#4),#2)}}}
+ }
+}
+
+\NewDocumentCommand{\ExpoC}{ s O{3} m m m }{%*=ing,2=prec,3=lbda,4=a,5=b
+ \def\BorneInf{#4}\def\BorneSup{#5}
+ \ifthenelse{\equal{#4}{*}}%
+ {\def\BorneInf{0}}
+ {}
+ \ifthenelse{\equal{#5}{*}}%
+ {\def\BorneSup{100/#3}}
+ {}
+ \IfBooleanTF{#1}%
+ {%
+ \num[exponent-mode=scientific]{\xintFloatToDecimal{\xintfloateval{round(exp(-#3*\BorneInf)-exp(-#3*\BorneSup),#2)}}}
+ }%
+ {%
+ \num[minimum-decimal-digits=#2]{\xintFloatToDecimal{\xintFloatToDecimal{\xintfloateval{round(exp(-#3*\BorneInf)-exp(-#3*\BorneSup),#2)}}}}
+ }
+}
+
+%%------ARBRESPROBAS
+\defKV[PLTIKZARBRE]{%
+ Unite=\def\PLAPunite{#1},%
+ EspaceNiveau=\def\PLAPespniv{#1},%
+ EspaceFeuille=\def\PLAPespfeuille{#1},%
+ Type=\def\PLAPtype{#1},%
+ Police=\def\PLAPfont{#1},%
+ PoliceProbas=\def\PLAPfontproba{#1},%
+ StyleTrait=\def\PLAPtypetrait{#1},%
+ EpaisseurTrait=\def\PLAPeptrait{#1}
+}
+
+\setKVdefault[PLTIKZARBRE]{%
+ Unite=1cm,%
+ EspaceNiveau=3.25,%
+ EspaceFeuille=1,%
+ Type=2x2,%
+ Police=\normalfont\normalsize,%
+ PoliceProbas=\normalfont\small,%
+ InclineProbas=true,%
+ Fleche=false,%
+ StyleTrait={},%
+ EpaisseurTrait=semithick
+}
+
+\NewDocumentCommand\ArbreProbasTikz{ O{} m }{%1=options,2=libellés
+ \useKVdefault[PLTIKZARBRE]%
+ \setKV[PLTIKZARBRE]{#1}%
+ \setsepchar[.]{,./}%
+ \readlist*\PLARBREDONNES{#2}%
+ \begin{tikzpicture}[x=\PLAPunite,y=\PLAPunite]
+ %styles
+ \tikzstyle{noeud} = [font=\PLAPfont]
+ \tikzstyle{probas}= [font=\PLAPfontproba]
+ \ifboolKV[PLTIKZARBRE]{InclineProbas}
+ {\tikzstyle{PLetiquette}=[pos=0.525,sloped,fill=white]}
+ {\tikzstyle{PLetiquette}=[pos=0.525,fill=white]}
+ \ifboolKV[PLTIKZARBRE]{Fleche}
+ {\tikzstyle{PLfleche}=[->,>=latex,\PLAPtypetrait,\PLAPeptrait]}
+ {\tikzstyle{PLfleche}=[\PLAPtypetrait,\PLAPeptrait]}
+ %arbre2x2
+ \IfEq{\PLAPtype}{2x2}
+ {%
+ \coordinate (R) at ({0*\PLAPespniv},{-1.5*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (A12)--(A23) ;}
+ {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ }{}
+ %arbre3x2
+ \IfEq{\PLAPtype}{3x2}
+ {%
+ %sommets
+ \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \node[noeud] (A13) at ({1*\PLAPespniv},{-4.5*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
+ \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
+ \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
+ %branches
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (A12)--(A23) ;}
+ {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[7,2]}
+ {\draw[PLfleche] (R)--(A13) ;}
+ {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[8,2]}
+ {\draw[PLfleche] (A13)--(A25) ;}
+ {\draw[PLfleche] (A13)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[9,2]}
+ {\draw[PLfleche] (A13)--(A26) ;}
+ {\draw[PLfleche] (A13)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
+ }{}
+ %arbre2x3
+ \IfEq{\PLAPtype}{2x3}
+ {%
+ %sommets
+ \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
+ \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
+ %branches
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (A11)--(A23) ;}
+ {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[7,2]}
+ {\draw[PLfleche] (A12)--(A25) ;}
+ {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[8,2]}
+ {\draw[PLfleche] (A12)--(A26) ;}
+ {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
+ }{}
+ %arbre2x3
+ \IfEq{\PLAPtype}{3x3}
+ {%
+ %sommets
+ \coordinate (R) at ({0*\PLAPespniv},{-4*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A13) at ({1*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
+ \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
+ \node[noeud] (A27) at ({2*\PLAPespniv},{-6*\PLAPespfeuille}) {\PLARBREDONNES[10,1]};
+ \node[noeud] (A28) at ({2*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[11,1]};
+ \node[noeud] (A29) at ({2*\PLAPespniv},{-8*\PLAPespfeuille}) {\PLARBREDONNES[12,1]};
+ %branches
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[9,2]}
+ {\draw[PLfleche] (R)--(A13) ;}
+ {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
+ %N2
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (A11)--(A23) ;}
+ {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[7,2]}
+ {\draw[PLfleche] (A12)--(A25) ;}
+ {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[8,2]}
+ {\draw[PLfleche] (A12)--(A26) ;}
+ {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[10,2]}
+ {\draw[PLfleche] (A13)--(A27) ;}
+ {\draw[PLfleche] (A13)--(A27) node[probas,PLetiquette,{\PLARBREDONNES[10,3]}] {{\PLARBREDONNES[10,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[11,2]}
+ {\draw[PLfleche] (A13)--(A28) ;}
+ {\draw[PLfleche] (A13)--(A28) node[probas,PLetiquette,{\PLARBREDONNES[11,3]}] {{\PLARBREDONNES[11,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[12,2]}
+ {\draw[PLfleche] (A13)--(A29) ;}
+ {\draw[PLfleche] (A13)--(A29) node[probas,PLetiquette,{\PLARBREDONNES[12,3]}] {{\PLARBREDONNES[12,2]}} ;}
+ }{}
+ \end{tikzpicture}
+}
+
+\NewDocumentEnvironment{EnvArbreProbasTikz}{ O{} m }%1=options,2=libellés
+{
+ \useKVdefault[PLTIKZARBRE]
+ \setKV[PLTIKZARBRE]{#1}
+ \setsepchar[.]{,./}%
+ \readlist*\PLARBREDONNES{#2}
+ \begin{tikzpicture}[x=\PLAPunite,y=\PLAPunite]
+ %styles
+ \tikzstyle{noeud} = [font=\PLAPfont]
+ \tikzstyle{probas}= [font=\PLAPfontproba]
+ \ifboolKV[PLTIKZARBRE]{InclineProbas}
+ {\tikzstyle{PLetiquette}=[pos=0.525,sloped,fill=white]}
+ {\tikzstyle{PLetiquette}=[pos=0.525,fill=white]}
+ \ifboolKV[PLTIKZARBRE]{Fleche}
+ {\tikzstyle{PLfleche}=[->,>=latex,\PLAPtypetrait,\PLAPeptrait]}
+ {\tikzstyle{PLfleche}=[\PLAPtypetrait,\PLAPeptrait]}
+ %arbre2x2
+ \IfEq{\PLAPtype}{2x2}
+ {%
+ \coordinate (R) at ({0*\PLAPespniv},{-1.5*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (A12)--(A23) ;}
+ {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ }{}
+ %arbre3x2
+ \IfEq{\PLAPtype}{3x2}
+ {%
+ %sommets
+ \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-0.5*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-2.5*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \node[noeud] (A13) at ({1*\PLAPespniv},{-4.5*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
+ \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
+ \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
+ %branches
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (A12)--(A23) ;}
+ {\draw[PLfleche] (A12)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[7,2]}
+ {\draw[PLfleche] (R)--(A13) ;}
+ {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[8,2]}
+ {\draw[PLfleche] (A13)--(A25) ;}
+ {\draw[PLfleche] (A13)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[9,2]}
+ {\draw[PLfleche] (A13)--(A26) ;}
+ {\draw[PLfleche] (A13)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
+ }{}
+ %arbre2x3
+ \IfEq{\PLAPtype}{2x3}
+ {%
+ %sommets
+ \coordinate (R) at ({0*\PLAPespniv},{-2.5*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
+ \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
+ %branches
+ \ifstrempty{\PLARBREDONNES[1,2]}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (A11)--(A23) ;}
+ {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[7,2]}
+ {\draw[PLfleche] (A12)--(A25) ;}
+ {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[8,2]}
+ {\draw[PLfleche] (A12)--(A26) ;}
+ {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
+ }{}
+ %arbre2x3
+ \IfEq{\PLAPtype}{3x3}
+ {%
+ %sommets
+ \coordinate (R) at ({0*\PLAPespniv},{-4*\PLAPespfeuille}) ;
+ \node[noeud] (A11) at ({1*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[1,1]};
+ \node[noeud] (A12) at ({1*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[5,1]};
+ \node[noeud] (A13) at ({1*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[9,1]};
+ \node[noeud] (A21) at ({2*\PLAPespniv},{-0*\PLAPespfeuille}) {\PLARBREDONNES[2,1]};
+ \node[noeud] (A22) at ({2*\PLAPespniv},{-1*\PLAPespfeuille}) {\PLARBREDONNES[3,1]};
+ \node[noeud] (A23) at ({2*\PLAPespniv},{-2*\PLAPespfeuille}) {\PLARBREDONNES[4,1]};
+ \node[noeud] (A24) at ({2*\PLAPespniv},{-3*\PLAPespfeuille}) {\PLARBREDONNES[6,1]};
+ \node[noeud] (A25) at ({2*\PLAPespniv},{-4*\PLAPespfeuille}) {\PLARBREDONNES[7,1]};
+ \node[noeud] (A26) at ({2*\PLAPespniv},{-5*\PLAPespfeuille}) {\PLARBREDONNES[8,1]};
+ \node[noeud] (A27) at ({2*\PLAPespniv},{-6*\PLAPespfeuille}) {\PLARBREDONNES[10,1]};
+ \node[noeud] (A28) at ({2*\PLAPespniv},{-7*\PLAPespfeuille}) {\PLARBREDONNES[11,1]};
+ \node[noeud] (A29) at ({2*\PLAPespniv},{-8*\PLAPespfeuille}) {\PLARBREDONNES[12,1]};
+ %branches
+ \ifstrempty{\PLARBREDONNES[1,2]}{}
+ {\draw[PLfleche] (R)--(A11) ;}
+ {\draw[PLfleche] (R)--(A11) node[probas,PLetiquette,{\PLARBREDONNES[1,3]}] {{\PLARBREDONNES[1,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[5,2]}{}
+ {\draw[PLfleche] (R)--(A12) ;}
+ {\draw[PLfleche] (R)--(A12) node[probas,PLetiquette,{\PLARBREDONNES[5,3]}] {{\PLARBREDONNES[5,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[9,2]}{}
+ {\draw[PLfleche] (R)--(A13) ;}
+ {\draw[PLfleche] (R)--(A13) node[probas,PLetiquette,{\PLARBREDONNES[9,3]}] {{\PLARBREDONNES[9,2]}} ;}
+ %N2
+ \ifstrempty{\PLARBREDONNES[2,2]}
+ {\draw[PLfleche] (A11)--(A21) ;}
+ {\draw[PLfleche] (A11)--(A21) node[probas,PLetiquette,{\PLARBREDONNES[2,3]}] {{\PLARBREDONNES[2,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[3,2]}
+ {\draw[PLfleche] (A11)--(A22) ;}
+ {\draw[PLfleche] (A11)--(A22) node[probas,PLetiquette,{\PLARBREDONNES[3,3]}] {{\PLARBREDONNES[3,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[4,2]}
+ {\draw[PLfleche] (A11)--(A23) ;}
+ {\draw[PLfleche] (A11)--(A23) node[probas,PLetiquette,{\PLARBREDONNES[4,3]}] {{\PLARBREDONNES[4,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[6,2]}
+ {\draw[PLfleche] (A12)--(A24) ;}
+ {\draw[PLfleche] (A12)--(A24) node[probas,PLetiquette,{\PLARBREDONNES[6,3]}] {{\PLARBREDONNES[6,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[7,2]}
+ {\draw[PLfleche] (A12)--(A25) ;}
+ {\draw[PLfleche] (A12)--(A25) node[probas,PLetiquette,{\PLARBREDONNES[7,3]}] {{\PLARBREDONNES[7,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[8,2]}
+ {\draw[PLfleche] (A12)--(A26) ;}
+ {\draw[PLfleche] (A12)--(A26) node[probas,PLetiquette,{\PLARBREDONNES[8,3]}] {{\PLARBREDONNES[8,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[10,2]}
+ {\draw[PLfleche] (A13)--(A27) ;}
+ {\draw[PLfleche] (A13)--(A27) node[probas,PLetiquette,{\PLARBREDONNES[10,3]}] {{\PLARBREDONNES[10,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[11,2]}
+ {\draw[PLfleche] (A13)--(A28) ;}
+ {\draw[PLfleche] (A13)--(A28) node[probas,PLetiquette,{\PLARBREDONNES[11,3]}] {{\PLARBREDONNES[11,2]}} ;}
+ \ifstrempty{\PLARBREDONNES[12,2]}
+ {\draw[PLfleche] (A13)--(A29) ;}
+ {\draw[PLfleche] (A13)--(A29) node[probas,PLetiquette,{\PLARBREDONNES[12,3]}] {{\PLARBREDONNES[12,2]}} ;}
+ }{}
+ }
+ {
+ \end{tikzpicture}
+}
+
+%%------SCHEMASPROBAS
+%densites utiles
+\def\densnorm#1{1/(sqrt(2*pi))*exp(-0.5*(#1*#1))}
+\def\densexpo#1{exp(-#1)}
+
+\defKV[GRPHPROBCONTINUES]{%
+ CouleurAire=\def\GRPHPROBcoulsurf{#1},%
+ CouleurCourbe=\def\GRPHPROBcoulcbe{#1},%
+ Largeur=\def\GRPHPROBlarg{#1},%
+ Hauteur=\def\GRPHPROBhauteur{#1}
+}
+
+\setKVdefault[GRPHPROBCONTINUES]{%
+ CouleurAire=LightGray,%
+ CouleurCourbe=red,%
+ Largeur=2,%
+ Hauteur=1,%
+ AfficheM=true,%
+ AfficheCadre=true
+}
+
+\NewDocumentCommand\LoiNormaleGraphe{ O{} D<>{} m m m m }{%1=options,2=optionstikz,3=m,4=s,5=a,6=b
+ %simplekv
+ \useKVdefault[GRPHPROBCONTINUES]%
+ \setKV[GRPHPROBCONTINUES]{#1}%
+ %unites
+ \def\UNITEX{\fpeval{\GRPHPROBlarg/8}}\def\UNITEY{\fpeval{\GRPHPROBhauteur/0.5}}%
+ %bornes
+ \def\BorneInf{\fpeval{(#5-#3)/#4}}\def\BorneSup{\fpeval{(#6-#3)/#4}}%
+ \ifthenelse{\equal{#5}{*}}{\def\BorneInf{-4}}{}%
+ \ifthenelse{\equal{#6}{*}}{\def\BorneSup{4}}{}%
+ %tikzpicture
+ \begin{tikzpicture}[x=\UNITEX cm,y=\UNITEY cm,#2]
+ \ifboolKV[GRPHPROBCONTINUES]{AfficheM}%
+ {\draw (0,-0.0375) node[font=\tiny,scale={2*\UNITEX}] {#3} ;}
+ {}
+ \ifboolKV[GRPHPROBCONTINUES]{AfficheCadre}%
+ {\draw[Gray] (-4,-0.075) rectangle (4,0.425) ;}
+ {}
+ \clip (-4,-0.075) rectangle (4,0.425) ;
+ \draw[black,semithick,fill=\GRPHPROBcoulsurf] ({\BorneInf},0) -- plot [domain={\BorneInf}:{\BorneSup},samples=100] (\x,{\densnorm{\x}}) -- ({\BorneSup},0) -- cycle;
+ \draw[thick,->,>=latex] (-4,0)--(4,0) ;
+ \draw[thick,densely dotted] (0,0)--(0,0.39894) ;
+ \draw[thick,domain=-4:4,samples=100,\GRPHPROBcoulcbe] plot (\x,{\densnorm{\x}}) ;
+ \end{tikzpicture}
+}
+
+\NewDocumentCommand\LoiExpoGraphe{ O{} D<>{} m m m }{%1=options,2=optionstikz,3=l,4=a,5=b
+ %simplekv
+ \useKVdefault[GRPHPROBCONTINUES]%
+ \setKV[GRPHPROBCONTINUES]{#1}%
+ %unites
+ \def\UNITEX{\fpeval{\GRPHPROBlarg/4}}\def\UNITEY{\fpeval{\GRPHPROBhauteur/1}}%
+ \def\MOYENNE{\fpeval{trunc(1/#3,0)}}%
+ %bornes
+ \def\BorneInf{\fpeval{#3*#4}}\def\BorneSup{\fpeval{#3*#5}}%
+ \ifthenelse{\equal{#4}{*}}{\def\BorneInf{0}}{}%
+ \ifthenelse{\equal{#5}{*}}{\def\BorneSup{4}}{}%
+ %tikzpicture
+ \begin{tikzpicture}[x=\UNITEX cm,y=\UNITEY cm,#2]
+ \ifboolKV[GRPHPROBCONTINUES]{AfficheCadre}%
+ {\draw[Gray] (-0.2,-0.15) rectangle (3.8,0.85) ;}
+ {}
+ \clip (-0.2,-0.15) rectangle (3.8,0.85) ;
+ \draw[black,semithick,fill=\GRPHPROBcoulsurf] ({\BorneInf},0) -- plot [domain={\BorneInf}:{\BorneSup},samples=100] (\x,{0.7*\densexpo{\x}}) -- ({\BorneSup},0) -- cycle;
+ \ifboolKV[GRPHPROBCONTINUES]{AfficheM}%
+ {\draw (1,-0.075) node[font=\tiny,scale={\UNITEX}] {\MOYENNE} ;
+ \draw[thick,densely dotted] (1,0)--(1,{0.7*\densexpo{1}}) ;}
+ {}
+ \draw[thick,->,>=latex] (-0.2,0)--(3.8,0) ;
+ \draw[thick,->,>=latex] (0,-0.15)--(0,0.85) ;
+ \draw[thick,domain=0:3.8,samples=100,\GRPHPROBcoulcbe] plot (\x,{0.7*\densexpo{\x}}) ;
+ \end{tikzpicture}
+}
+
+%%------aNp/Cnp
+\NewDocumentCommand\CalculAnp{ m m }{%avec et pour xint, p/n
+ pfactorial(#2-#1,#2)
+}
+
+\NewDocumentCommand\CalculCnp{ m m }{%avec et pour xint, p/n
+ binomial(#2,#1)
+}
+
+\setKVdefault[anpCnp]{%
+ Formule=false,%
+ Notation=false,%
+ NotationAncien=false
+}
+\NewDocumentCommand\Arrangement{ s O{} m m }{%p/n
+ \useKVdefault[anpCnp]%
+ \setKV[anpCnp]{#2}%
+ \ifboolKV[anpCnp]{Notation}{A_{#4}^{#3}=}{}%
+ \ifboolKV[anpCnp]{Formule}{\frac{#4!}{\inteval{#4-#3}!}=}{}%
+ \IfBooleanTF{#1}%
+ {\xinteval{\CalculAnp{#3}{#4}}}%non formaté
+ {\num{\xinteval{\CalculAnp{#3}{#4}}}}%formaté
+}
+\NewDocumentCommand\Combinaison{ s O{} m m }{%p/n
+ \useKVdefault[anpCnp]%
+ \setKV[anpCnp]{#2}%
+ \ifboolKV[anpCnp]{Notation}{\binom{#4}{#3} =}{}%
+ \ifboolKV[anpCnp]{NotationAncien}{C_{#4}^{#3}=}{}%
+ \ifboolKV[anpCnp]{Formule}{\frac{#4!}{#3! \times \inteval{#4-#3}!}=}{}%
+ \IfBooleanTF{#1}%
+ {\xinteval{\CalculCnp{#3}{#4}}}%non formaté
+ {\num{\xinteval{\CalculCnp{#3}{#4}}}}%formaté
+}
+
+\endinput \ No newline at end of file