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-%%%
-% Ronde infernale
-%%%
-\newcommand\TestNombrePremier[1]{%
- % #1 le nombre \`a tester
- \newcount\anp\newcount\bnp\newcount\cnp%
- \anp=#1\relax
- \bnp=2\relax
- \premier=-1\relax
- \whiledo{\anp > 1}{%
- \modulo{\the\anp}{\the\bnp}
- \ifnum\remainder=0\relax%
- \global\premier=\numexpr\premier+1\relax%
- \cnp=\numexpr\anp/\bnp\relax%
- \anp=\cnp\relax%
- \else%
- \bnp=\numexpr\bnp+1\relax%
- \fi%
- }%
-}%
-
-\newcommand\PfCRIListeDiviseur[1]{%#1 : nombre entier
- \newcount\anp\newcount\bnp%
- \anp=\fpeval{abs(#1)}%
- \bnp=2\relax%
- \xdef\PfCRIRetiensListeDiviseurs{}%
- \ifnum#1=0%
- \xdef\PfCRIRetiensListeDiviseurs{\fpeval{randint(2,5)},\fpeval{randint(6,9)}}%
- \else
- \whiledo{\bnp<\anp}{%
- \modulo{\the\anp}{\the\bnp}{}%
- \ifnum\remainder=0%
- \ifnum#1>0
- \xdef\PfCRIRetiensListeDiviseurs{\PfCRIRetiensListeDiviseurs \the\bnp,}%
- \else
- \xdef\PfCRIRetiensListeDiviseurs{\PfCRIRetiensListeDiviseurs \the\bnp,-\the\bnp,}%
- \fi
- \fi%
- \bnp=\numexpr\bnp+1%
- }%
- \ifnum#1>0
- \xdef\PfCRIRetiensListeDiviseurs{\PfCRIRetiensListeDiviseurs \the\anp,1}
- \else
- \xdef\PfCRIRetiensListeDiviseurs{\PfCRIRetiensListeDiviseurs \the\anp,-\the\anp}
- \fi
- \fi
-}%
-
-\setKVdefault[RondeInfernale]{Solution=false,Relatifs=false,Etapes=4,Perso=false,Cles=false,Vide,Rayon=2.5cm,Rectangle=false,Div=false,Cdot=false}%
-\defKV[RondeInfernale]{Graine=\PfCGraineAlea{#1}}
-\defKV[RondeInfernale]{Cle=\setKV[RondeInfernale]{Cles}\setKV[RondeInfernale]{Vide=false}}%
-\defKV[RondeInfernale]{ListeOperations=\setKV[RondeInfernale]{Perso}}%
-\defKV[RondeInfernale]{ListeNombres=\setKV[RondeInfernale]{Perso}}%
-%
-
-\NewDocumentCommand\RondeInfernale{ }{%Mise en place pour les germanistes : le " est actif :(
- \begingroup
- \catcode`\"12
- \RondeInfernaleaux
-}%
-
-\NewDocumentCommand\RondeInfernaleaux{o}{%
- \endgroup
- \useKVdefault[RondeInfernale]%
- \setKV[RondeInfernale]{#1}%
- % Graine
-% \ifboolKV[RondeInfernale]{Graines}{\PfCGraineAlea{\useKV[RondeInfernale]{Graine}}}{}%
- % Nombre clé
- \ifboolKV[RondeInfernale]{Cles}{%
- \xdef\PfCRINombreCle{\useKV[RondeInfernale]{Cle}}%
- }{%
- \ifboolKV[RondeInfernale]{Relatifs}{%
- \xdef\PfCRIListeNegatifs{-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10}
- \MelangeListe{\PfCRIListeNegatifs}{1}
- \readlist*\PfCRIListeCle{\faa}
- \xdef\PfCRINombreCle{\PfCRIListeCle[1]}%
- }{%
- \xdef\PfCRINombreCle{\fpeval{randint(2,9)}}%
- }%
- }%
- \ifboolKV[RondeInfernale]{Perso}{%
- \xdef\PfCRIRecupOperations{\useKV[RondeInfernale]{ListeOperations}}%
- \xdef\PfCRIRecupNombres{\useKV[RondeInfernale]{ListeNombres}}%
- }{%
- % On définit les éléments nécessaires
- \xdef\PfCRIListeToutesOperations{+,-,*,/}%
- \xdef\PfCRIListeOperationsSansDiv{+,-,*}%
- \xdef\PfCRIListeOperationsSansMul{+,-,/}%
- \xdef\PfCRIListeOperationsSimple{+,-}%
- \xdef\PfCRIRecupOperations{}%
- \xdef\PfCRIRecupNombres{}%
- \xdef\PfCRIRecupResultats{}%
- \xdef\PfCRINombreATester{\PfCRINombreCle}%
- \xdef\PfCRIRetiensNbEtapes{\useKV[RondeInfernale]{Etapes}}%
- \setsepchar{,}\ignoreemptyitems%
- % Liste des opérations jusqu'à l'étape n-1
- \xintFor* ##1 in{\xintSeq{1}{\fpeval{\useKV[RondeInfernale]{Etapes}-1}}}\do{%
- \TestNombrePremier{\PfCRINombreATester}\relax%
- \xintifboolexpr{\premier==0}{%
- % Définition des opérations
- \MelangeListe{\PfCRIListeOperationsSansDiv}{1}%
- \readlist*\PfCRIRetiensLoperation{\faa}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \xdef\PfCRIOperateur{\fpeval{randint(2,9)}}%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRIOperateur,}%
- \xdef\PfCRIResultat{\fpeval{\PfCRINombreATester\PfCRIRetiensLoperation[1]\PfCRIOperateur}}%
- \xdef\PfCRIRecupResultats{\PfCRIRecupResultats \PfCRIResultat,}%
- \xdef\PfCRINombreATester{\PfCRIResultat}%
- }{%
- \MelangeListe{\PfCRIListeToutesOperations}{1}%
- \readlist*\PfCRIRetiensLoperation{\faa}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \IfStrEq{\PfCRIRetiensLoperation[1]}{/}{%
- \PfCRIListeDiviseur{\PfCRINombreATester}%
- \MelangeListe{\PfCRIRetiensListeDiviseurs}{1}%
- \readlist*\PfCRIRetiensLeDiviseur{\faa}%
- \xdef\PfCRIOperateur{\PfCRIRetiensLeDiviseur[1]}%
- }{%
- \xdef\PfCRIOperateur{\fpeval{randint(2,9)}}%
- }%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRIOperateur,}%
- \xdef\PfCRIResultat{\fpeval{\PfCRINombreATester\PfCRIRetiensLoperation[1]\PfCRIOperateur}}%
- \xdef\PfCRIRecupResultats{\PfCRIRecupResultats \PfCRIResultat,}%
- \xdef\PfCRINombreATester{\PfCRIResultat}%
- }%
- }%
- % Dernière opération
- \xintifboolexpr{\fpeval{abs(\PfCRINombreATester)-abs(\PfCRINombreCle)}>0}{%
- \modulo{\PfCRINombreATester}{\PfCRINombreCle}{}%
- \xintifboolexpr{\remainder==0}{%
- \MelangeListe{\PfCRIListeOperationsSansMul}{1}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \ignoreemptyitems%
- \readlist*\PfCRIRetiensLoperation{\faa}%
- \IfStrEq{\PfCRIRetiensLoperation[1]}{/}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreATester/\PfCRINombreCle}}%
- }{%
- \IfStrEq{\PfCRIRetiensLoperation[1]}{-}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreATester-\PfCRINombreCle}}%
- }{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreCle-\PfCRINombreATester}}%
- }%
- }%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRINombreATester}%
- }{%
- \MelangeListe{\PfCRIListeOperationsSimple}{1}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \ignoreemptyitems%
- \readlist*\PfCRIRetiensLoperation{\faa}%
- \IfStrEq{\PfCRIRetiensLoperation[1]}{-}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreATester-\PfCRINombreCle}}%
- }{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreCle-\PfCRINombreATester}}%
- }%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRINombreATester}%
- }%
- }{%
- \xintifboolexpr{\fpeval{abs(\PfCRINombreATester)-abs(\PfCRINombreCle)}==0}{%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations *}%
- \ignoreemptyitems%
- \readlist*\PfCRIRIListeOperations{\PfCRIRecupOperations}%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres 1}%
- }{%
- \xintifboolexpr{\PfCRINombreATester==0}{%
- \MelangeListe{\PfCRIListeOperationsSimple}{1}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \ignoreemptyitems%
- \readlist*\PfCRIRetiensLoperation{\faa}%
- \IfStrEq{\PfCRIRetiensLoperation[1]}{-}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreATester-\PfCRINombreCle}}%
- }{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreCle-\PfCRINombreATester}}%
- }%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRINombreATester}%
- }{%
- \modulo{\PfCRINombreCle}{\PfCRINombreATester}{}%
- \xintifboolexpr{\remainder==0}{%-1
- \MelangeListe{\PfCRIListeToutesOperations}{1}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \readlist*\PfCRIRetiensLoperation{\faa}%
- \ignoreemptyitems%
- \readlist*\PfCRIRIListeOperations{\PfCRIRecupOperations}%
- \IfStrEq{\PfCRIRetiensLoperation[1]}{*}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreCle/\PfCRINombreATester}}%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRINombreATester}%
- }{
- \IfStrEq{\PfCRIRetiensLoperation[1]}{-}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreATester-\PfCRINombreCle}}%
- }{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreCle-\PfCRINombreATester}}%
- }%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRINombreATester}%
- }%
- }{%
- \MelangeListe{\PfCRIListeOperationsSimple}{1}%
- \xdef\PfCRIRecupOperations{\PfCRIRecupOperations \faa}%
- \ignoreemptyitems%
- \readlist*\PfCRIRIListeOperations{\PfCRIRecupOperations}%
- \IfStrEq{\PfCRIRIListeOperations[\PfCRIRetiensNbEtapes]}{-}{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreATester-\PfCRINombreCle}}%
- }{%
- \xdef\PfCRINombreATester{\fpeval{\PfCRINombreCle-\PfCRINombreATester}}%
- }%
- \xdef\PfCRIRecupNombres{\PfCRIRecupNombres \PfCRINombreATester}%
- }%
- }%
- }%
- }%
- }%
- \ignoreemptyitems%
- \readlist*\PfCRIRIOperations{\PfCRIRecupOperations}%
- \readlist*\PfCRIRINombres{\PfCRIRecupNombres}%
- \reademptyitems%
- % On prépare le dessin
- \xdef\PfCRINombresDessin{}%
- \xdef\PfCRIOperationsDessin{}%
- \foreachitem\compteur\in\PfCRIRINombres{%
- \xintifboolexpr{\PfCRIRINombres[\compteurcnt]<0}{%
- \xdef\PfCRINombresDessin{\PfCRINombresDessin "(\num{\PfCRIRINombres[\compteurcnt]})",}%
- }{%
- \xdef\PfCRINombresDessin{\PfCRINombresDessin "\num{\PfCRIRINombres[\compteurcnt]}",}%
- }%
- }%
- \foreachitem\compteur\in\PfCRIRIOperations{%
- \xdef\PfCRIOperationsDessin{\PfCRIOperationsDessin "\PfCRIRIOperations[\compteurcnt]",}%
- }%
- % On dessine
- \BuildRondeInfernale{\PfCRINombresDessin}{\PfCRIOperationsDessin}%
-}%
-
-\NewDocumentCommand\BuildRondeInfernale{m m}{%
- \ifluatex
- \mplibforcehmode
- \begin{mplibcode}
- boolean Vide,Rectangle,Perso;
- Vide=\useKV[RondeInfernale]{Vide};
- Rectangle=\useKV[RondeInfernale]{Rectangle};
- Perso=\useKV[RondeInfernale]{Perso};
- if Perso:
- string Depart;
- Depart=\useKV[RondeInfernale]{Cle};
- else:
- numeric Depart;
- Depart=\PfCRINombreCle;
- fi;
-
- numeric Rayon;
- Rayon=\useKV[RondeInfernale]{Rayon};
-
- string Nombre[];
-
- vardef Compte(text t)=%On compte le nb d'étapes et on retient les nombres
- nbcase:=0;
- for p_=t:
- nbcase:=nbcase+1;
- Nombre[nbcase]=p_;
- endfor;
- enddef;
-
- vardef AfficheRonde(text t)=%On fait l'affichage des opérations
- n:=0;
- for k=1 upto nbcase:
- fill cercles(rotation(A[k],O,0.5*(360/nbcase)),5mm) withcolor white;
- endfor;
- for p_=t:
- n:=n+1;
- if p_="*":
- label(TEX("$\times"&Nombre[n]&"$"),rotation(A[nbcase-n],O,0.5*(360/nbcase)));
- elseif p_="/":
- label(TEX("$\div"&Nombre[n]&"$"),rotation(A[nbcase-n],O,0.5*(360/nbcase)));
- else:
- label(TEX("$"&p_&Nombre[n]&"$"),rotation(A[nbcase-n],O,0.5*(360/nbcase)));
- fi;
- endfor;
- enddef;
-
- vardef AfficheRectangle(text t)=%On fait l'affichage des opérations
- n:=0;
- for p_=t:
- n:=n+1;
- if n=nbcase:
- if p_="*":
- label.bot(TEX("$\times"&Nombre[n]&"$"),1/2[A[n-1],A[0]]+u*(0,-1));
- elseif p_="/":
- label.bot(TEX("$\div"&Nombre[n]&"$"),1/2[A[n-1],A[0]]+u*(0,-1));
- else:
- label.bot(TEX("$"&p_&Nombre[n]&"$"),1/2[A[n-1],A[0]]+u*(0,-1));
- fi;
- else:
- if p_="*":
- label.top(TEX("$\times"&Nombre[n]&"$"),1/2[A[n-1],A[n]]);
- elseif p_="/":
- label.top(TEX("$\div"&Nombre[n]&"$"),1/2[A[n-1],A[n]]);
- else:
- label.top(TEX("$"&p_&Nombre[n]&"$"),1/2[A[n-1],A[n]]);
- fi;
- fi;
- endfor;
- enddef;
-
- vardef BaseRonde=
- pair O,A[];
- O=(0,0);
- path cc;
- cc=cercles(O,Rayon);
- A[0]=pointarc(cc,0);
- A[nbcase+1]=A[0];
- for k=1 upto nbcase:
- A[k]=rotation(A[0],O,k*(360/nbcase));
- endfor;
- for k=0 upto nbcase:
- drawarrow reverse(arccercle(A[k],A[k+1],O) cutbefore cercles(A[k],5mm) cutafter cercles(A[k+1],5mm)) withpen pencircle scaled 1.5;
- endfor;
- for k=0 upto nbcase:
- fill cercles(A[k],5mm) withcolor white;
- trace cercles(A[k],5mm) withpen pencircle scaled 1.5;
- endfor;
- enddef;
-
- vardef BoiteRectangle=
- save $;
- path $;
- $=u*(0.9,-0.5){dir 0}..{dir 90}(u*(1,-0.4))--(u*(1,0.4)){dir 90}..{dir180}(u*(0.9,0.5))--u*(-0.9,0.5){dir 180}..{dir-90}(u*(-1,0.4))--(u*(-1,-0.4)){dir-90}..{dir0}(u*(-0.9,-0.5))--cycle;
- $
- enddef;
-
- vardef BaseRectangle=
- pair O,A[];
- O=(0,0);
- A[0]=O;
- for k=1 upto nbcase:
- A[k]-A[k-1]=(Rayon+2cm,0);
- endfor;
- for k=0 upto nbcase-2:
- drawarrow (A[k]--A[k+1]) cutbefore (BoiteRectangle shifted A[k]) cutafter (BoiteRectangle shifted A[k+1]) withpen pencircle scaled 1.5;
- endfor;
- drawarrow (A[nbcase-1]--(A[nbcase-1]+u*(0,-1))--(A[0]+u*(0,-1))--A[0]) cutbefore (BoiteRectangle shifted A[nbcase-1]) cutafter (BoiteRectangle shifted A[0]) withpen pencircle scaled 1.5;
- for k=0 upto nbcase-1:
- trace (BoiteRectangle shifted A[k]) withpen pencircle scaled 1.5;
- endfor;
- enddef;
-
- Compte(#1);
-
- if Rectangle:
- BaseRectangle;
- AfficheRectangle(#2);
- else:
- BaseRonde;
- AfficheRonde(#2);
- fi;
- if Vide=false:
- if Perso:
- label(TEX("$"&Depart&"$"),A[0]);
- else:
- label(TEX("$"&decimal(Depart)&"$"),A[0]);
- fi;
- fi;
- \end{mplibcode}
- \else
- \begin{mpost}[mpsettings={%
- boolean Vide,Rectangle,Perso;Vide=\useKV[RondeInfernale]{Vide};Rectangle=\useKV[RondeInfernale]{Rectangle};Perso=\useKV[RondeInfernale]{Perso};if Perso:string Depart;Depart=\useKV[RondeInfernale]{Cle};else:numeric Depart;Depart=\PfCRINombreCle;fi;numeric Rayon;Rayon=\useKV[RondeInfernale]{Rayon};}]
- string Nombre[];
-
- vardef Compte(text t)=%On compte le nb d'étapes et on retient les nombres
- nbcase:=0;
- for p_=t:
- nbcase:=nbcase+1;
- Nombre[nbcase]=p_;
- endfor;
- enddef;
-
- vardef AfficheRonde(text t)=%On fait l'affichage des opérations
- n:=0;
- for k=1 upto nbcase:
- fill cercles(rotation(A[k],O,0.5*(360/nbcase)),5mm) withcolor white;
- endfor;
- for p_=t:
- n:=n+1;
- if p_="*":
- label(LATEX("$\times"&Nombre[n]&"$"),rotation(A[nbcase-n],O,0.5*(360/nbcase)));
- elseif p_="/":
- label(LATEX("$\div"&Nombre[n]&"$"),rotation(A[nbcase-n],O,0.5*(360/nbcase)));
- else:
- label(LATEX("$"&p_&Nombre[n]&"$"),rotation(A[nbcase-n],O,0.5*(360/nbcase)));
- fi;
- endfor;
- enddef;
-
- vardef AfficheRectangle(text t)=%On fait l'affichage des opérations
- n:=0;
- for p_=t:
- n:=n+1;
- if n=nbcase:
- if p_="*":
- label.bot(LATEX("$\times"&Nombre[n]&"$"),1/2[A[n-1],A[0]]+u*(0,-1));
- elseif p_="/":
- label.bot(LATEX("$\div"&Nombre[n]&"$"),1/2[A[n-1],A[0]]+u*(0,-1));
- else:
- label.bot(LATEX("$"&p_&Nombre[n]&"$"),1/2[A[n-1],A[0]]+u*(0,-1));
- fi;
- else:
- if p_="*":
- label.top(LATEX("$\times"&Nombre[n]&"$"),1/2[A[n-1],A[n]]);
- elseif p_="/":
- label.top(LATEX("$\div"&Nombre[n]&"$"),1/2[A[n-1],A[n]]);
- else:
- label.top(LATEX("$"&p_&Nombre[n]&"$"),1/2[A[n-1],A[n]]);
- fi;
- fi;
- endfor;
- enddef;
-
- vardef BaseRonde=
- pair O,A[];
- O=(0,0);
- path cc;
- cc=cercles(O,Rayon);
- A[0]=pointarc(cc,0);
- A[nbcase+1]=A[0];
- for k=1 upto nbcase:
- A[k]=rotation(A[0],O,k*(360/nbcase));
- endfor;
- for k=0 upto nbcase:
- drawarrow reverse(arccercle(A[k],A[k+1],O) cutbefore cercles(A[k],5mm) cutafter cercles(A[k+1],5mm)) withpen pencircle scaled 1.5;
- endfor;
- for k=0 upto nbcase:
- fill cercles(A[k],5mm) withcolor white;
- trace cercles(A[k],5mm) withpen pencircle scaled 1.5;
- endfor;
- enddef;
-
- vardef BoiteRectangle=
- save $;
- path $;
- $=u*(0.9,-0.5){dir 0}..{dir 90}(u*(1,-0.4))--(u*(1,0.4)){dir 90}..{dir180}(u*(0.9,0.5))--u*(-0.9,0.5){dir 180}..{dir-90}(u*(-1,0.4))--(u*(-1,-0.4)){dir-90}..{dir0}(u*(-0.9,-0.5))--cycle;
- $
- enddef;
-
- vardef BaseRectangle=
- pair O,A[];
- O=(0,0);
- A[0]=O;
- for k=1 upto nbcase:
- A[k]-A[k-1]=(Rayon+2cm,0);
- endfor;
- for k=0 upto nbcase-2:
- drawarrow (A[k]--A[k+1]) cutbefore (BoiteRectangle shifted A[k]) cutafter (BoiteRectangle shifted A[k+1]) withpen pencircle scaled 1.5;
- endfor;
- drawarrow (A[nbcase-1]--(A[nbcase-1]+u*(0,-1))--(A[0]+u*(0,-1))--A[0]) cutbefore (BoiteRectangle shifted A[nbcase-1]) cutafter (BoiteRectangle shifted A[0]) withpen pencircle scaled 1.5;
- for k=0 upto nbcase-1:
- trace (BoiteRectangle shifted A[k]) withpen pencircle scaled 1.5;
- endfor;
- enddef;
-
- Compte(#1);
-
- if Rectangle:
- BaseRectangle;
- AfficheRectangle(#2);
- else:
- BaseRonde;
- AfficheRonde(#2);
- fi;
- if Vide=false:
- if Perso:
- label(LATEX("$"&Depart&"$"),A[0]);
- else:
- label(LATEX("$"&decimal(Depart)&"$"),A[0]);
- fi;
- fi;
- \end{mpost}
- \fi
-}% \ No newline at end of file