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Diffstat (limited to 'macros/latex/contrib/profcollege/metapost/PfCArithmetiquePDF.mp')
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diff --git a/macros/latex/contrib/profcollege/metapost/PfCArithmetiquePDF.mp b/macros/latex/contrib/profcollege/metapost/PfCArithmetiquePDF.mp new file mode 100644 index 0000000000..8772c93b49 --- /dev/null +++ b/macros/latex/contrib/profcollege/metapost/PfCArithmetiquePDF.mp @@ -0,0 +1,237 @@ +% Fichier regroupant les macros pour les schémas des nombres premiers + +numeric retenirnb[]; + +vardef Estcepremier(expr NBa)= + boolean $; + c:=2; + departa:=NBa; + test:=1; + $=true; + if departa=1: + $:=false; + else: + forever: + if (departa mod c)=0: + departa:=departa div c; + test:=test+1; + else: + c:=c+1; + fi; + exitif departa=1; + endfor; + fi; + if test=2: + $:=true + else: + $:=false; + fi; + $ +enddef; + +vardef PremierSimple(expr NB)= + b:=2; + depart:=NB; + if Estcepremier(depart)=false: + forever: + if (depart mod b)=0: + Ancre[k+1]-Ancre[k]=(-decalage*0.5,-decalage); + Ancre[k+2]-Ancre[k+1]=(decalage,0); + depart:=depart div b; + retenirnb[k+1]=b; + retenirnb[k+2]=depart; + label(LATEX("\num{"&decimal(b)&"}"),Ancre[k+1]); + label(LATEX("\num{"&decimal(depart)&"}"),Ancre[k+2]); + draw 1/5[Ancre[k],Ancre[k+1]]--4/5[Ancre[k],Ancre[k+1]]; + draw 1/5[Ancre[k],Ancre[k+2]]--4/5[Ancre[k],Ancre[k+2]]; + k:=k+2; + racine:=depart; + depart:=1; + else: + b:=b+1; + fi; + exitif depart=1; + endfor; + else: + racine:=1; + fi; +enddef; + +vardef PremierSimplePdf(expr NB)= + b:=2; + depart:=NB; + if Estcepremier(depart)=false: + forever: + if (depart mod b)=0: + Ancre[k+1]-Ancre[k]=(-decalage*0.5,-decalage); + Ancre[k+2]-Ancre[k+1]=(decalage,0); + depart:=depart div b; + retenirnb[k+1]=b; + retenirnb[k+2]=depart; + label(LATEX("\num{"&decimal(b)&"}"),Ancre[k+1]); + label(LATEX("\num{"&decimal(depart)&"}"),Ancre[k+2]); + draw 1/5[Ancre[k],Ancre[k+1]]--4/5[Ancre[k],Ancre[k+1]]; + draw 1/5[Ancre[k],Ancre[k+2]]--4/5[Ancre[k],Ancre[k+2]]; + k:=k+2; + racine:=depart; + depart:=1; + else: + b:=b+1; + fi; + exitif depart=1; + endfor; + else: + racine:=1; + fi; +enddef; + +vardef PremierSimpleArbre(expr NB)= + b:=2; + depart:=NB; + if Estcepremier(depart)=false: + forever: + if (depart mod b)=0: + Ancre[k+1]-Ancre[k]=(-decalage*0.5,-decalage); + Ancre[k+2]-Ancre[k+1]=(decalage,0); + depart:=depart div b; + retenirnb[k+1]=b; + retenirnb[k+2]=depart; + draw Branche(Ancre[k],Ancre[k+1]); + draw Branche(Ancre[k],Ancre[k+2]); + k:=k+2; + racine:=depart; + depart:=1; + else: + b:=b+1; + fi; + exitif depart=1; + endfor; + else: + racine:=1; + fi; +enddef; + +vardef NbEtape(expr nb)= + b:=2; + depart:=nb; + etape:=0; + Stock[0][0]=depart; + forever: + if (depart mod b)=0: + etape:=etape+1; + if etape=1: + Stock[etape][0]=b; + Stock[etape][etape]:=depart div b; + else: + for k=0 upto etape-2: + Stock[etape][k]:=Stock[etape-1][k]; + endfor; + Stock[etape][etape-1]:=b; + Stock[etape][etape]:=depart div b; + fi; + depart:=depart div b; + else: + b:=b+1; + fi; + exitif depart=1; + endfor; + etape +enddef; + +vardef Positions(expr Step)= + for k=0 upto (Step-1): + for l=0 upto k: + N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy); + label(LATEX("\num{"&decimal(Stock[k][l])&"}"),N[k][l]); + endfor; + for l=0 upto k-1: + label(LATEX("$\times$"),1/2[N[k][l],N[k][l+1]]); + endfor; + endfor; + for k=0 upto (Step-1): + for l=0 upto (k-1): + draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]]; + endfor; + if k>0: + draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]]; + fi; + endfor; +enddef; + +vardef PositionsPdf(expr Step)= + for k=0 upto (Step-1): + for l=0 upto k: + N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy); + label(LATEX("\num{"&decimal(Stock[k][l])&"}"),N[k][l]); + endfor; + for l=0 upto k-1: + label(LATEX("$\times$"),1/2[N[k][l],N[k][l+1]]); + endfor; + endfor; + for k=0 upto (Step-1): + for l=0 upto (k-1): + draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]]; + endfor; + if k>0: + draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]]; + fi; + endfor; +enddef; + +vardef PositionsVide(expr Step)= + for k=0 upto (Step-1): + for l=0 upto k: + N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy); + endfor; + for l=0 upto k-1: + label(LATEX("$\times$"),1/2[N[k][l],N[k][l+1]]); + endfor; + endfor; + for k=0 upto (Step-1): + for l=0 upto (k-1): + draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]]; + endfor; + if k>0: + draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]]; + fi; + endfor; + label(LATEX("\num{"&decimal(Stock[0][0])&"}"),N[0][0]); +enddef; + +vardef PositionsVidePdf(expr Step)= + for k=0 upto (Step-1): + for l=0 upto k: + N[k][l]=(-k*dx+(l+k*.5)*dx,-k*dy); + endfor; + for l=0 upto k-1: + label(LATEX("$\times$"),1/2[N[k][l],N[k][l+1]]); + endfor; + endfor; + for k=0 upto (Step-1): + for l=0 upto (k-1): + draw 1/5[N[k][l],N[k-1][l]]--4/5[N[k][l],N[k-1][l]]; + endfor; + if k>0: + draw 1/5[N[k][k],N[k-1][k-1]]--4/5[N[k][k],N[k-1][k-1]]; + fi; + endfor; + label(LATEX("\num{"&decimal(Stock[0][0])&"}"),N[0][0]); +enddef; + +vardef Branche(expr nbd,nba)= + save $; + picture $; + pair UnitVector; + numeric AngleVector; + UnitVector=unitvector(nba-nbd) rotated 90; + AngleVector=angle(nba-nbd)+(-10+uniformdeviate(20)); + path branche; + branche=(nbd+UnitVector){dir AngleVector}..(nba+UnitVector)--reverse((nbd-UnitVector){dir AngleVector}..(nba-UnitVector))--cycle; + $=image( + fill branche withcolor gris; + draw branche; + ); + $ +enddef; + +endinput; |