Rev 18401 | Details | Compare with Previous | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 18401 | bpr | 1 | !set slib_header_coxaff=\ |
| 2 | \\ Polynome minimal de 2*cos(Pi/n)\ |
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| 3 | real_cyclo(n)={\ |
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| 4 | if(n==1,return(x+2));\ |
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| 5 | my(p=polcyclo(2*n),nn=eulerphi(2*n)/2,res=0,c);\ |
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| 6 | forstep(j=nn,0,-1,\ |
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| 7 | c = polcoeff(p,nn+j);\ |
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| 8 | res += c*x^j;\ |
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| 9 | p -= c*x^(nn-j)*(x^2+1)^j);\ |
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| 10 | res\ |
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| 11 | };\ |
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| 12 | \ |
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| 13 | \\ p(2*cos(t)) = 2*cos(n*t)\ |
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| 14 | cheby(n)=2*subst(polchebyshev(n),x,x/2);\ |
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| 15 | \ |
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| 16 | \\ m est une matrice de Coxeter\ |
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| 17 | \\ renvoie les generateurs\ |
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| 18 | cox_base(m)={\ |
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| 19 | my(n=#m,nn=1);\ |
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| 20 | for(i=1,n,for(j=i+1,n,if(m[i,j],nn=lcm(nn,m[i,j]))));\ |
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| 21 | xx=Mod(x,real_cyclo(nn));\ |
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| 22 | module=xx.mod;\ |
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| 23 | racine=2*cos(Pi/nn);\ |
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| 24 | gram=matrix(n,n,i,j,if(m[i,j],-cos(Pi/m[i,j]),-1));\ |
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| 25 | v=vector(n,k,matrix(n,n,i,j,\ |
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| 26 | (i==j)+(i==k)*lift(subst(if(m[k,j],cheby(nn/m[k,j]),2),x,xx))));\ |
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| 27 | Set(v)\ |
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| 28 | };\ |
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| 29 | \ |
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| 30 | longer(shorter,current,cb)={\ |
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| 31 | my(l=List());\ |
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| 32 | foreach(current,w,foreach(cb,s,\ |
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| 33 | listput(l,simplify((w*s)%module))));;\ |
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| 34 | setminus(Set(l),shorter)\ |
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| 35 | };\ |
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| 36 | \ |
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| 37 | \\ Sous l'hypothese 1/p+1/q+1/r=1\ |
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| 38 | \\ imprime le source tikz d'un pavage d'une partie\ |
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| 39 | \\ du plan avec des triangles d'angles Pi/p, etc.\ |
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| 40 | aff3(p,q,r,limite)={\ |
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| 18542 | bpr | 41 | my(g,t=matrix(3,3),u,v,acc,cb=cox_base([1,p/2,q/2;p/2,1,r/2;q/2,r/2,1]),\ |
| 18401 | bpr | 42 | sh=Set(),cr=Set(matid(3)),tmp,h,res,xmin,xmax,ymin,ymax,xm,ym);\ |
| 43 | for(i=1,3,\ |
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| 44 | g=subst(cb[i]*cb[1+(i%3)],x,racine);\ |
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| 45 | \\point fixe de g, moyenne des iteres : intersection de la droite de points fixes, puis z=1\ |
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| 18542 | bpr | 46 | u=if(i==1,p/2,if(i==2,r/2,q/2));\ |
| 18401 | bpr | 47 | v=[0,0,1];\ |
| 48 | acc=vector(3);\ |
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| 49 | for(i=1,u,acc+=v;v=v*g);\ |
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| 50 | t[i,]=acc/u);\ |
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| 51 | \\printf("p: %d, q: %d, r: %d\n",p, q, r);\ |
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| 52 | res=matrix(0,7);\ |
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| 53 | \\printf("\\begin{tikzpicture}[scale=%.3f]\n",7/limite);\ |
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| 54 | for(i=1,limite, tmp=longer(sh,cr,cb); sh=cr; cr=tmp;\ |
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| 18542 | bpr | 55 | foreach(sh,g,h=t*subst(g,x,racine)*[1,0;cos(2*Pi/p),sin(2*Pi/p);0,0];\ |
| 18401 | bpr | 56 | \\printf("\\%s(%.4f,%.4f)--(%.4f,%.4f)--(%.4f,%.4f)--cycle;\n",\ |
| 57 | \\if(i%2,"fill","draw"),h[1,1],h[1,2],h[2,1],h[2,2],h[3,1],h[3,2]);\ |
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| 58 | res=matconcat([res,[h[1,1],h[1,2],h[2,1],h[2,2],h[3,1],h[3,2],i%2]]~)\ |
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| 59 | ));\ |
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| 60 | \\print("\\end{tikzpicture}\n");\ |
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| 61 | for(i=1,matsize(res)[1],for(j=1,3,xm=res[i,2*j-1];ym=res[i,2*j];\ |
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| 62 | if(xm<xmin,xmin=xm);\ |
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| 63 | if(xm>xmax,xmax=xm);\ |
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| 64 | if(ym<ymin,ymin=ym);\ |
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| 65 | if(ym>ymax,ymax=ym)));\ |
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| 66 | [[xmin,xmax,ymin,ymax],res];\ |
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| 67 | };\ |
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| 68 | /*\ |
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| 69 | \p3\ |
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| 70 | print("\nAffines\n");\ |
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| 18542 | bpr | 71 | aff3(4,8,8,20);\ |
| 72 | aff3(6,6,6,20);\ |
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| 73 | aff3(4,6,12,20);\ |
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| 18401 | bpr | 74 | */\ |
| 75 | \ |