Verification of the polynomials:


*******************
allocatemem(2^33)
\p 3000
\r Hilbert.gp
*******************

l=13;
beta=5-2*sqrt(3);
betac=5+2*sqrt(3);


ch="(...)/Theta-Q3/Split/";
D=3;
PB3(x,y,z)=-x^4 - 2*x^2*y^2 + (4*z^2 + 4)*x*y -y^4 - 4*z^2;


MM=read("actionG24");
M=read(Str(ch,"../classeSLDG24-",D));

[b1,b2]=[3+7*I,-5+2*I];
b3=polroots(PB3(b1,b2,x))[1];
Z=taufromthetNivD(b1,b2,M,MM,D)[1];

MCl=read(Str(ch,"PolQ3Theta-",l,"/classeSLDG24-D3G",l));

DD=read(Str(ch,"PolQ3Theta-",l,"/DenThetD3G",l));
Den(xx,yy)=substvec(DD,[x,y],[xx,yy]);

L1=vector(2*(l+1),i,read(Str(ch,"PolQ3Theta-",l,"/NumPhi/numphi-",i)));
L2=vector(2*(l+1),i,read(Str(ch,"PolQ3Theta-",l,"/NumPsi2/numpsi2-",i)));
L3=vector(2*(l+1),i,read(Str(ch,"PolQ3Theta-",l,"/NumPsi3/numpsi3-",i)));

Tab=vector(2*(l+1),i,2);

Phi=X^(2*(l+1))+sum(i=1,2*(l+1),sum(k=1,2,substvec(L1[i][k],[x,y],[b1,b2])*b3^(k-1))*X^(i-1)/Den(b1,b2)^Tab[i]);
Phip=Phi';
Psi2=sum(i=1,2*(l+1),sum(k=1,2,substvec(L2[i][k],[x,y],[b1,b2])*b3^(k-1))/Den(b1,b2)^Tab[i]*X^(i-1))/Phip;
Psi3=sum(i=1,2*(l+1),sum(k=1,2,substvec(L3[i][k],[x,y],[b1,b2])*b3^(k-1))/Den(b1,b2)^Tab[i]*X^(i-1))/Phip;




for(i=1,length(MCl),z=mtauD(MCl[i],Z,D);[b1p,b2p,b3p]=EvalBjp(TauToOmega([z[1]/beta,z[2]/betac],D));print(i"  "round(10^1000*subst(Phi,X,b1p))"  "round(10^1000*(b2p-subst(Psi2,X,b1p)))"  "round(10^1000*(b3p-subst(Psi3,X,b1p)))));