Siegel Modular polynomials using Streng invariants for l=2,3.

******************

Invariants:
i1 = h4*h6/h10
i2 = h4^2*h12/h10^2
i3 = h4^5/h10^2

******************

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

ch="(...)/Streng/";

l=2
l=3

nb=l^3+l^2+l+1;
L1=vector(nb,i,read(Str(ch,"PolModStrNiv",l,"/NumStrNiv",l,"-Phi/numphi-",i)));
L2=vector(nb,i,read(Str(ch,"PolModStrNiv",l,"/NumStrNiv",l,"-Psi2/numpsi2-",i)));
L3=vector(nb,i,read(Str(ch,"PolModStrNiv",l,"/NumStrNiv",l,"-Psi3/numpsi3-",i)));


DD=read(Str(ch,"PolModStrNiv",l,"/DenStrNiv",l));
Den(xx,yy,zz)=substvec(DD,[x,y,z],[xx,yy,zz]);

[i1,i2,i3]=[1+3*I,2+4*I,3+5*I];


Phi=X^nb+sum(i=1,nb,substvec(L1[i],[x,y,z],[i1,i2,i3])*X^(i-1))/Den(i1,i2,i3);
Phip=Phi';
Psi2=sum(i=1,nb,substvec(L2[i],[x,y,z],[i1,i2,i3])*X^(i-1))/Den(i1,i2,i3)^2/Phip;
Psi3=sum(i=1,nb,substvec(L3[i],[x,y,z],[i1,i2,i3])*X^(i-1))/Den(i1,i2,i3)^2/Phip;

Om=TauFromJinvStr(i1,i2,i3);
M=ConjTauG2(l);

for(i=1,nb,om=l*Mtau(M[i],Om);[i1p,i2p,i3p]=EvalJinvStreng(om);print(i"  "round(10^1000*subst(Phi,X,i1p))"  "round(10^1000*(i2p-subst(Psi2,X,i1p)))"  "round(10^1000*(i3p-subst(Psi3,X,i1p)))));