Verification of the polynomials:


/*
Invariants for D=2
J1=G2^2/H4
J3=G2*H6/H4^2
 (J2=J1/J3=G2*H4/H6)

Invariants for D=5
J2=G2^5/H10
J4=H6*G2^2/H10
 (J1=J4/J2=H6/G2^3)
*/


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


ch="(...)/Gundlach-Q2/Split/";


l=2;
beta=2+sqrt(2);
betac=2-sqrt(2);

den=[[5*y^2, 25*y^3], [5*y^2, 25*y^3], [y, 5*y^2], [1, 1]];

M1=read("logJ1");
M2=read("logJ2");
M=concat(vector(l,i,[1,i-1;0,1]),[[0,-1;1,0]]);

L1=vector(l+1,i,read(Str(ch,"PolQ2Gundlach-",l,"/NumPhi/numphi",i)));
L2=vector(l+1,i,read(Str(ch,"PolQ2Gundlach-",l,"/NumPsi/numpsi",i)));

[J1,J2]=[3.23+7.2038*I,-5.209803+2.2382*I];
J3=J1*J2;
Z=taufromgundNiv2(J1,J3);

Phi=X^(l+1)+sum(i=1,l+1,substvec(L1[i],[x,y],[J1,J3])/substvec(den[i][1],[x,y],[J1,J3])*X^(i-1));
Phip=Phi';
Psi=sum(i=1,l+1,substvec(L2[i],[x,y],[J1,J3])/substvec(den[i][2],[x,y],[J1,J3])*X^(i-1))/Phip;


for(i=1,l+1,z=[1/beta,0;0,1/betac]*mtau(M[i],Z);[J1p,J3p]=JGundlachNiv2([z[1,1],z[2,2]],M1,M2);print(i"  "round(10^400*subst(Phi,X,J1p))"  "round(10^400*(J3p-subst(Psi,X,J1p)))));
for(i=1,l+1,z=[1/betac,0;0,1/beta]*mtau(M[i],Z);[J1p,J3p]=JGundlachNiv2([z[1,1],z[2,2]],M1,M2);print(i"  "round(10^400*subst(Phi,X,J1p))"  "round(10^400*(J3p-subst(Psi,X,J1p)))));



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

l=7;
beta=3+sqrt(2);
betac=3-sqrt(2);

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

l=17;
beta=5+2*sqrt(2);
betac=5-2*sqrt(2);

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

l=23;
beta=5+sqrt(2);
betac=5-sqrt(2);

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

l=31;
beta=7+3*sqrt(2);
betac=7-3*sqrt(2);

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

l=41;
beta=7+2*sqrt(2);
betac=7-2*sqrt(2);

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

l=47;
beta=7+sqrt(2);
betac=7-sqrt(2);

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

l=71;
beta=11+5*sqrt(2);
betac=11-5*sqrt(2);

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

DD=read(Str(ch,"PolQ2Gundlach-",l,"/DenQ2Gund",l));
D(xx,yy)=substvec(DD,[x,y],[xx,yy]);

J1='J1;J2='J2;j1='j1;j2='j2;j3='j3;
M1=read("logJ1");
M2=read("logJ2");

Tab1=vector(2*(l+1),i,4);Tab1[2*(l+1)]=2;
Tab2=vector(2*(l+1),i,6);Tab2[2*(l+1)]=4;

L1=vector(2*(l+1),i,read(Str(ch,"PolQ2Gundlach-",l,"/NumPhi/numphi",i)));
L2=vector(2*(l+1),i,read(Str(ch,"PolQ2Gundlach-",l,"/NumPsi/numpsi",i)));


[J1,J2]=[1.7+3*I,1.2+3.2*I]*1.;
J3=J1^2/J2;
M=concat(vector(l,i,[1,i-1;0,1]),[[0,-1;1,0]]);

Phi=X^(2*(l+1))+sum(i=1,2*(l+1),substvec(L1[i],[x,y],[J1,J3])/D(J1,J3)^Tab1[i]*X^(i-1));
Phip=Phi';
Psi=sum(i=1,2*(l+1),substvec(L2[i],[x,y],[J1,J3])/D(J1,J3)^Tab2[i]*X^(i-1))/Phip;


Z=taufromgundNiv2(J1,J3);
for(i=1,l+1,z=[1/beta,0;0,1/betac]*mtau(M[i],Z);[J1p,J3p]=JGundlachNiv2([z[1,1],z[2,2]],M1,M2);print(i"  "round(10^1000*subst(Phi,X,J1p))"  "round(10^1000*(J3p-subst(Psi,X,J1p)))));
for(i=1,l+1,z=[1/betac,0;0,1/beta]*mtau(M[i],Z);[J1p,J3p]=JGundlachNiv2([z[1,1],z[2,2]],M1,M2);print(i"  "round(10^1000*subst(Phi,X,J1p))"  "round(10^1000*(J3p-subst(Psi,X,J1p)))));