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)))));