Mbarek Haynoux
Problème:
m=[79,431,751,1039,1423,1759,1871,2143,2399,2447,3023,3343,3631,3727,4127];
{
for(i=1,#m,
bnf=bnfinit(x^4-m[i],1);
print(m[i],":", bnfisintnorm(bnf,2),":",bnfisintnorm(bnf,-2));
);
}
{
s = 0 ;s0 = 0 ;s1 = 0 ;s2 = 0 ;
forprime(q= 3, 1000000,
P=polredabs (x^4-2*q^2);
L=bnfinit(P);
C=L.cyc;
A=snfrank(L.cyc,2);s++;
if (A==0 , s0=s0+1) ;
if (A==1 , s1=s1+1) ;
if (A==2 , s2=s2+1);
if (s%1000==0,
print(" s= ",s " s0= ",s0" s1= ",s1" s2= ",s2);
print(s0/s* 1.," ",s1/s* 1.," ",s2/s* 1.);
print(1./4," ",5./8," ",1./8)));
}