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)));
    }