Annegret Weng on Mon, 19 Jun 2000 22:02:53 -0400 (EDT)

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I have a problem with the function "rnfisnorm". It seems that I do not
know how to work with it. 
I wrote a C++-program using Pari (see below) but I get an error. 

The program should do the following: Given a rational prime p (as an
element of a numberfield generated by y^3+b1*y^2+b2*y+b3), determine
wheter p is a relative norm in a field extension defined by

I entered for example b1=1, b2=-2 and b3=-1 and then a2=1, a1=2 and a0=1
and p=17. I got the error
  ***   incorrect type in principalideal.
  ***   Error in the PARI system. End of program.

Where is my mistake? 
Thank you very much for every advice!

Best regards,

My program:


extern "C" {

int main()
  long prec=DEFAULTPREC;

  long b1,b2,b3;
  long a0,a1,a2;
  const long vy=fetch_user_var("y"); 
  const long vx=0;                   

   GEN y=polx[vy];//Variable for number field
   GEN x=polx[vx];//Variable for relative extension
   GEN polynom1;//Polynomial for the number field
   GEN polynom2;//Polynomial for the relative extension
   long ltop;
   cout << "Enter a polynomial of degree 3!" << endl;
   cout << "First the coefficient of x^2, then x, then x^0:"<< endl;
   cin >> b1;
   cin >> b2;
   cin >> b3;
   //Polynomial defining the ground field of degree 3:
   polynom1=gaddsg(b3,gadd(polynom1, gmulsg(b2,y)));
   cout <<"Please enter an element alpha in Z[y]" << endl;
   cout <<"such that alpha=a0+a1w+a2w^2." << endl;
   cin >> a0;
   cin >> a1;
   cin >> a2;
   //Polynomial defining the relative extension:
   GEN puffer=gmodulcp(gaddsg(a0,gmul(y,gaddsg(a1,gmulsg(a2,y)))),polynom1);

   //Numberfield defined by y^3+b1*y^2+b2*y+b3
   GEN bnf=bnfinit0(polynom1,0,NULL,prec);
   //Producing the parameters required by rnfisnorm:  
   GEN yinx=rnfequation0(bnf,polynom2,1);
    //ext required for rnfisnorm:
    GEN ext=cgetg(4,t_VEC);
    ext[1]=(long) polynom2;
    ext[3]=(long) bnfinit0((GEN) yinx[1],0,NULL,prec);

    //The prime p which we want to satisfy a relative norm equation:
    long p; 
    cout<<"Enter a rational prime p!" << endl;
    cin >> p; 
    GEN element=algtobasis(bnf,stoi(p));