Slessor R. on Wed, 19 Aug 2009 11:56:42 +0200

 A number fields question

Dear all,

I was wondering if you would be able to help me with a quick question? I have the following relative number fields extension L/K (also Galois):

K=nfinit(y^2 + y + 1);
f= x^6 + Mod(3969*y+10584,y^2+y+1);
L=rnfinit(K,f);
lambda = Mod(Mod(-4/64827*y-1/43218,y^2+y+1)*x^5 + Mod(2/9261*y-1/9261,y^2+y+1)*x^4 + Mod(-1/294*y-1/441,y^2+y+1)*x^3 + Mod(1/441*y+1/147,y^2+y+1)*x^2 + Mod(-1/42*y-1/42,y^2+y+1)*x+1/3, x^6 + Mod(3969*y+10584,y^2+y+1));

lambda has been chosen in such a way that it is totally real under the action of Gal(L/K)

I would like to know if there is a way to get PARI to compute all elements x of the ring of integers O_L of L such that |Tr_{L/K}(lambda. \bar{x}. x)| = 1?

where \bar{x} is just the usual complex conjugation.

Thanks,

Rich