Re: Ideals

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Thu, Nov 19, 2009 at 01:21:54PM +0100, Vojtech Brtnik wrote:
> Hello,
> 
> I am trying to figure out how to list all prime ideals and ideals
> (with norm under certain bound) in a field Q(a) where a is a root of
> certain irreducible polynomial... I am relatively newbie to PARI so if
> there is a better place to ask these questions please let me kindly
> know.

Look at the function ideallist:

? ideallist(nfinit(x^3+x+1),10)
%2 = [[[1, 0, 0; 0, 1, 0; 0, 0, 1]], [], [[3, 1, 2; 0, 1, 0; 0, 0, 1]], [], [],
[], [], [[2, 0, 0; 0, 2, 0; 0, 0, 2]], [[9, 4, 2; 0, 1, 0; 0, 0, 1], [3, 0, 1; 0, 3, 1; 0, 0, 1]], []]

Cheers,
Bill.