Max Alekseyev on Sun, 28 Aug 2022 20:09:51 +0200


[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Re: all divisors of a cyclotomic integer

Dear Bill,

I've tried to run your code to find divisors of (2*x^30 + 4*x^26 + 2*x^22) modulo polcyclo(68).
This element has norm 2^32 = 4294967296. However, among the reported divisors I see norms that do not divide 2^32 (and some are even much larger).
For example, one of the reported divisors is (-x^22 + x^15 + x^12 - x^6 + 1) of the norm 23137.
What goes wrong here?

Regards,
Max


On Sat, Jul 2, 2022 at 5:26 PM Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> wrote:
On Sat, Jul 02, 2022 at 11:11:26PM +0200, Bill Allombert wrote:
> On Sat, Jul 02, 2022 at 03:16:27PM -0400, Max Alekseyev wrote:
> > Hello,
> >
> > What would be the easiest way to get all divisors of a cyclotomic integer?
> > For example, how to get all divisors of 4 modulo polcyclo(21).
>
> Use idealfactor and bnfisprincipal ?
>
> bnf=bnfinit(polcyclo(21,a),1);
> id=idealfactor(bnf,4);
> {
>   my(L=List());
>   forvec(v=apply(a->[1,a],id[,2]),

Sorry, it should be
  forvec(v=apply(a->[0,a],id[,2]),
but hopefully you get the idea.

Cheers,
Bill.