Re: all divisors of a cyclotomic integer

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

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]),
    my(v=bnfisprincipal(bnf,idealfactorback(bnf,id[,1],v)));
    if(v[1]==0,listput(~L,v[2])));
  Vec(L)
}

Cheers,
Bill.