Re: idealprimedec() behavior

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

On Wed, May 09, 2018 at 03:50:03AM +0000, Iwao Kimura wrote:
> Hi pari dev,
> 
> I found the following idealprimdec() behavior:
> (12:28) gp > nf=bnfinit(x^2+5);
> (12:28) gp > id=idealprimedec(nf,3)[1];id
> %5 = [3, [-1, 1]~, 1, 1, [1, -5; 1, 1]]
> (12:28) gp > idealfactor(nf,id)
> %6 =
> [[3, [-1, 1]~, 1, 1, [1, -5; 1, 1]] 1]
> 
> (12:29) gp > idtwo=idealtwoelt(nf,id);idtwo
> %7 = [3, [-1, 1]~]
> (12:29) gp > idealfactor(nf,idtwo)
> %8 =
> [ [3, [-1, 1]~, 1, 1, [1, -5; 1, 1]] 1]
> 
> [[3, [1, 1]~, 1, 1, [-1, -5; 1, -1]] 1]
> 
> What I expected is that %6 and %9 are the same.
> Am I missing something?

Yes, the problem is that PARI does not know idtwo is a pair of
generators.

You should do
idealfactor(nf,idealhnf(nf,idtwo[1],idtwo[2]))

idealfactor(nf,[3, [-1, 1]~]) is identical to idealfactor(nf,3).

Cheers,
Bill.