Re: rnfkummer() output issue

[Igor Schein <igor@txc.com>]

On Thu, Jan 22, 2004 at 07:31:29PM +0100, Karim Belabas wrote:
> * Igor Schein <igor@txc.com> [2004-01-21 05:25]:
> > ? p1=rnfkummer(bnrinit(bnfinit(y^8-76*y^6+1425*y^4-5776*y^2+5776),5,1),matdiagonal([2,1]))
> [...]
> > ? nfdisc(p1)
> >   ***   polynomial not in Z[X] in nfbasis.
> [...]
> > It's confusing that even though rnfkummer() appears to return an
> > absolute polynomial, it in fact isn't, at least internally.  
> 
> True. Fixed in CVS.
> 
> Btw, I investigated why this example was so slow (5s), and I have slightly
> modified rnfnormgroup() so that the computation of p1 is about 4 times faster:
> use only places of degree 1 from the base field.
> 
> Indeed, they have the same density as arbitrary places in the Galois group of
> the ray class field over the base, so we should not lose much.  And computing
> in their (prime) residue fields is much easier than in the general case [ we
> need to factor the defining relative polynomial in the residue fields ]
> 
> Does it break any rnfkummer() thing ?

Looks clean, no regression.

Thanks

Igor