Re: yet another rnfkummer() posting

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

On Mon, 9 Sep 2002, Igor Schein wrote:

> On Sun, Sep 08, 2002 at 05:52:06PM +0200, Karim BELABAS wrote:
> > On Sat, 7 Sep 2002, Igor Schein wrote:
> > > On Sat, Sep 07, 2002 at 03:39:31PM +0200, Karim BELABAS wrote:
> > > > I'm afraid you will have to re-run your regression suite now.
> > >
> > > 1 more type of bug is still present:
> > >
> > > ? setrand(6);rnfkummer(bnrinit(bnfinit(quadpoly(3409,y),1),25,1),[5,1;0,1]);
> > >   ***   bug in isvirtualunit, please report
>
> > All three are gone now. I think I owe you an explanation for what I was
> > trying to do, and the ensuing disasters.
>
> Not completely gone yet:
>
> ? setrand(863122475);rnfkummer(bnrinit(bnfinit(quadpoly(24485,y)),9,1),matdiagonal([3,1]));
>   ***   bug in isvirtualunit, please report

Still the same instance of a wrong bnf being computed (we cheat on Bach's
bound, remember:-), in yet another guise:

  setrand(867341586); bnf = bnfinit(y^4 - y^3 + 6122*y^2 + 6121*y + 37466641);

1) unit group (hence regulator) is correct
2) bnf structure = [60,2] (hence class number) is correct

BUT

3) the generators are incorrect !!! [first one has order 60, but the second
one is principal]

Again, no way to fix this without increasing the heuristic bound we use in
place of Bach's bound [ again 0.4 would do here ].

    Karim.
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
Dép. de Mathematiques, Bat. 425  Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
--
PARI/GP Home Page: http://www.parigp-home.de/