Re: yet another rnfkummer() posting

[Igor Schein <igor@txc.com>]

On Tue, Sep 10, 2002 at 06:05:24PM +0200, Karim BELABAS wrote:
> On Mon, 9 Sep 2002, Igor Schein wrote:
> > 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 ].

How expensive is it to check correctness of generators and rerun with
higher Bach's bound in worst case scenario?

Thanks

Igor