Karim BELABAS on Mon, 30 Jun 2003 10:48:45 +0200 (MEST)

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Re: polred() problem

On Mon, 30 Jun 2003, Igor Schein wrote:
> The output of the following command:
> polred(polcompositum(x^42+245*x^28+2499*x^14+7,quadpoly(-4))[1])
> is a vector of polynomials of degree strictly less than 84.  I've
> never seen it before, must be a bug.

Not necessarily; in fact, I don't think so. I'd rather read it as

  "you found a counter-example to a conjecture, please report!"

There is no theorem guaranteeing that one of the LLL-basis elements for the
maximal order will be primitive. It was a half-hearted conjecture, which many
people believed to be false.

I'll check your counter-example !

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