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