Karim BELABAS on Fri, 4 Apr 2003 01:36:01 +0200 (MEST) |
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Re: polredabs() again |
On Fri, 4 Apr 2003, Bill Allombert wrote: > On Fri, Apr 04, 2003 at 12:18:34AM +0200, Karim BELABAS wrote: > > On the other hand, the current specification of polredabs is quite useless. > > There's no application whatsoever for a "polynomial of absolute smallest > > T2-norm". It's not even guaranteed to have minimal discriminant, or to > > yield smallest coefficients. The only one I can see is to give a > > pseudo-canonical representative for the field (this helps table builders, > > less isomorphism tests...) > > I do not fully agree. Having a canonical defining polynomial is quite > useful when you are generating lots of (small) isomorphic files (try > galoisubfields on a large non abelian Galois groups). I said pseudo-canonical, it is not at all canonical. It depends in a complicated way on the available stack space (which affects the cache algorithm described in my previous post), the quality of the LLL-reduced basis (which depends on the original polynomial). There could be many polynomials with the same T2-bound (hundreds of them). I am not convinced that you save that many isomorphism tests [ also for quadratic and cubic fields, one has much better methods ] 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]