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 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]