Karim BELABAS on Mon, 13 Oct 2003 18:32:01 +0200 (MEST)

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Re: polredabs failure

On Mon, 13 Oct 2003, Karim BELABAS wrote:
> On the other hand, it won't help for polynomials of huge
> degrees with lots of subfields, if we're unlucky with the initial basis
> ordering. Especially when the fields contain lots of roots of 1. Like
>   polcompositum(x^12-2*x^9+2*x^6+2*x^3+1, polsubcyclo(9,3))[1]
> (in dimension 36). Just to see why, have a look at \g5, you'll see the
> (many) vectors of small L^2 norm that are being enumerated, but unfortunately
> do not generate the field. I do not see any obvious structure that would
> enable me to prune this. Essentially, as soon as one (small) generator is
> found, the show is over; but till then...
> For these guys, you simply _have_ to use polred. One could time the polredabs
> run and abort it after some point, but since we simply do not find any
> generator, it is all a waste of time.

Actually, it finishes in about 15minutes, which is not _that_ bad.

[ polred finds an optimal polynomial in < 30 seconds ].

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]