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. -- 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]