Karim BELABAS on Tue, 7 Oct 2003 21:25:55 +0200 (MEST) |
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Re: polgalois() precision strikes again |
On Mon, 6 Oct 2003, Igor Schein wrote: > GP/PARI CALCULATOR Version 2.2.7 (development CHANGES-1.827) > i686 running linux (ix86/GMP-4.1 kernel) 32-bit version > compiled: Oct 6 2003, gcc-3.2 20020903 (Red Hat Linux 8.0 3.2-7) > (readline v4.3 enabled, extended help available) > > ? \p48 > realprecision = 48 significant digits > ? polgalois(x^8+7250*x^4+3810781250) > [64, -1, 28] > ? \p57 > realprecision = 57 significant digits > ? polgalois(x^8+7250*x^4+3810781250) > [32, -1, 17] The algorithm is simply not rigorous, so I'm afraid there's not much I can do. [ The algorithm "recognizes" natural integers from their decimal expansion. Using proven bounds has a prohibitive cost when the field of decomposition has large degree ]. I've fiddled a little with my heuristic parameters, which were a trifle too restrictive (I had made a slight mistake in my computation); it's now easier to "pass" as an integer. It cures the above, without apparently hurting anything else. I ran a complete test suite ( try out polynomials for all possible groups 4 times, using Tschirnaus transforms to make them look different ) without runing into trouble. Takes 2 minutes, used to take an hour two or three versions ago. Igor, does it pass your test suite ? [ for some reason, I fear the answer... ] 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]