Re: polgalois() precision strikes again

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

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]