Re: polredabs(,16)

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

On Thu, 12 Sep 2002, Bill Allombert wrote:
> > We need a good routine for  "partial factorization of discriminants".
> > Many functions need this (and currently do trial division only).
>
> I have a simple algorithm for that.
> In fact I have even add the function FpX_gcd_check
> just for this purpose.
> The idea is to compute D=Disc(T)=Res(T,T') and
> try FpX_gcd_check(T, T', D).
> This must return a factor of D. If if is not one, we restart
> with the divisors: FpX_gcd_check(T, T', d),
> etc...
> This should be almost as good as polredabs(,,16).

... as a replacement for NFS :-)?

Just tried it with install(). If does not fare well with Igor's example:

   x^3 - 5*x - 86089842541292486305497862178148061265660715093760132420

The only factor it finds is '10' [ once you remove the factor 100 from the
discriminant, you don't get anything new ]

    Karim.
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Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
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