No, the van Hoeij / Belabas algorithms are for univariate polynomials,
over Q (and then over number fields). Pari does not have multivariate
polynomial factorization:
j...@selmer%sage -gp
Reading GPRC: /etc/gprc ...Done.
GP/PARI CALCULATOR Version 2.3.3 (released)
amd64 running linux (x86-64/GMP-4.2.1 kernel) 64-bit version
compiled: Jan 6 2010, gcc-4.3.3 (Ubuntu 4.3.3-5ubuntu4)
(readline v6.0 enabled, extended help available)
(...)
? factor(x^2-y^2)
*** factor: sorry, factor for general polynomials is not yet implemented.
I also tried this with a recent svn version 2.4.3 (development svn-12035) of gp.
John
2010/1/12 javier <vengor...@gmail.com>:
> Looking at Mark van Hoeij's website, he has a (maple) implementation
> of his algorithm:
> http://www.math.fsu.edu/~hoeij/knapsack.html
>
> he also mentions
>
> "My implementation is not tuned in the best possible way. A much
> better way (more efficient, more robust and simpler) to tune the
> algorithm is given by Karim Belabas in section 2 of his paper "A
> relative van Hoeij algorithm over number fields", to appear in J.
> Symbolic Computation"
>
> that paper is available at Belabas' website:
>
> http://www.ufr-mi.u-bordeaux.fr/~belabas/research/vanhoeij.pdf
>
> and the end of the introduction reads
>
> "Our implementations are part of the PARI library [23]. All timings
> were obtained
> with PARI-2.2.6 configured to use GMP-4.1 as its multiprecision
> kernel,
> on a 1GHz Athlon under Linux (lucrezia.medicis.polytechnique.fr), and
> are given in seconds."
>
> so it seems PARI already contains an algorithm similar to what you are
> looking for.
>
> Alternatively, since it seems that van Hoeijs algorithm reduces to a
> knapsack problem, so maybe it could be easily built upon the brand new
> fast graphs methods that we got?
>
> Cheers
> J
>
> On Jan 12, 2:08 pm, YannLC <yannlaiglecha...@gmail.com> wrote:
>> On Jan 12, 2:46 pm, javier <vengor...@gmail.com> wrote:
>>
>> > There are indeed well known (sort of) fast algorithms for
>> > factorization of multivariable polynomials over finite
>> > fields:http://portal.acm.org/citation.cfm?id=808748http://www.jstor.org/stab...
>>
>> > In the second paper there is a particular (probabilistic) algorithm
>> > for bivariate polynomials. Maybe magma has something like that?
>>
>> Citing Magma's help (http://magma.maths.usyd.edu.au/magma/htmlhelp/
>> text315.htm):
>>
>> For bivariate polynomials, a polynomial-time algorithm in the same
>> spirit as van Hoeij's Knapsack factoring algorithm [vH02] is used.
>
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