On Nov 15, 2:38 pm, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote:
> On 2010-11-15 13:53, Niels wrote:
>
> > Hi,
>
> > I think the following is a bug (only complete factorization after 2 steps):
>
> Yes, it is a bug.  The problem is with the upstream package PARI/GP.

Yes, it is a bug in pari. Note also the following:

gp: poly = t^3 + (-4*a^3 + 2*a)*t^2 - 11/3*a^2*t + 2/3*a^3 - 4/3*a
t^3 + (-4*a^3 + 2*a)*t^2 - 11/3*a^2*t + (2/3*a^3 - 4/3*a)
gp: factornf(poly, a^4 - a^2 +1)

[t + Mod(-2*a^3 + a, a^4 - a^2 + 1) 1]

[t + Mod(-4/3*a^3 + 2/3*a, a^4 - a^2 + 1) 1]

[t + Mod(-2/3*a^3 + 1/3*a, a^4 - a^2 + 1) 1]

Which is the correct answer.

Note that with the new pari, it is not needed nfinit any more. We
should avoid calling R.nfinit in self.factor() and only use the
nffactor command if the nf structure is already computed and cached.
This is another issue that would not solve the problem though.

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