#10279: Bug in factor of polynomials over number fields
-----------------------------+----------------------------------------------
Reporter: lftabera | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone:
Component: factorization | Keywords: pari, factor, number field
Author: | Upstream: Reported upstream. Little or no
feedback.
Reviewer: | Merged:
Work_issues: |
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Bug raised in sage-devel by Niels Lubbes
[http://groups.google.com/group/sage-
devel/browse_thread/thread/33aa40a7685f37aa/d6a6230ee023fd06?show_docid=d6a6230ee023fd06]
{{{
sage: R = PolynomialRing( QQ, var( 't' ), order = 'lex' )
sage: t = R.gens()[0]
sage: f = t^4 - t^2 + 1
sage: T = NumberFieldTower( [f], 'a0' )
sage: R1 = R.change_ring( T )
sage: a0 = T.gens()[0]
sage: t = R1.gens()[0]
sage: poly = t^3 + (-4*a0^3 + 2*a0)*t^2 - 11/3*a0^2*t + 2/3*a0^3 - 4/3*a0
sage: poly.factor()
(t - 2*a0^3 + a0) * (t^2 + (-2*a0^3 + a0)*t - 2/3*a0^2)
sage: fact = poly.factor()[1][0]
sage: fact.factor()
(t - 4/3*a0^3 + 2/3*a0) * (t - 2/3*a0^3 + 1/3*a0)
}}}
As Jeroen Demeyer points, it is a bug in Pari.
{{{
gp> t; nf = nfinit(a^4 - a^2 + 1);
gp> poly = t^3 + (-4*a^3 + 2*a)*t^2 - 11/3*a^2*t + 2/3*a^3 - 4/3*a
%1 = t^3 + (-4*a^3 + 2*a)*t^2 - 11/3*a^2*t + (2/3*a^3 - 4/3*a)
gp> F = nffactor(nf, poly)
%2 =
[t + Mod(-2*a^3 + a, a^4 - a^2 + 1) 1]
[t^2 + Mod(-2*a^3 + a, a^4 - a^2 + 1)*t + Mod(-2/3*a^2, a^4 - a^2 + 1) 1]
gp> nffactor(nf, F[2,1])
%3 =
[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]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10279>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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