#19611: Error in gcd for polynomials modulo p^n
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Reporter: roed | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.10
Component: algebra | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: Not yet reported upstream;
Work issues: | Will do shortly.
Commit: | Branch:
Stopgaps: | Dependencies:
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We've observed an error in gcds for polynomials over `Zmod(5^2)` and
`Zmod(5^3)`. This seems to be a problem in FLINT's `nmod_poly_gcd`, since
Sage essentially calls that function directly.
{{{
sage: R.<x> = QQ['x']
sage: f1old = x^5 + 7*x^3 + 8*x^2 + 15*x + 19
sage: f1old.is_irreducible()
True
sage: f2 = f1old.derivative()
sage: factor((f1old).discriminant())
181654981
sage: for i in range(1,5):
....: K.<x> = Zmod(5^i)['x'] #reducing over ZZ/(5^i ZZ)
....: f1 = K(f1old)
....: f2 = f1.derivative()
....: h = gcd(f1,f2)
....: if h.degree() > 0:
....: r = -h.constant_coefficient()
....: print 'over (ZZ/5^%s)[x], gcd is %s, evaluations of f1, f2
at the root are %s, %s'%(i, h, f1(r), f2(r))
over (ZZ/5^2)[x], gcd is x + 1, evaluations of f1, f2 at the root are 4, 0
over (ZZ/5^3)[x], gcd is x + 101, evaluations of f1, f2 at the root are 4,
0
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/19611>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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