#11239: Incorrect coercion of polynomials over finite fields
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Reporter: johanbosman | Owner: robertwb
Type: defect | Status:
Priority: major | needs_info
Component: coercion | Milestone:
Keywords: finite fields, polynomials, | sage-5.11
coercion | Resolution:
Authors: | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
Stopgaps: | Dependencies:
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Comment (by pbruin):
The problem lies in the ''NTL implementation'' of polynomials over finite
fields. This is the default implementation for polynomials over finite
fields, even though the fields themselves are only implemented via NTL in
characteristic 2, and via Givaro or PARI otherwise.
The following example demonstrates this (after applying #8335 plus a patch
that I will upload shortly):
{{{
sage: K.<a> = GF(5^2, conway=True, prefix='z')
sage: L.<b> = GF(5^4, conway=True, prefix='z')
sage: type(K)
<class
'sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro_with_category'>
sage: R = PolynomialRing(K, 'x', implementation='NTL')
sage: S = PolynomialRing(L, 'x', implementation='NTL')
sage: f = R.gen() + a; f
x + a
sage: type(f)
<type 'sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX'>
sage: S(f)
x + b
sage: R = PolynomialRing(K, 'x', implementation='generic')
sage: S = PolynomialRing(L, 'x', implementation='generic')
sage: f = R.gen() + a; f
x + a
sage: type(f)
<class
'sage.rings.polynomial.polynomial_element_generic.Polynomial_generic_dense_field'>
sage: S(f)
x + b^3 + b^2 + b + 3
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/11239#comment:7>
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