#11057: GCD in Polynomial Rings over Extension Fields
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Reporter: cswiercz | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-4.7
Component: algebra | Keywords: gcd, polynomialring, extension fields
Author: cswiercz | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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During an `ask.sagemath.org` response (see
[http://ask.sagemath.org/question/461/symbolic-polynomial-euclidean-
algorithm?answer=818#818 symbolic polynomial euclidean algorithm]) I came
across a bug in computing the GCD of two elements of a polynomial ring
over an extension field. For example:
{{{
sage: R.<x> = PolynomialRing(QQ,'x')
sage: p = x^2-2
sage: q = x^2-3
sage: K.<a,b> = QQ.extension([p,q])
sage: S.<x> = PolynomialRing(K,'x')
sage: f = a*x^2 * (x-1); g = a*x^2 * (x-b)
sage: f.gcd(g)
x^2
}}}
However, the result should be `a*x^2`.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11057>
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