#11057 closed defect (invalid)
GCD in Polynomial Rings over Extension Fields
Reported by: | cswiercz | Owned by: | AlexGhitza |
---|---|---|---|
Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | algebra | Keywords: | gcd, polynomialring, extension fields |
Cc: | Merged in: | ||
Authors: | cswiercz | Reviewers: | cswiercz |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
During an ask.sagemath.org
response (see 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
.
Change History (2)
comment:1 Changed 10 years ago by
- Resolution set to invalid
- Reviewers set to cswiercz
- Status changed from new to closed
comment:2 Changed 10 years ago by
- Milestone changed from sage-4.7 to sage-duplicate/invalid/wontfix
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Mathematical mistake.
a
is a unit in $QQ(a,b)$ so it's not part of the GCD. This ticket is not an issue / defect.