Opened 12 years ago

Closed 12 years ago

Last modified 12 years ago

#11057 closed defect (invalid)

GCD in Polynomial Rings over Extension Fields

Reported by: Chris Swierczewski Owned by: Alex Ghitza
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:

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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 12 years ago by Chris Swierczewski

Resolution: invalid
Reviewers: cswiercz
Status: newclosed

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.

comment:2 Changed 12 years ago by Minh Van Nguyen

Milestone: sage-4.7sage-duplicate/invalid/wontfix
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