#20722: Comparison in polynomial quotient rings
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Reporter: nbruin | Owner:
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-7.3
Component: PLEASE CHANGE | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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see [https://groups.google.com/forum/?hl=en#!topic/sage-devel/lAHT1sENv9w
this sage-devel discussion]:
{{{
sage: R = PolynomialRing(GF(4), ('x', 'y'))
sage: x, y = R.gens()
sage: I = R.ideal([x^2 + y^2, x + y^3])
sage: S = R.quotient(I, 'ab')
sage: a, b = S.gens()
sage: c, d, e = a + b^2, a*b, b^2
sage: c*(d + e) == c*d + c*e
False
}}}
The problem is `QuotientRingElement._cmp_`, where it is assumed that the
reduction of an element with respect to an ideal I is a unique
representative of its residue class modulo I. In general, it is not.
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Ticket URL: <http://trac.sagemath.org/ticket/20722>
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