#16268: Better normalization for function field elements
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.2
Component: algebra | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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If K is a field then K(u), the function field, has a reduce() method which
cancels the gcd but does not put into a canonical form by (for example)
dividing through by the leading coefficient of the denominator to make the
denominator monic. This means that equal elements may have different
hashes, and hence that putting function field elements into a set does not
work as a mathematician would expect. For example:
{{{
sage: Ku.<u> = FractionField(PolynomialRing(QQ,'u'))
sage: a = 27*u^2+81*u+243
sage: b = 27*u-81
sage: c = u^2 + 3*u + 9
sage: d = u-3
sage: s = a/b
sage: t = c/d
sage: s==t
True
sage: len(Set([s,t]))
2
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16268>
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