#16964: Speed up comparisons in QQbar
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Reporter: gagern | Owner:
Type: defect | Status: positive_review
Priority: critical | Milestone: sage-6.5
Component: number fields | Resolution:
Keywords: variety qqbar cmp | Merged in:
singular | Reviewers: Vincent Delecroix
Authors: Martin von Gagern | Work issues:
Report Upstream: N/A | Commit:
Branch: | 3f4afef46ab6a042cb2678394031cb5c26d89b1a
u/vdelecroix/16964 | Stopgaps:
Dependencies: |
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Comment (by jdemeyer):
Replying to [comment:24 vdelecroix]:
> But I am not completely convinced that this is optimal. Do you know if
there is a cheap way to assert if two roots of a given (irreducible)
polynomial have the same real value?
Using resultants, you can find a polynomial which has (a - b) as a root.
And then you use interval arithmetic to find which root. Determining
whether the imaginary parts are equal then is equivalent to checking
whether a real polynomial has a pure imaginary root. The latter can
probably be done using some Sturm-like algorithm.
--
Ticket URL: <http://trac.sagemath.org/ticket/16964#comment:30>
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