#16964: Speed up comparisons in QQbar
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Reporter: gagern | Owner:
Type: defect | Status: needs_info
Priority: critical | Milestone: sage-6.5
Component: number fields | Resolution:
Keywords: variety qqbar cmp | Merged in:
singular | Reviewers:
Authors: Martin von Gagern | Work issues:
Report Upstream: N/A | Commit:
Branch: | e7acd96040fb43eebed0e3df0f1b1c7613d49bc1
u/gagern/ticket/16964 | Stopgaps:
Dependencies: |
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Changes (by vdelecroix):
* status: needs_review => needs_info
Comment:
Hello,
This improvement is really cool!
Couldn't we do a little bit better? In some cases we might identify
numerically pairs of conjugated roots (and possibly one real root) and
still be able to decide which one is which. There exists polynomials whose
roots have the same real part:
{{{
sage: x = polygen(ZZ)
sage: P = x^4 - 4*x^3 + 9*x^2 - 10*x + 5
sage: P.roots(CC,False)
[1.00000000000000 - 1.61803398874989*I,
1.00000000000000 - 0.618033988749895*I,
1.00000000000000 + 0.618033988749895*I,
1.00000000000000 + 1.61803398874989*I]
}}}
With the implementation proposed in this ticket, the comparison of the
roots of the above polynomial falls back to the generic implementation. We
could at least compare the conjugated ones without exactification of the
real part. But we can leave that for a further ticket.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/16964#comment:14>
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