#17895: Computing all roots is faster than computing a single one
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Reporter: gagern | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: number | Keywords: qqbar polynomial_root roots
fields | performance
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The following example comes from comment:27:ticket:16964 via
comment:2:ticket:17886.
{{{
sage: x,y = polygens(QQ,"x,y")
sage: p1 = x^5 + 6*x^4 - 42*x^3 - 142*x^2 + 467*x + 422
sage: p2 = p1(x=(x-1)^2)
sage: p3 = p2(x=x*y).resultant(p2,x).univariate_polynomial()
sage: p4, = [f[0] for f in p3.factor() if f[0].degree() == 80]
sage: ival = CIF((0.77, 0.78), (-0.08, -0.07))
sage: %time z1, = [r for r in p4.roots(QQbar, False) if r in ival]
CPU times: user 1.43 s, sys: 195 ms, total: 1.62 s
Wall time: 1.47 s
sage: %time z2 = QQbar.polynomial_root(p4, ival)
CPU times: user 1min 5s, sys: 212 ms, total: 1min 5s
Wall time: 1min 5s
}}}
The computation for `z1` works reasonably well and completes in under 2
seconds, but the one for `z2` takes over a minute on my system. Which I
find really strange, since computing all roots and then choosing the right
one should be ''more'' work, not ''less'' than just computing a single
one. Should we change `QQbar.polynomial_root` to go via the list of all
roots, or is there a better solution?
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Ticket URL: <http://trac.sagemath.org/ticket/17895>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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