#20243: Count real roots of polynomials using Sturm sequences
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Reporter: kedlaya | Owner: kedlaya
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-7.2
Component: algebra | Resolution:
Keywords: polynomials, | Merged in:
root-counting, days71 | Reviewers:
Authors: Kiran Kedlaya | Work issues:
Report Upstream: N/A | Commit:
Branch: | 264f2b33a895463e71ad84739a5dc74952eb95bb
u/kedlaya/count_real_roots_of_polynomials_using_sturm_sequences| Stopgaps:
Dependencies: #20256 |
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Comment (by kedlaya):
Merged #20256 to do the Infinity conversion.
I don't know what to do about type-checking. If you have a polynomial over
C but whose coefficients actually belong to R, then PARI seems to handle
this correctly (I added a doctest to this effect). However, we have
trouble with inexact polynomials which are (apparently) not squarefree:
{{{
sage: P.<x> = PolynomialRing(RR)
sage: pol = (x-1)^2*(x-2)^2*(x-3)
sage: pol.is_squarefree() # Should be False
True
sage: pari(pol).issquarefree # Should be 0
1
sage: pol.count_roots_in_interval()
...
PariError: domain error in polsturm: issquarefree(pol) = 0
}}}
I created ticket #20282 for this issue, in case we decide not to deal with
it here (which would be my preference).
--
Ticket URL: <http://trac.sagemath.org/ticket/20243#comment:20>
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