#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: | 3f52ae0a26e0c8427013c29c2f2262a3d5eaea84
u/kedlaya/count_real_roots_of_polynomials_using_sturm_sequences| Stopgaps:
Dependencies: #20256 |
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Comment (by kedlaya):
Replying to [comment:9 jdemeyer]:
> Replying to [comment:8 kedlaya]:
> > PARI's polsturm allows infinite arguments by omission: a first
argument of None translates to -Infinity, a second argument of None
translates to +Infinity. I just pushed a commit allowing these.
>
> That's undocumented in PARI, so I think it's a bad idea to rely on that.
It's in the 2.7 documentation:
{{{
polsturm(pol, {a}, {b}): Number of real roots of the real squarefree
polynomial pol in the interval ]a,b], using Sturm's algorithm. a (resp. b)
is taken to be -infinity (resp. +infinity) if omitted.
}}}
Or have you seen the 2.8 user guide yet (which I haven't found)? There
does need to be a change of text to change the interval from ]a,b] (open
on the left, closed on the right) to [a,b] (closed both sides).
--
Ticket URL: <http://trac.sagemath.org/ticket/20243#comment:10>
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