#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):
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.
I agree with adding an alias for all real roots, but I'm not sure what to
call it. My first thought would be is_self-adjoint().
I'm not sure what is the best way to check for a valid base ring. One
option would be to force the coefficients into RR, but I really want this
to be an exact computation on exact input. I suppose I could check for
coefficients in QQ or ZZ, and in those cases pass exact coefficients, and
in all other cases force the coefficients into RR. But then one should be
careful not to clobber the precision of the input in case it is higher
than usual.
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Ticket URL: <http://trac.sagemath.org/ticket/20243#comment:8>
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