#20243: Count real roots of polynomials using Sturm sequences
-------------------------------------+-------------------------------------
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: | 81e9366b072db5dc772f3ea9b91b54e20116504b
u/kedlaya/count_real_roots_of_polynomials_using_sturm_sequences| Stopgaps:
Dependencies: #20256 |
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Comment (by kedlaya):
Replying to [comment:37 kdilks]:
> Patchbot doesn't like something about the way errors are raised. I think
it would be a bit more straightforward to make the arguments be
{{{(self,lower_bound=None,upper_bound=None)}}}, and just not allow for the
option of specifying the bounds as a two-element list.
>
See if patchbot does better with this.
> In terms of the names of functions, I think
{{{count_roots_in_interval}}} would make more sense as
{{{number_of_roots_in_interval}}} (that's the naming convention used for
most combinatorial statistics). And {{{has_all_real_roots}}} should
probably be named {{{is_real_rooted}}}. Things that return a boolean
almost always start with {{{is_}}}, and calling polynomials with all real
roots "real rooted" is prevalent, at least in the literature that I read.
Not a term I had seen before. I suppose it's actually "real-rooted"
(otherwise a "real rooted polynomial" would be a polynomial which is real
and also "rooted"), but I think there is a convention to convert both
spaces and hyphens into underscores in method names (as in
{{{Matrix.is_skew_symmetric}}}). However, I don't have a suitable "is"
reformulation of {{{all_roots_in_interval}}}.
Bonus edit: I added {{{number_of_real_roots}}} as an alias for
{{{number_of_roots_in_interval}}} with no arguments.
--
Ticket URL: <http://trac.sagemath.org/ticket/20243#comment:40>
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