#18282: Fixes, cleanup and improvements to the default evaluation method for
univariate polynomials
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Reporter: mmezzarobba | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: commutative | Resolution:
algebra | Merged in:
Keywords: | Reviewers:
Authors: Marc Mezzarobba | Work issues:
Report Upstream: N/A | Commit:
Branch: | 84d6a1b874c241e8eed8196cc42fd9075be40206
u/mmezzarobba/pol_call | Stopgaps:
Dependencies: |
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Comment (by bruno):
In view of #18600 (and older sisters #18518 and #18585), I think
`__call__` may be at the same time improved and adapted to high degree
sparse polynomials: Basically, when a univariate polynomial `p` is
evaluated on a value `v` (other than a symbolic variable), it uses a
Horner scheme that ranges over all the coefficients of `p`, including the
zeroes. One could easily modify lines 755-756 in
`src/sage/rings/polynomial/polynomial_element.pyx` to make the loop ranges
over the nonzero coefficients. I've not checked already whether it is
slower in a sensible way for really dense polynomials or not, but it would
be faster for sparse polynomials. And as a side benefit, one would be able
to evaluate polynomials such as `x^2^500`, at least on "easy" values such
as `1` or `-1` or on finite fields.
What do you think of my proposal?
--
Ticket URL: <http://trac.sagemath.org/ticket/18282#comment:15>
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