#10304: PolynomialRing_field.lagrange_polynomial doesn't always return a
polynomial
-----------------------------------+----------------------------------------
Reporter: mguaypaq | Owner: mguaypaq
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.6.1
Component: algebra | Keywords: polynomial ring, lagrange
polynomial
Author: Mathieu Guay-Paquet | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* cc: mvngu (added)
* status: new => needs_review
* author: => Mathieu Guay-Paquet
Comment:
I've put up a patch that should fix the problem, at least in the case of
{{{algorithm='divided_difference'}}}, and includes a new doctest to verify
this.
For the {{{algorithm='neville'}}} case, I've taken the liberty of
rewriting the code, to clean it up and unify it a bit in addition to
fixing the original problem. However:
* This changes the default value of {{{previous_row}}} from {{{None}}} to
{{{[]}}}. I doubt this would break anything, but it is a slight change in
the function signature.
* In the case of an empty list of points, I wasn't sure whether to return
{{{[]}}} or {{{[0]}}}. The former is more consistent with the
{{{previous_row}}} option, but the latter preserves the property that the
last element of the returned list is the interpolating polynomial (as
opposed to non-existent). I opted for the first one, but there's
definitely a choice to be made here. (I'll note that neither choice is
really backwards-incompatible, since the method used to fail in this
case.)
Minh, I've put you on CC, since (I think) you wrote the original code for
the {{{algorithm='neville'}}} part. Do you approve of the changes?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10304#comment:1>
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