#16813: symbolic Legendre / associated Legendre functions / polynomials
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Reporter: rws | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: Ralf Stephan | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/rws/symbolic_legendre___associated_legendre_functions___polynomials|
74ca8ea0fd8ef0eab57ceb1405e0887efd971bc9
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Ralf Stephan', 'oldvalue': ''}):
* status: new => needs_review
* author: => Ralf Stephan
Comment:
Replying to [comment:24 maldun]:
> Nevertheless I think we should stick to the recursion with W(n,x),
because from a computational view it is a lot better since:
>
> 1) The computational complexity is the same (solving a two term
recursion)
>
> 2) we save computation time since we don't have to simplify expressions
containing logarithms but only polynomials which are much simpler to
handle and expand.
Well, I have implemented your recurrence using multivariate polynomials
where the generator `l` stands for the `log` term and gets substituted
subsequently. This is already twice as fast as Maxima. However, your
intuition was right that the `W(n,x)` formula is still faster, my guess
because univariate polys are faster than multi. Note that the `P(n,x)`
have to be computed, too, but nevertheless it's about 10x the speed of
Maxima (which BTW uses the wrong log branch as well).
I might add some introductory doc cleanup but the functions themselves are
now finished. Please review.
--
Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:26>
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