#16813: symbolic Legendre / associated Legendre functions / polynomials
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: Ralf Stephan, | Reviewers:
Stefan Reiterer | Work issues:
Report Upstream: N/A | Commit:
Branch: | 9df78de81e0c307a1181a6ad4453bc56a93870b2
u/rws/symbolic_legendre___associated_legendre_functions___polynomials|
Stopgaps:
Dependencies: |
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Comment (by rws):
Replying to [comment:52 mmezzarobba]:
> Is the idea that calls to `legendre_P(n, x)` with no `algorithm` keyword
will always take the branch corresponding to `x` in `SR`, but the user can
obtain faster evaluations at integers etc. by specifying
`algorithm='pari'` is they know what they are doing?
Effectively, one of the `__call__` methods (at this point of time
`OrthogonalPolynomial.__call__`) dispatches to the resp. `eval_...`
method. If no match is found (and `algorithm` is `None`) `__call__`
returns to somewhere in the `BuiltinFunction/Function` classes to either
return a held object or call `evalf`. Jeroen wanted to implement a default
list of `algorithm/eval_...` pairs checked automatically but, if this
keeps coming up, I'll put it high on my list.
> I'm not sure being holonomic or not makes a big difference for a
symbolic function. What do you have in mind?
It's just a natural category for special functions, corresponding to a
D-finite series expansion.
--
Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:62>
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