#17151: symbolic Laguerre / associated Laguerre polynomials
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: symbolics | Resolution:
Keywords: special, | Merged in:
function, holonomic, orthogonal | Reviewers:
Authors: Ralf Stephan | Work issues:
Report Upstream: N/A | Commit:
Branch: u/rws/17151 | ea2ff9b11a520edd58b1db527ef41eed6b0e7f85
Dependencies: | Stopgaps:
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Comment (by rws):
Replying to [comment:13 mmezzarobba]:
> Are the three separate cases in `_pol_laguerre()` necessary? Couldn't
one just do something like
> {{{
> R = PolynomialRing(QQ, 'x')
> pol = R([binomial(n,k)*(-1)**k/factorial(k) for k in xrange(n+1)])
> return pol(x)
> }}}
> no matter what `x` is?
No, because (apart from speed reasons) the R([...]) construction is not
available in all parents. However, when investigating this I found that
the argument is coerced into `SR` by the superclasses
`BuiltinFunction/Function`, so it must be unwrapped for the real parent.
OTOH, for simplicity the branch with `sum` would be a catch-all. Let's see
if going polynomial really is faster and, if not, do only summing for all
parents.
--
Ticket URL: <http://trac.sagemath.org/ticket/17151#comment:18>
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