#9706: Symbolic Chebyshev polynomials
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Reporter: maldun | Owner: burcin, maldun
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.13
Component: symbolics | Resolution:
Keywords: orthogonal | Merged in:
polynomials, symbolics | Reviewers: Burcin Erocal, Travis
Authors: Stefan Reiterer, | Scrimshaw, Stefan Reiterer
Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by jdemeyer):
Replying to [comment:86 maldun]:
> @clenshaw_method: there is a difference. clenshaw method also applies a
direct formula for small n and calls the recursive method else. The
difference is that the recursive evaluation does not give an expanded
representation of the polynomial, which is wanted for small n
OK, fine. But for simplicity, you could simply call
`_cheb_recur_(...).expand()` instead which would achieve the same thing
without an additional method.
> _eval cares about evaluating the polynomial (e.g return a number if x is
a number etc.)
> Look into the symbolic.function module for more details
> And eval is so complicated because there are several cases to consider:
correct evaluation of symbolic expressions, numerical expressions and
numpy arrays etc.
If you really think the complexity is justified (I have a hard time
believing that), you should add comments in the code to describe the
various cases, because I'm having a hard time understanding the logic. A
comment like {{{# A faster check would be nice...}}} doesn't mean much to
me because I don't understand what you're trying to do.
--
Ticket URL: <http://trac.sagemath.org/ticket/9706#comment:88>
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