#16812: use FLINT to speed up Chebyshev T polynomial creation
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: flint, speedup | Merged in:
Authors: Ralf Stephan | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/rws/use_flint_to_speed_up_chebyshev_t_polynomial_creation|
61972b5574632e914e178fe211062d0dd0e35b87
Dependencies: | Stopgaps:
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Comment (by rws):
On another note, the behaviour of the function up to this is unexpectedly
complicated and not documented. Given integer n, if the second argument is
symbolic then if `n<32` a formula is applied else the recursive algorithm.
With this ticket, additionally polynomials are handled with FLINT (modulo
the refinements discussed).
Now, I have a patch ready for an `algorithm` keyword
(`flint`/`recursive`). Also, I want to remove that `n<32` bit together
with the `eval_formula` method that really is no longer necessary now we
have FLINT. It also leads to such inconsistencies as
{{{
sage: var('n,x')
(n, x)
sage: chebyshev_T(5,x)
16*x^5 - 20*x^3 + 5*x
sage: chebyshev_T(64, x)
2*(2*(2*(2*(2*(2*x^2 - 1)^2 - 1)^2 - 1)^2 - 1)^2 - 1)^2 - 1
}}}
which I would like to have either so or so, not both.
I think I propose to handle a symbolic argument exactly as a polynomial.
No one expects such a nested result except if explicitly requested. It's
also only faster because it's not expanded.
Do you have any objections?
--
Ticket URL: <http://trac.sagemath.org/ticket/16812#comment:20>
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