Opened 6 years ago
Last modified 3 years ago
#16670 new enhancement
Symbolic orthogonal and some other holonomic polynomials
Reported by: | rws | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-wishlist |
Component: | symbolics | Keywords: | orthogonal, holonomic |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
At the moment just the Chebyshev polynomials are symbolic. Missing are hermite
, laguerre
, legendreP
, legendreQ
, ultraspherical
(=gegenbauer
), and, while the Stirling and Euler polynomials are not orthogonal, they are holonomic and belong to the standard repertoire, so we're including them here.
- symbolic Associated Legendre P(n,m,x) / Q(n,m,x) and P(n,x) / Q(n,x) polynomials / functions (#16813)
- symbolic Laguerre / associated Laguerre polynomials (#17151)
- symbolic Gegenbauer polynomials (#20475)
- symbolic Hermite polynomials (#20475)
- symbolic Jacobi P polynomials (#22326)
- symbolic Euler polynomials
- symbolic Stirling polynomials
Change History (8)
comment:1 Changed 6 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:2 follow-up: ↓ 3 Changed 6 years ago by
comment:3 in reply to: ↑ 2 Changed 6 years ago by
Really? For me flint constructs T_10000 in 0.009 seconds while Sage's chebyshev_T takes 1 second.
But *evaluating* a Chebyshev polynomial is a completely different problem. You want to do that by recurrence relations, not by constructing the polynomial and evaluating it.
comment:4 Changed 6 years ago by
Ah, that's true. I only tested at T_500.
comment:5 Changed 6 years ago by
- Branch set to u/rws/make_all_orthogonal_polynomials_symbolic
comment:6 Changed 6 years ago by
- Branch u/rws/make_all_orthogonal_polynomials_symbolic deleted
- Description modified (diff)
- Milestone changed from sage-6.4 to sage-wishlist
The speed issue is now #16812
I think the scope of the ticket is too broad. Let's make it a meta-ticket.
comment:7 Changed 5 years ago by
- Description modified (diff)
comment:8 Changed 3 years ago by
- Description modified (diff)
- Summary changed from make all orthogonal polynomials symbolic to Symbolic orthogonal and some other holonomic polynomials
For the record, using FLINT's
arith_chebyshev_t_polynomial
forchebyshev_T
inZZ[]
is twice as slow as the current Sage implementation.