Opened 5 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 rws)

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 5 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:2 follow-up: Changed 5 years ago by rws

For the record, using FLINT's arith_chebyshev_t_polynomial for chebyshev_T in ZZ[] is twice as slow as the current Sage implementation.

comment:3 in reply to: ↑ 2 Changed 5 years ago by fredrik.johansson

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 5 years ago by rws

Ah, that's true. I only tested at T_500.

comment:5 Changed 5 years ago by rws

  • Branch set to u/rws/make_all_orthogonal_polynomials_symbolic

comment:6 Changed 5 years ago by rws

  • 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 rws

  • Description modified (diff)

comment:8 Changed 3 years ago by rws

  • Description modified (diff)
  • Summary changed from make all orthogonal polynomials symbolic to Symbolic orthogonal and some other holonomic polynomials
Note: See TracTickets for help on using tickets.