Symbolic Quadrature and Orthogonal Polynomials Recurrence

[6baab83c-76f4-4804-a70b-e51e5d41585b]

I'm working on two functions that are related to orthogonal polynomials. Given a finite interval and a polynomial measure on it, i.e. dmu = q(x)dx for some q(x) polynomial, I calculate

1) The recurrence relations of the respective orthogonal polynomials. 2) The quadrature points and weights (in the sense of numerical-integration Gaussian quadrature).

This will all be done symbolically,, results given in algebraic numbers (AA) using linear-algebra techniques. Albeit slow, this has the advantage of accuracy.

Inasmuch as I know, there is no parallel scipy or matlab code that does it generically for all measures.

The basic codes now work. I still have some thoughts:

1. What to do with non-polynomial measures and/or infinite intervals? To keep it in AA I see no alternative to this assumptions.
2. Where should these functions "live", just as functions?

Amir

Component: numerical

Keywords: sagedays79, newFeature

Issue created by migration from https://trac.sagemath.org/ticket/21956

[videlec]

comment:2

Hi Amir,

If you put your ticket in "needs review" it means that you have some code to propose... but where is it? You need to push it on the git server and upload the "branch" field of the ticket. The relevant section of the developer manual is http://doc.sagemath.org/html/en/developer/manual_git.html