Orthogonal polynomials and Gauss Quadrature: s.th. in Maple?

Axel Vogt's picture

There is a Mathematica package OrthogonalPolynomials by Milovanovic sketched in facta.junis.ni.ac.yu/mai/mai19/f19-017-036.pdf
( ~ 200 kb and 20 pages). Is anybody aware of something similar for Maple?

JacquesC's picture

OrthogonalSeries

Some of the functionality is in OrthogonalSeries, while other bits are buried in `evalf/int` itself, some are in the numapprox package.

The documentation, as usual, is awful.  For OrthogonalSeries, you can blame me if you wish -- I am the one who rewrote most of the code to integrate this into Maple [it was originally written at one of the universities that does research-oriented development for Maplesoft; that code usually works, but even then written in an antique Maple style.  This is usually because this was written by students who learned their Maple style from the Maple books (which mostly are quaint in their obsolescence), from their supervisors (too many of whom stopped reading the "What's New" 10 years ago, or from their supervisor's code which tends to be very old.  In any case, I had time to modernize the code but did not have the time to do much with the documentation.  And then I moved on to the next project, and the next, and ... 

Axel Vogt's picture

outing

Thx for your outing, no reason to blame you :-)

My interest was for some stand-alone package to have routines for specific quadratures without carrying together from books & papers and coding (& testing) it

Computational Mathematics at University of Kassel

The Computational Mathematics group at University of Kassel has experts on this topic. Please see www.mathematik.uni-kassel.de/~koepf/ for more information. Prof. Koepf has contributed many routines to Maple, e.g. the convert/FormalPowerSeries in Maple 11.

Axel Vogt's picture

i had just quadrature rules in mind

Thanks for the hint, however I just had in mind some routines to produce Gauss quadrature rules (for given weight functions for example), there are some standard ways (sketched in the cited document) - certainly easier then the theory around Koepf's work.

Axel Vogt's picture

example sheet

Not that complete as the package as described in the linked paper above (especially they do have various methods), but the following fits my basic needs (and I am too 'lazy' for a full solution, that's on Maple, if they want to compete ...):

Download 102_computing_Gauss_integration_rules.mws (30 kb)

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