MOPS: Multivariate Orthogonal Polynomials (symbolically)

Dumitriu, Ioana; Edelman, Alan; Shuman, Gene

MOPS: Multivariate Orthogonal Polynomials (symbolically)

Authors

Dumitriu, Ioana

Edelman, Alan

Shuman, Gene

Description

In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also compute multivariate hypergeometric functions, and offer both symbolic and numerical evaluations for all these quantities. We prove that all algorithms are well-defined, analyze their complexity, and illustrate their performance in practice. Finally, we also present a few of the possible applications of this library.
42 pages, 5 figures