MOPS: Multivariate orthogonal polynomials (symbolically)

Authors:
Ioana Dumitriu;Alan Edelman;Gene Shuman
Affiliations:
Department of Mathematics, University of Washington, Seattle, WA 98195, United States;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States;Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, CAmbridge, MA 02139, United States
Venue:
Journal of Symbolic Computation
Year:
2007

Citing 2
Cited 1

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Journal of Multivariate Analysis
Selberg integrals and hypergeometric functions associated with Jack polynomials

SIAM Journal on Mathematical Analysis

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Abstract

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 present a few applications of this library.