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MOPS: multivariate orthogonal polynomials (symbolically). (English) Zbl 1122.33019
Summary: 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.

MSC:
33F05 Numerical approximation and evaluation of special functions
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
68W30 Symbolic computation and algebraic computation
Software:
Maple; MOPS ; SF; LUC
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References:
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