MOPS: multivariate orthogonal polynomials (symbolically). 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.

References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Forrester, Peter J.; Rahman, Anas A.: Relations between moments for the Jacobi and Cauchy random matrix ensembles (2021)
  2. Jiang, Tiefeng; Wang, Ke: Statistical properties of eigenvalues of Laplace-Beltrami operators (2021)
  3. Jonnadula, Bhargavi; Keating, Jonathan P.; Mezzadri, Francesco: Symmetric function theory and unitary invariant ensembles (2021)
  4. Chafaï, Djalil; Lehec, Joseph: On Poincaré and logarithmic Sobolev inequalities for a class of singular Gibbs measures (2020)
  5. Ehler, Martin; Gräf, Manuel: Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians (2019)
  6. Mayerhofer, Eberhard: On Wishart and noncentral Wishart distributions on symmetric cones (2019)
  7. Aggarwal, Amol: An arithmetic property of moments of the (\beta)-Hermite ensemble and certain map enumerators (2018)
  8. Slater, Paul B.: Formulas for generalized two-qubit separability probabilities (2018)
  9. Breger, Anna; Ehler, Martin; Gräf, Manuel: Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians (2017)
  10. Forrester, Peter J.; Rahman, Anas A.; Witte, Nicholas S.: Large (N) expansions for the Laguerre and Jacobi (\beta)-ensembles from the loop equations (2017)
  11. Mezzadri, Francesco; Reynolds, Alexi K.; Winn, Brian: Moments of the eigenvalue densities and of the secular coefficients of (\beta)-ensembles (2017)
  12. Sommariva, Alvise; Vianello, Marco: Numerical hyperinterpolation over nonstandard planar regions (2017)
  13. Wirtz, Tim; Waltner, Daniel; Kieburg, Mario; Kumar, Santosh: The correlated Jacobi and the correlated Cauchy-Lorentz ensembles (2016)
  14. Passemier, Damien; McKay, Matthew R.; Chen, Yang: Hypergeometric functions of matrix arguments and linear statistics of multi-spiked Hermitian matrix models (2015)
  15. Wang, Dong: The largest eigenvalue of real symmetric, Hermitian and Hermitian self-dual random matrix models with rank one external source. I (2012)
  16. Barrio, Roberto; Peña, Juan Manuel; Sauer, Tomas: Three term recurrence for the evaluation of multivariate orthogonal polynomials (2010)
  17. Albrecht, James T.; Chan, Cy P.; Edelman, Alan: Sturm sequences and random eigenvalue distributions (2009)
  18. Wang, Dong: The largest sample eigenvalue distribution in the rank 1 quaternionic spiked model of Wishart ensemble (2009)
  19. Anshelevich, Michael: Monic non-commutative orthogonal polynomials (2008)
  20. Iliopoulos, George: UMVU estimation of the ratio of powers of normal generalized variances under correlation (2008)

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