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jackpolynomials: Jack, zonal, and Schur polynomials

[ algebra, gpl, library, math ] [ Propose Tags ]

This library can evaluate Jack polynomials, zonal polynomials and Schur polynomials. It is also able to compute them in symbolic form.

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Versions [RSS] 1.0.0.0, 1.0.0.1, 1.1.0.0, 1.1.0.1, 1.1.1.0, 1.1.2.0, 1.2.0.0, 1.2.1.0, 1.2.2.0
Change log CHANGELOG.md
Dependencies array (>=0.5.4.0), base (>=4.7 && <5), hspray (>=0.1.0.0), ilist (>=0.4.0.1), lens (>=5.0.1), math-functions (>=0.3.4.2), numeric-prelude (>=0.4.4) [details]
License GPL-3.0-only
Copyright 2022 Stéphane Laurent
Author Stéphane Laurent
Maintainer laurent_step@outlook.fr
Category Math, Algebra
Home page https://github.com/stla/jackpolynomials#readme
Source repo head: git clone https://github.com/stla/jackpolynomials
Uploaded by stla at 2022-12-12T05:56:12Z
Distributions NixOS:1.1.1.0
Downloads 251 total (75 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2022-12-12 [all 1 reports]

Readme for jackpolynomials-1.1.0.1

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jackpolynomials

Schur polynomials have applications in combinatorics and zonal polynomials have applications in multivariate statistics. They are particular cases of Jack polynomials. This package allows to evaluate these polynomials. It can also compute their symbolic form.

import Math.Algebra.Jack
import Data.Ratio
jack [1, 1] [3, 1] (2%1)
-- 48 % 1

import Math.Algebra.JackPol
import Data.Ratio
import Math.Algebra.Spray
jp = jackPol 2 [3, 1] (2%1)
prettySpray show "x" jp
-- "(18 % 1) * x^(1, 3) + (12 % 1) * x^(2, 2) + (18 % 1) * x^(3, 1)"
evalSpray jp [1, 1]
-- 48 % 1

References

  • I.G. Macdonald. Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1995.

  • J. Demmel and P. Koev. Accurate and efficient evaluation of Schur and Jack functions. Mathematics of computations, vol. 75, n. 253, 223-229, 2005.

  • Jack polynomials. https://www.symmetricfunctions.com/jack.htm.