# 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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• Math
• Algebra

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Versions [RSS] 1.0.0.0, 1.0.0.1, 1.1.0.0, 1.1.0.1 CHANGELOG.md 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] GPL-3.0-only 2022 Stéphane Laurent Stéphane Laurent laurent_step@outlook.fr Math, Algebra https://github.com/stla/jackpolynomials#readme head: git clone https://github.com/stla/jackpolynomials by stla at 2022-12-12T05:56:12Z NixOS:1.1.0.1 125 total (1 in the last 30 days) (no votes yet) [estimated by Bayesian average] λ λ λ Docs available Last success reported on 2022-12-12

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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.