jackpolynomials: Jack, zonal, and Schur polynomials
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, 1.3.0.0, 1.4.0.0, 1.4.1.0, 1.4.2.0, 1.4.3.0, 1.4.4.0, 1.4.5.0, 1.4.6.0, 1.4.7.0 |
|---|---|
| Change log | CHANGELOG.md |
| Dependencies | array (>=0.5.4.0 && <0.6), base (>=4.7 && <5), hspray (>=0.2.2.0 && <1), ilist (>=0.4.0.1 && <0.4.1), lens (>=5.0.1 && <5.3), math-functions (>=0.3.4.2 && <0.3.5), numeric-prelude (>=0.4.4 && <0.5) [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 2024-03-26T12:05:53Z |
| Distributions | |
| Downloads | 628 total (85 in the last 30 days) |
| Rating | (no votes yet) [estimated by Bayesian average] |
| Your Rating | |
| Status | Docs available [build log] Last success reported on 2024-03-26 [all 1 reports] |
Readme for jackpolynomials-1.1.1.0
[back to package description]jackpolynomials
Jack, zonal, and Schur polynomials.
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.Hspray
jp = jackPol 2 [3, 1] (2%1)
putStrLn $ prettySpray' jp
-- (18 % 1) x1^3x2 + (12 % 1) x1^2x2^2 + (18 % 1) x1x2^3
evalSpray jp [1, 1]
-- 48 % 1
References
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I.G. Macdonald. Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1995.
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J. Demmel and P. Koev. Accurate and efficient evaluation of Schur and Jack functions. Mathematics of computations, vol. 75, n. 253, 223-229, 2005.
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Jack polynomials. https://www.symmetricfunctions.com/jack.htm.