https://github.com/stla/jackpolynomials.jl

Jack, Zonal, and Schur polynomials.
https://github.com/stla/jackpolynomials.jl

jack-polynomials julia schur-polynomials zonal-polynomials

Last synced: 7 months ago
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Jack, Zonal, and Schur polynomials.

• Host: GitHub
• URL: https://github.com/stla/jackpolynomials.jl
• Owner: stla
• License: mit
• Created: 2020-12-15T08:59:28.000Z (over 5 years ago)
• Default Branch: master
• Last Pushed: 2022-07-22T09:20:40.000Z (almost 4 years ago)
• Last Synced: 2025-02-23T14:09:20.083Z (over 1 year ago)
• Topics: jack-polynomials, julia, schur-polynomials, zonal-polynomials
• Language: Julia
• Homepage: https://stla.github.io/JackPolynomials.jl/dev/
• Size: 140 KB
• Stars: 1
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# JackPolynomials.jl

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://stla.github.io/JackPolynomials.jl/dev)

Schur polynomials have applications in combinatorics and zonal polynomials have

applications in multivariate statistics. They are particular cases of

[Jack polynomials](https://en.wikipedia.org/wiki/Jack_function). This package

allows to evaluate these polynomials. It can also compute their symbolic form:

```julia

julia> jack = JackPolynomial(2, [3 ; 1], 2.5)

24.5x₁³x₂ + 14.0x₁²x₂² + 24.5x₁x₂³

julia> jack(1,2)

301.0

```

Here `2.5` is the value of the `alpha` parameter. One can use a rational

number instead:

```julia

JackPolynomial(2, [3; 1], 1//4)

25//8x₁³x₂ + 5//1x₁²x₂² + 25//8x₁x₂³

```

It is also possible to deal with a symbolic `alpha`:

```julia

julia> jack = JackPolynomial(2, [2 ; 1])

(alpha + 2)*x_1^2*x_2 + (alpha + 2)*x_1*x_2^2

julia> jack(1,2)

6*alpha + 12

```