# jackpolynomials

*Jack, zonal, and Schur polynomials.*

<!-- badges: start -->
[![Stack-lts](https://github.com/stla/jackpolynomials/actions/workflows/Stack-lts.yml/badge.svg)](https://github.com/stla/jackpolynomials/actions/workflows/Stack-lts.yml)
[![Stack-nightly](https://github.com/stla/jackpolynomials/actions/workflows/Stack-nightly.yml/badge.svg)](https://github.com/stla/jackpolynomials/actions/workflows/Stack-nightly.yml)
<!-- badges: end -->

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.

___

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

```haskell
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

* 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>.