jackpolynomials

Jack, zonal, Schur and skew 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

• 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.