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
jackPol [1, 1] [3, 1] (2%1)
-- 48 % 1

import Math.Algebra.JackPol
import Data.Ratio
import Math.Algebra.MultiPol
jp = jackPol 2 [3, 1] (2%1)
jp
-- (M (Monomial {coefficient = 18 % 1, powers = fromList [1,3]}) 
--  :+: 
--  M (Monomial {coefficient = 12 % 1, powers = fromList [2,2]})) 
--  :+: 
--  M (Monomial {coefficient = 18 % 1, powers = fromList [3,1]})
prettyPol show "x" jp
-- "(18 % 1) * x^(1, 3) + (12 % 1) * x^(2, 2) + (18 % 1) * x^(3, 1)"
evalPoly jp [1, 1]
-- 48 % 1