JackPolynomials.jl

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:

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:

JackPolynomial(2, [3; 1], 1//4)
25//8x₁³x₂ + 5//1x₁²x₂² + 25//8x₁x₂³

It is also possible to deal with a symbolic alpha:

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