JackPolR {jack}

Jack polynomial

Description

Returns the Jack polynomial.

Usage

JackPolR(n, lambda, alpha, algorithm = "DK", basis = "canonical", which = "J")

Arguments

n

number of variables, a positive integer

lambda

an integer partition, given as a vector of decreasing integers

alpha

parameter of the Jack polynomial, a number, possibly (and preferably) a bigq rational number

algorithm

the algorithm used, either "DK" or "naive"

basis

the polynomial basis for algorithm = "naive", either "canonical" or "MSF" (monomial symmetric functions); for algorithm = "DK" the canonical basis is always used and this parameter is ignored

which

which Jack polynomial, "J", "P" or "Q"; this argument is taken into account only if alpha is a bigq number and algorithm = "DK"

Value

A mvp multivariate polynomial (see mvp-package), or a qspray multivariate polynomial if alpha is a bigq rational number and algorithm = "DK", or a character string if basis = "MSF".

Examples

JackPolR(3, lambda = c(3,1), alpha = gmp::as.bigq(2,3),
                  algorithm = "naive")
JackPolR(3, lambda = c(3,1), alpha = 2/3, algorithm = "DK")
JackPolR(3, lambda = c(3,1), alpha = gmp::as.bigq(2,3), algorithm = "DK")
JackPolR(3, lambda = c(3,1), alpha= gmp::as.bigq(2,3),
        algorithm = "naive", basis = "MSF")
# when the Jack polynomial is a `qspray` object, you can
# evaluate it with `qspray::evalQspray`:
jack <- JackPolR(3, lambda = c(3, 1), alpha = gmp::as.bigq(2))
evalQspray(jack, c("1", "1/2", "3"))