ZonalQ: Evaluation of quaternionic zonal polynomials

In jack: Jack, Zonal, and Schur Polynomials

Evaluation of quaternionic zonal polynomials

Description

Evaluates a quaternionic (or symplectic) zonal polynomial.

Usage

ZonalQ(x, lambda, algorithm = "DK")

Arguments

x	numeric or complex vector or bigq vector
lambda	an integer partition, given as a vector of decreasing integers
algorithm	the algorithm used, either "DK" (Demmel-Koev) or "naive"

Value

A numeric or complex scalar or a bigq rational number.

References

F. Li, Y. Xue. Zonal polynomials and hypergeometric functions of quaternion matrix argument. Comm. Statist. Theory Methods, 38 (8), 1184-1206, 2009

See Also

ZonalQPol

Examples

lambda <- c(2,2)
ZonalQ(c(3,1), lambda)
ZonalQ(c(gmp::as.bigq(3),gmp::as.bigq(1)), lambda)
##
x <- c(3,1)
ZonalQ(x, c(1,1)) + ZonalQ(x, 2) # sum(x)^2
ZonalQ(x, 3) + ZonalQ(x, c(2,1)) + ZonalQ(x, c(1,1,1)) # sum(x)^3

jack documentation built on July 9, 2023, 7:09 p.m.