jack (version 5.3.0)

ZonalQ: Evaluation of quaternionic zonal polynomials

Description

Evaluates a quaternionic (or symplectic) zonal polynomial.

Usage

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

Value

A numeric or complex scalar or a bigq rational number.

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"

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