jack (version 5.3.0)

Zonal: Evaluation of zonal polynomials

Description

Evaluates a zonal polynomial.

Usage

Zonal(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

• Robb Muirhead. Aspects of multivariate statistical theory. Wiley series in probability and mathematical statistics. Probability and mathematical statistics. John Wiley & Sons, New York, 1982.

• Akimichi Takemura. Zonal Polynomials, volume 4 of Institute of Mathematical Statistics Lecture Notes – Monograph Series. Institute of Mathematical Statistics, Hayward, CA, 1984.

• Lin Jiu & Christoph Koutschan. Calculation and Properties of Zonal Polynomials. http://koutschan.de/data/zonal/

See Also

ZonalPol

Examples

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