Jack: Evaluation of Jack polynomials

In jack: Jack, Zonal, and Schur Polynomials

Evaluation of Jack polynomials

Description

Evaluates a Jack polynomial.

Usage

Jack(x, lambda, alpha, algorithm = "DK")

Arguments

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

Value

A numeric or complex scalar or a bigq rational number.

References

• I.G. Macdonald. Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1995.

• J. Demmel & P. Koev. Accurate and efficient evaluation of Schur and Jack functions. Mathematics of computations, vol. 75, n. 253, 223-229, 2005.

• Jack polynomials. https://www.symmetricfunctions.com/jack.htm

See Also

JackPol

Examples

lambda <- c(2,1,1)
Jack(c(1/2, 2/3, 1), lambda, alpha = 3)
# exact value:
Jack(c(gmp::as.bigq(1,2), gmp::as.bigq(2,3), gmp::as.bigq(1)), lambda,
     alpha = gmp::as.bigq(3))

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