ZonalQPolR function

Quaternionic zonal polynomial

Returns the quaternionic (or symplectic) zonal polynomial.

ZonalQPolR(n, lambda, algorithm = "DK", basis = "canonical", exact = TRUE)

Arguments

• n: number of variables, a positive integer
• lambda: an integer partition, given as a vector of decreasing integers
• 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
• exact: logical, whether to get rational coefficients

Returns

A mvp multivariate polynomial (see mvp-package ), or a qspray multivariate polynomial if exact = TRUE and algorithm = "DK", or a character string if basis = "MSF".

Examples

ZonalQPolR(3, lambda = c(3,1), algorithm = "naive")
ZonalQPolR(3, lambda = c(3,1), algorithm = "DK")
ZonalQPolR(3, lambda = c(3,1), algorithm = "DK", exact = FALSE)
ZonalQPolR(3, lambda = c(3,1), algorithm = "naive", basis = "MSF")