ZonalQPolR

Returns the quaternionic (or symplectic) zonal polynomial.

Schur polynomials appear in combinatorics and zonal
polynomials appear in random matrix theory. They are particular cases
of Jack polynomials. This package allows to compute these polynomials
and other symmetric multivariate polynomials: flagged Schur
polynomials, factorial Schur polynomials, t-Schur polynomials,
Hall-Littlewood polynomials, Macdonald polynomials, and modified
Macdonald polynomials. In addition, it can compute the Kostka-Jack
numbers, the Kostka-Foulkes polynomials, the Kostka-Macdonald
polynomials, and the Hall polynomials. Mainly based on Demmel &
Koev's paper (2006) <doi:10.1090/S0025-5718-05-01780-1> and
Macdonald's book (1995) <doi:10.1093/oso/9780198534891.003.0001>.

Stc3<a9>phane Laurent

jack

Jack, Zonal, Schur, and Other Symmetric Polynomials

Stéphane Laurent

ZonalQPolR function

<dl><dt>n</dt>
<dd>number of variables, a positive integer</dd>
<dt>lambda</dt>
<dd>an integer partition, given as a vector of decreasing
integers</dd>
<dt>algorithm</dt>
<dd>the algorithm used, either <code>"DK"</code> or <code>"naive"</code></dd>
<dt>basis</dt>
<dd>the polynomial basis for <code>algorithm = "naive"</code>,
either <code>"canonical"</code> or <code>"MSF"</code> (monomial symmetric functions);
for <code>algorithm = "DK"</code> the canonical basis is always used and
this parameter is ignored</dd>
<dt>exact</dt>
<dd>logical, whether to get rational coefficients</dd></dl>

Arguments

Quaternionic zonal polynomial — ZonalQPolR

<dl>

<dt>n</dt>
<dd>number of variables, a positive integer</dd>


<dt>lambda</dt>
<dd>an integer partition, given as a vector of decreasing
integers</dd>


<dt>algorithm</dt>
<dd>the algorithm used, either <code>"DK"</code> or <code>"naive"</code></dd>


<dt>basis</dt>
<dd>the polynomial basis for <code>algorithm = "naive"</code>,
either <code>"canonical"</code> or <code>"MSF"</code> (monomial symmetric functions);
for <code>algorithm = "DK"</code> the canonical basis is always used and
this parameter is ignored</dd>


<dt>exact</dt>
<dd>logical, whether to get rational coefficients</dd>

</dl>

ZonalQPolR: Quaternionic zonal polynomial

Description

Usage

Value

Arguments

Examples