A Maple package for the Fast Computations of Certain Poincaré Series Introduced by Allan Berele in the Theory of Polynomial Identity Rings and Invariant Theory

By Shalosh B. Ekhad and Doron Zeilberger

Posted: Aug. 10, 2022

Abstract: This Maple package implements Allan Berele's constant-term expressions for certain Poincaré series called Cbar(n,k), described in his paper

Denominators for One Variable Poincaré series of generic matrices .

It arose in the theory of Polynomial Identity Rings and Invariant Theory, that thanks to Wilf-Zeilberger algorithmic proof theory can be used to derive linear recurrences for n=2 and n=3. This enables very fast computations of these series for many values of k. Alas, while the analogous recurrences exist for n=4 and above, finding them is currently beyond our meager computational powers.

Note: There is no accompanying article. Everything is contained in the Maple package and the output files.

Maple package

Sample Input and Output for Berele.txt

Persoanl Journal of SBE and Doron Zeilberger's Home Page

Papers of Doron Zeilberger's Home Page

Doron Zeilberger's Home Page