The authors show how to use the Maple symbolic manipulation system to manipulate descent algebras. They base their representation on a linear basis of quasi-idempotents, which, with some manipulations, results in expressions that can be expressed and manipulated with Maple. Their techniques are not specific to Maple, and can be implemented in Mathematica and Gauss.

Given this technique, the authors present a variety of Maple expressions and functions for manipulating descent algebras. A variety of mathematical structures are presented, along with derivations that result in expressions expressible in Maple. All in all, this work is a nice example of mapping abstract algebra into a symbolic manipulation system.