Calculations with Simplicial and Cubical Groups in AXIOM

Work on calculations with simplicial and cubical groups in AXIOM was carried out using loan equipment and software from IBM UK and guidance from L A Lambe. We report on the results of this work, and present the AXIOM code written by the second author during this period. This includes an implementation of the monoids which model cubes and simplices, together with a new AXIOM category of near-rings with which to carry out non-abelian calculations. Examples of the use of this code in interactive AXIOM sessions are also given.