MacMahon’s Partition Analysis: The Omega Package

Authors: Andrews G.E.¹; Paule P.²; Riese A.³

Source: European Journal of Combinatorics, Volume 22, Number 7, October 2001 , pp. 887-904(18)

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Abstract:

In his famous book ‘Combinatory Analysis’ MacMahon introduced Partition Analysis (‘Omega Calculus’) as a computational method for solving problems in connection with linear homogeneous diophantine inequalities and equations. The object of this paper is to show that partition analysis is ideally suited for being implemented in computer algebra. To this end we have developed the computer algebra packageOmega. In addition to an introduction to basic facts of ‘Omega Calculus’, we present a number of applications that illustrate the usage of the package. Copyright 2001 Academic Press

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A. 2: Research Institute for Symbolic Computation, Johannes Kepler University Linz, A–4040 Linz, Austria 3: Research Institute for Symbolic Computation, Johannes Kepler University Linz, A–4040 Linz, Austria

Publication date: 2001-10-01