MacMahon’s Partition Analysis: The Omega Package

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.