"Contributions to MacMahon's Partition Analysis"
, Serie Johannes Kepler University, 1-2009
Contributions to MacMahon's Partition Analysis
Sprache des Titels:
About a century ago P. A. MacMahon introduced Partition Analysis as a method for solving problems in connection with systems of linear Diophantine inequalities and equations. Due to its arithmetical complexity the method lay dorment until G. E. Andrews, P. Paule and A. Riese discovered that it could be implemented in today's computer algebra systems and presented their Omega package written in Mathematica. Inspired by their work, Guo-Niu Han was able to derive an algorithm for more general expressions than those covered with the Omega package, which resulted in his GenOmega package written in Maple. In this thesis we present an account of these accomplishments and introduce the new GenOmega package which was implemented in the course of the thesis. This new GenOmega package is written in Mathematica and is also based on Han's algorithm but is more general than the Maple version.