MacMahon's partition analysis. VI: A new reduction algorithm (Q1600815)

In [Eur. J. Comb. 22, 887-904 (2001; Zbl 0979.05008)], the authors introduced \textit{Omega}, a computer algebra package that implements operators used in MacMahon's method of partition analysis. The paper under review provides an algorithmic improvement to the Omega package. This improvement involves a more general partial fraction decomposition than that used in the original package, which makes an algorithm more efficient and avoids handling roots of unity, with slow computation. The paper also includes a brief introduction to partition analysis and several applications, including the computation of the generating function for the number of magic pentagrams.