In his famous book ldquoCombinatory Analysisrdquo MacMahon introduced Partition Analysis (ldquoOmega Calculusrdquo) as a computational method for solving problems in connection with linear diophantine inequalities and equations. The technique has recently been given a new life by G.E. Andrews and his coauthors, who had the idea of marrying it with the tools of to-dayrsquos Computer Algebra. The theory consists of evaluating a certain type of rational function of the form A(lambda)-1 B(1/lambda)-1 by the MacMahon OHgr operator. So far, the case where the two polynomials A and B are factorized as products of polynomials with two terms has been studied in details. In this paper we study the case of arbitrary polynomials A and B. We obtain an algorithm for evaluating the OHgr operator using the coefficients of those polynomials without knowing their roots. Since the program efficiency is a persisting problem in several-variable polynomial Calculus, we did our best to make the algorithm as fast as possible. As an application, we derive new combinatorial identities.
