Towards computing vector partition functions by iterated partial fraction decomposition

We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an algorithm to compute the numerators in their partial fraction decomposition “formally,” i.e., as a formal expression in the parameter. We also analyze the type of generalized rational functions that appear during the execution of an algorithm based on iterated partial fraction decomposition and explain how to handle these objects.