  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.
