Parallel Computation and Indefinite Summation: a MAPLE Application for the Rational Case

The problem of computing a closed form for sums of special functions arises in many parts of mathematical and computer science, especially in combinatorics and complexity analysis. Here we discuss two algorithms for indefinite summation of rational functions, due to Abramov (1975) and Paule (1993). We describe some improvements and a parallel implementation on a workstation network in MAPLE (read: parallel Maple). Our best implementation achieves a speedup of up to eight over the fastest available sequential implementation. Finally, further applications of parallel computing in this field are outlined.