Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Symbolic Summation: Algorithms and Missed Opportunities
Peter Paule, RISC, Johannes Kepler University, Austria
Friday, September 13, 2002, at U. of Waterloo.

Abstract:

The problem of simplifying complicated sum expressions arises not only in special functions but in many mathematical fields. Nevertheless, symbolic algorithms that assist in this task do not have a very long history.

The starting point of symbolic summation with the computer is Gosper's algorithm (1978), a decision procedure for indefinite hypergeometric summation. Despite being a first breakthrough, for a long time its applicability has been considered as quite restricted since most hypergeometric summations arising in practice are definite ones. Zeilberger's 'creative telescoping' (1990) dissolved this limitation. Since then symbolic summation has turned into an active subarea of computer algebra on its own.

This talk presents a survey on algorithms and methods for definite (multiple) sums along a historical chain of missed opportunities.

 

Last modified on Sunday, 04 November 2012, at 20:42 hours.