Automatic Proofs of Identities

Abstract

In the past 30 years, computer algebra has made a lot of progress in the design of algorithms operating on mathematical objects. In particular, a few simple but fruitful ideas make it possible to compute sums or integrals of a wide variety of functions. Early work concentrated on hypergeometric identities. This was generalized by Zeilberger to deal with what he called "holonomic" systems. Recently, we generalized this further In a joint work with Chyzak and Kauers so that even more functions and sequences can be handled automatically. The talk will focus on the basic principles that underly all these algorithms."

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