Title：                 Efficient Rational Creative Telescoping

Speaker：           Huang Hui  ( University of Waterloo )

Time&Venue：   2019.08.05  16:00pm  N226

Abstract:：          In this talk, we present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. This is the first step towards the long-term goal of developing fast creative telescoping algorithms for special functions that circumvent intermediate expression swell. As with the reduction-based approach, our algorithm also has the nice feature that the computation of a telescoper is independent of its certificate. Moreover, our algorithm uses a sparse representation of the certificate, which allows to be more easily manipulated and analyzed without knowing the precise expanded form. This sparse representation hides any potential exponential expression swell until the final (and optional) expansion. A complexity analysis, along with a Maple implementation, suggests that our algorithm has better theoretical and practical performances than the reduction-based approach when restricted to the rational case. This is joint work with M. Giesbrecht, G. Labahn and E. Zima.