Efficient Rational Creative Telescoping
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We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approach, our algorithm 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 it to be easily manipulated and analyzed without knowing the precise expanded form. This representation hides potential expression swell until the final (and optional) expansion, which can be accomplished in time polynomial in the size of the expanded certificate. A complexity analysis, along with a Maple implementation, suggests that our algorithm has better theoretical and practical performance than the reduction-based approach in the rational case.
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