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Complexity of Creative Telescoping for Bivariate Rational Functions

Abstract : The long-term goal initiated in this work is to obtain fast algorithms and implementations for definite integration in Almkvist and Zeilberger's framework of (differential) creative telescoping. Our complexity-driven approach is to obtain tight degree bounds on the various expressions involved in the method. To make the problem more tractable, we restrict to bivariate rational functions. By considering this constrained class of inputs, we are able to blend the general method of creative telescoping with the well-known Hermite reduction. We then use our new method to compute diagonals of rational power series arising from combinatorics.
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https://hal.inria.fr/hal-00780066
Contributor : Alin Bostan <>
Submitted on : Wednesday, January 23, 2013 - 10:06:20 AM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM

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  • HAL Id : hal-00780066, version 1
  • ARXIV : 1301.5045

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Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li. Complexity of Creative Telescoping for Bivariate Rational Functions. ISSAC'10 - International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.203-210. ⟨hal-00780066⟩

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