Hermite Reduction and Creative Telescoping for Hyperexponential Functions

Abstract : We present a reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive decomposition and allows to decide hyperexponential integrability. Based on this reduction algorithm, we design a new method to compute minimal telescopers for bivariate hyperexponential functions. One of its main features is that it can avoid the costly computation of certificates. Its implementation outperforms Maple's function DEtools[Zeilberger]. Moreover, we derive an order bound on minimal telescopers, which is more general and tighter than the known one.
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https://hal.inria.fr/hal-00780067
Contributor : Alin Bostan <>
Submitted on : Wednesday, January 23, 2013 - 10:08:14 AM
Last modification on : Wednesday, August 21, 2019 - 10:38:02 AM

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Alin Bostan, Shaoshi Chen, Frédéric Chyzak, Ziming Li, Guoce Xin. Hermite Reduction and Creative Telescoping for Hyperexponential Functions. ISSAC'13 - 38th International Symposium on Symbolic and Algebraic Computation, Northeastern University, Boston, Massachusetts, USA, Jul 2013, Boston, United States. pp.77-84, ⟨10.1145/2465506.2465946⟩. ⟨hal-00780067⟩

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