Work

Complexity of Creative Telescoping for Bivariate Rational Functions

Year: 2013

Type: article

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.

DOI: 10.48550/arxiv.1301.5045

Authors: Bostan, Alin, Chen, Shaoshi, Chyzak, Frédéric, Li, Ziming

Institutions: Institut national de recherche en sciences et technologies du numérique, Academy of Mathematics and Systems Science

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Microsoft Research, National Natural Science Foundation of China

Award: G5932878250

OpenAlex ID: W2952199487

FWCI:

Cites: 9

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Related to: 10