Creative telescoping for rational functions using the griffiths: dwork method

Authors:
Alin Bostan;Pierre Lairez;Bruno Salvy
Affiliations:
Inria, Saclay, France;Inria, Saclay, France;Inria, Lyon, France
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

Citing 8
Cited 0

An algorithm of constructing the integral of a module--an infinite dimensional analog of Gröbner basis

ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
A holonomic systems approach to special functions identities

Journal of Computational and Applied Mathematics
The method of creative telescoping

Journal of Symbolic Computation
An extension of Zeilberger's fast algorithm to general holonomic functions

Discrete Mathematics
Modern Computer Algebra

Modern Computer Algebra
Essentially optimal computation of the inverse of generic polynomial matrices

Journal of Complexity - Special issue: Foundations of computational mathematics 2002 workshops
Complexity of creative telescoping for bivariate rational functions

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Telescopers for rational and algebraic functions via residues

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of rational functions. This leads to bounds on the order and degree of the coefficients of the differential equation, and to the first complexity result which is single exponential in the number of variables. One of the important features of the algorithm is that it does not need to compute certificates. The approach is vindicated by a prototype implementation.