Creative telescoping for rational functions using the Griffiths-Dwork method

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 simply 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.

Cited by in corpus (17)

• Computing periods of rational integrals
• Creative Telescoping for Holonomic Functions
• Multiple binomial sums
• Algorithms for minimal Picard-Fuchs operators of Feynman integrals
• Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Functions
• New Bounds for Hypergeometric Creative Telescoping
• Tableau sequences, open diagrams, and Baxter families
• Efficient Algorithms for Mixed Creative Telescoping
• Computing the volume of compact semi-algebraic sets
• Diagonals of rational functions, pullbacked 2F1 hypergeometric functions and modular forms (unabrigded version)
• Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems
• A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
• Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables
• Mahler discrete residues and summability for rational functions
• Effective homology and periods of complex projective hypersurfaces
• A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line
• A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping