Computing periods of rational integrals
Symbolic Computation
2023-06-12 v3 Algebraic Geometry
Abstract
A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period under consideration satisfies a linear differential equation, the Picard-Fuchs equation. I give a reduction algorithm that extends the Griffiths-Dwork reduction and apply it to the computation of Picard-Fuchs equations. The resulting algorithm is elementary and has been successfully applied to problems that were previously out of reach.
Keywords
Cite
@article{arxiv.1404.5069,
title = {Computing periods of rational integrals},
author = {Pierre Lairez},
journal= {arXiv preprint arXiv:1404.5069},
year = {2023}
}
Comments
To appear in Math. comp. Supplementary material at http://pierre.lairez.fr/supp/periods/