Faster multivariate integration in D-modules

2025/04/17 by Hadrien Brochet, Frédéric Chyzak, Brochet, Hadrien +3 · 1 voice · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Computer and information sciences #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC

paper · pdf · doi:10.48550/arxiv.2504.12724

openalex publication_date 2025/04/17 · arxiv published 2025/04/17 · openalex created_date 2025/10/10 · arxiv updated 2026/03/19 · openalex updated_date 2026/07/28

Abstract

We present a new algorithm for solving the reduction problem in the context of holonomic integrals, which in turn provides an approach to integration with parameters. Our method extends the Griffiths--Dwork reduction technique to holonomic systems and is implemented in Julia. While not yet outperforming creative telescoping in D-finite cases, it enhances computational capabilities within the holonomic framework. As an application, we derive a previously unattainable differential equation for the generating series of 8-regular graphs.

Citations

• Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach
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Cited by

• Differential Space of Feynman Integrals: Annihilators and D-module

Discussions

• Hadrien Brochet, Fr\'ed\'eric Chyzak, Pierre Lairez: Faster multivariate integration in D-modules https://arxiv.org/abs/2504.12724 https://arxiv.org/pdf/2504.12724 https://arxiv.org/html/2504.12724 [bsky, 0 points, 1 comments]

Related

• D-Modules and Holonomic Functions
• Computing a holonomic submodule of the partial Weyl closure
• Differential Equations for Moving Hyperplane Arrangements
• Comprehensive Restriction Algorithm for Hypergeometric Systems
• Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm