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arXiv · 2504.12724

Faster multivariate integration in D-modules

Hadrien Brochet·Frédéric Chyzak·Pierre Lairez
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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.

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Hadrien Brochet, Frédéric Chyzak, Pierre Lairez. 2025-04-17. Faster multivariate integration in D-modules. https://arxiv.org/abs/2504.12724

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