Article Dans Une Revue Journal of Symbolic Computation Année : 2026

Faster multivariate integration in D-modules

Résumé

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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Dates et versions

hal-05289785 , version 1 (30-09-2025)
hal-05289785 , version 2 (19-03-2026)

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Hadrien Brochet, Frédéric Chyzak, Pierre Lairez. Faster multivariate integration in D-modules. Journal of Symbolic Computation, 2026, 137, pp.102569. ⟨10.1016/j.jsc.2026.102569⟩. ⟨hal-05289785v2⟩
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