Faster multivariate integration in D-modules
This work addresses computational bottlenecks in holonomic integration for researchers in algebraic combinatorics and mathematical physics, though it is incremental as it builds on existing reduction techniques.
The authors tackled the problem of multivariate integration in D-modules by extending the Griffiths-Dwork reduction technique to holonomic systems, resulting in a new algorithm implemented in Julia that derived a previously unattainable differential equation for the generating series of 8-regular graphs.
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.