Connection Matrices in Macaulay2
Algebraic Geometry
2026-05-26 v2 Symbolic Computation
Abstract
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of finite holonomic rank, we implement the computation of the encoded system of linear PDEs in connection form with respect to an elimination term order that depends on a chosen positive weight vector. We also implement the gauge transformation for carrying out a change of basis over the field of rational functions. We demonstrate all implemented algorithms with examples.
Keywords
Cite
@article{arxiv.2504.01362,
title = {Connection Matrices in Macaulay2},
author = {Paul Görlach and Joris Koefler and Anna-Laura Sattelberger and Mahrud Sayrafi and Hendrik Schroeder and Nicolas Weiss and Francesca Zaffalon},
journal= {arXiv preprint arXiv:2504.01362},
year = {2026}
}