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arXiv · 2504.01362

Connection Matrices in Macaulay2

Paul Görlach·Joris Koefler·Anna-Laura Sattelberger·Mahrud Sayrafi·Hendrik Schroeder·Nicolas Weiss·Francesca Zaffalon
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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.

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Paul Görlach, Joris Koefler, Anna-Laura Sattelberger, Mahrud Sayrafi, Hendrik Schroeder, Nicolas Weiss, Francesca Zaffalon. 2025-04-02. Connection Matrices in Macaulay2. https://arxiv.org/abs/2504.01362

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