Connection Matrices in Macaulay2
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913160632467456 |
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| author | Görlach, Paul Koefler, Joris Sattelberger, Anna-Laura Sayrafi, Mahrud Schroeder, Hendrik Weiss, Nicolas Zaffalon, Francesca |
| author_facet | Görlach, Paul Koefler, Joris Sattelberger, Anna-Laura Sayrafi, Mahrud Schroeder, Hendrik Weiss, Nicolas Zaffalon, Francesca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connection Matrices in Macaulay2 Görlach, Paul Koefler, Joris Sattelberger, Anna-Laura Sayrafi, Mahrud Schroeder, Hendrik Weiss, Nicolas Zaffalon, Francesca Algebraic Geometry Symbolic Computation 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. |
| title | Connection Matrices in Macaulay2 |
| topic | Algebraic Geometry Symbolic Computation |
| url | https://arxiv.org/abs/2504.01362 |