Certifying Galois/monodromy Actions via Homotopy Graphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917351251771392 |
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| author | Duff, Timothy Lee, Kisun |
| author_facet | Duff, Timothy Lee, Kisun |
| contents | We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guarantee the correctness of the monodromy action produced by the algorithm, and builds on previous ``homotopy graph" frameworks. We conduct extensive experiments with an implementation of this algorithm, which we have used to certify properties of several notable Galois/monodromy groups which arise in several examples drawn from pure and applied mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17288 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Certifying Galois/monodromy Actions via Homotopy Graphs Duff, Timothy Lee, Kisun Algebraic Geometry Symbolic Computation 65H14 We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guarantee the correctness of the monodromy action produced by the algorithm, and builds on previous ``homotopy graph" frameworks. We conduct extensive experiments with an implementation of this algorithm, which we have used to certify properties of several notable Galois/monodromy groups which arise in several examples drawn from pure and applied mathematics. |
| title | Certifying Galois/monodromy Actions via Homotopy Graphs |
| topic | Algebraic Geometry Symbolic Computation 65H14 |
| url | https://arxiv.org/abs/2603.17288 |