Numerically Computing Galois Groups of Minimal Problems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911054704934912 |
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| author | Duff, Timothy |
| author_facet | Duff, Timothy |
| contents | I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely "Random Sampling and Consensus", aka "RanSaC".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerically Computing Galois Groups of Minimal Problems Duff, Timothy Computer Vision and Pattern Recognition Symbolic Computation Algebraic Geometry 68W30 I discuss a seemingly unlikely confluence of topics in algebra, numerical computation, and computer vision. The motivating problem is that of solving multiples instances of a parametric family of systems of algebraic (polynomial or rational function) equations. No doubt already of interest to ISSAC attendees, this problem arises in the context of robust model-fitting paradigms currently utilized by the computer vision community (namely "Random Sampling and Consensus", aka "RanSaC".) This talk will give an overview of work in the last 5+ years that aspires to measure the intrinsic difficulty of solving such parametric systems, and makes strides towards practical solutions. |
| title | Numerically Computing Galois Groups of Minimal Problems |
| topic | Computer Vision and Pattern Recognition Symbolic Computation Algebraic Geometry 68W30 |
| url | https://arxiv.org/abs/2507.10407 |