Computing braids from approximate data
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910006222258176 |
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| author | Guillemot, Alexandre Lairez, Pierre |
| author_facet | Guillemot, Alexandre Lairez, Pierre |
| contents | We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under numerical uncertainty. Instead, we formalize an input model for approximate data, based on a separation predicate. It applies, for example, to paths obtained by tracking the roots of a parametrized polynomial with complex coefficients, thereby connecting certified path tracking outputs to exact braid computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23073 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing braids from approximate data Guillemot, Alexandre Lairez, Pierre Computational Geometry Symbolic Computation We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under numerical uncertainty. Instead, we formalize an input model for approximate data, based on a separation predicate. It applies, for example, to paths obtained by tracking the roots of a parametrized polynomial with complex coefficients, thereby connecting certified path tracking outputs to exact braid computation. |
| title | Computing braids from approximate data |
| topic | Computational Geometry Symbolic Computation |
| url | https://arxiv.org/abs/2601.23073 |