Computing the connected components of real algebraic curves
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911522012266496 |
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| author | Rocchi, Elisabetta Din, Mohab Safey El |
| author_facet | Rocchi, Elisabetta Din, Mohab Safey El |
| contents | Connected components of real algebraic sets are semi-algebraic, i.e. they are described by a boolean formula whose atoms are polynomial constraints with real coefficients. Computing such descriptions finds topical applications in optical system design and robotics. In this paper, we design a new algorithm for computing such semi-algebraic descriptions for real algebraic curves. Notably, its complexity is less than the best known one for computing a graph which is isotopic to the real space curve under study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16283 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing the connected components of real algebraic curves Rocchi, Elisabetta Din, Mohab Safey El Symbolic Computation Algebraic Geometry Connected components of real algebraic sets are semi-algebraic, i.e. they are described by a boolean formula whose atoms are polynomial constraints with real coefficients. Computing such descriptions finds topical applications in optical system design and robotics. In this paper, we design a new algorithm for computing such semi-algebraic descriptions for real algebraic curves. Notably, its complexity is less than the best known one for computing a graph which is isotopic to the real space curve under study. |
| title | Computing the connected components of real algebraic curves |
| topic | Symbolic Computation Algebraic Geometry |
| url | https://arxiv.org/abs/2603.16283 |