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arXiv · 2603.16283

Computing the connected components of real algebraic curves

Elisabetta Rocchi·Mohab Safey El Din
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Abstract

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.

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Elisabetta Rocchi, Mohab Safey El Din. 2026-03-17. Computing the connected components of real algebraic curves. https://arxiv.org/abs/2603.16283

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