Computing the connected components of real algebraic curves
Symbolic Computation
2026-03-18 v1 Algebraic Geometry
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.
Cite
@article{arxiv.2603.16283,
title = {Computing the connected components of real algebraic curves},
author = {Elisabetta Rocchi and Mohab Safey El Din},
journal= {arXiv preprint arXiv:2603.16283},
year = {2026}
}