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.

翻译：实代数集的连通分量是半代数的，即它们由布尔公式描述，其原子为具有实系数的多项式约束。计算此类描述在光学系统设计和机器人学中具有前沿应用。本文设计了一种新算法，用于计算实代数曲线的此类半代数描述。值得注意的是，其复杂度低于已知最佳算法，后者需计算与研究中的实空间曲线同胚的图。