论文标题
Urysohn行动：通过多项式分开半ge
Urysohn in action: separating semialgebraic sets by polynomials
论文作者
论文摘要
拓扑的经典结果称为Uryshon的引理，认为存在一个在足够规则的拓扑空间中的两个不连接封闭组的连续分离器。在这项工作中，我们在实际代数几何形状的背景下搜索了该分离器的建设性和高效。也就是说，给定两个紧凑的脱节基本的半隔板集，其中包含在$ n $维盒中，我们提供了一种算法，该算法计算出在第一组中大于或等于1的分离多项式的算法，第二组中的分离算数大于或等于0。
A classical result from topology called Uryshon's lemma asserts the existence of a continuous separator of two disjoint closed sets in a sufficiently regular topological space. In this work we make a search for this separator constructive and efficient in the context of real algebraic geometry. Namely, given two compact disjoint basic semialgebraic sets which are contained in an $n$-dimensional box, we provide an algorithm that computes a separating polynomial greater than or equal to 1 on the first set and less than or equal to 0 on the second one.
