标题： 从近似数据中计算辫子 显示英文标题

标题： Computing braids from approximate data

摘要： 我们研究了计算由平面上路径的近似描述所定义的辫子的理论和实际方面。 精确算法依赖于平面上点的字典序排列，在数值不确定性下是不稳定的。 相反，我们形式化了一个基于分离谓词的近似数据输入模型。 例如，它适用于通过跟踪具有复系数的参数多项式的根得到的路径，从而将认证的路径跟踪输出与精确的辫子计算联系起来。 显示英文摘要

摘要： We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under numerical uncertainty. Instead, we formalize an input model for approximate data, based on a separation predicate. It applies, for example, to paths obtained by tracking the roots of a parametrized polynomial with complex coefficients, thereby connecting certified path tracking outputs to exact braid computation.