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.

翻译：本文研究了基于平面路径近似描述计算辫群的理论与实践问题。精确算法依赖于平面上点的字典序，这种排序在数值不确定性下是不稳定的。为此，我们基于分离谓词形式化了一种近似数据的输入模型。该模型适用于通过追踪复系数参数化多项式根所获得的路径，从而将认证路径追踪输出与精确辫群计算联系起来。