This paper presents an algorithm to compute the topology of an algebraic space curve. This is a modified version of the previous algorithm. Furthermore, the authors also analyse the bit complexity of the algorithm, which is \(\widetilde{\cal O}\left( {{N^{20}}} \right)\), where N = max{d, τ}, d and τ are the degree bound and the bit size bound of the coefficients of the defining polynomials of the algebraic space curve. To our knowledge, this is the best bound among the existing work. It gains the existing results at least N². Meanwhile, the paper contains some contents of the conference papers (CASC 2014 and SNC 2014).

本文提出了一种计算代数空间曲线拓扑的算法。这是先前算法的修改版本。此外，作者还分析了算法的位复杂度，即\（\ widetilde {\ cal O} \ left（{{N ^ {20}}} \ right）\），其中N = max { d，τ }，d和τ是代数空间曲线的定义多项式的系数的度界和位大小界。就我们所知，这是现有工作之间的最佳界限。获得至少N ²的现有结果。同时，本文包含会议论文的某些内容（CASC 2014和SNC 2014）。