On the Complexity of Computing the Topology of Real Algebraic Space Curves

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 O similar to(N-20), where N = max{d, tau}, d and tau 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 N-2. Meanwhile, the paper contains some contents of the conference papers (CASC 2014 and SNC 2014).

Automated summary

The paper presents an algorithm for computing the topology of an algebraic space curve, which is a modified version of a previous algorithm. The authors also analyze the bit complexity of the algorithm, which has the best bounds among existing work. Additionally, the paper includes content from conference papers CASC 2014 and SNC 2014.