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 $$\widetilde{\cal O}\left( {{N^{20}}} \right)$$ O ˜ ( N 20 ) , 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 N 2 . Meanwhile, the paper contains some contents of the conference papers (CASC 2014 and SNC 2014).

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