论文信息 - On algorithms for real algebraic plane curves

On algorithms for real algebraic plane curves

During the last years several researchers have considered the problem of finding polynomial-time sequential algorithms for the computation of the topology of a real algebraic plane curve. Up till now, we can divide these algorithms into two main groups: those coding real algebraic numbers by means of isolating intervals (see for instance [3] and [7]) and those coding them a la Thom (see [9]). The aim of this note is to survey the state of the art as far as the second group is concerned. In particular we introduce two new such algorithms, one of which is, to our knowledge, the algorithm computing the topology of a real algebraic plane curve with the lowest running time, while the other one has been successfully implemented.

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