Computation of the topology of real algebraic space curves

Abstract

An algorithm for computing the topology of a real algebraic space curve C , implicitly defined as the intersection of two surfaces, is presented. Given C , the algorithm generates a space graph which is topologically equivalent to the real variety on the Euclidean space. The algorithm is based on the computation of the graphs of at most two projections of C . For this purpose, we introduce the notion of space general position for space curves, we show that any curve under the above conditions can always be linearly transformed to be in general position, and we present effective methods for checking whether space general position has been reached.