Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter
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Given a family of algebraic surfaces, implicitly defined, depending on a parameter t, here we provide an algorithm for computing the different shapes arising in the family. The algorithm decomposes the real line into finitely many pieces (points and intervals) so that over each interval the shape is invariant, in the sense that the topology of the family can be described by means of the same simplicial complex. As a consequence, by applying known algorithms (, , , ) the different shapes in the family can be computed. The algorithm is due to a generalization of the ideas in  to the surface case.
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