Computation of topological invariants for real projective surfaces with isolated singularities

Given a real algebraic surface S   in RP3RP3, we propose a procedure to determine the topology of S   and to compute non-trivial topological invariants for the pair (RP3,S)(RP3,S) under the hypothesis that the real singularities of S are isolated. In particular, starting from an implicit equation of the surface, we compute the number of connected components of S, their Euler characteristics and the labeled 2-adjacency graph of the surface.