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We present an algorithm for the symbolic and numerical computation of thedegrees of the Chern-Schwartz-MacPherson classes of a closed subvariety ofprojective space P^n. As the degree of the top Chern-Schwartz-MacPherson classis the topological Euler characteristic, this also yields a method to computethe topological Euler characteristic of projective varieties. The method isbased on Aluffi's symbolic algorithm to compute degrees ofChern-Schwartz-MacPherson classes, a symbolic method to compute degrees ofSegre classes, and the regenerative cascade by Hauenstein, Sommese and Wampler.The new algorithm complements the existing algorithms. We also give an examplefor using a theorem by Huh to compute an invariant from algebraic statistics,the maximum likelihood degree of an implicit model.

An algorithm for computing the topological Euler characteristic of complex projective varieties