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