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Let $V$ be a closed subscheme of a projective space $\mathbb{P}^n$. We givean algorithm to compute the Chern-Schwartz-MacPherson class, Eulercharacteristic and Segre class of $ V$. The algorithm can be implemented usingeither symbolic or numerical methods. The algorithm is based on a new methodfor calculating the projective degrees of a rational map defined by ahomogeneous ideal. Using this result and known formulas for theChern-Schwartz-MacPherson class of a projective hypersurface and the Segreclass of a projective variety in terms of the projective degrees of certainrational maps we give algorithms to compute the Chern-Schwartz-MacPherson classand Segre class of a projective variety. Since the Euler characteristic of $V$is the degree of the zero dimensional component of theChern-Schwartz-MacPherson class of $V$ our algorithm also computes the Eulercharacteristic $\chi(V)$. Relationships between the algorithm developed hereand other existing algorithms are discussed. The algorithm is tested on severalexamples and performs favourably compared to current algorithms for computingChern-Schwartz-MacPherson classes, Segre classes and Euler characteristics.

An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties