polyTop: Software for Computing Topology of Smooth Real Surfaces.

A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geometry computations from Bertini and Bertini real with topological computations in javaPlex to compute the Euler characteristic, genus, Betti numbers, and generators of the fundamental group of a smooth real surface. Several examples are used to demonstrate this new software.