Singular points of real sextic curves

Abstract

Complete classifications of the individual types of singular points are given for irreducible real quartic curves, reducible real quartic curves, irreducible real quintic curves, reducible real quintic curves, irreducible real sextic curves, and reducible real sextic curves. These classifications are derived by using the computer algebra system Maple. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.