Real Parametrization of Algebraic Curves

There are various algorithms known for deciding the parametrizability (rationality) of a plane algebraic curve, and if the curve is rational, actually computing a parametrization. Optimality criteria such as low degrees in the parametrization or low degree field extensions are met by some parametrization algorithms. In this paper we investigate real curves. Given a parametrizable plane curve over the complex numbers, we decide whether it is in fact real. Furthermore, we discuss methods for actually computing a real parametrization for a parametrizable real curve.

• Type: Conference
• Year: 1998
• Where: AISC
• Authors: J. Rafael Sendra, Franz Winkler
• Keywords: AISC 1998, Artificial Intelligence, Parametrization Algorithms, Plane Algebraic Curve, Real Curve