ALGORITHMS FOR REAL NUMERICAL VARIETIES WITH APPLICATION TO PARAMETERIZING QUADRATIC SURFACE INTERSECTION CURVES

Abstract

A numerical method for analyzing and parameterizing quadratic surface intersection curves (QSIC) is proposed. This method is based on numerical fractional linear transformations, numerical irreducible decomposition and a numerical version of a classical method for replacing an irreducible QSIC with a numerically birationally equivalent cubic plane curve. Ultimately each component of the QSIC is parameterized by a plane curve of the form $y=u(x)$ or $y^2=u(x)$ where $u(x)$ is a numerical polynomial of degree $3$ or less.