Automatic parameterization of rational curves and surfaces III: Algebraic plane curves

Abstract

We present algorithms to compute the genus and rational parametric equations, for implicitly defined irreducible plane algebraic curves of arbitrary degree. Rational parameterizations exist for all irreducible algebraic curves of genus 0. The genus is computed by a complete analysis of the singularities of plane algebraic curves, using affine quadratic transformations. The rational parameterization techniques, essentially, reduce to solving symbolically systems of homogeneous linear equations and the computation of polynomial resultants.