Implicitization of Rational Parametric Equations

Based on the Grobner basis method, we present algorithms for a complete solution of the following problems in the implicitization of a set of rational parametric equations. (1) To find a basis of the implicit prime ideal determined by a set of rational parametric equations. (2) To decide whether the parameters of a set of rational parametric equations are independent. (3) If the parameters of a set of rational parametric equations are not independent, to reparameterize the parametric equations so that the new parametric equations have independent parameters. (4) To compute the inversion maps of parametric equations, and as a consequence, to give a method to decide whether a set of parametric equations is proper. (5) In the case of algebraic curves, to find proper reparameterization for a set of improper parametric equations.

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