Using polynomial interpolation for implicitizing algebraic curves

A simple algorithm for finding the implicit equation of a rational plane al gebraic curve given by its parametric equations is presented. The algorithm is based on an efficient computation of the resultant by means of classica l bivariate polynomial interpolation. One of the main features of the used approach is the fact that it considerably reduces the problem of intermedia te expression swell, which is usually present in many computer algebra algo rithms. (C) 2001 Elsevier Science B.V. All rights reserved.