An implicitization algorithm with fewer variables Original Research Article

In this paper we present a general implicitization algorithm for rational parameterizations, using Gröbner Bases, which: (i) is valid for general parametric varieties (i.e. allowing both rational or polynomial parameterizations), (ii) computes the greatest ideal of polynomials vanishing over the variety and (iii) uses only as many variables as the number of parameters plus coordinates. We give examples of the performance of our algorithm in the CoCoa system, comparing the obtained results with other algorithms.