Numerical implicitization of parametric hypersurfaces with linear algebra, Artificial intelligence and symbolic computation

Abstract. We present a new method for implicitization of paramet-ric curves, surfaces and hypersurfaces using essentially numerical linear algebra. The method is applicable for polynomial, rational as well as trigonometric parametric representations. The method can also handle monoparametric families of parametric curves, surfaces and hypersur-faces with a small additional amount of human interaction. We illustrate the method with a number of examples. The eÆciency of the method compares well with the other available methods for implicitization.