Implicitization using univariate resultants
Rational curves and surfaces can either be represented implicitly by polynomial equations, or parametrically by rational parametrizations. Transforming one representation into the other is a problem near the top of the list in constructive algebraic geometry. It is also the source for a variety of symbolic algebraic and also numerical algorithms. Implicitization -- transforming a parametric representation into an implicit one -- is a problem in elimination theory; the rational relation between the space coordinates and the parameters of the variety are first transformed into polynomial ones, and then we want to have relations only between the space coordinates. Gröbner bases, resultants, and any other methods in elimination theory may be employed. In this paper the authors present a specific resultant based approach to the implicitization of a certain class of space curves and surfaces. No formal complexity analysis is given. But an experimental implementation seems to support the claim to lower computational complexity.
scientific article; zbMATH DE number 5857558