An application of Groebner bases to planarity of intersection of surfaces

Abstract

In this paper we use Groebner bases theory in order to determine planarity of intersections of two algebraic surfaces in ${\mathbf{R}}^3$. We specially considered plane sections of certain type of conoid which has a cubic egg curve as one of the directrices. The paper investigates a possibility of conic plane sections of this type of conoid.