The mu-basis of a rational ruled surface

The mu-basis of a planar rational curve is a polynomial ideal basis compris ed of two polynomials that greatly facilitates computing the implicit equat ion of the curve. This paper defines a mu-basis for a rational ruled surfac e, and presents a simple algorithm for computing the mu-basis. The mu-basis consists of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linea r in x, y, z and degree mu and m - mu in s respectively, where m is the deg ree of the implicit equation. The implicit equation of the surface is then obtained by merely taking the resultant of p and q with respect to s, This implicitization algorithm is faster and/or more robust than previous method s. (C) 2001 Elsevier Science B.V, All rights reserved.