Fast Computation of the Entries of the Bezout and Dixon Resultants
by
Ron Goldman
Rice University
Coauthors: Eng-Wee Chionh, Ming Zhang

The Dixon resultant for three bivariate polynomials of bidegree (m, n) is the most commonly used resultant formulation for investigating tensor product surfaces. But while in principle the Dixon resultant is easy to construct from Cayley's determinant device, in practice the entries of the Dixon resultant are complicated expressions in the coefficients of the original three polynomials and explicit formulas for these expression are difficult to compute. Here we provide a simple recursive algorithm for calculating the entries of the Dixon resultant. We introduce this procedure first for the Bezout resultant of two univariate polynomials, and then show how this technique extends to three bivariate polynomials of bidegree (m, n).

Date received: December 17, 1998