Resultants and Moving Surfaces

We prove a conjectured relationship among resultants and the determinants arising in the formulation of the method of moving surfaces for computing the implicit equation of rational surfaces formulated by Sederberg. In addition, we extend the validity of this method to the case of not properly parametrized surfaces without base points.Comment: 21 pages, LaTex, uses academic.cls. To appear: Journal of Symbolic Computatio

Subresultants and Generic Monomial Bases

Given n polynomials in n variables of respective degrees d_1,...,d_n, and a set of monomials of cardinality d_1...d_n, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in n variables modulo the ideal generated by the system of polynomials. This approach allows us to clarify the algorithms for the Bezout construction of the resultant.Comment: 22 pages, uses elsart.cls. Revised version accepted for publication in the Journal of Symbolic Computatio

Explicit formulas for the multivariate resultant

We present formulas for the homogenous multivariate resultant as a quotient of two determinants. They extend classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the given polynomials and coefficients of their Bezoutian. These formulas can also be viewed as an explicit computation of the morphisms and the determinant of a resultant complex.Comment: 30 pages, Late

A matrix-based approach to properness and inversion problems for rational surfaces

We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.Comment: 12 pages, latex, revised version accepted for publication in the Journal AAEC