MUTIVARIATE POLYNOMIALS, DUALITY AND STRUCTURED MATRICES

BERNARD MOURRAIN VICTOR Y. PAN

Abstract. We study multivariate Bezoutians and other structured matrices, dual spaces of linear maps on a polynomial ring, and algebraic residues. By combining various old and new techniques developed in this study, we obtain a better insight into the major problems of multivariate polynomial computations and improve substantially the known techniques of the study of these major problems. From algorithmic point, we yield acceleration by order of magnitude of the known methods for some fundamental problems of solving multivariate polynomial systems of equations.