Consider a system of polynomials generating a zero-dimensional ideal I. We study the computation of matrices of traces for the factor algebra A, i.e. matrices with entries which are trace functions of the roots of I. Such matrices of traces in turn allow us to compute a system of multiplication matrices of the radical I. We first propose a method using Macaulay type resultant matrices to compute moment matrices, and in particular matrices of traces for A. We prove bounds on the degrees needed for the Macaulay matrix in the case when I has finitely many projective roots. We also extend previous results which work only for the case where A is Gorenstein to the non-Gorenstein case. The second proposed method uses Bezoutian matrices to compute matrices of traces of A. This second method also works if we have higher dimensional components at infinity. A new explicit description of the generators of the radical are given in terms of Bezoutians.
This work was done in collaboration with Bernard Mourrain, Lajos Ronyai and Agnes Szanto.