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.