Moment matrices, trace matrices and the radical of ideals

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Let f₁,...,fₛ ∈ K[x₁,...,xₘ] be a system of polynomials generating a zero-dimensional ideal, where K is an arbitrary algebraically closed field. Assume that the factor algebra =K[x₁,...,xₘ]/ is Gorenstein and that we have a bound δ>0 such that a basis for can be computed from multiples of f₁,...,fₛ of degrees at most δ. We propose a method using Sylvester or Macaulay type resultant matrices of f₁,...,fₛ and J, where J is a polynomial of degree δ generalizing the Jacobian, to compute moment matrices, and in particular matrices of traces for. These matrices of traces in turn allow us to compute a system of multiplication matrices {Mₓᵢ|i=1,...,m} of the radical √, following the approach in the previous work by Janovitz-Freireich, Rónyai and Szántó. Additionally, we give bounds for δ for the case when has finitely many projective roots in Pᵐ.