Moment matrices, trace matrices and the radical of ideals

  • Authors:

  • Itnuit Janovitz-Freireich;Agnes Szántó;Bernard Mourrain;Lajos Ronyai

  • Affiliations:

  • North Carolina State University, Raleigh, NC, USA;North Carolina State University, Raleigh, NC, USA;GALAAD INRIA, Sophia Antipolis, France;MTA SZTAKI, Budapest, Hungary

  • Venue:
  • Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
  • Year:
  • 2008

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Abstract

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