Moment matrices, trace matrices and the radical of ideals

Itnuit Janovitz-Freireich, Ágnes Szántó, Bernard Mourrain, Lajos Rónyai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Let f1, . . . , fs ∈ K{double-struck}[x 1, . . . , xm] be a system of polynomials generating a zero-dimensional ideal I, where K{double-struck} is an arbitrary algebraically closed field. Assume that the factor algebra. A = K{double-struck}[x 1, . . . , xm]/I is Gorenstein and that we have a bound δ > 0 such that a basis for A can be computed from multiples of f 1, . . . , 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 A. These matrices of traces in turn allow us to compute a system of multiplication matrices {Mxi|i = 1, . . . , m} of the radical √I, following the approach in the previous work by Janovitz-Freireich, Rónyai and Szántó. Additionally, we give bounds for δ for the case when I has finitely many projective roots in ℙ mK{double-struck}.

Original languageEnglish
Title of host publicationISSAC'08
Subtitle of host publicationProceedings of the 21st International Symposium on Symbolic and Algebraic Computation 2008
Pages125-132
Number of pages8
DOIs
Publication statusPublished - 2008
Event21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 - Linz, Hagenberg, Austria
Duration: Jul 20 2008Jul 23 2008

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Other

Other21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008
CountryAustria
CityLinz, Hagenberg
Period7/20/087/23/08

Keywords

  • Matrices of traces
  • Moment matrices
  • Radical ideal
  • Solving polynomial systems

ASJC Scopus subject areas

  • Mathematics(all)

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    Janovitz-Freireich, I., Szántó, Á., Mourrain, B., & Rónyai, L. (2008). Moment matrices, trace matrices and the radical of ideals. In ISSAC'08: Proceedings of the 21st International Symposium on Symbolic and Algebraic Computation 2008 (pp. 125-132). (Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC). https://doi.org/10.1145/1390768.1390788