### Abstract

Let f_{1}, . . . , f_{s} ∈ K{double-struck}[x _{1}, . . . , x_{m}] 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}, . . . , x_{m}]/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}, . . . , f_{s} of degrees at most δ. We propose a method using Sylvester or Macaulay type resultant matrices of f_{1}, . . . , f_{s} 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 {M_{xi}|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 ^{m}_{K{double-struck}}.

Original language | English |
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Title of host publication | ISSAC'08 |

Subtitle of host publication | Proceedings of the 21st International Symposium on Symbolic and Algebraic Computation 2008 |

Pages | 125-132 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2008 |

Event | 21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 - Linz, Hagenberg, Austria Duration: Jul 20 2008 → Jul 23 2008 |

### Publication series

Name | Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC |
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### Other

Other | 21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 |
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Country | Austria |

City | Linz, Hagenberg |

Period | 7/20/08 → 7/23/08 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*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