Title | **Hilbert Stratification and Parametric Gröbner Bases** |

Author(s) | Laureano Gonzalez-Vega, Carlo Traverso, Alberto Zanoni |

Type | Article in Conference Proceedings |

Abstract | In this paper we generalize a method to analyze inhomogeneous polynomial systems containing parameters. In particular, the Hilbert function is used as a tool to check that the specialization of a “generic” Gröbner basis of the parametric polynomial system (computed in a polynomial ring having both parameters and unknowns as variables) is a Gröbner basis of the specialized system. Extending the analysis, we can also build the so-called Hilbert stratification of the associated variety. We classify the possible specializations according to the value of the Hilbert function of the specialized system. Some computation examples with the PoSSoLib are reported. |

Keywords | Gröbner bases, Hilbert function, Specialization |

ISBN | 3-540-28966-6 |

Language | English |

Journal | Lecture Notes in Computer Science |

Volume | 3718 |

Pages | 220-235 |

Publisher | Springer |

Year | 2005 |

Editor | Victor G. Ganzha, Ernst W. Mayr, Evgenii V. Vorozhtsov |

Edition | 0 |

Translation |
No |

Refereed |
No |

Book | Computer Algebra in Scientific Computing: 8th International Workshop, CASC 2005, Kalamata, Greece, September 12-16, 2005. Proceedings |

Conferencename | Computer Algebra in Scientific Computing: 8th International Workshop, CASC 2005 |