Title | **Dimension-dependent bounds for Gröbner bases of polynomial ideals** |

Author(s) | Ernst W. Mayr, Stephan Ritscher |

Type | Article in Journal |

Abstract | Given a basis F of a polynomial ideal I in K [x_1, … ,x_n] with degrees deg(F) ≤ d , the degrees of the reduced Gröbner basis G w.r.t. any admissible monomial ordering are known to be double exponential in the number of indeterminates in the worst case, i.e. deg(G) = d^2^Θ(n). This was established in Mayr and Meyer (1982) andDubé (1990). We modify both constructions in order to give worst case bounds depending on the ideal dimension proving that deg(G) = d^n^Θ(1)2^Θ(r) for r -dimensional ideals (in the worst case). |

Keywords | Polynomial ideal, Ideal dimension, Regular sequence, Noether normalization, Cone decomposition |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717111002112 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 49 |

Number | 0 |

Pages | 78 - 94 |

Year | 2013 |

Note | The International Symposium on Symbolic and Algebraic Computation |

Edition | 0 |

Translation |
No |

Refereed |
No |