Title | **Applying IsRewritten criterion on Buchberger algorithm** |

Author(s) | Amir Hashemi, Benyamin M.-Alizadeh |

Type | Article in Journal |

Abstract | Faugère’s F 5 algorithm is one of the fastest algorithms to compute Gröbner bases. It uses two criteria namely the F 5 criterion and the IsRewritten criterion to detect the useless critical pairs (see Faugère (2002) [8]). The IsRewritten criterion has been used in the F 5 algorithm, but it has not been explicitly declared in the related paper. In this paper, we give first a complete proof for the IsRewritten criterion and then using a signature structure on Buchberger’s algorithm, we apply this criterion on Buchberger’s algorithm. We have implemented a new algorithm (based on the above results) in Maple to compute a Gröbner basis of a general ideal and we evaluate its performance via some examples. |

Keywords | Gröbner bases, Buchberger’s algorithm, IsRewritten criterion |

ISSN | 0304-3975 |

URL |
http://www.sciencedirect.com/science/article/pii/S0304397511003495 |

Language | English |

Journal | Theoretical Computer Science |

Volume | 412 |

Number | 35 |

Pages | 4592 - 4603 |

Year | 2011 |

Edition | 0 |

Translation |
No |

Refereed |
No |