Title | **Computing inhomogeneous Gröbner bases** |

Author(s) | Anna M. Bigatti, Massimo Caboara, Lorenzo Robbiano |

Type | Article in Journal |

Abstract | In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner bases via Buchberger’s Algorithm. In a nutshell, the idea is to extend the advantages of computing with homogeneous polynomials or vectors to the general case. When the input data are not homogeneous, we use as a main tool the procedure of a self-saturating Buchberger’s Algorithm. Another strictly related topic is treated later when a mathematical foundation is given to the sugar trick which is nowadays widely used in most of the implementations of Buchberger’s Algorithm. A special emphasis is also given to the case of a single grading, and subsequently some timings and indicators showing the practical merits of our approach. |

Keywords | Gröbner bases, Buchberger’s Algorithm |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717110001719 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 46 |

Number | 5 |

Pages | 498 - 510 |

Year | 2011 |

Note | Groebner Bases and Applications |

Edition | 0 |

Translation |
No |

Refereed |
No |