Title | **On the Computation of Comprehensive Boolean Gröbner Bases** |

Author(s) | Shutaro Inoue |

Type | Article in Conference Proceedings |

Abstract | We show that a comprehensive Boolean Gröbner basis of an ideal <em>I</em> in a Boolean polynomial ring B $(\bar A,\bar X)$ with main variables $\bar X$ and parameters $\bar A$ can be obtained by simply computing a usual Boolean Gröbner basis of <em>I</em> regarding both $\bar X$ and $\bar A$ as variables with a certain block term order such that $\bar X \gg \bar A$. The result together with a fact that a finite Boolean ring is isomorphic to a direct product of the Galois field $\mathbb{GF}_2$ enables us to compute a comprehensive Boolean Gröbner basis by only computing corresponding Gröbner bases in a polynomial ring over $\mathbb{GF}_2$. Our implementation in a computer algebra system Risa/Asir shows that our method is extremely efficient comparing with existing computation algorithms of comprehensive Boolean Gröbner bases. |

Length | 12 |

ISBN | 978-3-642-04102-0 |

URL |
http://dx.doi.org/10.1007/978-3-642-04103-7_13 |

Language | English |

Series | CASC '09 |

Pages | 130--141 |

Publisher | Springer-Verlag |

Address | Berlin, Heidelberg |

Year | 2009 |

Translation |
No |

Refereed |
No |

How published | CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing |

Conferencename | CASC '09, 11th International Workshop on Computer Algebra in Scientific Computing |