Title | **Gröbner bases and logarithmic -modules** |

Author(s) | Francisco Jesus Castro-Jimenez, Jose Maria Ucha-Enriquez |

Type | Article in Journal |

Abstract | Let C[x] = C[x_1, … ,x_n] be the ring of polynomials with complex coefficients and A n the Weyl algebra of order n over C . Elements in A n are linear differential operators with polynomial coefficients. For each polynomial f , the ring M = C[x] f of rational functions with poles along f has a natural structure of a left A n -module which is finitely generated by a classical result of I.N. Bernstein. A central problem in this context is how to find a finite presentation of M starting from the input f . In this paper we use Gröbner base theory in the non-commutative frame of the ring A n to compare M to some other A n -modules arising in Singularity Theory as the so-called logarithmic A n -modules. We also show how the analytic case can be treated with computations in the Weyl algebra if the input data f is a polynomial. |

Keywords | Gröbner bases, Weyl algebra, D -modules, Free divisors, Spencer divisors |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717105001355 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 41 |

Number | 3–4 |

Pages | 317 - 335 |

Year | 2006 |

Note | Logic, Mathematics and Computer Science: Interactions in honor of Bruno Buchberger (60th birthday) |

Edition | 0 |

Translation |
No |

Refereed |
No |