Title | **Implicitizing rational hypersurfaces using approximation complexes** |

Author(s) | Laurent Buse, Claude Marche |

Type | Article in Journal |

Abstract | We describe an algorithm for implicitizing rational hypersurfaces with at most a finite number of base points, based on a technique described in Busé, Laurent, Jouanolou, Jean-Pierre [2003. On the closed image of a rational map and the implicitization problem. J. Algebra 265, 312–357], where implicit equations are obtained as determinants of certain graded parts of an approximation complex. We detail and improve this method by providing an in-depth study of the cohomology of such a complex. In both particular cases of interest of curve and surface implicitization we also present algorithms which involve only linear algebra routines. |

Keywords | Implicitization, Base points, Syzygies, Approximation complexes |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S074771710500101X |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 40 |

Number | 4–5 |

Pages | 1150 - 1168 |

Year | 2005 |

Note | Applications of Computer Algebra (ACA) 2001 and 2002 ACA Applications of Computer Algebra (ACA) 2001 and 2002 |

Edition | 0 |

Translation |
No |

Refereed |
No |