Title | **On inverse systems and squarefree decomposition of zero-dimensional polynomial ideals** |

Author(s) | Werner Heiß, Ulrich Oberst, Franz Pauer |

Type | Article in Journal |

Abstract | Let I be a zero-dimensional ideal in a polynomial ring F[s]:= F[s_1, … ,s_n] over an arbitrary field F . We show how to compute an F -basis of the inverse system I^⊥ of I . We describe the F[s] -module I^⊥ by generators and relations and characterise the minimal length of a system of F[s] -generators of I^⊥. If the primary decomposition of I is known, such a system can be computed. Finally we generalise the well-known notion of squarefree decomposition of a univariate polynomial to the case of zero-dimensional ideals in F[s] and present an algorithm to compute this decomposition. |

Keywords | Dual basis, Inverse system, Squarefree decomposition, Systems of generators of minimal length |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S074771710500132X |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 41 |

Number | 3–4 |

Pages | 261 - 284 |

Year | 2006 |

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

Edition | 0 |

Translation |
No |

Refereed |
No |