Title | **Rational invariants of a group action. Construction and rewriting** |

Author(s) | Evelyne Hubert, Irina A. Kogan |

Type | Article in Journal |

Abstract | Geometric constructions applied to a rational action of an algebraic group lead to a new algorithm for computing rational invariants. A finite generating set of invariants appears as the coefficients of a reduced Gröbner basis. The algorithm comes in two variants. In the first construction the ideal of the graph of the action is considered. In the second one the ideal of a cross-section is added to the ideal of the graph. Zero-dimensionality of the resulting ideal brings a computational advantage. In both cases, reduction with respect to the computed Gröbner basis allows us to express any rational invariant in terms of the generators. |

Keywords | Rational invariants, Algebraic group actions, Cross-section, Gröbner basis, Differential invariants, Moving frame |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717106000721 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 42 |

Number | 1–2 |

Pages | 203 - 217 |

Year | 2007 |

Note | Effective Methods in Algebraic Geometry (MEGA 2005) |

Edition | 0 |

Translation |
No |

Refereed |
No |