## Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001

### Robert Cori and Jacques Mazoyer and Michel Morvan and Rémy Mosseri (eds.)

### DMTCS Conference Volume AA (2001), pp. 315-328

author: | Nicolas M. Thiéry |
---|---|

title: | Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGB I-Gröbner Basis |

keywords: | Invariant Theory, Permutation Group, Discrete Mathematics, Minimal Generating Set, Hironaka Decomposition, SAGBI-Gröbner basis, permuvar, mupad |

abstract: | We present a characteristic-free algorithm for computing minimal generating sets of invariant rings of permutation groups. We circumvent the main weaknesses of the usual approaches (using classical Gröbner basis inside the full polynomial ring, or pure linear algebra inside the invariant ring) by relying on the theory of SAGBI-Gröbner basis. This theory takes, in this special case, a strongly combinatorial flavor, which makes it particularly effective. Our algorithm does not require the computation of a Hironaka decomposition, nor even the computation of a system of parameters, and could be parallelized. Our implementation, as part of the library permuvar for mupad, is in many cases much more efficient than the other existing software. |

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reference: | Nicolas M. Thiéry
(2001), Computing Minimal Generating Sets of Invariant Rings
of Permutation Groups with
SAGB
I-Gröbner Basis, in Discrete
Models: Combinatorics, Computation, and Geometry, DM-CCG
2001, Robert Cori and Jacques Mazoyer and Michel Morvan
and Rémy Mosseri (eds.), Discrete Mathematics and
Theoretical Computer Science Proceedings AA, pp.
315-328 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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