Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2001

Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis

Nicolas M. Thiéry

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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Dates and versions

hal-01182965 , version 1 (06-08-2015)

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Nicolas M. Thiéry. Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis. Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2001, 2001, Paris, France. pp.315-328, ⟨10.46298/dmtcs.2285⟩. ⟨hal-01182965⟩
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