Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner BasisReport as inadecuate




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1 Laboratoire de Mathématiques Discrètes

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.

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





Author: Nicolas Thiéry -

Source: https://hal.archives-ouvertes.fr/



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