Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis
Thiéry, Nicolas,
HAL, hal-01182965 / Harvested from HAL
Text on HAL
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.
Publié le : 2001-07-04
Classification:  Hironaka Decomposition,  SAGBI-Gröbner basis,  permuvar,  mupad,  Minimal Generating Set,  Discrete Mathematics,  Invariant Theory,  Permutation Group,  [INFO]Computer Science [cs],  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],  [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],  [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC] 
@article{hal-01182965,
     author = {Thi\'ery, Nicolas, },
     title = {Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gr\"obner Basis},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01182965}
}

Thiéry, Nicolas, . Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01182965/