Computing gröbner bases associated with lattices
We specialize Möller’s algorithm to the computation of Gröbner bases related to lattices. We give the complexity analysis of our algorithm. Then we provide experiments showing that our algorithm is more efficient than Buchberger’s algorithm for computing the associated Gröbner bases. Furthermore we show that the binomial ideal associated to the lattice can be constructed from a set of binomials associated with a set of generators of the corresponding label code. This result is presented in a general way by means of three ideal constructions associated with group codes that constitute the same ideal. This generalizes earlier results for specific cases of group codes such as linear codes, codes over ℤm and label codes of lattices.
|Keywords||Group codes, Gröbner bases, Label codes, Lattices, Möller algorithm|
|Journal||Advances in Mathematics of Communications|
Álvarez-Barrientos, I. (Ismara), Borges-Quintana, M. (Mijail), Borges-Trenard, M.A. (Miguel Angel), & Panario, D. (2016). Computing gröbner bases associated with lattices. Advances in Mathematics of Communications, 10(4), 851–860. doi:10.3934/amc.2016045