Truncated Groebner fans and lattice ideals

Details Truncated Groebner fans and lattice ideals Truncated Groebner fans and lattice ideals

2005-09-11

arxiv.org/abs/math/0509247v1

Mathematics

Commutative Algebra

Scientific paper

We outline a generalization of the Groebner fan of a homogeneous ideal with maximal cells parametrizing truncated Groebner bases. This "truncated" Groebner fan is usually much smaller than the full Groebner fan and offers the natural framework for conversion between truncated Groebner bases. The generic Groebner walk generalizes naturally to this setting by using the Buchberger algorithm with truncation on facets. We specialize to the setting of lattice ideals. Here facets along the generic walk are given by unique (facet) binomials. This along with the representation of binomials as integer vectors give an especially simple version of the generic Groebner walk. Computational experience with the special Aardal-Lenstra integer programming knapsack problems is reported.

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