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TitleComputing Gröbner bases of pure binomial ideals via submodules of Z^n
Author(s) Giandomenico Boffi, Alessandro Logar
TypeArticle in Journal
AbstractA binomial ideal is an ideal of the polynomial ring which is generated by binomials. In a previous paper, we gave a correspondence between pure saturated binomial ideals of K[x_1, ,x_n] and submodules of Z n and we showed that it is possible to construct a theory of Gröbner bases for submodules of Z_n . As a consequence, it is possible to follow alternative strategies for the computation of Gröbner bases of submodules of Z_n (and hence of binomial ideals) which avoid the use of Buchberger algorithm. In the present paper, we show that a Gröbner basis of a Z -module M ⊆ Z n of rank m lies into a finite set of cones of Z m which cover a half-space of Z_m . More precisely, in each of these cones C , we can find a suitable subset Y(C) which has the structure of a finite abelian group and such that a Gröbner basis of the module M (and hence of the pure saturated binomial ideal represented by M ) is described using the elements of the groups Y(C) together with the generators of the cones.
KeywordsBinomial ideal, Gröbner basis, Polyhedral cone, Buchberger algorithm, Smith normal form, Hilbert basis
URL http://www.sciencedirect.com/science/article/pii/S0747717111002495
JournalJournal of Symbolic Computation
Pages1297 - 1308
NoteSymbolic Computation and its Applications
Translation No
Refereed No