Details:
Title  Computing Gröbner bases of pure binomial ideals via submodules of Z^n  Author(s)  Giandomenico Boffi, Alessandro Logar  Type  Article in Journal  Abstract  A 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 halfspace 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.  Keywords  Binomial ideal, Gröbner basis, Polyhedral cone, Buchberger algorithm, Smith normal form, Hilbert basis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111002495 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  10  Pages  1297  1308  Year  2012  Note  Symbolic Computation and its Applications  Edition  0  Translation 
No  Refereed 
No 
