Computing Gr枚bner bases of pure binomial ideals via submodules of

详细信息	查看全文 | 推荐本文 |

• 作者：Giandomenico Boffi^a ; ^{giandomenico.boffi@luspio.it} ; Alessandro Logar^b ; ¹ ; ^{logar@units.it}
• 关键词：Binomial ideal ; Grö ; bner basis ; Polyhedral cone ; Buchberger algorithm ; Smith normal form ; Hilbert basis
• 刊名：Journal of Symbolic Computation
• 出版年：2012
• 期刊代码：140_07477171
• 类别：cp
• 出版时间：October, 2012
• 卷：47
• 期：10
• 页码：1297-1308
• 文件大小：286 K

摘要

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 and submodules of and we showed that it is possible to construct a theory of Gr枚bner bases for submodules of . As a consequence, it is possible to follow alternative strategies for the computation of Gr枚bner bases of submodules of (and hence of binomial ideals) which avoid the use of Buchberger algorithm. In the present paper, we show that a Gr枚bner basis of a -module of rank lies into a finite set of cones of which cover a half-space of . More precisely, in each of these cones , we can find a suitable subset which has the structure of a finite abelian group and such that a Gr枚bner basis of the module (and hence of the pure saturated binomial ideal represented by ) is described using the elements of the groups together with the generators of the cones.