Small Groebner Fans of Ideals of Points
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866909391879405568 |
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| author | Dimitrova, Elena He, Qijun Robbiano, Lorenzo Stigler, Brandilyn |
| author_facet | Dimitrova, Elena He, Qijun Robbiano, Lorenzo Stigler, Brandilyn |
| contents | In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this property. Moreover, we provide methodologies for constructing such ideals. We then relax the condition of uniqueness. The second and most relevant topic discussed here is to consider and identify pairs of ideals with the same number of reduced Groebner bases, that is, with the same cardinality of their associated Groebner fan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_03680 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Small Groebner Fans of Ideals of Points Dimitrova, Elena He, Qijun Robbiano, Lorenzo Stigler, Brandilyn Commutative Algebra 13P10, 13P25, 13-04, 68W30, 92B05 In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this property. Moreover, we provide methodologies for constructing such ideals. We then relax the condition of uniqueness. The second and most relevant topic discussed here is to consider and identify pairs of ideals with the same number of reduced Groebner bases, that is, with the same cardinality of their associated Groebner fan. |
| title | Small Groebner Fans of Ideals of Points |
| topic | Commutative Algebra 13P10, 13P25, 13-04, 68W30, 92B05 |
| url | https://arxiv.org/abs/1704.03680 |