Smith Form Equivalence for Several Classes of Multivariate Polynomial Matrices
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908987725709312 |
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| author | Chen, Zuo Guan, Jiancheng Li, Dongmei |
| author_facet | Chen, Zuo Guan, Jiancheng Li, Dongmei |
| contents | This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to study this equivalence problem. We then leverage the Quillen-Suslin and Lin-Bose theorems to extend these results to non-square and rank-deficient matrices. Moreover, the verification of our criteria is achievable algorithmically via existing Gröbner basis methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smith Form Equivalence for Several Classes of Multivariate Polynomial Matrices Chen, Zuo Guan, Jiancheng Li, Dongmei Commutative Algebra 15A06, 15A23, 68W30 This paper investigates the equivalence reduction for several classes of multivariate polynomial matrices and their Smith forms, establishing some criteria for such reduction. In particular, we employ algebra isomorphisms as a key tool to study this equivalence problem. We then leverage the Quillen-Suslin and Lin-Bose theorems to extend these results to non-square and rank-deficient matrices. Moreover, the verification of our criteria is achievable algorithmically via existing Gröbner basis methods. |
| title | Smith Form Equivalence for Several Classes of Multivariate Polynomial Matrices |
| topic | Commutative Algebra 15A06, 15A23, 68W30 |
| url | https://arxiv.org/abs/2604.20929 |