The smith form of a multivariate polynomial matrix over an arbitrary coefficient field

被引：7
|
作者：
Li, Dongmei [1 ,2 ]
Liu, Jinwang [1 ]
Chu, Delin [2 ]
机构：
[1] Hunan Univ Sci & Technol, Sch Math & Comp Sci, Xiangtan 411201, Hunan, Peoples R China
[2] Natl Univ Singapore, Dept Math, Singapore, Singapore
来源：
LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Multidimensional system; multivariate polynomial matrix; Smith form; 2-D SYSTEMS-THEORY; FACTORIZATION; EQUIVALENCE;
D O I：
10.1080/03081087.2020.1726275
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The equivalence of multidimensional systems is closely related to the equivalence of multivariate polynomial matrices, for which the Smith form plays an important role. In this paper we study multivariate polynomial matrices with their entries in the polynomial ring , where is an arbitrary field. We derive some new conditions on reducing these matrices to their Smith forms. These conditions can be verified by computing the reduced Grobner bases of the associated ideals.
引用
收藏
页码：366 / 379
页数：14
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