On factor left prime factorization problems for multivariate polynomial matrices

被引：4

作者：

Lu, Dong ^{[1
,2
]}

Wang, Dingkang ^{[3
,4
]}

Xiao, Fanghui ^{[5
]}

机构：

[1] Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China

[2] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[3] Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China

[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[5] Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China

来源：

MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING | 2021年 / 32卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Multivariate polynomial matrices; Matrix factorizations; Factor left prime (FLP); Column reduced minors; Free modules;

D O I：

10.1007/s11045-021-00768-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper is concerned with factor left prime factorization problems for multivariate polynomial matrices without full row rank. We propose a necessary and sufficient condition for the existence of factor left prime factorizations of a class of multivariate polynomial matrices, and then design an algorithm to compute all factor left prime factorizations if they exist. We implement the algorithm on the computer algebra system Maple, and two examples are given to illustrate the effectiveness of the algorithm. The results presented in this paper are also true for the existence of factor right prime factorizations of multivariate polynomial matrices without full column rank.

引用

页码：975 / 992

页数：18

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