论文标题
在因子上，多元多项式矩阵的左质量分解问题
On Factor Left Prime Factorization Problems for Multivariate Polynomial Matrices
论文作者
论文摘要
本文涉及多元多项式矩阵的因子左质量分解问题，而没有全行等级。我们提出了一个必要且充分的条件，以使一类多元多项式矩阵的因子左质量因素的存在，然后设计算法以计算所有因子左质量因素（如果存在）。我们在计算机代数系统枫树上实现算法，并给出了两个示例以说明算法的有效性。本文介绍的结果也是如此，对于没有完整列等级的多元多项式矩阵的因子右质量因素的存在也是如此。
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.
