论文标题
关于多元多项式矩阵的小左质分解问题
On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices
论文作者
论文摘要
提出了一个新的必要条件，用于存在没有完整排名的多元多项式矩阵的次要左质量因素。关键思想是建立矩阵与其完整排等级子序列之间的关系。基于新结果，我们提出了一种用于分解矩阵的算法，并已在计算机代数系统枫树上实现。给出了两个示例以说明算法的有效性，实验数据表明该算法是有效的。
A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is presented. The key idea is to establish a relationship between a matrix and its full row rank submatrix. Based on the new result, we propose an algorithm for factorizing matrices and have implemented it on the computer algebra system Maple. Two examples are given to illustrate the effectiveness of the algorithm, and experimental data shows that the algorithm is efficient.
