多项式环上一次不定方程组的矩阵解法与程序设计

Matrix Solution of Indefinite Equations of First Degree over a Polynomial Ring and the Program Design

利用欧几里德算法和多项式环上的可逆线性变换,从理论上对多项式环上的一次不定方程组的解进行深入的研究,给出了用矩阵的初等变换求解多项式环上的一次不定方程组的矩阵解法,并利用MATLAB数学软件开发了相应的计算机程序。

By using the Euclidean algorithm and invertible linear transformation over a polynomial ring, the solutions of polynomial indeterminate equations of first degree was investigated in theory, and its matrix solution based on the elementary matrix transformation was proposed. In addition, the program for the matrix solution was given by using MAT-LAB mathematical software.