使用改进后的Bareiss消去法,在求解具有符号系数的线性方程组时可以避免普通Gauss消去法在计算过程中出现所谓中间系数爆炸的问题,还可以求解系数矩阵不是方阵以及系数矩阵奇异的线性方程组的情况.并且以这一改进算法与syzygy算法为基础,给出了求解多项式系数线性方程组的多项式解的算法.已经在自行开发的自动推理平台软件MMP上实现了这个算法.

Comparing with the Gauss method for solving linear equations, the Bareiss elimination method can be used to avoid the phenomenon of coefficient explosion in the computation process. Using the improved Bareiss elimination method, we can solve linear equations whose coefficient matrix is singular or the coefficient matrix is not square. Based on this improvement and the syzygy algorithm, we give an algorithm to find polynomial solutions to a system of linear equations with polynomial coefficients. We implemen...