The Improved Bareiss Algorithm of Solving Linear Equations Symbolically

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 implement the algorithms in the software MMP (Mathematics Mechanization Platform) developed by ourselves.