The Grobner basis of a module over KUX1,...,Xne and polynomial solutions of a system of linear equations

Abstract

Many computations relating polynomial ideals are reduced to calculating polynomial solutions of a system of linear equations with polynomial coefficients[1]. Zacharias[2] pointed out that Buchberger's algorithm[3] for Gröbner basis can be applied to solving such a linear equation. From the computational viewpoint, Zacharias' method seems to be much better than the previous methods. Hence, we have generalized his method to solve a system of equations directly. After completing the paper, we knew that similar works had been done by several authors[4,5]. This paper describes our method briefly.