The Grobner basis of a module over KUX1,...,Xne and polynomial solutions of a system of linear equations
The Grobner basis of a module over KUX1,...,Xne and polynomial solutions of a system of linear equations
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KUX1,...,Xne 模块的 Grobner 基和线性方程组的多项式解
DOI：
10.1145/32439.32483
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
H. Kobayashi
中科院分区：
文献类型：
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作者：
A. Furukawa;T. Sasaki;H. Kobayashi
许多与多项式理想相关的计算都被简化为计算具有多项式系数的线性方程组的多项式解[1]。 Zacharias[2]指出Gröbner基的Buchberger算法[3]可以应用于求解这样的线性方程。从计算的角度来看，撒迦利亚的方法似乎比以前的方法要好得多。因此，我们将他的方法推广到直接求解方程组。完成论文后，我们知道有几位作者也做过类似的工作[4,5]。本文简要描述了我们的方法。
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.