Rationalizing Denominators Using Gröbner Bases
Rationalizing Denominators Using Gröbner Bases
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DOI：
10.1155/2022/1288357
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Dongmei Li;Man Wu;Jinwang Liu;Yiman Gao
中科院分区：
文献类型：
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作者：
Dongmei Li;Man Wu;Jinwang Liu;Yiman Gao
本文讨论了两类分式的有理化算子问题。利用Gröbner基的理论和算法，首先介绍了分式平方根和立方根的有理化算子的一种方法，然后，对于一般形式的高阶根的有理化算子，将有理化算子的有理化问题转化为求极小多项式的问题.一些有趣的结果和可执行的算法合理化这些类型的分数的分母。最后，通过一个算例验证了算法的有效性.
The problem of rationalizing denominators for two types of fractions is discussed in the paper. By using the theory and algorithms of Gröbner bases, we first introduce a method to rationalize the denominators of fractions with square root and cube root, and then, for the denominators with higher radical of the general form, the problem of rationalizing denominators is converted into the related problem of finding the minimal polynomials. Some interesting results and an executable algorithm for rationalizing the denominator of these type fractions are presented. Furthermore, an example is also established to illustrate the effectiveness of the algorithm.