Rationalizing Denominators Using Gröbner Bases. (6th January 2022)

• Record Type: Journal Article
• Authors: Li, Dongmei; Wu, Man; Liu, Jinwang; Gao, Yiman
• Other Names: Gao Zhiwei Academic Editor.
• Is Part Of: Complexity. Volume 2022(2022)
• Publication Date: 2022-01-06
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2022/1288357
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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.