具有重根的三次多项式的拓扑共轭分类
Topological Conjugate Classification of Cubic Polynomials with Multiple Roots
王思如 1邢秋菊1
作者信息
- 1. 南昌航空大学 数学与信息科学学院,南昌 330063
- 折叠
摘要
为解决具有重根的三次多项式在拓扑共轭意义下的分类问题,分别对具有一个三重根和具有一个二重根及一个单根的三次多项式进行分析.通过构造共轭函数,得到具有重根的三次多项式的分类结果,并给出证明.结果表明:对于具有一个三重根的三次多项式,如果首项系数为正,可以将其分为 3类;如果首项系数为负,可以将其归为 1类.对于首项系数为正的三次多项式,如果具有一个二重根0和一个单根a≠0,可以将其分为2类;如果具有一个二重根a≠0和一个单根0,也可以将其分为2类.
Abstract
To classify cubic polynomials with multiple roots in the sense of topological conjugation,this study specifically analyses the following two classes of cubic polynomials.One class is the cubic polynomials with a triple root and the other class is the cubic polynomials with a double root and a single root.By constructing the conjugate functions,the conclusions for the classification of cubic polynomials with multiple roots are presented.Also,the proofs of the conclusions are given.The results show that the cubic polynomials with a triple root can be categorized into three classes if the first coefficient is positive,and into one class if the first coefficient is negative.If the first coefficient is positive,the cubic polynomials which have a double root of 0 and a single root a≠0 can be divided into two classes.Similarly,the cubic polynomials which have a double root a≠0 and a single root 0 can also be divided into two classes.
关键词
三次多项式/重根/拓扑共轭/分类Key words
cubic polynomials/multiple roots/topological conjugate/classification引用本文复制引用
基金项目
国家自然科学基金(1196010189)
江西省自然科学基金(20232ACB201004)
南昌航空大学博士启动基金(EA201207226)
出版年
2024
NETL
NSTL
万方数据