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

作　　者：王思如 邢秋菊 WANG Si-ru;XING Qiu-ju(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2024年第1期57-63,84,共8页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：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金(EA201207226)。

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。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 Ioot.By constructing the conjugate functions,the conchusions 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 cefficient is positive,and into one class if the fust coefficient is negative.If the first coefficient is postive,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 anda 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 

分 类 号：O17[理学—数学]