关于四元数系数多项式特殊根的研究  

A Research on Special Roots of Quaternion Coefficient Polynomials

作　　者：姜莲霞 Jiang Lian-xia(College of Mathematics and Statistics,Kashi University,Kashi 844000,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000

出　　处：《广东工业大学学报》2019年第3期80-82,98,共4页Journal of Guangdong University of Technology

基　　金：新疆维吾尔自治区自然科学基金资助项目(2017D01A13)

摘　　要：探讨了四元数系数多项式Q(t)的球形根、实根、孤立复根、纯虚数四元数根的集合,通过将这些集合对应于由Q(t)确定的某些实(复)系数多项式的实(复)根集合,确定了Q(t)在■和■中根的集合,得到的实(复)系数多项式根的计数和分类方法可用于四元数系数多项式根的计数和分类上.In this research,the sets of spherical roots,real roots,isolated complex roots,pure imaginary quaternion roots and roots in R+Rj and R+Rk of a quaternion polynomial Q(t) are determined by corresponding these sets to the sets of real or complex roots of some real or complex polynomials determined by Q(t).Thus,the counting and classifying methods for such polynomials can be used for the counting and classifying of the aforementioned roots of quaternion polynomials.

关 键 词：四元数 多项式 球形根 孤立根 复根 

分 类 号：O151[理学—数学]