A Research on Special Roots of Quaternion Coefficient Polynomials

Jiang Lian-xia

doi:10.12052/gdutxb.180109

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A Research on Special Roots of Quaternion Coefficient Polynomials

更新时间：2026-05-27

- A Research on Special Roots of Quaternion Coefficient Polynomials
- Vol. 36, Issue 3, Pages: 80-82, 98(2019)
- 作者机构：
  
  喀什大学　数学与统计学院,新疆,喀什,844000
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.180109
  CLC： O151
- Online First：09 May 2019，
  
  Published：2019
- 稿件说明：
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姜莲霞. 关于四元数系数多项式特殊根的研究[J]. 广东工业大学学报, 2019, 36(3): 80-82, 98.

Jiang Lian-xia. A Research on Special Roots of Quaternion Coefficient Polynomials[J]. 2019, 36(3): 80-82, 98.
姜莲霞. 关于四元数系数多项式特殊根的研究[J]. 广东工业大学学报, 2019, 36(3): 80-82, 98. DOI： 10.12052/gdutxb.180109.

Jiang Lian-xia. A Research on Special Roots of Quaternion Coefficient Polynomials[J]. 2019, 36(3): 80-82, 98. DOI： 10.12052/gdutxb.180109.

摘要

探讨了四元数系数多项式

$Q(t)$

img text_id='M370' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M370.jpg'>

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

$Q(t)$

img text_id='M370' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M370.jpg'>

确定的某些实(复)系数多项式的实(复)根集合

确定了

$Q(t)$

img text_id='M370' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M370.jpg'>

在

$\mathbb{R} + \mathbb{R}{j}$

img text_id='M400' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M400.jpg'>

和

$\mathbb{R} + \mathbb{R}{k}$

img text_id='M401' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M401.jpg'>

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.

Abstract

In this research

the sets of spherical roots

real roots

isolated complex roots

pure imaginary quaternion roots and roots in

$\mathbb{R} + \mathbb{R}{j}$

img text_id='M402' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M402.jpg'>

and

$\mathbb{R} + \mathbb{R}{k}$

img text_id='M403' class='formula-img' style='display:none;' src='gdgydxxb-36-3-80_M403.jpg'>

of a quaternion polynomial

(

) are determined by corresponding these sets to the sets of real or complex roots of some real or complex polynomials determined by

(

). 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

Keywords

references

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ZHU F J. Distribution of polynomial real roots and algorithm on calculating all real roots [J]. Journal of Northwest Minorities University(Natural Science), 2001, 22(3): 5-9.

谢彦麟. 多项式理论研究综述[M]. 哈尔滨: 哈尔滨工业大学出版社, 2016.

庄瓦金. 体上矩阵理论导引[M]. 北京: 科学出版社, 2006.

LIANG S, JEFFREY D J. Automatic computation of the complete root classification for a parametric polynomial [J]. Journal of Symbolic Computation, 2009, 44(10): 1487-1501.

杨路, 侯晓荣. 多项式的完全判别系统[J]. 中国科学: 技术科学, 1996(5): 424-441.

YANG C H, ZHU S M, LIANG Z J. Complete discrimination of the roots of polynomials and its applications [J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2003, 42(1): 5-8.

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