| 引用本文: | 许伟,冯良贵.一元二次四元数单边多项式的求根公式.[J].国防科技大学学报,2013,35(5):74-78.[点击复制] |
| XU Wei,FENG Lianggui.Formulae for finding all roots of quadratic one-sided polynomials over quaternions[J].Journal of National University of Defense Technology,2013,35(5):74-78[点击复制] |
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| 一元二次四元数单边多项式的求根公式 |
| 许伟, 冯良贵 |
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(国防科技大学 理学院， 湖南 长沙 410073)
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| 摘要: |
| 随着四元数代数广泛应用于量子力学、惯性导航及控制论等学科，四元数多项式的求根问题被许多学者关注。最近Janovska和Opfer从理论上给出了一种n次四元数单边多项式零点的求解方法，Feng和Zhao进一步给出了一般n次四元数单边多项式的零点显性表达式。本文根据Feng和Zhao的结果对一元二次四元数单边方程的根进行了讨论，并利用复数域上四次多项式的Ferrari求根公式建立了一元二次四元数单边方程的求解公式。与文献中现有的结果相比，本文建立的求根公式在许多方面展现了优越性。 |
| 关键词: 四元数 二次方程 根式求解 |
| DOI： |
| 投稿日期：2013-01-20 |
| 基金项目:国防科技大学基础研究项目;湖南省自然科学基金资助项目（11JJ7002） |
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| Formulae for finding all roots of quadratic one-sided polynomials over quaternions |
| XU Wei, FENG Lianggui |
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(College of Science,National University of Defense Technology,Changsha 410073, China)
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| Abstract: |
| Quaternion algebra has been widely applied to many subjects such as quantum mechanics, control theory and inertial navigation, and it has won attention from many scholars in the field of effectively obtaining the roots of a quaternionic polynomial. Recently, Janovska and Opfer have theoretically provided a method of finding all zeros of a simple quaternionic polynomial of degree n. Furthermore, Feng and Zhao have given a formula of finding all zeros of a general simple quaternionic polynomial of degree n in terms of solving polynomials over the field of complex numbers. Based on the results given by Feng and Zhao in this paper, the roots of a quaternionic one-sided polynomial with degree 2 were discussed and classified, and a quadratic formula for quaternions with the help of the Ferrari's quadratic formula over the field of complex numbers was produced. Compared with the results in literature, the formula built in this paper displays its advantages in many aspects. |
| Keywords: quaternion quadratic equation root |
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