数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 1004-1012.doi: 10.1016/S0252-9602(10)60097-5

• 论文 • 上一篇    下一篇

ON SETS OF ZEROES OF CLIFFORD ALGEBRA-VALUED POLYNOMIALS

杨燕, 钱涛   

  1. School of Mathematics and Computational Science, Sun Yat-Sen University and Department of Mathematics, Faculty of Science and Technology, University of |Macau
  • 收稿日期:2009-02-08 修回日期:2009-04-26 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

    This project sponsored by the National Natural Science Funds for Young Scholars (10901166), the Scientific Research Foundation for the Youth Scholars of Sun Yat-Sen University, and the Research Grant of University of Macau on Applications of Hyper-Complex Analysis (cativo: 7560).

ON SETS OF ZEROES OF CLIFFORD ALGEBRA-VALUED POLYNOMIALS

 YANG Yan, QIAN Tao   

  1. School of Mathematics and Computational Science, Sun Yat-Sen University and Department of Mathematics, Faculty of Science and Technology, University of |Macau
  • Received:2009-02-08 Revised:2009-04-26 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This project sponsored by the National Natural Science Funds for Young Scholars (10901166), the Scientific Research Foundation for the Youth Scholars of Sun Yat-Sen University, and the Research Grant of University of Macau on Applications of Hyper-Complex Analysis (cativo: 7560).

摘要:

In this note, we study zeroes of Clifford algebra-valued polynomials. We prove that if such a polynomial has only real coefficients, then it has two types of zeroes: the real isolated zeroes  and the spherical conjugate ones. The total number of zeroes does not exceed the degree of the polynomial. We also present a technique for computing the zeroes.

关键词: Clifford algebra, zeroes of polynomials

Abstract:

In this note, we study zeroes of Clifford algebra-valued polynomials. We prove that if such a polynomial has only real coefficients, then it has two types of zeroes: the real isolated zeroes  and the spherical conjugate ones. The total number of zeroes does not exceed the degree of the polynomial. We also present a technique for computing the zeroes.

Key words: Clifford algebra, zeroes of polynomials

中图分类号: 

  • 30G35