SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 5

Resultants of quaternion polynomials

Xiangui Zhao
Yang Zhang
Pages
1304–1311
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We generalize the concept of resultants to quaternion polynomials and investigate the relationships among resultants, greatest common right divisors and repeated right roots of quaternion polynomials.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We generalize the concept of resultants to quaternion polynomials and investigate the relationships among resultants, greatest common right divisors and repeated right roots of quaternion polynomials.
📊
Key Findings & Data:We generalize the concept of resultants to quaternion polynomials and investigate the relationships among resultants, greatest common right divisors and repeated right roots of quaternion polynomials.
💡
Conclusion & Impact:We generalize the concept of resultants to quaternion polynomials and investigate the relationships among resultants, greatest common right divisors and repeated right roots of quaternion polynomials.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:quaternion · (double) resultant · greatest common right divisor

Abstract

We generalize the concept of resultants to quaternion polynomials and investigate the relationships among resultants, greatest common right divisors and repeated right roots of quaternion polynomials.

🔖

Cite This Article

Zhao, X., Zhang, Y. (2022). Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1304–1311. https://ajindex.com/articles/529728

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. L. Chen, Definition of determinant and Cramer solutions over the quaternion field, Acta Math. Sin. 7 (2), 171-180, 1991
  2. D.A. Cox, J. Little and D. O’Shea, Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra, 10, Springer, 2007
  3. J. Dieudonné, Les déterminants sur un corps non commutatif, Bull. Soc. Math. France 71, 27-45, 1943
  4. A.Lj. Erić, The resultant of non-commutative polynomials, Mat. Vesnik 60, 3-8, 2008
  5. L. Feng and K. Zhao, Classifying zeros of two-sided quaternionic polynomials and computing zeros of two-sided polynomials with complex coefficients, Pac. J. Math. 262 (2), 317-337, 2013
  6. I. Gelfand, S. Gelfand, V. Retakh and R. Lee Wilson, Quasideterminants, Adv. Math. 193 (1), 56-141, 2005
  7. I.I. Kyrchei, Cramer’s rule for quaternionic systems of linear equations, J. Math. Sci. 155 (6), 839-858, 2008
  8. T.Y. Lam, A first course in noncommutative rings, Graduate Texts in Mathematics 131, Springer-Verlag New York, 2001
  9. I. Niven, Equations in quaternions, Amer. Math. Monthly 48 (10), 654-661, 1941
  10. O. Ore, Theory of non-commutative polynomials, Ann. Math. 34 (3), 480–508, 1933
  11. P. Rastall, Quaternions in relativity, Rev. Mod. Phys. 36 (3), 820-832, 1964
  12. K. Shoemake, Animating rotation with quaternion curves, ACM SIGGRAPH Com- puter Graphics 19 (3), 245–254, 1985
  13. G. Song and Q. Wang, Condensed Cramer rule for some restricted quaternion linear equations, Appl. Math. Comput. 218, 3110-3121, 2011
  14. G. Song, Q. Wang and H. Chang, Cramer rule for the unique solution of restricted matrix equations over the quaternion skew fields, Comput. Math. Appl. 61 (6), 1576- 1589, 2011
  15. R. Szeliski, Computer vision: algorithms and applications, Springer, 2011
  16. J. von zur Gathen and J. Gerhard, Modern computer algebra, Cambridge University Press, 2013.