KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 5

Resultants of quaternion polynomials

Xiangui Zhao0000-0001-7613-0539
Yang Zhang0000-0002-0540-0893
Sayfa
—
Yayın Tarihi
2019-10-08
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

Zhao, X., Zhang, Y. (2019). Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 5. https://ajindex.com/articles/1402730

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (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.