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Resultants of quaternion polynomials

Yıl 2019, Cilt: 48 Sayı: 5, 1304 - 1311, 08.10.2019

Öz

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.

Kaynakça

  • [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.
Yıl 2019, Cilt: 48 Sayı: 5, 1304 - 1311, 08.10.2019

Öz

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Xiangui Zhao Bu kişi benim 0000-0001-7613-0539

Yang Zhang Bu kişi benim 0000-0002-0540-0893

Yayımlanma Tarihi 8 Ekim 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 48 Sayı: 5

Kaynak Göster

APA Zhao, X., & Zhang, Y. (2019). Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics, 48(5), 1304-1311.
AMA Zhao X, Zhang Y. Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics. Ekim 2019;48(5):1304-1311.
Chicago Zhao, Xiangui, ve Yang Zhang. “Resultants of Quaternion Polynomials”. Hacettepe Journal of Mathematics and Statistics 48, sy. 5 (Ekim 2019): 1304-11.
EndNote Zhao X, Zhang Y (01 Ekim 2019) Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics 48 5 1304–1311.
IEEE X. Zhao ve Y. Zhang, “Resultants of quaternion polynomials”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 5, ss. 1304–1311, 2019.
ISNAD Zhao, Xiangui - Zhang, Yang. “Resultants of Quaternion Polynomials”. Hacettepe Journal of Mathematics and Statistics 48/5 (Ekim 2019), 1304-1311.
JAMA Zhao X, Zhang Y. Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics. 2019;48:1304–1311.
MLA Zhao, Xiangui ve Yang Zhang. “Resultants of Quaternion Polynomials”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 5, 2019, ss. 1304-11.
Vancouver Zhao X, Zhang Y. Resultants of quaternion polynomials. Hacettepe Journal of Mathematics and Statistics. 2019;48(5):1304-11.