对称Max Plus半环上热带多项式的根
Roots of Tropical Polynomials over Symmetric Max-Plus Semiring
DOI: 10.12677/PM.2022.1210189, PDF,    科研立项经费支持
作者: 苏 瑞, 秦靖玻：云南财经大学，统计与数学学院，云南 昆明
关键词: 热带几何；半环；多项式；Tropical Geometry； Semiring； Polynomial
摘要: 多项式的求根是数学的核心内容之一。本文将讨论系数在热带对称max-plus半环Smax上的一元热带多项式根的存在性与求根公式。
Abstract: Finding roots of polynomials is one of the core contents of mathematics. In this paper, we discuss the existence and formula of roots of unitary tropical polynomials with coefficients on tropical symmetrized max-plus semiring Smax.
文章引用：苏瑞, 秦靖玻. 对称Max Plus半环上热带多项式的根[J]. 理论数学, 2022, 12(10): 1751-1756. https://doi.org/10.12677/PM.2022.1210189

参考文献

[1] Pin, J.E. (1994) Tropical Semirings. In: Gunawardena, J., Ed., Idempotency, Cambridge University Press, Cambridge, 50-69. [Google Scholar] [CrossRef] 
[2] Simon, I. (1988) Recognizable Sets with Multiplic-ities in the Tropical Semiring. In: Chytil, M.P., Koubek, V. and Janiga, L., Eds., Lecture Notes in Computer Science, Vol. 324, Springer, Berlin, Heidelberg, 107-120. [Google Scholar] [CrossRef] 
[3] Wilding, D. (2014) Linear Algebra over Semirings. Doctoral Dissertation, The University of Manchester, Manchester.
[4] Gaubert, S. and Sharify, M. (2009) Tropical Scaling of Polynomial Matrices. In: Bru, R. and Romero-Vivó, S., Eds., Lecture Notes in Control and Information Sciences, Vol. 389, Springer, Berlin, Heidelberg, 291-303. [Google Scholar] [CrossRef] 
[5] Plus, M. (1990) Linear Systems in (Max, +)-Algebra. Pro-ceedings of the 29th Conference on Decision and Control, Honolulu, 6 p.
[6] Baccelli, F., Cohen, G., Olsder, G.J., et al. (1992) Synchronization and Linearity: An Algebra for Discrete Event Systems. John Wiley & Sons, New York.
[7] Brualdi, R.A. and Shader, B.L. (1995) Matrices of Sign-Solvable Linear Systems. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef] 
[8] Thomassen, C. (1986) Sign-Nonsingular Matrices and Even Cycles in Directed Graphs. Linear Algebra and Its Applications, 75, 27-41. [Google Scholar] [CrossRef] 
[9] Norton, J. and Spiroff, S. (2018) The Tropical Semiring in Higher Dimensions. Involve a Journal of Mathematics, 11, 477-488. [Google Scholar] [CrossRef] 
[10] Zonnefeld, C.G. (2021) Directed Graphs of the Finite Tropical Semiring. Rose-Hulman Undergraduate Mathematics Journal, 22, Article No. 4.
[11] Cuninghame-Green, R. (1979) Minimax Algebra. In: Fandel, G. and Trockel, W., Eds., Lecture Notes in Economics and Mathematical Systems, Springer Berlin, Heidelberg, 13-15. [Google Scholar] [CrossRef] 

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