Overdetermined Strata for Degree 5 Hyperbolic Polynomials

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• 作者：Ezzaldine Hayssam (1)
  Khalil Houssam (2)
  Sarrage Mouhamad (3)
  Hossein Mouhamad (1)
  
  1. D茅partement de Math茅matiques ; Facult茅 des Sciences III ; Universit茅 Libanaise ; Baabda ; Lebanon
  2. Institut Camille Jordan ; 43 Boulevard du 11 Novembre 1918 ; 69622 ; Villeurbanne Cedex ; France
  3. Laboratoire J.A. Dieudonn茅 ; parc Valrose ; 06108 ; Nice Cedex 02 ; France
  
• 关键词：Hyperbolic polynomials ; Gegenbauer polynomials ; Overdetermined strata ; Resultants ; 12D10 ; 14P05 ; 26C10 ; 13P15 ; 13P10
• 刊名：Vietnam Journal of Mathematics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：43
• 期：1
• 页码：139-150
• 全文大小：493 KB
• 参考文献：1. Basu, S, Pollack, R, Roy, M-F (2006) Algorithms in Real Algebraic Geometry, 2nd ed. Algorithms and Computation in Mathematics, 10. Springer, Berlin
  2. Cox, D, Little, J, O鈥橲hea, D (1996) Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics, 2nd ed. Springer, New York
  3. Kostov, VP (2002) Discriminant sets of families of hyperbolic polynomials of degree 4 and 5. Serdica Math. J. 28: pp. 117-152
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2305-2228

文摘

In the present paper, we consider degree 5 hyperbolic polynomials (HPs) in one variable (i.e., real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and its derivatives is greater or equal to 4. We give a new method, based on resultants and subresultants, to calculate the overdetermined strata for degree 5 hyperbolic polynomials.