Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials

Zhi-Yong Zhang (), Chun-Ming Yuan () and Xiao-Shan Gao ()
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Zhi-Yong Zhang: Chinese Academy of Sciences, KLMM, Academy of Mathematics and Systems Science
Chun-Ming Yuan: Chinese Academy of Sciences, KLMM, Academy of Mathematics and Systems Science
Xiao-Shan Gao: Chinese Academy of Sciences, KLMM, Academy of Mathematics and Systems Science

A chapter in Computer Mathematics, 2014, pp 479-503 from Springer

Abstract: Abstract In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomials $$f_1$$ f 1 and $$f_2$$ f 2 in the differential indeterminate $$y$$ y with order one and arbitrary degree is given. That is, a nonsingular matrix is constructed such that its determinant contains the differential resultant as a factor. Furthermore, the algebraic sparse resultant of $$f_1, f_2, {\updelta } f_1$$ f 1 , f 2 , δ f 1 and $${\updelta } f_2$$ δ f 2 treated as polynomials in $$y, y^{\prime }, y^{\prime \prime }$$ y , y ′ , y ″ is shown to be a nonzero multiple of the differential resultant of $$f_1$$ f 1 and $$f_2$$ f 2 . Although very special, this seems to be the first matrix representation for a class of nonlinear generic differential polynomials.

Keywords: Matrix formula; Differential resultant; Sparse resultant; Macaulay resultant (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-662-43799-5_32

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