Functional Analysis and Its Applications

, Volume 46, Issue 1, pp 33–40 | Cite as

Resultants and contour integrals

  • A. Morozov
  • Sh. Shakirov


Resultants are important special functions used to describe nonlinear phenomena. The resultant \(R_{r_1 \ldots r_n }\) determines a consistency condition for a system of n homogeneous polynomials of degrees r 1, ..., r n in n variables in precisely the same way as the determinant does for a system of linear equations. Unfortunately, there is a lack of convenient formulas for resultants in the case of a large number of variables. In this paper we use Cauchy contour integrals to obtain a polynomial formula for resultants, which is expected to be useful in applications.

Key words

rezultant algebraic equation contour integral 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia

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