Resultants and Contour Integrals

Details Resultants and Contour Integrals Resultants and Contour Integrals

2008-07-28

arxiv.org/abs/0807.4539v1

Mathematics

Algebraic Geometry

9 pages

Scientific paper

Resultants are important special functions used in description of non-linear phenomena. Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$ variables, just in the same way as determinant does for a system of linear equations. Unfortunately, there is a lack of convenient formulas for resultants when the number of variables is large. In this paper we use Cauchy contour integrals to obtain a polynomial formula for resultants, which is expected to be useful in applications.

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