Resultants and Contour Integrals

Abstract

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.

9 pages

References in corpus (7)

• Nonperturbative Results on the Point Particle Limit of N=2 Heterotic String Compactifications
• String triality, black hole entropy and Cayley's hyperdeterminant
• Strings, Black Holes, and Quantum Information
• Hidden symmetries of the Nambu-Goto action
• Algebraic Geometry of Discrete Dynamics. The case of one variable
• Analogue of the identity Log Det = Trace Log for resultants
• Explicit formulas for the multivariate resultant

Cited by in corpus (6)

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• New and Old Results in Resultant Theory
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• Resultant as Determinant of Koszul Complex
• Symmetry Breaking: A New Paradigm for Non-Perturbative QFT and Topological Transitions
• Complanart of polynomial equations