Resultant of an equivariant polynomial system with respect to the symmetric group

2014/07/10 by Laurent Busé, Busé, Laurent, Άννα Καρασούλου +1 · 2 citations
Agricultural and Biological Sciences · Chemistry · Engineering · #Advanced Data Processing Techniques #Advanced Scientific Research Methods #Analytical Chemistry and Chromatography #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1407.2799

openalex publication_date 2014/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a system of n homogeneous polynomials in n variables which is equivariant with respect to the canonical actions of the symmetric group of n symbols on the variables and on the polynomials, it is proved that its resultant can be decomposed into a product of several smaller resultants that are given in terms of some divided differences. As an application, we obtain a decomposition formula for the discriminant of a multivariate homogeneous symmetric polynomial.

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