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

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