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Journal Articles Journal of Symbolic Computation Year : 2016

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

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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Dates and versions

hal-01022345 , version 1 (10-07-2014)
hal-01022345 , version 2 (22-02-2016)

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Cite

Laurent Busé, Anna Karasoulou. Resultant of an equivariant polynomial system with respect to the symmetric group. Journal of Symbolic Computation, 2016, 76, pp.142-157. ⟨10.1016/j.jsc.2015.12.004⟩. ⟨hal-01022345v2⟩
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