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.
https://hal.inria.fr/hal-01022345
Contributor : Laurent Busé
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Submitted on : Monday, February 22, 2016 - 9:17:27 PM
Last modification on : Wednesday, October 10, 2018 - 10:09:41 AM
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Laurent Busé, Anna Karasoulou. Resultant of an equivariant polynomial system with respect to the symmetric group. Journal of Symbolic Computation, Elsevier, 2016, 76, pp.142-157. ⟨10.1016/j.jsc.2015.12.004⟩. ⟨hal-01022345v2⟩
