Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din, Éric Schost, Thi Xuan Vu · 2023
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the action of the symmetric group. We construct and analyze a Monte Carlo probabilistic algorithm which solves this problem, under some regularity assumptions on the input, by taking advantage of the symmetry invariance property.