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Computer algebra tools used to solve the problem

For dealing with polynomial systems, we used recently-developed computer algebra tools which provide facilities for the computation of Gröbner bases (Gb, RealSolving), and related functionality (Hilbert function, lexicographic Gröbner basis computations by change of ordering, Triangular sets computations, Real Root counting, Rational Univariate representation of zero-dimensional systems). In addition, because of the complexity of the computations (size of the input/output), we designed a special change of variables and an adapted strategy to solve the problem.