Rational Univariate Reduction via toric resultants

We describe algorithms for solving a given system of multivariate polynomial equations via the Rational Univariate Reduction (RUR). We compute the RUR from the toric resultant of the input system. Our algorithms derandomize several of the choices made in similar prior algorithms. We also propose a new derandomized algorithm for solving an overdetermined system. Finally, we analyze the computational complexity of the algorithm, and discuss its implementation and performance.