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. Key words: Polynomial system solving, Rational univariate representation, Geometric resolution, Toric (or sparse) resultant. 1991 MSC: 68W30, 33F10

• Type: Journal
• Year: 2008
• Where: JSC
• Authors: Koji Ouchi, John Keyser
• Keywords: Algorithm, JSC 2008, Multivariate Polynomial Equations, Rational Univariate Reduction