Solving Polynomial Equations -- Resultants -- Computation in Local Rings -- Modules -- Free Resolutions -- Polytopes, Resultants, and Equations -- Polyhedral Regions and Polynomials -- Algebraic Coding Theory -- The Berlekamp-Massey-Sakata Decoding Algorithm.In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpens…