A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for algebraic independence by the well-known Jacobian criterion. For fields of other characteristic p > 0, no analogous characterization is known. In this paper we give the first such criterion. Essentially, it boils down to a non-degeneracy condition on a lift of the Jacobian polynomial over (an unra...

A package for solving time-dependent partial differential equations (PDEs), MathPDE, is presented. It implements finitedifference methods. After making a sequence of symbolic transformations on the PDE and its initial and boundary conditions, MathPDE automatically generates a problem-specific set of Mathematica functions to solve the numerical problem, which is essentially a system of algebraic...