Automatic variable order selection for polynomial system solving (abstract only)

The goal of a general purpose solver is to allow a user to compute the solutions of a system of equations with minimal interactions. Modern tools for polynomial system solving, namely triangular decomposition and Groebner basis computation, can be highly sensitive to the ordering of the variables. Our goal is to examine the structure of a given system and use it to compute a variable ordering that will cause the solving algorithm to complete quickly (or alternately, to give compact output). We explore methods based on the dependency graph of coincident variables and terms between the equations. Desirable orderings are gleaned from connected components and other topological properties of these graphs, under different weighting schemes. We present experimental results suggesting that these methods work well in practice.