An Algorithm For Spliting Polynomial Systems Based On F4

Abstract

We present algorithms for splitting polynomial systems using Gröbner bases. For zero dimensional systems, we use FGLM to compute univariate polynomials and factor them, placing the ideal into general position if necessary. For positive dimensional systems, we successively eliminate variables using F4 and use the leading co-efficients of the last variable to split the system. We also present a known optimization to reduce the cost of zero-reductions in F4, an improvement for FGLM over the rationals, and an algorithm for quickly detecting redundant ideals in a decomposition.