Solving via modular methods

In this chapter we present a parallel modular algorithm to compute all solutions with multiplicities of a given zero-dimensional polynomial system of equations over the rationals. In fact, we compute a triangular decomposition using Möller's algorithm (Möller, Appl. Algebra Eng. Commun. Comput. 4:217-230, 1993) of the corresponding ideal in the polynomial ring over the rationals using modular methods, and then apply a solver for univariate polynomials.