Solving Decomposable Sparse Systems

Amendola et al. proposed a method for solving systems of polynomial equations lying in a family which exploits a recursive decomposition into smaller systems. A family of systems admits such a decomposition if and only if the corresponding monodromy group is imprimitive. A consequence of Esterov's classification of sparse polynomial systems with imprimitive monodromy groups is that this decomposition is obtained by inspection. Using these ideas, we present a recursive algorithm to numerically solve decomposable sparse systems. This is joint work with Frank Sottile, Jose Rodriguez, and Thomas Yahl.