Améndola 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 Galois group is imprimitive. When the Galois group is imprimitive, we consider the problem of computing an explicit decomposition. A consequence of Esterov’s classification of sparse polynomial systems with imprimitive Galois groups is that this decomposition is obtained by inspection. This leads to a recursive algorithm to compute complex isolated solutions to decomposable sparse systems, which we present and give evidence for its efficiency.

Améndola等。提出了一种解决族中多项式方程组系统的方法，该方法利用递归分解成较小的系统。当且仅当相应的Galois组是极小值时，一个系统族才允许这种分解。当伽罗瓦群是极点时，我们考虑计算显式分解的问题。Esterov对具有定性Galois组的稀疏多项式系统进行分类的结果是，这种分解是通过检查获得的。这导致了一种递归算法，可计算可分解稀疏系统的复杂隔离解决方案，我们对其进行了介绍并为其有效性提供了证据。