论文标题
求解可分解的稀疏系统
Solving Decomposable Sparse Systems
论文作者
论文摘要
Amendola等。提出了一种解决位于家庭中的多项式方程系统的方法，该系统将递归分解利用为较小的系统。当且仅当相应的GALOIS组不适合时，一个系统家庭就承认了这种分解。当Galois群体是不适的时，我们会考虑计算显式分解的问题。埃斯特罗夫（Esterov）将稀疏多项式系统分类的结果是，这种分解是通过检查获得的。这导致了一种递归算法来求解可分解的稀疏系统，我们提出并提供证据证明其效率。
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 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 solve decomposable sparse systems, which we present and give evidence for its efficiency.
