Solving Decomposable Sparse Systems
Algebraic Geometry
2020-12-01 v2 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2001.04228,
title = {Solving Decomposable Sparse Systems},
author = {Taylor Brysiewicz and Jose Israel Rodriguez and Frank Sottile and Thomas Yahl},
journal= {arXiv preprint arXiv:2001.04228},
year = {2020}
}
Comments
20 pages