Abstract
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.
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Research of Sottile supported by grant 636314 from the Simons Foundation.
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Brysiewicz, T., Rodriguez, J.I., Sottile, F. et al. Solving decomposable sparse systems. Numer Algor 88, 453–474 (2021). https://doi.org/10.1007/s11075-020-01045-x
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DOI: https://doi.org/10.1007/s11075-020-01045-x