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Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 21, 19:15 ~ 19:45 UTC-3

Decomposable Sparse Polynomial Systems

Jose Israel Rodriguez

University of Wisconsin --- Madison, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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. In this talk, I will discuss how this leads to a recursive algorithm to solve decomposable sparse systems.

Joint work with Taylor Brysiewicz (Max Planck Institute for Mathematics in the Sciences in Leipzig), Frank Sottile (Texas A&M) and Thomas Yahl (Texas A&M).

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