## View abstract

### 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. document.getElementById('cloak47120c901fb78e23dc43463121b44d31').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy47120c901fb78e23dc43463121b44d31 = 'jr&#111;dr&#105;g&#117;&#101;z43' + '&#64;'; addy47120c901fb78e23dc43463121b44d31 = addy47120c901fb78e23dc43463121b44d31 + 'w&#105;sc' + '&#46;' + '&#101;d&#117;'; var addy_text47120c901fb78e23dc43463121b44d31 = 'jr&#111;dr&#105;g&#117;&#101;z43' + '&#64;' + 'w&#105;sc' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak47120c901fb78e23dc43463121b44d31').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy47120c901fb78e23dc43463121b44d31 + '\'>'+addy_text47120c901fb78e23dc43463121b44d31+'<\/a>';

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).