C++ library Geomsolvex of MATHEMAGIX: Implementation of the Kronecker polynomial solver for a reduced regular sequence. The geometric resolution algorithm is a Gröbner-free alternative for solving polynomial systems of equations and inequations. It computes a lifting fiber of the system (see e.g. [Giusti, Lecerf, Salvy - A Gröbner free alternative for polynomial system solving]). Its current implementation in Mathemagix handles only certain polynomial systems in input, that are systems of equations that form a regular reduced sequence. This restriction implies in particular that there are the same number of equations and variables and that the solutions of the system are a set of points.

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  1. Bank, Bernd; Giusti, Marc; Heintz, Joos; Lecerf, Grégoire; Matera, Guillermo; Solernó, Pablo: Degeneracy loci and polynomial equation solving (2015)