# A Gröbner Free Alternative for Polynomial System Solving

@article{Giusti2001AGF, title={A Gr{\"o}bner Free Alternative for Polynomial System Solving}, author={Marc Giusti and Gr{\'e}goire Lecerf and Bruno Salvy}, journal={J. Complex.}, year={2001}, volume={17}, pages={154-211} }

Given a system of polynomial equations and inequations with coefficients in the field of rational numbers, we show how to compute a geometric resolution of the set of common roots of the system over the field of complex numbers. A geometric resolution consists of a primitive element of the algebraic extension defined by the set of roots, its minimal polynomial, and the parametrizations of the coordinates. Such a representation of the solutions has a long history which goes back to Leopold…

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