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General Theory of Algebraic Equations by Etienne Bézout, Eric Feron

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Translator’s Foreword

This document is a literal translation of Bézout’s seminal work on the theory of algebraic equations in several unknowns. The notation of this translation strictly follows that of the original manuscript. Bézout’s purpose was to provide an in-depth analysis of systems of algebraic equations. His main push was devoted to determining the degree of the final equation in one unknown, resulting from the original set of polynomial equations.

Translating Bézout’s research centerpiece became necessary to me after attending an illuminating presentation made by Pablo Parrilo at MIT sometime around 2002. His presentation was devoted to polynomially constrained polynomial optimization via sum-of-square arguments. It was illuminating ...

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