Definition

A simple example of a system of polynomial equations is
:Its solutions are the four pairs . These solutions can easily be checked by substitution, but more work is needed for proving that there are no other solutions.

The subject of this article is the study of generalizations of such an examples, and the description of the methods that are used for computing the solutions.

A system of polynomial equations, or polynomial system is a collection of equations
:where each is a polynomial

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