Editing Elimination theory (section)

{{short description|Part of algebraic geometry devoted to the elimination of variables between polynomials}}
In [[commutative algebra]] and [[algebraic geometry]], '''elimination theory''' is the classical name for algorithmic approaches to eliminating some variables between [[polynomial]]s of several variables, in order to solve [[systems of polynomial equations]].

Classical elimination theory culminated with the work of [[Francis Sowerby Macaulay|Francis Macaulay]] on [[multivariate resultant]]s, as described in the chapter on ''Elimination theory'' in the first editions (1930) of [[Bartel Leendert van der Waerden|Bartel van der Waerden]]'s ''[[Moderne Algebra]]''. After that, elimination theory was ignored by most algebraic geometers for almost thirty years, until the introduction of new methods for solving polynomial equations, such as [[Gröbner bases]], which were needed for [[computer algebra]].