Elimination theory

In <a href="/facts/Commutative_algebra/mKtUdPCT">commutative algebra</a> and <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, elimination theory is the classical name for algorithmic approaches to eliminating some variables between <a href="/facts/Polynomial/Lzak8VVx">polynomials</a> of several variables, in order to solve <a href="/facts/Systems_of_polynomial_equations/1456MrT2">systems of polynomial equations</a>.
Classical elimination theory culminated with the work of <a href="/facts/Francis_Sowerby_Macaulay/4XTyDBNa">Francis Macaulay</a> on <a href="/facts/Multivariate_resultant/A5g2MdhT">multivariate resultants</a>, as described in the chapter on Elimination theory in the first editions (1930) of <a href="/facts/Bartel_Leendert_van_der_Waerden/rITfcujK">Bartel van der Waerden</a>'s <a href="/facts/Moderne_Algebra/bnnBkY3Y">Moderne Algebra</a>. 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 <a href="/facts/Gr%25C3%25B6bner_bases/efMrjM7w">Gröbner bases</a>, which were needed for <a href="/facts/Computer_algebra/hjun1KAX">computer algebra</a>.

Elimination theory open-in-new

Elimination theory