Elimination Theory

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High Quality Content by WIKIPEDIA articles! In commutative algebra and algebraic geometry, elimination theory is the classical nam...

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High Quality Content by WIKIPEDIA articles! In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables. The linear case would now routinely be handled by Gaussian elimination, rather than the theoretical solution provided by Cramer's rule. In the same way, computational techniques for elimination can in practice be based on Gröbner basis methods. There is however older literature on types of eliminant, including resultants to find common roots of polynomials, discriminants and so on. In particular the discriminant appears in invariant theory, and is often constructed as the invariant of either a curve or an n-ary k-ic form. Whilst discriminants are always constructed resultants,