This talk by Adam Strzebonski at the Wolfram Technology Conference 2011 gives a survey of Mathematica functions related to solving algebraic equations and inequalities. It also discusses the choice of the most appropriate solvers for various types of problems and the ways of formulating the problems so that they can be solved most efficiently. For more information about Mathematica, please visit: www.wolfram.com
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Getting the Most from Algebraic Solvers in Mathematica