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The complexity of robot motion planning
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Solving systems of nonlinear polynomial equations faster
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Using multivariate resultants to find the implicit equation of a rational surface
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Motivated by revived interest in elimination techniques, we survey methods for constructing bivariate and multivariate resultants. This tutorial consists of two parts: Part 1 introduces elimination theory, presents properties of resultants, and develops explicit expressions for bivariate resultants; Part 2 explains multivariate resultants and includes the Dixon and Macaulay resultants as well as special resultant expressions for three polynomials of the same degree.