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What is an extremely important problem that requires one to solve large systems of polynomial equations? I've heard of a number of "general areas" where the problems crop up (robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, machine learning, control theory), but never an explicit problem.

Perhaps one that is easy to state without too much domain knowledge?

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    Multivariate polynomials model many geometric objects and curves well. So anything that could have anything to do with geometry, surfaces or paths on surfaces.2016-05-04

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