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Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure. Particularly fruitful--both for information on real solutions and for applicability--are systems whose additional structure comes from geometry. Such equations from geometry for which we havearXiv:math/0609829v2 fatcat:xqnyznyvsrfbvbe35k2w37rutq