Abstract
Bézout’s Theorem is the n-dimensional generalization of the Fundamental Theorem of Algebra. It “counts” the number of solutions of a system of n complex polynomial equations in n-unknowns. It is the goal of this chapter to prove Bézout’s Theorem. In Chapter 16 we use Bézout’s Theorem as a tool to derive geometric upper bounds on the number of connected components of semi-algebraic sets and complexity-theoretic lower bounds on some problems such as the Knapsack.
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© 1998 Springer Science+Business Media New York
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Blum, L., Cucker, F., Shub, M., Smale, S. (1998). Bézout’s Theorem. In: Complexity and Real Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0701-6_10
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DOI: https://doi.org/10.1007/978-1-4612-0701-6_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6873-4
Online ISBN: 978-1-4612-0701-6
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