A constructive version of Laplace's proof on the existence of complex roots

Abstract : Laplace presented an algebraic proof of the fundamental theorem of algebra which relied on the existence of a splitting field. This proof can be generalized by replacing real numbers by any real closed field. Although it is possible to build a splitting field in a classical context, it is not true anymore in an constructive context. We present a constructive version of Laplace's proof as the result of a general method to make constructive sense of the notion of splitting fields.
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https://hal.inria.fr/inria-00592284
Contributor : Cyril Cohen <>
Submitted on : Thursday, May 12, 2011 - 1:21:38 AM
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Cyril Cohen, Thierry Coquand. A constructive version of Laplace's proof on the existence of complex roots. Journal of Algebra, Elsevier, 2013, 381, pp.110-115. ⟨10.1016/j.jalgebra.2013.01.016⟩. ⟨inria-00592284v1⟩

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