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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Submitted on : Friday, March 22, 2013 - 9:47:09 PM
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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-00592284v2⟩

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