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

JOURNAL OF ALGEBRA

卷:381

Article

Cohen, Cyril¹  Coquand, Thierry¹ 

[1] Univ Gothenburg, Gothenburg, Sweden

关键词: Constructive algebra;    Fundamental theorem of algebra;   

DOI  :  10.1016/j.jalgebra.2013.01.016

来源: Elsevier

【 摘 要 】

We present a constructive analysis of Laplace's proof that the field of complex numbers is algebraically closed. This proof was criticized by Gauss, who presented later a rigorous and constructive version of this proof. Our argument is different, and closer to the one of Laplace. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free