https://hal.inria.fr/hal-01647563Bernard, SophieSophieBernardCOMUE UCA - COMUE Université Côte d'Azur (2015-2019)MARELLE - Mathematical, Reasoning and Software - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en AutomatiqueFormalization of the Lindemann-Weierstrass TheoremHAL CCSD2017CoqFormal proofsMultivariate polynomialsPolynomial conjugatesTranscendance[INFO] Computer Science [cs][INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO][INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS]Bernard, Sophie2017-11-24 13:55:262023-03-15 08:58:092017-11-24 17:32:23enConference papersapplication/pdf1This article details a formalization in Coq of the Lindemann-Weierstrass theorem which gives a transcendence criterion for complex numbers: this theorem establishes a link between the linear independence of a set of algebraic numbers and the algebraic independence of the exponentials of these numbers. As we follow Baker's proof, we discuss the difficulties of its formalization and explain how we resolved them in Coq. Most of these difficulties revolve around multivariate polynomials and their relationship with the conjugates of a univariate polynomial. Their study ultimately leads to alternative forms of the fundamental theorem of symmetric polynomials. This formalization uses mainly the Mathcomp library for the part relying on algebra, and the Coquelicot library and the Coq standard library of real numbers for the calculus part.