Formalization of the Lindemann-Weierstrass Theorem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2017

Formalization of the Lindemann-Weierstrass Theorem

Abstract

This 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.
Fichier principal
Vignette du fichier
main.pdf (295.27 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01647563 , version 1 (24-11-2017)

Identifiers

  • HAL Id : hal-01647563 , version 1

Cite

Sophie Bernard. Formalization of the Lindemann-Weierstrass Theorem. Interactive Theorem Proving, Sep 2017, Brasilia, Brazil. ⟨hal-01647563⟩
299 View
759 Download

Share

Gmail Facebook X LinkedIn More