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Unsolvability of the Quintic Formalized in Dependent Type Theory

Abstract : In this paper, we describe an axiom-free Coq formalization that there does not exists a general method for solving by radicals polynomial equations of degree greater than 4. This development includes a proof of Galois’ Theorem of the equivalence between solvable extensions and extensions solvable by radicals. The unsolvability of the general quintic follows from applying this theorem to a well chosen polynomial with unsolvable Galois group.
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Contributor : Cyril Cohen <>
Submitted on : Sunday, May 2, 2021 - 1:44:47 AM
Last modification on : Wednesday, May 5, 2021 - 3:07:53 AM


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  • HAL Id : hal-03136002, version 4


Sophie Bernard, Cyril Cohen, Assia Mahboubi, Pierre-Yves Strub. Unsolvability of the Quintic Formalized in Dependent Type Theory. ITP 2021 - 12th International Conference on Interactive Theorem Proving, Jun 2021, Rome / Virtual, France. ⟨hal-03136002v4⟩



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