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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2021.8
URN: urn:nbn:de:0030-drops-139038
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13903/
Bernard, Sophie ;
Cohen, Cyril ;
Mahboubi, Assia ;
Strub, Pierre-Yves
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.
BibTeX - Entry
@InProceedings{bernard_et_al:LIPIcs.ITP.2021.8,
author = {Bernard, Sophie and Cohen, Cyril and Mahboubi, Assia and Strub, Pierre-Yves},
title = {{Unsolvability of the Quintic Formalized in Dependent Type Theory}},
booktitle = {12th International Conference on Interactive Theorem Proving (ITP 2021)},
pages = {8:1--8:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-188-7},
ISSN = {1868-8969},
year = {2021},
volume = {193},
editor = {Cohen, Liron and Kaliszyk, Cezary},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13903},
URN = {urn:nbn:de:0030-drops-139038},
doi = {10.4230/LIPIcs.ITP.2021.8},
annote = {Keywords: Galois theory, Coq, Mathematical Components, Dependent Type Theory, Abel-Ruffini, General quintic}
}
