I am happy to announce that we -- Sophie Bernard, Cyril Cohen, Assia Mahboubi and Pierre-Yves Strub -- were able to formalize in Coq **a proof of Abel-Ruffini Theorem**, which states that there are polynomials of degree 5 that are not solvable by radicals, e.g. $X^5 - 4X + 2$.

```
Lemma example_not_solvable_by_radicals :
~ solvable_by_radical_poly ('X^5 - 4 *: 'X + 2).
```

This is a consequence of Abel-Galois theorem (also formalized) which states the equivalence between being solvable by radicals and having a solvable Galois group.

The proofs are accessible in the repository https://github.com/math-comp/Abel and will soon be released as the opam package `coq-mathcomp-abel.1.0.0`

and as a nix package. This development uses and extends non trivially the Mathematical Components library especially the Galois Theory part.

NB: all the proofs in this repository are constructive.

–

Cyril Cohen, for the contributors of https://github.com/math-comp/Abel

Cross posted to #Coq users and #math-comp users **please follow-up on** #math-comp users

Last updated: Jan 28 2023 at 06:30 UTC