(WIP) Galois group of x^n - x - 1

[tb65536]

---

[github-actions]

PR summary dde1cfffb6

Import changes exceeding 2%

%	File
+15.20%	Mathlib.FieldTheory.Galois.IsGaloisGroup
+20.84%	Mathlib.RingTheory.Polynomial.Selmer

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.Polynomial.Selmer	2557	3090	+533 (+20.84%)
Mathlib.FieldTheory.Galois.IsGaloisGroup	1691	1948	+257 (+15.20%)

Import changes for all files

Files	Import difference
Mathlib.FieldTheory.Galois.IsGaloisGroup	257
Mathlib.RingTheory.Polynomial.Selmer	533

---

Declarations diff

+ AddSubgroup.subgroupOf_inertia
+ Ideal.card_inertiaSubgroup
+ Ideal.inertiaSubgroup_eq_ker
+ IsFractionRing.nontrivial'
+ IsGaloisGroup.toIsFractionRing
+ X_pow_sub_X_sub_one_gal
+ _root_.Polynomial.Monic.mem_rootSet
+ aeval_smul
+ card_fixingSubgroup_eq_finrank
+ card_subgroup_eq_finrank_fixedpoints
+ finite
+ fixedPoints_bot
+ fixedPoints_fixingSubgroup
+ fixedPoints_le_of_le
+ fixedPoints_top
+ fixingSubgroup_bot
+ fixingSubgroup_fixedPoints
+ fixingSubgroup_le_of_le
+ fixingSubgroup_top
+ genthm
+ genthm₀
+ inst4
+ instance (K : Type*) [Field K] [NumberField K]
+ instance {R S : Type*} [CommRing R] [CommRing S] [IsDomain S] [Algebra R S]
+ le_fixedPoints_iff_le_fixingSubgroup
+ switchinglemma
+ tada
+ tada'
+ tada''
+ to_intermediateField
+ to_subgroup

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[AntoineChambert-Loir]

Question: would one want to have this framed in this way or as a MulEquiv?

[AntoineChambert-Loir]

The same argument also works in the geometric context, for galois groups over Q(X) (see Serre Topics in Galois theory, §4.4) and I hope it will be possible to set up such a framework.