feat(CMField): add IsCyclotomicExtension.Rat.isCMField

[xroblot]

We remove the NumberField hypothesis in two more results and thus can deduce that any nontrivial cyclotomic extension of ℚ is CM. In particular, we add the instance:

instance (K : Type*) [Field K] [CharZero K] [IsCyclotomicExtension ⊤ ℚ K] : IsCMField K

---

• depends on: chore(CMField): generalize definitions and results #31811
• depends on: feat(FieldTheory/IsGaloisGroup): prove the Galois correspondence for IsGaloisGroup #29688

[github-actions]

PR summary 66b2a6571b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ IsComplex.of_comap
+ NumberField.CMExtension.of_isMulCommutative
+ card_fixingSubgroup_eq_finrank
+ card_subgroup_eq_finrank_fixedpoints
+ fixedPoints_bot
+ fixedPoints_fixingSubgroup
+ fixedPoints_le_of_le
+ fixedPoints_top
+ fixingSubgroup_bot
+ fixingSubgroup_fixedPoints
+ fixingSubgroup_le_of_le
+ fixingSubgroup_top
+ instance [CharZero K] [Algebra.IsIntegral ℚ K] [IsAlgClosed A] : Nonempty (K →+* A) := by
+ instance [IsCyclotomicExtension ⊤ ℚ K] :
+ instance [IsTotallyReal K] (F : Subfield K) [Algebra.IsIntegral F K] : IsTotallyReal F
+ instance [IsTotallyReal K] [CharZero K] (F : IntermediateField ℚ K) [Algebra.IsAlgebraic F K] :
+ instance [Nonempty (K →+* ℂ)] : Nonempty (NumberField.InfinitePlace K) := Set.instNonemptyRange _
+ instance _root_.IntermediateField.isTotallyReal_bot [CharZero K] :
+ instance _root_.Subfield.isTotallyReal_bot [CharZero K] :
+ intermediateFieldEquivSubgroup
+ intermediateFieldEquivSubgroup_apply
+ intermediateFieldEquivSubgroup_symm_apply
+ intermediateFieldEquivSubgroup_symm_apply_toDual
+ isCMField
+ isTotallyComplex
+ isTotallyComplex_of_algebra
+ le_fixedPoints_iff_le_fixingSubgroup
+ map_mulEquivAlgEquiv_fixingSubgroup
+ ofCMExtension
+ ofDual_intermediateFieldEquivSubgroup_apply
+ of_fixed_field
+ of_forall_isConj
+ of_isAbelianGalois
+ of_mulEquiv_algEquiv
+ to_intermediateField
+ to_subgroup
- _root_.NumberField.IsCMField.ofCMExtension
- _root_.NumberField.IsCMField.of_forall_isConj
- instance [IsTotallyReal K] (F : IntermediateField ℚ K) : IsTotallyReal F
- instance [IsTotallyReal K] (F : Subfield K) : IsTotallyReal F
- instance [NumberField K] : Nonempty (NumberField.InfinitePlace K) := Set.instNonemptyRange _
- of_isMulCommutative

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• chore(CMField): generalize definitions and results #31811
• feat(FieldTheory/IsGaloisGroup): prove the Galois correspondence for IsGaloisGroup #29688
  By Dependent Issues (🤖). Happy coding!