chore(CMField): generalize definitions and results

[xroblot]

We continue the work in #31810 but removing the NumberField hypothesis in the definition of CM-fields. Many results still hold if it is replaced by the hypothesis that the field is of characteristic zero and some integrality hypothesis.

---

• depends on: chore(TotallyReal/TotallyComplex): remove the NumberField hypothesis #31810

[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

+ NumberField.CMExtension.of_isMulCommutative
+ instance [CharZero K] [Algebra.IsIntegral ℚ K] [IsAlgClosed A] : Nonempty (K →+* A) := by
+ 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] :
+ of_isAbelianGalois
- 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(TotallyReal/TotallyComplex): remove the NumberField hypothesis #31810
  By Dependent Issues (🤖). Happy coding!