[Merged by Bors] - chore(NumberTheory/NumberField/AdeleRing): refactor adele rings

[kbuzzard]

The current AdeleRing ℚ explicitly involves 𝓞 ℚ and is not much fun to work with. This PR enables AdeleRing ℤ ℚ.

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[github-actions]

PR summary d4abfe627f

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ instance : Algebra K (AdeleRing R K) := Prod.algebra _ _ _
+ instance : CommRing (AdeleRing R K) := Prod.instCommRing
+ instance : Inhabited (AdeleRing R K) := ⟨0⟩
+ instance : TopologicalRing (AdeleRing R K) := instTopologicalRingProd
+ instance : TopologicalSpace (AdeleRing R K) := instTopologicalSpaceProd
- instance : Algebra K (AdeleRing K) := Prod.algebra _ _ _
- instance : CommRing (AdeleRing K) := Prod.instCommRing
- instance : Inhabited (AdeleRing K) := ⟨0⟩
- instance : TopologicalRing (AdeleRing K) := instTopologicalRingProd
- instance : TopologicalSpace (AdeleRing K) := instTopologicalSpaceProd

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.

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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).

[alexjbest]

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by alexjbest.

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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