perf: lower the priority of Comm*.to* instances

[astrainfinita]

CommRing.toRing is an exception. CommRing is so important that it needs to be looked up early. An important goal of #7873 is also to search for Zero/One/Add/Mul instances first along Zero/One/Add/Mul -> ... -> Ring -> CommRing -> Field.

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• depends on: perf: lower the priority of *WithOne.to* instances #18474
• depends on: perf: change the priority of *.toRing instances #18641

From #7873.

[github-actions]

PR summary 51ade5646b

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas	1543	1336	-207 (-13.42%)
Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity	1552	1352	-200 (-12.89%)
Mathlib.NumberTheory.NumberField.Discriminant.Defs	1646	1441	-205 (-12.45%)
Mathlib.NumberTheory.Padics.PadicNumbers	1290	1142	-148 (-11.47%)
Mathlib.Topology.MetricSpace.Polish	1268	1259	-9 (-0.71%)

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas	-207
Mathlib.NumberTheory.NumberField.Discriminant.Defs	-205
Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity Mathlib.NumberTheory.SumTwoSquares	-200
Mathlib.NumberTheory.Padics.PadicNumbers Mathlib.NumberTheory.Harmonic.Int	-148
Mathlib.NumberTheory.Padics.PadicIntegers	-109
Mathlib.Algebra.Homology.Embedding.Basic	-101
Mathlib.NumberTheory.Padics.RingHoms	-89
Mathlib.RingTheory.WittVector.Compare	-84
Mathlib.Algebra.Module.LinearMap.Rat Mathlib.Algebra.Module.Rat	-37
12 files Mathlib.Algebra.Star.Module Mathlib.CategoryTheory.Monoidal.Linear Mathlib.Algebra.Category.ModuleCat.Monoidal.Symmetric Mathlib.Algebra.Category.ModuleCat.Monoidal.Basic Mathlib.Algebra.Algebra.Unitization Mathlib.CategoryTheory.Quotient.Linear Mathlib.Algebra.Homology.ShortComplex.Linear Mathlib.RepresentationTheory.Action.Limits Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed Mathlib.CategoryTheory.Monoidal.Subcategory Mathlib.Algebra.Homology.Linear Mathlib.CategoryTheory.Linear.LinearFunctor	-33
4 files Mathlib.Algebra.Homology.Embedding.HomEquiv Mathlib.Algebra.Homology.Embedding.Extend Mathlib.Algebra.Homology.Embedding.Boundary Mathlib.Algebra.Homology.Embedding.Restriction	-29
21 files Mathlib.Data.Matrix.Auto Mathlib.Data.Matrix.Invertible Mathlib.Data.Matrix.Composition Mathlib.Data.Matrix.Basic Mathlib.Data.Matrix.Basis Mathlib.GroupTheory.Coxeter.Matrix Mathlib.Data.Matrix.PEquiv Mathlib.Data.Matrix.CharP Mathlib.Data.Matrix.Block Mathlib.CategoryTheory.Preadditive.Mat Mathlib.Data.Matrix.Reflection Mathlib.LinearAlgebra.Matrix.Trace Mathlib.LinearAlgebra.Matrix.Symmetric Mathlib.Data.Matrix.RowCol Mathlib.Data.Matrix.DualNumber Mathlib.Data.Matrix.Hadamard Mathlib.Combinatorics.Optimization.ValuedCSP Mathlib.Combinatorics.SimpleGraph.IncMatrix Mathlib.Data.Matrix.Notation Mathlib.LinearAlgebra.Matrix.Circulant Mathlib.LinearAlgebra.Matrix.Orthogonal	-25
10 files Mathlib.LinearAlgebra.FinsuppVectorSpace Mathlib.Algebra.Category.ModuleCat.Adjunctions Mathlib.LinearAlgebra.Matrix.Ideal Mathlib.LinearAlgebra.Matrix.DotProduct Mathlib.Algebra.Module.Projective Mathlib.RepresentationTheory.Action.Monoidal Mathlib.LinearAlgebra.TensorProduct.Basis Mathlib.RingTheory.Localization.FractionRing Mathlib.LinearAlgebra.FreeModule.Basic Mathlib.LinearAlgebra.StdBasis	-10
Mathlib.Topology.MetricSpace.Polish Mathlib.Topology.MetricSpace.Perfect	-9
Mathlib.GroupTheory.Coxeter.Basic	-8
3 files Mathlib.Data.Rat.Denumerable Mathlib.MeasureTheory.Constructions.Polish.EmbeddingReal Mathlib.MeasureTheory.Constructions.Polish.Basic	-5

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

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.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• perf: lower the priority of *WithOne.to* instances #18474
• perf: change the priority of *.toRing instances #18641
  By Dependent Issues (🤖). Happy coding!

[astrainfinita]

!bench