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feat(LinearAlgebra/Multilinear/DirectSum, LinearAlgebra/DirectSum/{PiTensorProduct,Finsupp}): interaction between `MultilinearMap` and `DirectSum`, and between `PiTensorProduct` and `DirectSum`

Open smorel394 opened this issue 1 year ago • 1 comments

This does three things:

  • MultilinearMap.fromDirectSumEquiv (in LinearAlgebra/MultilinearMap/DirectSum.lean) calculates MultilinearMaps on a family of DirectSums. More precisely, if 'ιis aFintype, if κ iis a family of types indexed byιand we have aR-module M i jfor everyi : ιandj : κ i, this is the linear equivalence between Π p : (i : ι) → κ i, MultilinearMap R (fun i ↦ M i (p i)) M'andMultilinearMap R (fun i ↦ ⨁ j : κ i, M i j) M'`.
  • PiTensorProduct.directSum (in LinearAlgebra/DirectSum/PiTensorProduct.lean): the distributivity property of a PiTensorProduct with respect to DirectSums in all its arguments.
  • finsuppPiTensorProduct (in LinearAlgebra/DirectSum/Finsupp.lean): If ι is a Fintype, κ i is a family of types indexed by ι and M i is a family of R-modules indexed by ι, then the tensor product of the family κ i →₀ M i is linearly equivalent to ∏ i, κ i →₀ ⨂[R] i, M i.
  • [x] depends on: #11152
  • [x] depends on: #11196

Open in Gitpod

smorel394 avatar Mar 04 '24 18:03 smorel394

PR summary 707c205109

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.LinearAlgebra.DirectSum.Finsupp 992 1009 +17 (+1.71%)
Import changes for all files
Files Import difference
Mathlib.LinearAlgebra.ExteriorPower.Pairing 5
Mathlib.Analysis.NormedSpace.PiTensorProduct.InjectiveSeminorm Mathlib.Analysis.NormedSpace.PiTensorProduct.ProjectiveSeminorm 6
392 files Mathlib.Algebra.Category.ModuleCat.ExteriorPower Mathlib.Analysis.Analytic.Basic Mathlib.Analysis.Analytic.CPolynomialDef Mathlib.Analysis.Analytic.CPolynomial Mathlib.Analysis.Analytic.ChangeOrigin Mathlib.Analysis.Analytic.Composition Mathlib.Analysis.Analytic.Constructions Mathlib.Analysis.Analytic.Inverse Mathlib.Analysis.Analytic.IsolatedZeros Mathlib.Analysis.Analytic.IteratedFDeriv Mathlib.Analysis.Analytic.Linear Mathlib.Analysis.Analytic.OfScalars Mathlib.Analysis.Analytic.Order Mathlib.Analysis.Analytic.Polynomial Mathlib.Analysis.Analytic.RadiusLiminf Mathlib.Analysis.Analytic.Uniqueness Mathlib.Analysis.Analytic.Within Mathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.CStarAlgebra.CStarMatrix Mathlib.Analysis.CStarAlgebra.CompletelyPositiveMap Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral 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5 files Mathlib.Analysis.Calculus.FormalMultilinearSeries Mathlib.Analysis.NormedSpace.Multilinear.Curry Mathlib.RepresentationTheory.GroupCohomology.Functoriality Mathlib.RepresentationTheory.GroupCohomology.Hilbert90 Mathlib.RepresentationTheory.GroupCohomology.LowDegree
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719 files Mathlib.Algebra.Category.Ring.Under.Limits Mathlib.Algebra.DirectSum.LinearMap Mathlib.Algebra.GCDMonoid.IntegrallyClosed Mathlib.Algebra.Lie.CartanExists Mathlib.Algebra.Lie.Classical Mathlib.Algebra.Lie.Derivation.Killing Mathlib.Algebra.Lie.Killing Mathlib.Algebra.Lie.LieTheorem Mathlib.Algebra.Lie.Matrix Mathlib.Algebra.Lie.Rank Mathlib.Algebra.Lie.Semisimple.Lemmas Mathlib.Algebra.Lie.SkewAdjoint Mathlib.Algebra.Lie.TraceForm Mathlib.Algebra.Lie.Weights.Basic Mathlib.Algebra.Lie.Weights.Cartan Mathlib.Algebra.Lie.Weights.Chain Mathlib.Algebra.Lie.Weights.Killing Mathlib.Algebra.Lie.Weights.Linear Mathlib.Algebra.Lie.Weights.RootSystem Mathlib.Algebra.Module.DedekindDomain Mathlib.Algebra.Module.LinearMap.Polynomial Mathlib.Algebra.Module.PID Mathlib.Algebra.Module.ZLattice.Basic Mathlib.Algebra.Module.ZLattice.Covolume Mathlib.Algebra.Polynomial.Bivariate Mathlib.Algebra.Polynomial.Module.FiniteDimensional Mathlib.AlgebraicGeometry.AffineScheme 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6 files Mathlib.Analysis.NormedSpace.Alternating.Basic Mathlib.Analysis.NormedSpace.Multilinear.Basic Mathlib.RepresentationTheory.GroupCohomology.Basic Mathlib.RepresentationTheory.GroupCohomology.Resolution Mathlib.Topology.Algebra.Module.Alternating.Topology Mathlib.Topology.Algebra.Module.Multilinear.Topology
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51 files Mathlib.Algebra.Category.FGModuleCat.Basic Mathlib.Algebra.Category.FGModuleCat.Limits Mathlib.Algebra.Category.ModuleCat.Differentials.Basic Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf Mathlib.Algebra.Lie.InvariantForm Mathlib.Algebra.Module.Presentation.Differentials Mathlib.CategoryTheory.Preadditive.HomOrthogonal Mathlib.LinearAlgebra.BilinearForm.DualLattice Mathlib.LinearAlgebra.BilinearForm.Orthogonal Mathlib.LinearAlgebra.BilinearForm.Properties Mathlib.LinearAlgebra.BilinearForm.TensorProduct Mathlib.LinearAlgebra.Coevaluation Mathlib.LinearAlgebra.Contraction Mathlib.LinearAlgebra.Dimension.Torsion.Basic Mathlib.LinearAlgebra.Dimension.Torsion.Finite Mathlib.LinearAlgebra.Dual.Lemmas Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber Mathlib.LinearAlgebra.PerfectPairing.Basic Mathlib.LinearAlgebra.RootSystem.Base Mathlib.LinearAlgebra.RootSystem.Chain Mathlib.LinearAlgebra.RootSystem.Defs Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear Mathlib.LinearAlgebra.RootSystem.Finite.G2 Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas Mathlib.LinearAlgebra.RootSystem.Hom Mathlib.LinearAlgebra.RootSystem.Irreducible Mathlib.LinearAlgebra.RootSystem.IsValuedIn Mathlib.LinearAlgebra.RootSystem.OfBilinear Mathlib.LinearAlgebra.RootSystem.Reduced Mathlib.LinearAlgebra.RootSystem.RootPairingCat Mathlib.LinearAlgebra.RootSystem.RootPositive Mathlib.LinearAlgebra.RootSystem.WeylGroup Mathlib.RepresentationTheory.Basic Mathlib.RepresentationTheory.Coinduced Mathlib.RepresentationTheory.Rep Mathlib.RepresentationTheory.Submodule Mathlib.RingTheory.AdicCompletion.AsTensorProduct Mathlib.RingTheory.Extension.Basic Mathlib.RingTheory.Extension.Cotangent.Basic Mathlib.RingTheory.Extension.Cotangent.LocalizationAway Mathlib.RingTheory.Extension.Generators Mathlib.RingTheory.Extension.Presentation.Basic Mathlib.RingTheory.Ideal.Cotangent Mathlib.RingTheory.Kaehler.Basic Mathlib.RingTheory.Kaehler.JacobiZariski Mathlib.RingTheory.Kaehler.Polynomial Mathlib.RingTheory.Kaehler.TensorProduct Mathlib.RingTheory.LocalRing.Module Mathlib.RingTheory.Regular.Depth Mathlib.RingTheory.Regular.IsSMulRegular Mathlib.RingTheory.Regular.RegularSequence
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106 files Mathlib.Algebra.Algebra.Subalgebra.IsSimpleOrder Mathlib.Algebra.Category.Ring.LinearAlgebra Mathlib.Algebra.Central.TensorProduct Mathlib.Algebra.Lie.CartanSubalgebra Mathlib.Algebra.Lie.Character Mathlib.Algebra.Lie.EngelSubalgebra Mathlib.Algebra.Lie.Engel Mathlib.Algebra.Lie.Nilpotent Mathlib.Algebra.Lie.Semisimple.Basic Mathlib.Algebra.Lie.Semisimple.Defs Mathlib.Algebra.Lie.Sl2 Mathlib.Algebra.Lie.Solvable Mathlib.Algebra.LinearRecurrence Mathlib.Analysis.BoxIntegral.Partition.Additive Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Pi Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unitary Mathlib.Analysis.CStarAlgebra.ContinuousMap Mathlib.Analysis.CStarAlgebra.Multiplier Mathlib.Analysis.CStarAlgebra.Unitization Mathlib.Analysis.Calculus.Deriv.Basic Mathlib.Analysis.Calculus.Deriv.Comp Mathlib.Analysis.Calculus.Deriv.Slope Mathlib.Analysis.Calculus.Deriv.Support Mathlib.Analysis.Calculus.FDeriv.Basic Mathlib.Analysis.Calculus.FDeriv.Comp Mathlib.Analysis.Calculus.FDeriv.RestrictScalars Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn Mathlib.Analysis.Convex.AmpleSet Mathlib.Analysis.Convex.BetweenList Mathlib.Analysis.Convex.Between Mathlib.Analysis.Convex.Radon Mathlib.Analysis.Convex.Side Mathlib.Analysis.Convex.StrictConvexBetween Mathlib.Analysis.Convex.Visible Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar Mathlib.Analysis.Normed.Algebra.Unitization Mathlib.Analysis.Normed.Group.ZeroAtInfty Mathlib.Analysis.Normed.Operator.BanachSteinhaus Mathlib.Analysis.Normed.Operator.Banach Mathlib.Analysis.Normed.Unbundled.InvariantExtension Mathlib.Analysis.NormedSpace.Connected Mathlib.Analysis.NormedSpace.Extend Mathlib.Analysis.NormedSpace.OperatorNorm.Mul Mathlib.Analysis.NormedSpace.RCLike Mathlib.Analysis.RCLike.BoundedContinuous Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic Mathlib.Data.Real.GoldenRatio Mathlib.FieldTheory.MvRatFunc.Rank Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional Mathlib.LinearAlgebra.Dimension.ErdosKaplansky Mathlib.LinearAlgebra.FreeModule.Finite.Matrix Mathlib.LinearAlgebra.FreeModule.Finite.Quotient Mathlib.LinearAlgebra.FreeModule.IdealQuotient Mathlib.LinearAlgebra.LinearDisjoint Mathlib.LinearAlgebra.Matrix.FiniteDimensional Mathlib.MeasureTheory.Function.ConvergenceInMeasure Mathlib.MeasureTheory.Function.LpOrder Mathlib.MeasureTheory.Function.LpSpace.Basic Mathlib.MeasureTheory.Function.LpSpace.Complete Mathlib.MeasureTheory.Function.LpSpace.ContinuousFunctions Mathlib.MeasureTheory.Function.LpSpace.Indicator Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic Mathlib.NumberTheory.Padics.AddChar Mathlib.NumberTheory.Padics.MahlerBasis Mathlib.RingTheory.FiniteStability Mathlib.RingTheory.Flat.Basic Mathlib.RingTheory.Flat.CategoryTheory Mathlib.RingTheory.Flat.Domain Mathlib.RingTheory.Flat.Equalizer Mathlib.RingTheory.Flat.EquationalCriterion Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra Mathlib.RingTheory.Flat.FaithfullyFlat.Basic Mathlib.RingTheory.Flat.Localization Mathlib.RingTheory.Flat.Stability Mathlib.RingTheory.LinearDisjoint Mathlib.RingTheory.LocalProperties.Projective Mathlib.RingTheory.LocalRing.Quotient Mathlib.RingTheory.Localization.Algebra Mathlib.RingTheory.Localization.Finiteness Mathlib.RingTheory.Localization.Free Mathlib.RingTheory.MvPolynomial.Localization Mathlib.RingTheory.MvPolynomial Mathlib.RingTheory.RingHom.FiniteType Mathlib.RingTheory.Support Mathlib.RingTheory.TensorProduct.MvPolynomial Mathlib.RingTheory.TensorProduct.Nontrivial Mathlib.Topology.ContinuousMap.Bounded.Star Mathlib.Topology.ContinuousMap.Compact Mathlib.Topology.ContinuousMap.CompactlySupported Mathlib.Topology.ContinuousMap.ContinuousMapZero Mathlib.Topology.ContinuousMap.ContinuousSqrt Mathlib.Topology.ContinuousMap.Ideals Mathlib.Topology.ContinuousMap.StarOrdered Mathlib.Topology.ContinuousMap.StoneWeierstrass Mathlib.Topology.ContinuousMap.Weierstrass Mathlib.Topology.ContinuousMap.ZeroAtInfty Mathlib.Topology.Instances.Complex Mathlib.Topology.MetricSpace.GromovHausdorffRealized Mathlib.Topology.MetricSpace.GromovHausdorff Mathlib.Topology.MetricSpace.Ultra.ContinuousMaps Mathlib.Topology.Separation.NotNormal Mathlib.Topology.TietzeExtension
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13 files Mathlib.Analysis.LocallyConvex.StrongTopology Mathlib.Analysis.Normed.Affine.ContinuousAffineMap Mathlib.Analysis.Normed.Field.WithAbs Mathlib.Analysis.Normed.Module.Completion Mathlib.Analysis.NormedSpace.OperatorNorm.Asymptotics Mathlib.Analysis.NormedSpace.OperatorNorm.Basic Mathlib.Analysis.NormedSpace.OperatorNorm.Bilinear Mathlib.Analysis.NormedSpace.OperatorNorm.Completeness Mathlib.Analysis.NormedSpace.OperatorNorm.NNNorm Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace Mathlib.Analysis.NormedSpace.OperatorNorm.Prod Mathlib.Topology.ContinuousMap.Bounded.Normed Mathlib.Topology.ContinuousMap.BoundedCompactlySupported
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59 files Mathlib.Algebra.Algebra.Subalgebra.Centralizer Mathlib.Algebra.Azumaya.Basic Mathlib.Algebra.Azumaya.Defs Mathlib.Algebra.Azumaya.Matrix Mathlib.Algebra.Category.ModuleCat.Presheaf.Free Mathlib.Algebra.Category.ModuleCat.Presheaf.Generator Mathlib.Algebra.Category.ModuleCat.Presheaf.Pullback Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous Mathlib.Algebra.Category.ModuleCat.Simple Mathlib.Algebra.Homology.LocalCohomology Mathlib.Algebra.Module.FinitePresentation Mathlib.Algebra.Module.Lattice Mathlib.Algebra.Module.Presentation.Finite Mathlib.Condensed.AB Mathlib.Condensed.Discrete.Characterization Mathlib.Condensed.Discrete.Module Mathlib.Condensed.Epi Mathlib.Condensed.Explicit Mathlib.Condensed.Light.AB Mathlib.Condensed.Light.Epi Mathlib.Condensed.Light.Explicit Mathlib.Condensed.Light.Limits Mathlib.Condensed.Light.Module Mathlib.Condensed.Limits Mathlib.Condensed.Module Mathlib.Condensed.Solid Mathlib.FieldTheory.Finiteness Mathlib.LinearAlgebra.Dimension.Constructions Mathlib.LinearAlgebra.Dimension.DivisionRing Mathlib.LinearAlgebra.Dimension.Finite Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition Mathlib.LinearAlgebra.Dimension.LinearMap Mathlib.LinearAlgebra.Dimension.Localization Mathlib.LinearAlgebra.Dimension.RankNullity Mathlib.LinearAlgebra.Eigenspace.Basic Mathlib.LinearAlgebra.Eigenspace.Matrix Mathlib.LinearAlgebra.FiniteDimensional.Basic Mathlib.LinearAlgebra.FiniteDimensional.Lemmas Mathlib.LinearAlgebra.Matrix.Diagonal Mathlib.LinearAlgebra.Projectivization.Basic Mathlib.LinearAlgebra.Projectivization.Cardinality Mathlib.LinearAlgebra.Projectivization.Independence Mathlib.LinearAlgebra.Projectivization.Subspace Mathlib.LinearAlgebra.TensorProduct.Subalgebra Mathlib.LinearAlgebra.TensorProduct.Submodule Mathlib.LinearAlgebra.TensorProduct.Vanishing Mathlib.RingTheory.Adjoin.Dimension Mathlib.RingTheory.Ideal.Quotient.Index Mathlib.RingTheory.Length Mathlib.RingTheory.LocalProperties.Basic Mathlib.RingTheory.LocalProperties.Reduced Mathlib.RingTheory.Localization.BaseChange Mathlib.RingTheory.RingHom.Finite Mathlib.RingTheory.RingHom.Locally Mathlib.RingTheory.RingHom.Surjective Mathlib.RingTheory.SimpleModule.Rank Mathlib.RingTheory.TensorProduct.Free Mathlib.RingTheory.TensorProduct.IsBaseChangePi Mathlib.Topology.Compactification.OnePointEquiv
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Mathlib.Analysis.Normed.Operator.Compact Mathlib.Topology.Algebra.Module.StrongTopology 16
7 files Mathlib.Algebra.Category.ModuleCat.Adjunctions Mathlib.Algebra.Category.ModuleCat.Projective Mathlib.Algebra.Module.Projective Mathlib.LinearAlgebra.DirectSum.Finsupp Mathlib.LinearAlgebra.TensorProduct.Basis Mathlib.RingTheory.Finiteness.Projective Mathlib.Topology.Algebra.SeparationQuotient.Section
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Mathlib.LinearAlgebra.Multilinear.DirectSum (new file) 987
Mathlib.LinearAlgebra.DFinsupp.PiTensorProduct (new file) 995
Mathlib.LinearAlgebra.DirectSum.PiTensorProduct (new file) 1001

Declarations diff

+ dfinsupp + dfinsupp_symm_single_tprod + dfinsupp_tprod_apply + dfinsupp_tprod_single + directSum + directSum_ext + directSum_symm_lof_tprod + directSum_tprod_apply + directSum_tprod_lof + finsuppPiTensorProduct + finsuppPiTensorProduct' + finsuppPiTensorProduct'_apply_apply + finsuppPiTensorProduct'_tprod_single + finsuppPiTensorProduct_apply + finsuppPiTensorProduct_symm_single_tprod + finsuppPiTensorProduct_tprod_single + fromDFinsuppEquiv + fromDFinsuppEquiv_apply + fromDFinsuppEquiv_single + fromDFinsuppEquiv_symm_apply + fromDirectSumEquiv + fromDirectSumEquiv_apply + fromDirectSumEquiv_lof + fromDirectSumEquiv_symm_apply

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.

Increase in tech debt: (relative, absolute) = (1.00, 0.00)
Current number Change Type
872 1 erw

Current commit 707c205109 Reference commit 7ed4f8133a

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).

github-actions[bot] avatar Oct 13 '24 11:10 github-actions[bot]

(sorry, pushed by accident)

eric-wieser avatar Oct 19 '24 00:10 eric-wieser

This PR/issue depends on:

  • ~~leanprover-community/mathlib4#11152~~
  • ~~leanprover-community/mathlib4#11196~~
  • ~~leanprover-community/mathlib4#17881~~
  • ~~leanprover-community/mathlib4#17932~~ By Dependent Issues (🤖). Happy coding!

mathlib4-dependent-issues-bot avatar Oct 27 '24 10:10 mathlib4-dependent-issues-bot

This pull request has conflicts, please merge master and resolve them.

mathlib4-merge-conflict-bot avatar Nov 19 '25 07:11 mathlib4-merge-conflict-bot