feature(LinearAlgebra/QuadraticForm/TensorProduct): Extend baseChange_ext to work over a free module

[mans0954]

This PR continues the work from #21814.

Original PR: #21814

[mans0954]

Comments from Original PR #21814

This section contains 1 comment(s) from the original PR, excluding bot comments.

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@github-actions (2025-02-13 07:46 UTC):

PR summary 4dda80b3a0

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.Basis.Bilinear	798	799	+1 (+0.13%)
Mathlib.LinearAlgebra.QuadraticForm.TensorProduct	1500	1501	+1 (+0.07%)

Import changes for all files

Files

Import difference

128 files Mathlib.Algebra.Category.ModuleCat.ExteriorPower Mathlib.Algebra.Lie.Classical Mathlib.Algebra.Lie.SkewAdjoint Mathlib.Algebra.Lie.Weights.RootSystem Mathlib.Analysis.Calculus.LineDeriv.QuadraticMap Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.Combinatorics.SimpleGraph.LapMatrix Mathlib.FieldTheory.Finite.Trace Mathlib.FieldTheory.Laurent Mathlib.FieldTheory.NormalizedTrace Mathlib.FieldTheory.RatFunc.AsPolynomial Mathlib.FieldTheory.RatFunc.Degree Mathlib.LinearAlgebra.Basis.Bilinear Mathlib.LinearAlgebra.CliffordAlgebra.BaseChange Mathlib.LinearAlgebra.CliffordAlgebra.Basic Mathlib.LinearAlgebra.CliffordAlgebra.CategoryTheory Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation Mathlib.LinearAlgebra.CliffordAlgebra.Contraction Mathlib.LinearAlgebra.CliffordAlgebra.Equivs Mathlib.LinearAlgebra.CliffordAlgebra.EvenEquiv Mathlib.LinearAlgebra.CliffordAlgebra.Even Mathlib.LinearAlgebra.CliffordAlgebra.Fold Mathlib.LinearAlgebra.CliffordAlgebra.Grading Mathlib.LinearAlgebra.CliffordAlgebra.Inversion Mathlib.LinearAlgebra.CliffordAlgebra.Prod Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup Mathlib.LinearAlgebra.CliffordAlgebra.Star Mathlib.LinearAlgebra.ExteriorAlgebra.Basic Mathlib.LinearAlgebra.ExteriorAlgebra.Grading Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating Mathlib.LinearAlgebra.ExteriorPower.Basic Mathlib.LinearAlgebra.ExteriorPower.Pairing Mathlib.LinearAlgebra.Matrix.BilinearForm Mathlib.LinearAlgebra.Matrix.LDL Mathlib.LinearAlgebra.Matrix.PosDef Mathlib.LinearAlgebra.Matrix.SchurComplement Mathlib.LinearAlgebra.Matrix.SesquilinearForm Mathlib.LinearAlgebra.QuadraticForm.Basic Mathlib.LinearAlgebra.QuadraticForm.Complex Mathlib.LinearAlgebra.QuadraticForm.Dual Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv Mathlib.LinearAlgebra.QuadraticForm.Isometry Mathlib.LinearAlgebra.QuadraticForm.Prod Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat Mathlib.LinearAlgebra.QuadraticForm.Real Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries Mathlib.LinearAlgebra.QuadraticForm.TensorProduct Mathlib.LinearAlgebra.RootSystem.Basic Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate Mathlib.NumberTheory.ClassNumber.Finite Mathlib.NumberTheory.ClassNumber.FunctionField Mathlib.NumberTheory.Cyclotomic.Basic Mathlib.NumberTheory.Cyclotomic.Discriminant Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.NumberTheory.Cyclotomic.Gal Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots Mathlib.NumberTheory.Cyclotomic.Rat Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Fermat Mathlib.NumberTheory.FunctionField Mathlib.NumberTheory.GaussSum Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Completion Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Discriminant.Defs Mathlib.NumberTheory.NumberField.Embeddings Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.FractionalIdeal Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Norm Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.PrimesCongruentOne Mathlib.NumberTheory.RamificationInertia.Galois Mathlib.RingTheory.Complex Mathlib.RingTheory.DedekindDomain.AdicValuation Mathlib.RingTheory.DedekindDomain.Different Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing Mathlib.RingTheory.DedekindDomain.IntegralClosure Mathlib.RingTheory.DedekindDomain.SInteger Mathlib.RingTheory.DedekindDomain.SelmerGroup Mathlib.RingTheory.Discriminant Mathlib.RingTheory.FractionalIdeal.Norm Mathlib.RingTheory.Frobenius Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.RingTheory.IntegralClosure.IntegralRestrict Mathlib.RingTheory.Invariant Mathlib.RingTheory.LaurentSeries Mathlib.RingTheory.LittleWedderburn Mathlib.RingTheory.Localization.NormTrace Mathlib.RingTheory.NormTrace Mathlib.RingTheory.Polynomial.Cyclotomic.Basic Mathlib.RingTheory.Polynomial.Cyclotomic.Eval Mathlib.RingTheory.Polynomial.Cyclotomic.Expand Mathlib.RingTheory.Polynomial.Cyclotomic.Roots Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed Mathlib.RingTheory.Trace.Basic Mathlib.RingTheory.Trace.Defs Mathlib.RingTheory.Trace.Quotient Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic Mathlib.Topology.Algebra.Valued.WithVal

1

---

Declarations diff

+ BilinearMap.map_finsuppSum
+ apply_linearCombination

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).

[github-actions]

PR summary b3e5f6991f

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.Basis.Bilinear	801	802	+1 (+0.12%)
Mathlib.LinearAlgebra.QuadraticForm.TensorProduct	1523	1524	+1 (+0.07%)

Import changes for all files

Files

Import difference

141 files Mathlib.Algebra.Category.ModuleCat.ExteriorPower Mathlib.Algebra.Lie.Classical Mathlib.Algebra.Lie.SkewAdjoint Mathlib.Algebra.Lie.Weights.RootSystem Mathlib.Analysis.Calculus.LineDeriv.QuadraticMap Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.Combinatorics.SimpleGraph.LapMatrix Mathlib.FieldTheory.Finite.Trace Mathlib.FieldTheory.Laurent Mathlib.FieldTheory.NormalizedTrace Mathlib.FieldTheory.RatFunc.AsPolynomial Mathlib.FieldTheory.RatFunc.Degree Mathlib.LinearAlgebra.Basis.Bilinear Mathlib.LinearAlgebra.CliffordAlgebra.BaseChange Mathlib.LinearAlgebra.CliffordAlgebra.Basic Mathlib.LinearAlgebra.CliffordAlgebra.CategoryTheory Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation Mathlib.LinearAlgebra.CliffordAlgebra.Contraction Mathlib.LinearAlgebra.CliffordAlgebra.Equivs Mathlib.LinearAlgebra.CliffordAlgebra.EvenEquiv Mathlib.LinearAlgebra.CliffordAlgebra.Even Mathlib.LinearAlgebra.CliffordAlgebra.Fold Mathlib.LinearAlgebra.CliffordAlgebra.Grading Mathlib.LinearAlgebra.CliffordAlgebra.Inversion Mathlib.LinearAlgebra.CliffordAlgebra.Prod Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup Mathlib.LinearAlgebra.CliffordAlgebra.Star Mathlib.LinearAlgebra.ExteriorAlgebra.Basic Mathlib.LinearAlgebra.ExteriorAlgebra.Grading Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating Mathlib.LinearAlgebra.ExteriorPower.Basic Mathlib.LinearAlgebra.ExteriorPower.Pairing Mathlib.LinearAlgebra.Matrix.BilinearForm Mathlib.LinearAlgebra.Matrix.LDL Mathlib.LinearAlgebra.Matrix.PosDef Mathlib.LinearAlgebra.Matrix.SchurComplement Mathlib.LinearAlgebra.Matrix.SesquilinearForm Mathlib.LinearAlgebra.QuadraticForm.Basic Mathlib.LinearAlgebra.QuadraticForm.Complex Mathlib.LinearAlgebra.QuadraticForm.Dual Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv Mathlib.LinearAlgebra.QuadraticForm.Isometry Mathlib.LinearAlgebra.QuadraticForm.Prod Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Monoidal Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat.Symmetric Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat Mathlib.LinearAlgebra.QuadraticForm.Real Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries Mathlib.LinearAlgebra.QuadraticForm.TensorProduct Mathlib.LinearAlgebra.RootSystem.Basic Mathlib.LinearAlgebra.RootSystem.CartanMatrix Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate Mathlib.LinearAlgebra.RootSystem.GeckConstruction Mathlib.NumberTheory.ClassNumber.Finite Mathlib.NumberTheory.ClassNumber.FunctionField Mathlib.NumberTheory.Cyclotomic.Basic Mathlib.NumberTheory.Cyclotomic.Discriminant Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.NumberTheory.Cyclotomic.Gal Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots Mathlib.NumberTheory.Cyclotomic.Rat Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Fermat Mathlib.NumberTheory.FunctionField Mathlib.NumberTheory.GaussSum Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.NumberTheory.NumberField.AdeleRing Mathlib.NumberTheory.NumberField.Basic Mathlib.NumberTheory.NumberField.CMField Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.NumberTheory.NumberField.Completion Mathlib.NumberTheory.NumberField.DedekindZeta Mathlib.NumberTheory.NumberField.Discriminant.Basic Mathlib.NumberTheory.NumberField.Discriminant.Defs Mathlib.NumberTheory.NumberField.Discriminant.Different Mathlib.NumberTheory.NumberField.Embeddings Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.FractionalIdeal Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Ideal.Asymptotics Mathlib.NumberTheory.NumberField.Ideal Mathlib.NumberTheory.NumberField.InfinitePlace.Basic Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex Mathlib.NumberTheory.NumberField.Norm Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.PrimesCongruentOne Mathlib.NumberTheory.RamificationInertia.Galois Mathlib.RingTheory.Complex Mathlib.RingTheory.DedekindDomain.AdicValuation Mathlib.RingTheory.DedekindDomain.Different Mathlib.RingTheory.DedekindDomain.FiniteAdeleRing Mathlib.RingTheory.DedekindDomain.IntegralClosure Mathlib.RingTheory.DedekindDomain.SInteger Mathlib.RingTheory.DedekindDomain.SelmerGroup Mathlib.RingTheory.Discriminant Mathlib.RingTheory.FractionalIdeal.Norm Mathlib.RingTheory.Frobenius Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.RingTheory.IntegralClosure.IntegralRestrict Mathlib.RingTheory.Invariant.Basic Mathlib.RingTheory.Invariant.Profinite Mathlib.RingTheory.Invariant Mathlib.RingTheory.LaurentSeries Mathlib.RingTheory.LittleWedderburn Mathlib.RingTheory.Localization.NormTrace Mathlib.RingTheory.NormTrace Mathlib.RingTheory.Polynomial.Cyclotomic.Basic Mathlib.RingTheory.Polynomial.Cyclotomic.Eval Mathlib.RingTheory.Polynomial.Cyclotomic.Expand Mathlib.RingTheory.Polynomial.Cyclotomic.Roots Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed Mathlib.RingTheory.Trace.Basic Mathlib.RingTheory.Trace.Defs Mathlib.RingTheory.Trace.Quotient Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic Mathlib.Topology.Algebra.Valued.WithVal

1

---

Declarations diff

+ BilinearMap.map_finsuppSum
+ apply_linearCombination

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).