WIP: Bipolar theorem absconvex refactor

[mans0954]

Experiment to see what happens when #26345 and #29342 are merged.

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[github-actions]

PR summary 7014959348

Import changes exceeding 2%

%	File
+29.15%	Mathlib.Analysis.LocallyConvex.Polar
+49.92%	Mathlib.Topology.Algebra.Module.WeakBilin

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.Module.WeakBilin	1206	1808	+602 (+49.92%)
Mathlib.Analysis.LocallyConvex.Polar	1417	1830	+413 (+29.15%)
Mathlib.Analysis.Normed.Module.Dual	2024	2033	+9 (+0.44%)
Mathlib.Analysis.LocallyConvex.WeakDual	1803	1809	+6 (+0.33%)

Import changes for all files

Files	Import difference
229 files Mathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.CStarAlgebra.CStarMatrix Mathlib.Analysis.CStarAlgebra.CompletelyPositiveMap Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Range Mathlib.Analysis.CStarAlgebra.GelfandDuality Mathlib.Analysis.CStarAlgebra.Hom Mathlib.Analysis.CStarAlgebra.Module.Constructions Mathlib.Analysis.CStarAlgebra.Module.Defs Mathlib.Analysis.CStarAlgebra.PositiveLinearMap Mathlib.Analysis.CStarAlgebra.Projection Mathlib.Analysis.CStarAlgebra.SpecialFunctions.PosPart Mathlib.Analysis.CStarAlgebra.Spectrum Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts Mathlib.Analysis.Calculus.LogDerivUniformlyOn Mathlib.Analysis.Complex.AbsMax Mathlib.Analysis.Complex.CauchyIntegral Mathlib.Analysis.Complex.Hadamard Mathlib.Analysis.Complex.Harmonic.Analytic Mathlib.Analysis.Complex.Harmonic.MeanValue Mathlib.Analysis.Complex.HasPrimitives Mathlib.Analysis.Complex.JensenFormula Mathlib.Analysis.Complex.Liouville Mathlib.Analysis.Complex.LocallyUniformLimit Mathlib.Analysis.Complex.MeanValue Mathlib.Analysis.Complex.OpenMapping Mathlib.Analysis.Complex.Periodic Mathlib.Analysis.Complex.PhragmenLindelof Mathlib.Analysis.Complex.Polynomial.Basic Mathlib.Analysis.Complex.Polynomial.GaussLucas Mathlib.Analysis.Complex.Polynomial.UnitTrinomial Mathlib.Analysis.Complex.Positivity Mathlib.Analysis.Complex.RemovableSingularity Mathlib.Analysis.Complex.Schwarz Mathlib.Analysis.Complex.SummableUniformlyOn Mathlib.Analysis.Complex.TaylorSeries Mathlib.Analysis.Complex.UpperHalfPlane.Exp Mathlib.Analysis.Complex.UpperHalfPlane.Manifold Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem Mathlib.Analysis.Complex.ValueDistribution.ProximityFunction Mathlib.Analysis.Distribution.FourierSchwartz Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Analysis.Fourier.AddCircleMulti Mathlib.Analysis.Fourier.AddCircle Mathlib.Analysis.Fourier.FourierTransformDeriv Mathlib.Analysis.Fourier.Inversion Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.Analysis.InnerProductSpace.Harmonic.Constructions Mathlib.Analysis.InnerProductSpace.StarOrder Mathlib.Analysis.Matrix.Order Mathlib.Analysis.MellinInversion Mathlib.Analysis.MellinTransform Mathlib.Analysis.Meromorphic.Complex Mathlib.Analysis.Normed.Algebra.Basic Mathlib.Analysis.Normed.Algebra.GelfandFormula Mathlib.Analysis.NormedSpace.MultipliableUniformlyOn Mathlib.Analysis.ODE.PicardLindelof Mathlib.Analysis.Polynomial.Factorization Mathlib.Analysis.Polynomial.MahlerMeasure Mathlib.Analysis.Real.Pi.Chudnovsky Mathlib.Analysis.Real.Pi.Irrational Mathlib.Analysis.Real.Pi.Leibniz Mathlib.Analysis.Real.Pi.Wallis Mathlib.Analysis.SpecialFunctions.Complex.Analytic Mathlib.Analysis.SpecialFunctions.Complex.Arctan Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.Analysis.SpecialFunctions.Complex.LogBounds Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Isometric Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Isometric Mathlib.Analysis.SpecialFunctions.Gamma.Basic Mathlib.Analysis.SpecialFunctions.Gamma.Beta Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup Mathlib.Analysis.SpecialFunctions.Gamma.Deligne Mathlib.Analysis.SpecialFunctions.Gamma.Deriv Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.Analysis.SpecialFunctions.ImproperIntegrals Mathlib.Analysis.SpecialFunctions.Integrability.Basic Mathlib.Analysis.SpecialFunctions.Integrability.LogMeromorphic Mathlib.Analysis.SpecialFunctions.Integrals.Basic Mathlib.Analysis.SpecialFunctions.Integrals.LogTrigonometric Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage Mathlib.Analysis.SpecialFunctions.JapaneseBracket Mathlib.Analysis.SpecialFunctions.Log.Summable Mathlib.Analysis.SpecialFunctions.MulExpNegMulSqIntegral Mathlib.Analysis.SpecialFunctions.NonIntegrable Mathlib.Analysis.SpecialFunctions.Pow.Integral Mathlib.Analysis.SpecialFunctions.Stirling Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd Mathlib.Combinatorics.SimpleGraph.LapMatrix Mathlib.Data.Real.Pi.Irrational Mathlib.Data.Real.Pi.Leibniz Mathlib.Data.Real.Pi.Wallis Mathlib.Geometry.Manifold.Complex Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique Mathlib.Geometry.Manifold.IntegralCurve.UniformTime Mathlib.Geometry.Manifold.Riemannian.Basic Mathlib.MeasureTheory.Constructions.HaarToSphere Mathlib.MeasureTheory.Integral.CircleAverage Mathlib.MeasureTheory.Integral.CircleIntegral Mathlib.MeasureTheory.Integral.CircleTransform Mathlib.MeasureTheory.Integral.ExpDecay Mathlib.MeasureTheory.Integral.FundThmCalculus Mathlib.MeasureTheory.Integral.Gamma Mathlib.MeasureTheory.Integral.IntegralEqImproper Mathlib.MeasureTheory.Integral.IntegrationByParts Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus Mathlib.MeasureTheory.Integral.IntervalIntegral.IntegrationByParts Mathlib.MeasureTheory.Integral.IntervalIntegral Mathlib.MeasureTheory.Integral.PeakFunction Mathlib.MeasureTheory.Integral.TorusIntegral Mathlib.MeasureTheory.Measure.CharacteristicFunction Mathlib.MeasureTheory.Measure.DiracProba Mathlib.MeasureTheory.Measure.FiniteMeasureExt Mathlib.MeasureTheory.Measure.FiniteMeasurePi Mathlib.MeasureTheory.Measure.FiniteMeasureProd Mathlib.MeasureTheory.Measure.FiniteMeasure Mathlib.MeasureTheory.Measure.IntegralCharFun Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls Mathlib.MeasureTheory.Measure.LevyProkhorovMetric Mathlib.MeasureTheory.Measure.Portmanteau Mathlib.MeasureTheory.Measure.ProbabilityMeasure Mathlib.NumberTheory.AbelSummation Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.Cyclotomic.Three Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.EulerProduct.DirichletLSeries Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.Fermat Mathlib.NumberTheory.GaussSum Mathlib.NumberTheory.Harmonic.Bounds Mathlib.NumberTheory.Harmonic.GammaDeriv Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.NumberTheory.JacobiSum.Basic Mathlib.NumberTheory.LSeries.AbstractFuncEq Mathlib.NumberTheory.LSeries.Deriv Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.NumberTheory.LSeries.MellinEqDirichlet Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.Positivity Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.NumberTheory.LSeries.RiemannZeta Mathlib.NumberTheory.LSeries.SumCoeff Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.NumberTheory.LucasLehmer Mathlib.NumberTheory.ModularForms.Basic Mathlib.NumberTheory.ModularForms.DedekindEta Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.ModularForms.LevelOne Mathlib.NumberTheory.ModularForms.QExpansion Mathlib.NumberTheory.NumberField.AdeleRing 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.Embeddings Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.NumberTheory.NumberField.FinitePlaces Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Ideal.Asymptotics Mathlib.NumberTheory.NumberField.Ideal.Basic Mathlib.NumberTheory.NumberField.Ideal Mathlib.NumberTheory.NumberField.InfinitePlace.Basic Mathlib.NumberTheory.NumberField.InfinitePlace.Completion Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex Mathlib.NumberTheory.NumberField.ProductFormula Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart Mathlib.NumberTheory.ZetaValues Mathlib.Probability.Distributions.Beta Mathlib.Probability.Distributions.Exponential Mathlib.Probability.Distributions.Gamma Mathlib.Probability.Distributions.Gaussian.Basic Mathlib.Probability.Distributions.Gaussian.Fernique Mathlib.Probability.Distributions.Gaussian.Real Mathlib.Probability.Distributions.Gaussian Mathlib.Probability.Distributions.Pareto Mathlib.Probability.HasLawExists Mathlib.Probability.Independence.CharacteristicFunction Mathlib.Probability.Independence.InfinitePi Mathlib.Probability.Kernel.IonescuTulcea.Traj Mathlib.Probability.Moments.ComplexMGF Mathlib.Probability.Moments.MGFAnalytic Mathlib.Probability.Moments.SubGaussian Mathlib.Probability.Moments.Tilted Mathlib.Probability.ProductMeasure Mathlib.RingTheory.Polynomial.Selmer Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic	1
Mathlib.Analysis.Normed.Algebra.Spectrum	2
Mathlib.Analysis.LocallyConvex.WeakDual	6
Mathlib.Analysis.Normed.Module.Dual Mathlib.Analysis.Normed.Module.WeakDual	9
Mathlib.Analysis.LocallyConvex.WeakSpace	21
Mathlib.Topology.ContinuousMap.Ideals	147
Mathlib.Analysis.LocallyConvex.Polar Mathlib.Topology.Algebra.Module.StrongDual	413
Mathlib.Topology.Algebra.Module.CharacterSpace	497
Mathlib.Topology.Algebra.Module.WeakBilin Mathlib.Topology.Algebra.Module.WeakDual	602
Mathlib.Topology.Algebra.Module.LinearSpan (new file)	1802
Mathlib.Analysis.LocallyConvex.Bipolar (new file)	2033

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Declarations diff

+ _root_.LinearMap.CLMtoLinearMap₂
+ closedAbsConvexHull_empty
+ closureOperator_polar_gc_nonempty
+ dualEmbedding_injective_of_separatingRight
+ dualEmbedding_surjective
+ flip_polar_polar_eq
+ leftDualEquiv
+ polar_absConvex
+ rightDualEquiv

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).