[Merged by Bors] - feat: the real exponential is analytic #17218
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PR summary 9998b349b7
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.Analysis.SpecialFunctions.ExpDeriv | 1648 | 1653 | +5 (+0.30%) |
| Mathlib.Analysis.SpecialFunctions.Complex.Analytic | 1886 | 1891 | +5 (+0.27%) |
Import changes for all files
| Files | Import difference |
|---|---|
6 filesMathlib.Analysis.Normed.Algebra.Spectrum Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique Mathlib.Analysis.Normed.Algebra.Basic Mathlib.LinearAlgebra.Matrix.HermitianFunctionalCalculus |
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20 filesMathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Distribution.FourierSchwartz Mathlib.NumberTheory.EulerProduct.DirichletLSeries Mathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.Analysis.Fourier.FourierTransformDeriv Mathlib.NumberTheory.LSeries.RiemannZeta Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.ZetaValues Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.Analysis.Distribution.SchwartzSpace |
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125 filesMathlib.NumberTheory.Cyclotomic.Rat Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv Mathlib.Analysis.SpecialFunctions.Gamma.Basic Mathlib.Analysis.Complex.Angle Mathlib.Analysis.SpecialFunctions.Integrals Mathlib.NumberTheory.Cyclotomic.Discriminant Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds Mathlib.Tactic.FunProp.ContDiff Mathlib.NumberTheory.GaussSum Mathlib.Analysis.Complex.AbsMax Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv Mathlib.Geometry.Manifold.Complex Mathlib.MeasureTheory.Integral.CircleIntegral Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral Mathlib.Analysis.SpecialFunctions.Gamma.Beta Mathlib.MeasureTheory.Integral.TorusIntegral Mathlib.Analysis.Complex.TaylorSeries Mathlib.Analysis.FunctionalSpaces.SobolevInequality Mathlib.Probability.Distributions.Exponential Mathlib.Analysis.SpecialFunctions.Complex.Arctan Mathlib.NumberTheory.NumberField.Discriminant Mathlib.Analysis.SpecialFunctions.Log.NegMulLog Mathlib.NumberTheory.NumberField.EquivReindex Mathlib.Analysis.SpecialFunctions.ImproperIntegrals Mathlib.RingTheory.Polynomial.Hermite.Gaussian Mathlib.Analysis.Fourier.ZMod Mathlib.Analysis.SpecialFunctions.Complex.LogBounds Mathlib.Analysis.SpecialFunctions.Gamma.Deligne Mathlib.Analysis.Complex.PhragmenLindelof Mathlib.Analysis.InnerProductSpace.NormPow Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls Mathlib.NumberTheory.Cyclotomic.Three Mathlib.Geometry.Manifold.PoincareConjecture Mathlib.NumberTheory.LSeries.Deriv Mathlib.Analysis.Fourier.AddCircle Mathlib.Analysis.Fourier.Inversion Mathlib.Computability.AkraBazzi.AkraBazzi Mathlib.Analysis.SpecialFunctions.NonIntegrable Mathlib.Analysis.SpecialFunctions.Complex.Analytic Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic Mathlib.Probability.Distributions.Gaussian Mathlib.Geometry.Manifold.BumpFunction Mathlib.NumberTheory.Harmonic.GammaDeriv Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone Mathlib.Analysis.Complex.CauchyIntegral Mathlib.Analysis.SpecialFunctions.Pow.Deriv Mathlib.Analysis.SpecialFunctions.PolarCoord Mathlib.Analysis.Complex.UpperHalfPlane.Metric Mathlib.NumberTheory.Cyclotomic.Embeddings Mathlib.Analysis.Complex.Schwarz Mathlib.Data.Real.Pi.Leibniz Mathlib.NumberTheory.FLT.Three Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody Mathlib.NumberTheory.NumberField.Units.Basic Mathlib.NumberTheory.DirichletCharacter.GaussSum Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Analysis.SpecialFunctions.BinaryEntropy Mathlib.Analysis.SpecialFunctions.SmoothTransition Mathlib.Combinatorics.Additive.AP.Three.Behrend Mathlib.MeasureTheory.Integral.IntegralEqImproper Mathlib.Analysis.Complex.Polynomial.Basic Mathlib.Analysis.Complex.RemovableSingularity Mathlib.Analysis.Complex.Liouville Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum Mathlib.NumberTheory.LSeries.MellinEqDirichlet Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol Mathlib.Analysis.Complex.LocallyUniformLimit Mathlib.NumberTheory.Harmonic.EulerMascheroni Mathlib.Analysis.SpecialFunctions.Log.Deriv Mathlib.NumberTheory.LegendreSymbol.AddCharacter Mathlib.NumberTheory.Cyclotomic.PID Mathlib.NumberTheory.JacobiSum.Basic Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup Mathlib.Data.Real.Pi.Bounds Mathlib.MeasureTheory.Integral.PeakFunction Mathlib.NumberTheory.NumberField.Units.DirichletTheorem Mathlib.MeasureTheory.Integral.ExpDecay Mathlib.NumberTheory.NumberField.Units.Regulator Mathlib.Analysis.SpecialFunctions.Stirling Mathlib.Analysis.ODE.Gronwall Mathlib.RingTheory.Polynomial.Selmer Mathlib.Geometry.Manifold.IntegralCurve Mathlib.MeasureTheory.Constructions.HaarToSphere Mathlib.Analysis.SpecialFunctions.JapaneseBracket Mathlib.MeasureTheory.Integral.CircleTransform Mathlib.Analysis.SpecialFunctions.Arsinh Mathlib.Tactic.FunProp.Differentiable Mathlib.Analysis.MellinInversion Mathlib.Analysis.Complex.Polynomial.UnitTrinomial Mathlib.Geometry.Manifold.PartitionOfUnity Mathlib.Analysis.Complex.Hadamard Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts Mathlib.Probability.Distributions.Pareto Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv Mathlib.Analysis.Calculus.Rademacher Mathlib.Analysis.Calculus.BumpFunction.InnerProduct Mathlib.NumberTheory.NumberField.House Mathlib.NumberTheory.NumberField.Embeddings Mathlib.NumberTheory.Harmonic.Bounds Mathlib.Analysis.MellinTransform Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar Mathlib.MeasureTheory.Integral.Gamma Mathlib.Analysis.Convex.SpecificFunctions.Deriv Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension Mathlib.Probability.Distributions.Gamma Mathlib.Analysis.SpecialFunctions.ExpDeriv Mathlib.Analysis.Complex.OpenMapping Mathlib.Analysis.ODE.PicardLindelof Mathlib.NumberTheory.NumberField.ClassNumber Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv Mathlib.Tactic Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.NumberTheory.Bertrand Mathlib.Analysis.SpecialFunctions.Pow.Integral Mathlib.Geometry.Manifold.WhitneyEmbedding Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.Data.Real.Pi.Wallis Mathlib.NumberTheory.LSeries.AbstractFuncEq Mathlib.Data.Complex.ExponentialBounds Mathlib.Geometry.Manifold.Instances.Sphere |
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Declarations diff
+ AnalyticAt.restrictScalars
+ AnalyticAt.rexp
+ AnalyticOn.restrictScalars
+ AnalyticOn.rexp
+ AnalyticOnNhd.contDiff
+ AnalyticOnNhd.restrictScalars
+ AnalyticOnNhd.rexp
+ AnalyticWithinAt.restrictScalars
+ AnalyticWithinAt.rexp
+ HasFPowerSeriesAt.restrictScalars
+ HasFPowerSeriesOnBall.restrictScalars
+ HasFPowerSeriesWithinAt.restrictScalars
+ HasFPowerSeriesWithinOnBall.restrictScalars
+ analyticAt_rexp
+ analyticOnNhd_inverse
+ analyticOnNhd_rexp
+ analyticOn_rexp
-++- contDiff_exp
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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leanprover-community-mathlib4-bot
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Currently, mathlib proves that the complex exponential is analytic as a consequence of its differentiability, quite late in the import hierarchy -- and this is specific to complexes. On the other hand, we also know that the exponential on a general normed algebra is analytic, thanks to its power series expansion. We switch to deduce the former from the latter, earlier in the import hierarchy, and use this occasion to also prove analyticity of the real exponential in the same file.
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fbarroero
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Currently, mathlib proves that the complex exponential is analytic as a consequence of its differentiability, quite late in the import hierarchy -- and this is specific to complexes. On the other hand, we also know that the exponential on a general normed algebra is analytic, thanks to its power series expansion. We switch to deduce the former from the latter, earlier in the import hierarchy, and use this occasion to also prove analyticity of the real exponential in the same file.
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Currently, mathlib proves that the complex exponential is analytic as a consequence of its differentiability, quite late in the import hierarchy -- and this is specific to complexes. On the other hand, we also know that the exponential on a general normed algebra is analytic, thanks to its power series expansion. We switch to deduce the former from the latter, earlier in the import hierarchy, and use this occasion to also prove analyticity of the real exponential in the same file.