path stringlengths 11 71 | content stringlengths 75 124k |
|---|---|
Analysis\Calculus\LocalExtr\LineDeriv.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.LocalExtr.Basic
import Mathlib.Analysis.Calculus.LineDeriv.Basic
/-!
# Local extremum and line derivatives
If `f` has a local ext... |
Analysis\Calculus\LocalExtr\Polynomial.lean | /-
Copyright (c) 2021 Benjamin Davidson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Benjamin Davidson, Yury Kudryashov
-/
import Mathlib.Algebra.Star.Order
import Mathlib.Analysis.Calculus.LocalExtr.Rolle
import Mathlib.Analysis.Calculus.Deriv.Polynomial
import Mat... |
Analysis\Calculus\LocalExtr\Rolle.lean | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Anatole Dedecker
-/
import Mathlib.Analysis.Calculus.LocalExtr.Basic
import Mathlib.Topology.Algebra.Order.Rolle
/-!
# Rolle's Theorem
In this file we prove Rolle's... |
Analysis\Complex\AbelLimit.lean | /-
Copyright (c) 2024 Jeremy Tan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Tan
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Tactic.Peel
/-!
# Abel's limit theorem
If a real or complex power series ... |
Analysis\Complex\AbsMax.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Complex.CauchyIntegral
import Mathlib.Analysis.Normed.Module.Completion
import Mathlib.Analysis.NormedSpace.Extr
import Mathlib.Topolo... |
Analysis\Complex\Angle.lean | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds
import Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic
/-!
# Angle between complex numbers
This file rel... |
Analysis\Complex\Arg.lean | /-
Copyright (c) 2022 Eric Rodriguez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Rodriguez
-/
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.SpecialFunctions.Complex.Arg
/-!
# Rays in the complex numbers
This file links the definitio... |
Analysis\Complex\Asymptotics.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Asymptotics.Theta
/-!
# Lemmas about asymptotics and the natural embedding `ℝ → ℂ`
In this file we p... |
Analysis\Complex\Basic.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Data.Complex.Module
import Mathlib.Data.Complex.Order
import Mathlib.Data.Complex.Exponential
import Mathlib.Analysis.RCLike.Basic
import Mathlib... |
Analysis\Complex\CauchyIntegral.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.MeasureTheory.Measure.Lebesgue.Complex
import Mathlib.MeasureTheory.Integral.DivergenceTheorem
import Mathlib.MeasureTheory.Integral.CircleIntegral
i... |
Analysis\Complex\Circle.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.SpecialFunctions.Exp
import Mathlib.Topology.ContinuousFunction.Basic
import Mathlib.Analysis.Normed.Field.UnitBall
/-!
# The circle
This ... |
Analysis\Complex\Conformal.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import Mathlib.Analysis.Complex.Isometry
import Mathlib.Analysis.NormedSpace.ConformalLinearMap
import Mathlib.Analysis.Normed.Module.FiniteDimension
import Mathlib.Data.... |
Analysis\Complex\Convex.lean | /-
Copyright (c) 2023 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Complex.Basic
/-!
# Theorems about convexity on the complex plane
-/
open Set
open scoped... |
Analysis\Complex\Hadamard.lean | /-
Copyright (c) 2023 Xavier Généreux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Généreux
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
import Mathlib.Analysis.Complex.PhragmenLindelof
/-!
# Hadamard three-lines Theorem
In this file we present a ... |
Analysis\Complex\HalfPlane.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Topology.Instances.EReal
/-!
# Half-planes in ℂ are open
We state that open left, right, upper and lower half-pla... |
Analysis\Complex\Isometry.lean | /-
Copyright (c) 2021 François Sunatori. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: François Sunatori
-/
import Mathlib.Analysis.Complex.Circle
import Mathlib.LinearAlgebra.Determinant
import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic
/-!
# Isometries o... |
Analysis\Complex\Liouville.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Complex.CauchyIntegral
import Mathlib.Analysis.Calculus.FDeriv.Analytic
import Mathlib.Analysis.Normed.Module.Completion
/-!
# Liouvi... |
Analysis\Complex\LocallyUniformLimit.lean | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara
-/
import Mathlib.Analysis.Complex.RemovableSingularity
import Mathlib.Analysis.Calculus.UniformLimitsDeriv
import Mathlib.Analysis.NormedSpace.FunctionSeries
/-!
# L... |
Analysis\Complex\OpenMapping.lean | /-
Copyright (c) 2022 Vincent Beffara. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vincent Beffara
-/
import Mathlib.Analysis.Analytic.IsolatedZeros
import Mathlib.Analysis.Complex.CauchyIntegral
import Mathlib.Analysis.Complex.AbsMax
import Mathlib.Topology.MetricS... |
Analysis\Complex\OperatorNorm.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.Data.Complex.Determinant
/-! # The basic cont... |
Analysis\Complex\PhragmenLindelof.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.AbsMax
import Mathlib.Analysis.Asymptotics.SuperpolynomialDecay
/-!
# Phragmen-Lindelöf principle
In this file we prove several ve... |
Analysis\Complex\RealDeriv.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yourong Zang
-/
import Mathlib.Analysis.Calculus.ContDiff.Basic
import Mathlib.Analysis.Calculus.Deriv.Linear
import Mathlib.Analysis.Complex.Conformal
import Mat... |
Analysis\Complex\ReImTopology.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle
/-!
# Closure, interior, and frontier of preimages under `re`... |
Analysis\Complex\RemovableSingularity.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Calculus.FDeriv.Analytic
import Mathlib.Analysis.Asymptotics.SpecificAsymptotics
import Mathlib.Analysis.Complex.CauchyIntegral
/-!
# Remov... |
Analysis\Complex\Schwarz.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Complex.AbsMax
import Mathlib.Analysis.Complex.RemovableSingularity
/-!
# Schwarz lemma
In this file we prove several versions of th... |
Analysis\Complex\TaylorSeries.lean | /-
Copyright (c) 2024 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
import Mathlib.Analysis.Complex.CauchyIntegral
/-!
# Convergence of Taylor series of holomorphic functions
We show that the Taylor series around some point `c : ℂ` of... |
Analysis\Complex\Tietze.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.RCLike.Lemmas
import Mathlib.Topology.TietzeExtension
import Mathlib.Analysis.NormedSpace.HomeomorphBall
i... |
Analysis\Complex\Polynomial\Basic.lean | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Junyan Xu, Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Liouville
import Mathlib.Analysis.Calculus.Deriv.Polynomial
import Mathlib.FieldTheory.PolynomialGaloisGroup
i... |
Analysis\Complex\Polynomial\UnitTrinomial.lean | /-
Copyright (c) 2022 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
import Mathlib.Algebra.Polynomial.UnitTrinomial
import Mathlib.Analysis.Complex.Polynomial.Basic
/-!
# Irreducibility of unit trinomials
## TODO
Develop more the... |
Analysis\Complex\UnitDisc\Basic.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.Circle
import Mathlib.Analysis.NormedSpace.BallAction
/-!
# Poincaré disc
In this file we define `Complex.UnitDisc` to be the unit... |
Analysis\Complex\UpperHalfPlane\Basic.lean | /-
Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
-/
import Mathlib.Algebra.GroupWithZero.Action.Defs
import Mathlib.Analysis.Complex.Basic
import Ma... |
Analysis\Complex\UpperHalfPlane\Exp.lean | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
/-!
# Exp on the upper half plane
This file contai... |
Analysis\Complex\UpperHalfPlane\FunctionsBoundedAtInfty.lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck, David Loeffler
-/
import Mathlib.Algebra.Module.Submodule.Basic
import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
import Mathlib.Order.Filter.ZeroAndBoundedAtFilter
... |
Analysis\Complex\UpperHalfPlane\Manifold.lean | /-
Copyright (c) 2022 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
import Mathlib.Geometry.Manifold.MFDeriv.Basic
/-!
# Manifold structure on the upper half plane.
In this fil... |
Analysis\Complex\UpperHalfPlane\Metric.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Topology
import Mathlib.Analysis.SpecialFunctions.Arsinh
import Mathlib.Geometry.Euclidean.Inversion.Basic
/-!
# Met... |
Analysis\Complex\UpperHalfPlane\Topology.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
import Mathlib.Analysis.Convex.Contractible
import Mathlib.Analysis.Convex.Normed
import Mathlib.Analysis... |
Analysis\Convex\AmpleSet.lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Floris van Doorn
-/
import Mathlib.Analysis.Convex.Normed
import Mathlib.Analysis.NormedSpace.Connected
import Mathlib.LinearAlgebra.AffineSpace.ContinuousAffineEqu... |
Analysis\Convex\Basic.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov, Yaël Dillies
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Module.OrderedSMul
import Mathlib.Analysis.C... |
Analysis\Convex\Between.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Algebra.CharP.Invertible
import Mathlib.Algebra.Order.Interval.Set.Group
import Mathlib.Analysis.Convex.Segment
import Mathlib.LinearAlgebra.AffineSpace.Fi... |
Analysis\Convex\Body.lean | /-
Copyright (c) 2022 Paul A. Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul A. Reichert
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Topology.MetricSpace.HausdorffDistance
/-!
# Convex bodies
This ... |
Analysis\Convex\Caratheodory.lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Scott Morrison
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.LinearAlgebra.AffineSpace.Independent
import Mathlib.Tactic.FieldSimp
/-!
# Carathéodory's ... |
Analysis\Convex\Combination.lean | /-
Copyright (c) 2019 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov
-/
import Mathlib.Algebra.Order.BigOperators.Ring.Finset
import Mathlib.Analysis.Convex.Hull
import Mathlib.LinearAlgebra.AffineSpace.Basis
/-!
# Convex combinations
... |
Analysis\Convex\Complex.lean | /-
Copyright (c) 2019 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov, Yaël Dillies
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Data.Complex.Module
/-!
# Convexity of half spaces in ℂ
The open and closed half-spaces in ℂ giv... |
Analysis\Convex\Contractible.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Star
import Mathlib.Topology.Homotopy.Contractible
/-!
# A convex set is contractible
In this file we prove that a (star) convex se... |
Analysis\Convex\Deriv.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov, David Loeffler
-/
import Mathlib.Analysis.Calculus.MeanValue
import Mathlib.Analysis.Convex.Slope
/-!
# Convexity of functions and derivatives
... |
Analysis\Convex\EGauge.lean | /-
Copyright (c) 2024 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Seminorm
/-!
# The Minkowski functional, normed field version
In this file we define `(egauge 𝕜 s ·)`
to be the Minkowski functional (gau... |
Analysis\Convex\Exposed.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Extreme
import Mathlib.Analysis.Convex.Function
import Mathlib.Topology.Algebra.Module.Basic
import Mathlib.Top... |
Analysis\Convex\Extrema.lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Convex.Function
import Mathlib.Topology.Algebra.Affine
import Mathlib.Topology.MetricSpace.Pseudo.Lemmas
import Mathlib.Topology.Order.Local... |
Analysis\Convex\Extreme.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Hull
/-!
# Extreme sets
This file defines extreme sets and extreme points for sets in a module.
An extreme s... |
Analysis\Convex\Function.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, François Dupuis
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Order.Filter.Extr
import Mathlib.Tactic.NormNum
/-!
# Convex and concave functions
This... |
Analysis\Convex\Gauge.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Topology
import Mathlib.Analysis.NormedSpace.Pointwise
import Mathlib.Analysis.Seminorm
import Mathlib.Analysis... |
Analysis\Convex\GaugeRescale.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Gauge
import Mathlib.Analysis.Convex.Normed
/-!
# "Gauge rescale" homeomorphism between convex sets
Given two convex von Neumann bou... |
Analysis\Convex\Hull.lean | /-
Copyright (c) 2020 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov, Yaël Dillies
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Order.Closure
/-!
# Convex hull
This file defines the convex hull of a set `s` in a module. `con... |
Analysis\Convex\Independent.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Extreme
/-!
# Convex independence
This file defines convex indepen... |
Analysis\Convex\Integral.lean | /-
Copyright (c) 2020 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Convex.Function
import Mathlib.Analysis.Convex.StrictConvexSpace
import Mathlib.MeasureTheory.Function.AEEqOfIntegral
import Mathlib.M... |
Analysis\Convex\Intrinsic.lean | /-
Copyright (c) 2023 Paul Reichert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Paul Reichert, Yaël Dillies
-/
import Mathlib.Analysis.NormedSpace.AddTorsorBases
/-!
# Intrinsic frontier and interior
This file defines the intrinsic frontier, interior and closure ... |
Analysis\Convex\Jensen.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudriashov
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Function
import Mathlib.Tactic.FieldSimp
/-!
# Jensen's inequality... |
Analysis\Convex\Join.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.Convex.Hull
/-!
# Convex join
This file defines the convex join of two sets. The convex join of `s` and `t` is the union of the
segments with on... |
Analysis\Convex\KreinMilman.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.Convex.Exposed
import Mathlib.Analysis.NormedSpace.HahnBanach.Separation
import Mathlib.Topology.Algebra.ContinuousAffineMap
/-!
# The Krein-Milm... |
Analysis\Convex\Measure.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Topology
import Mathlib.Analysis.NormedSpace.AddTorsorBases
import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
/-!
# Convex sets a... |
Analysis\Convex\Mul.lean | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Order.Monovary
import Mathlib.Algebra.Order.Ring.Basic
import Mathlib.Analysis.Convex.Function
import Mathlib.Tactic.FieldSimp
/-!
# Product of co... |
Analysis\Convex\Normed.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Between
import Mathlib.Analysis.Convex.Jensen
import Mathlib.Analysis.Convex.Topology
import Mathlib.Analysis.Nor... |
Analysis\Convex\PartitionOfUnity.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Topology.PartitionOfUnity
import Mathlib.Analysis.Convex.Combination
/-!
# Partition of unity and convex sets
In this file we prove the following l... |
Analysis\Convex\Quasiconvex.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.Convex.Function
/-!
# Quasiconvex and quasiconcave functions
This file defines quasiconvexity, quasiconcavity and quasilinearity of functions, w... |
Analysis\Convex\Radon.lean | /-
Copyright (c) 2023 Vasily Nesterov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Vasily Nesterov
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Data.Set.Card
import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional
import Mathlib.Topology.Separatio... |
Analysis\Convex\Segment.lean | /-
Copyright (c) 2019 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov, Yaël Dillies
-/
import Mathlib.Algebra.Order.Invertible
import Mathlib.Algebra.Order.Module.OrderedSMul
import Mathlib.LinearAlgebra.AffineSpac... |
Analysis\Convex\Side.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Analysis.Convex.Between
import Mathlib.Analysis.Convex.Normed
import Mathlib.Analysis.Normed.Group.AddTorsor
/-!
# Sides of affine subspaces
This file de... |
Analysis\Convex\Slope.lean | /-
Copyright (c) 2021 Yury Kudriashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudriashov, Malo Jaffré
-/
import Mathlib.Analysis.Convex.Function
import Mathlib.Tactic.AdaptationNote
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
/-!
# Slop... |
Analysis\Convex\Star.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Algebra.Module.LinearMap.Prod
import Mathlib.Algebra.Order.Group.Instances
import Mathlib.Analysis.Convex.Segment
import Mathlib.Tactic.GCongr
/-!
# Star-... |
Analysis\Convex\StoneSeparation.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Join
/-!
# Stone's separation theorem
This file proves Stone's separation theorem. This tells ... |
Analysis\Convex\Strict.lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Topology.Algebra.Group.Basic
import Mathlib.Topology.Order.Basic
/-!
# Strictly convex sets
This file defines strict... |
Analysis\Convex\StrictConvexBetween.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers
-/
import Mathlib.Analysis.Convex.Between
import Mathlib.Analysis.Convex.StrictConvexSpace
import Mathlib.Analysis.NormedSpace.AffineIsometry
/-!
# Betweenness in affine sp... |
Analysis\Convex\StrictConvexSpace.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Normed
import Mathlib.Analysis.Convex.Strict
import Mathlib.Analysis.Normed.Order.Basic
import Mathlib.Analysis.NormedSpac... |
Analysis\Convex\Strong.lean | /-
Copyright (c) 2023 Yaël Dillies, Chenyi Li. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chenyi Li, Ziyu Wang, Yaël Dillies
-/
import Mathlib.Analysis.InnerProductSpace.Basic
/-!
# Uniformly and strongly convex functions
In this file, we define uniformly convex ... |
Analysis\Convex\Topology.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Yury Kudryashov
-/
import Mathlib.Analysis.Convex.Combination
import Mathlib.Analysis.Convex.Strict
import Mathlib.Topology.Connected.PathConnected
import Mathlib.... |
Analysis\Convex\Uniform.lean | /-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import Mathlib.Analysis.Convex.StrictConvexSpace
/-!
# Uniformly convex spaces
This file defines uniformly convex spaces, which are real normed vector spaces in which f... |
Analysis\Convex\Cone\Basic.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Frédéric Dupuis
-/
import Mathlib.Analysis.Convex.Hull
/-!
# Convex cones
In a `𝕜`-module `E`, we define a convex cone as a set `s` such that `a • x + b • y ∈ s` w... |
Analysis\Convex\Cone\Closure.lean | /-
Copyright (c) 2023 Apurva Nakade. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Apurva Nakade
-/
import Mathlib.Analysis.Convex.Cone.Pointed
/-!
# Closure of cones
We define the closures of convex and pointed cones. This construction is primarily needed for
defin... |
Analysis\Convex\Cone\Extension.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Frédéric Dupuis
-/
import Mathlib.Analysis.Convex.Cone.Basic
import Mathlib.Data.Real.Archimedean
import Mathlib.LinearAlgebra.LinearPMap
/-!
# Extension theorems
W... |
Analysis\Convex\Cone\InnerDual.lean | /-
Copyright (c) 2021 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
import Mathlib.Analysis.Convex.Cone.Basic
import Mathlib.Analysis.InnerProductSpace.Projection
/-!
# Convex cones in inner product spaces
We define `Set.inn... |
Analysis\Convex\Cone\Pointed.lean | /-
Copyright (c) 2023 Apurva Nakade. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Apurva Nakade
-/
import Mathlib.Analysis.Convex.Cone.InnerDual
import Mathlib.Algebra.Order.Nonneg.Module
import Mathlib.Algebra.Module.Submodule.Basic
/-!
# Pointed cones
A *pointed ... |
Analysis\Convex\Cone\Proper.lean | /-
Copyright (c) 2022 Apurva Nakade. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Apurva Nakade
-/
import Mathlib.Analysis.Convex.Cone.Closure
import Mathlib.Analysis.InnerProductSpace.Adjoint
/-!
# Proper cones
We define a *proper cone* as a closed, pointed cone. ... |
Analysis\Convex\SimplicialComplex\Basic.lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import Mathlib.Analysis.Convex.Hull
import Mathlib.LinearAlgebra.AffineSpace.Independent
/-!
# Simplicial complexes
In this file, we define ... |
Analysis\Convex\SpecificFunctions\Basic.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Heather Macbeth
-/
import Mathlib.Analysis.Convex.Slope
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Tactic.LinearCombination
... |
Analysis\Convex\SpecificFunctions\Deriv.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.Deriv.ZPow
import Mathlib.Analysis.SpecialFunctions.Sqrt
import Mathlib.Analysis.SpecialFunctions.Log.Deriv
impo... |
Analysis\Convex\SpecificFunctions\Pow.lean | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Convex.SpecificFunctions.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
/-!
# Convexity properties of `rpow`
We prove basic co... |
Analysis\CStarAlgebra\Basic.lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Normed.Operator.LinearIsometry
import Mathlib.Algebra.S... |
Analysis\CStarAlgebra\Exponential.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Normed.Algebra.Exponential
/-! # The exponential map from selfadjoint to unitary
In this file, we establish various properties related to the m... |
Analysis\CStarAlgebra\GelfandDuality.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.Spectrum
import Mathlib.Analysis.Normed.Group.Quotient
import Mathlib.Analysis.Normed.Algebra.Basic
import Mathlib.Topology.Continu... |
Analysis\CStarAlgebra\Matrix.lean | /-
Copyright (c) 2022 Hans Parshall. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Hans Parshall
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Analysis.Matrix
import Mathlib.Analysis.RCLike.Basic
import Mathlib.LinearAlgebra.UnitaryGroup
import M... |
Analysis\CStarAlgebra\Module.lean | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order
/-!
# Hilbert C⋆-modules
A Hilbert C⋆-module is a complex module `E` together with a righ... |
Analysis\CStarAlgebra\Multiplier.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux, Jon Bannon
-/
import Mathlib.Analysis.NormedSpace.OperatorNorm.Completeness
import Mathlib.Analysis.CStarAlgebra.Unitization
import Mathlib.Analysis.SpecialFunctions.Pow.... |
Analysis\CStarAlgebra\Spectrum.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.Basic
import Mathlib.Analysis.Normed.Algebra.Spectrum
import Mathlib.Analysis.SpecialFunctions.Exponential
import Mathlib.Algebra.S... |
Analysis\CStarAlgebra\Unitization.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.Basic
import Mathlib.Analysis.Normed.Algebra.Unitization
/-! # The minimal unitization of a C⋆-algebra
This file shows that when `... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Basic.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.GelfandDuality
import Mathlib.Topology.Algebra.StarSubalgebra
/-! # Continuous functional calculus
In this file we construct the ... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Instances.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic
import Mathlib.Analys... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\NonUnital.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Quasispectrum
import Mathlib.Topology.ContinuousFunction.Compact
import Mathlib.Topology.ContinuousFunction.ContinuousMapZero
import Math... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Order.lean | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances
import Mathlib.Topology.ContinuousFunction.StarOrdered
import Mathlib.Analysis.CStarAlg... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Restrict.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Normed.Algebra.Spectrum
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital
/-! # Restriction of the continuous functio... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Unique.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Normed.Algebra.Spectrum
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital
import Mathlib.Topology.ContinuousFunction.S... |
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