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[Merged by Bors] - chore: Move smooth_barycentric_coord #14666

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[Merged by Bors] - chore: Move smooth_barycentric_coord #14666

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3 changes: 2 additions & 1 deletion Mathlib.lean
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Expand Up @@ -859,7 +859,8 @@ import Mathlib.Analysis.BoxIntegral.Partition.Measure
import Mathlib.Analysis.BoxIntegral.Partition.Split
import Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction
import Mathlib.Analysis.BoxIntegral.Partition.Tagged
import Mathlib.Analysis.Calculus.AffineMap
import Mathlib.Analysis.Calculus.AddTorsor.AffineMap
import Mathlib.Analysis.Calculus.AddTorsor.Coord
import Mathlib.Analysis.Calculus.BumpFunction.Basic
import Mathlib.Analysis.Calculus.BumpFunction.Convolution
import Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension
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0 Mathlib/Analysis/Calculus/AffineMap.lean → ...nalysis/Calculus/AddTorsor/AffineMap.lean
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22 changes: 22 additions & 0 deletions Mathlib/Analysis/Calculus/AddTorsor/Coord.lean
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@@ -0,0 +1,22 @@
/-
Copyright (c) 2021 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Analysis.Calculus.AddTorsor.AffineMap
import Mathlib.Analysis.NormedSpace.AddTorsorBases

#align_import analysis.normed_space.add_torsor_bases from "leanprover-community/mathlib"@"2f4cdce0c2f2f3b8cd58f05d556d03b468e1eb2e"

/-!
# Barycentric coordinates are smooth
-/

variable {ι 𝕜 E P : Type*} [NontriviallyNormedField 𝕜] [CompleteSpace 𝕜]
variable [NormedAddCommGroup E] [NormedSpace 𝕜 E]
variable [MetricSpace P] [NormedAddTorsor E P]
variable [FiniteDimensional 𝕜 E]

theorem smooth_barycentric_coord (b : AffineBasis ι 𝕜 E) (i : ι) : ContDiff 𝕜 ⊤ (b.coord i) :=
(⟨b.coord i, continuous_barycentric_coord b i⟩ : E →ᴬ[𝕜] 𝕜).contDiff
#align smooth_barycentric_coord smooth_barycentric_coord
7 changes: 1 addition & 6 deletions Mathlib/Analysis/NormedSpace/AddTorsorBases.lean
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Expand Up @@ -4,8 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Analysis.NormedSpace.FiniteDimension
import Mathlib.Analysis.Calculus.AffineMap
import Mathlib.Analysis.Convex.Combination
import Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional

#align_import analysis.normed_space.add_torsor_bases from "leanprover-community/mathlib"@"2f4cdce0c2f2f3b8cd58f05d556d03b468e1eb2e"
Expand All @@ -24,6 +22,7 @@ This file contains results about bases in normed affine spaces.
* `interior_convexHull_nonempty_iff_affineSpan_eq_top`
-/

assert_not_exists HasFDerivAt

section Barycentric

Expand All @@ -45,10 +44,6 @@ theorem continuous_barycentric_coord (i : ι) : Continuous (b.coord i) :=
(b.coord i).continuous_of_finiteDimensional
#align continuous_barycentric_coord continuous_barycentric_coord

theorem smooth_barycentric_coord (b : AffineBasis ι 𝕜 E) (i : ι) : ContDiff 𝕜 ⊤ (b.coord i) :=
(⟨b.coord i, continuous_barycentric_coord b i⟩ : E →ᴬ[𝕜] 𝕜).contDiff
#align smooth_barycentric_coord smooth_barycentric_coord

end Barycentric

open Set
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