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This commit is contained in:
Stefan Kebekus 2024-04-30 08:20:57 +02:00
parent 0c15de05b8
commit f85fafd05f
8 changed files with 38 additions and 40 deletions

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def hello := "world"
import Nevanlinna.cauchyRiemann

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import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Calculus.LineDeriv.Basic
import Mathlib.Analysis.Calculus.ContDiff.Defs
import Mathlib.Analysis.Calculus.FDeriv.Basic
import Nevanlinna.cauchyRiemann
noncomputable def Complex.laplace : () → () := by
intro f
let f₁ := fun x ↦ lineDeriv f x 1
let f₁₁ := fun x ↦ lineDeriv f₁ x 1
let f₂ := fun x ↦ lineDeriv f x Complex.I
let f₂₂ := fun x ↦ lineDeriv f₂ x Complex.I
exact f₁₁ + f₂₂
def Harmonic (f : ) : Prop :=
(ContDiff 2 f) ∧ (∀ z, Complex.laplace f z = 0)
theorem re_comp_holomorphic_is_harmonic (f : ) :
Differentiable f → Harmonic (Complex.reCLM ∘ f) := by
intro h
constructor
· -- f is two times real continuously differentiable
sorry
· -- Laplace of f is zero
intro z
unfold Complex.laplace
simp
let ZZ := (CauchyRiemann₃ (h z)).left
rw [ZZ]
sorry

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import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Calculus.LineDeriv.Basic
import Mathlib.Analysis.Calculus.ContDiff.Defs
import Mathlib.Analysis.Calculus.FDeriv.Basic
noncomputable def Real.laplace : ( × ) → ( × ) := by
intro f
let f₁ := fun x ↦ lineDeriv f x ⟨1,0⟩
let f₁₁ := fun x ↦ lineDeriv f₁ x ⟨1,0⟩
let f₂ := fun x ↦ lineDeriv f x ⟨0,1⟩
let f₂₂ := fun x ↦ lineDeriv f₂ x ⟨0,1⟩
exact f₁₁ + f₂₂
noncomputable def Complex.laplace : () → () := by
intro f
let f₁ := fun x ↦ lineDeriv f x 1
let f₁₁ := fun x ↦ lineDeriv f₁ x 1
let f₂ := fun x ↦ lineDeriv f x Complex.I
let f₂₂ := fun x ↦ lineDeriv f₂ x Complex.I
exact f₁₁ + f₂₂
theorem xx : ∀ f : → , f = 0 := by
intro f
let f₁ := fun x ↦ lineDeriv f x 1
let f₂ := fun x ↦ lineDeriv f x Complex.I
have : ∀ z, fderiv f z = 0 := by
sorry
have : (fun x ↦ lineDeriv f x 1) = (fun x ↦ lineDeriv f x Complex.I) := by
unfold lineDeriv
sorry
sorry