working...

nevanlinna/cauchyRiemann.lean

@@ -1,15 +1,14 @@
-import Mathlib.Analysis.Complex.CauchyIntegral
-import Mathlib.Analysis.Complex.Basic
-import Mathlib.Analysis.Calculus.LineDeriv.Basic
-import Mathlib.Analysis.Calculus.ContDiff.Defs
-import Mathlib.Analysis.Calculus.FDeriv.Basic
-import Mathlib.Analysis.Complex.RealDeriv
-import Mathlib.Analysis.Calculus.ContDiff.Basic
-import Mathlib.Analysis.Calculus.Deriv.Linear
-import Mathlib.Analysis.Complex.Conformal
 import Mathlib.Analysis.Calculus.Conformal.NormedSpace
+import Mathlib.Analysis.Calculus.ContDiff.Basic
+import Mathlib.Analysis.Calculus.ContDiff.Defs
+import Mathlib.Analysis.Calculus.Deriv.Linear
 import Mathlib.Analysis.Calculus.FDeriv.Basic
 import Mathlib.Analysis.Calculus.FDeriv.RestrictScalars
+import Mathlib.Analysis.Calculus.LineDeriv.Basic
+import Mathlib.Analysis.Complex.Basic
+import Mathlib.Analysis.Complex.CauchyIntegral
+import Mathlib.Analysis.Complex.Conformal
+import Mathlib.Analysis.Complex.RealDeriv
 
 variable {z : ℂ} {f : ℂ → ℂ}
 

nevanlinna/complexHarmonic.lean

@@ -0,0 +1,39 @@
+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 : (ℝ × ℝ → ℝ) → (ℝ × ℝ → ℝ) := by
+  intro f
+  let f₁ := fun x ↦ lineDeriv ℝ f x ⟨1,0⟩
+  let f₁₁ := fun x ↦ lineDeriv ℝ f₁ x ⟨1,0⟩
+  let f₂ := fun x ↦ lineDeriv ℝ f x ⟨0,1⟩
+  let f₂₂ := fun x ↦ lineDeriv ℝ f₂ x ⟨0,1⟩
+  exact f₁₁ + f₂₂
+
+noncomputable def Complex.laplace : (ℂ → ℝ) → (ℂ → ℝ) := by
+  intro f
+  let f₁ := fun x ↦ lineDeriv ℝ f x 1
+  let f₁₁ := fun x ↦ lineDeriv ℝ f₁ x 1
+  let f₂ := fun x ↦ lineDeriv ℝ f x Complex.I
+  let f₂₂ := fun x ↦ lineDeriv ℝ f₂ x Complex.I
+  exact f₁₁ + f₂₂
+
+
+theorem xx : ∀ f : ℂ → , f = 0  := by
+  intro f
+
+  let f₁ := fun x ↦ lineDeriv ℝ f x 1
+  let f₂ := fun x ↦ lineDeriv ℝ f x Complex.I
+
+  have : ∀ z, fderiv ℂ f z = 0 := by
+    sorry
+
+
+  have : (fun x ↦ lineDeriv ℝ f x 1) = (fun x ↦ lineDeriv ℝ f x Complex.I) := by
+
+    unfold lineDeriv
+
+    sorry
+
+  sorry

nevanlinna/realHarmonic.lean

@@ -11,6 +11,6 @@ noncomputable def Real.laplace : (ℝ × ℝ → ℝ) → (ℝ × ℝ → ℝ) :
 
   exact f₁₁ + f₂₂
 
-structure Harmonic (f : ℝ × ℝ → ℝ) : Prop where
-  ker_Laplace : ∀ x, Real.laplace f x = 0
-  cont_Diff : ContDiff ℝ 2 f
+
+def Harmonic (f : ℝ × ℝ → ℝ) : Prop :=
+  (ContDiff ℝ 2 f) ∧ (∀ x, Real.laplace f x = 0)