26 lines
939 B
Plaintext
26 lines
939 B
Plaintext
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import Mathlib.Data.Fin.Tuple.Basic
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import Mathlib.Analysis.Complex.Basic
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import Mathlib.Analysis.Complex.TaylorSeries
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import Mathlib.Analysis.Calculus.LineDeriv.Basic
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import Mathlib.Analysis.Calculus.ContDiff.Defs
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import Mathlib.Analysis.Calculus.FDeriv.Basic
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import Mathlib.Analysis.Calculus.FDeriv.Symmetric
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import Mathlib.Data.Complex.Module
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import Mathlib.Data.Complex.Order
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import Mathlib.Data.Complex.Exponential
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import Mathlib.Analysis.RCLike.Basic
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import Mathlib.Topology.Algebra.InfiniteSum.Module
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import Mathlib.Topology.Instances.RealVectorSpace
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import Nevanlinna.cauchyRiemann
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import Nevanlinna.partialDeriv
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variable {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F]
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noncomputable def Complex.laplace : (ℂ → F) → (ℂ → F) := by
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intro f
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let fx := partialDeriv ℝ 1 f
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let fxx := partialDeriv ℝ 1 fx
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let fy := partialDeriv ℝ Complex.I f
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let fyy := partialDeriv ℝ Complex.I fy
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exact fxx + fyy
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