45 lines
1.5 KiB
Text
45 lines
1.5 KiB
Text
/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.SpaceTime.LorentzTensor.IndexNotation.IndexListColor
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import HepLean.SpaceTime.LorentzTensor.Basic
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/-!
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# The structure of a tensor with a string of indices
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-/
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namespace TensorStructure
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open TensorColor
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open IndexNotation
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variable {R : Type} [CommSemiring R] (𝓣 : TensorStructure R)
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variable {d : ℕ} {X Y Y' Z W : Type} [Fintype X] [DecidableEq X] [Fintype Y] [DecidableEq Y]
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[Fintype Y'] [DecidableEq Y'] [Fintype Z] [DecidableEq Z] [Fintype W] [DecidableEq W]
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{cX cX2 : X → 𝓣.Color} {cY : Y → 𝓣.Color} {cZ : Z → 𝓣.Color}
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{cW : W → 𝓣.Color} {cY' : Y' → 𝓣.Color} {μ ν η : 𝓣.Color}
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variable [IndexNotation 𝓣.Color] [Fintype 𝓣.Color] [DecidableEq 𝓣.Color]
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structure TensorIndex (cn : Fin n → 𝓣.Color) where
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tensor : 𝓣.Tensor cn
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index : IndexListColor 𝓣.toTensorColor
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nat_eq : n = index.1.length
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quot_eq : 𝓣.colorQuot ∘ index.1.colorMap ∘ Fin.cast nat_eq = 𝓣.colorQuot ∘ cn
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namespace TensorIndex
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variable {𝓣 : TensorStructure R} [IndexNotation 𝓣.Color] [Fintype 𝓣.Color] [DecidableEq 𝓣.Color]
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variable {n m : ℕ} {cn : Fin n → 𝓣.Color} {cm : Fin m → 𝓣.Color} (T : TensorIndex 𝓣 cn)
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section noncomputable
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def smul (r : R) : TensorIndex 𝓣 cn := ⟨r • T.tensor, T.index, T.nat_eq, T.quot_eq⟩
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end
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end TensorIndex
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end TensorStructure
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