58 lines
1.5 KiB
Text
58 lines
1.5 KiB
Text
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/-
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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.Indices.Color
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import HepLean.SpaceTime.LorentzTensor.IndexNotation.Indices.UniqueDualInOther
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import HepLean.SpaceTime.LorentzTensor.Basic
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import Init.Data.List.Lemmas
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/-!
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# Index lists with color conditions
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Here we consider `IndexListColor` which is a subtype of all lists of indices
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on those where the elements to be contracted have consistent colors with respect to
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a Tensor Color structure.
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-/
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namespace IndexNotation
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namespace ColorIndexList
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variable {𝓒 : TensorColor} [IndexNotation 𝓒.Color] [Fintype 𝓒.Color] [DecidableEq 𝓒.Color]
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variable (l l' : ColorIndexList 𝓒)
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/-!
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## Reindexing
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-/
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def Reindexing : Prop := l.length = l'.length ∧
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∀ (h : l.length = l'.length), l.colorMap = l'.colorMap ∘ Fin.cast h ∧
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Option.map (Fin.cast h) ∘ l.getDual? = l'.getDual? ∘ Fin.cast h
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/-!
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## Permutation
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Test whether two `ColorIndexList`s are permutations of each other.
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To prevent choice problems, this has to be done after contraction.
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-/
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def ContrPerm : Prop := l.contr.length = l'.contr.length ∧
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l.contr.withUniqueDualInOther l'.contr.toIndexList = Finset.univ ∧
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l'.contr.colorMap ∘ Subtype.val ∘ (l.contr.getDualInOtherEquiv l'.contr.toIndexList)
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= l.contr.colorMap ∘ Subtype.val
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end ColorIndexList
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end IndexNotation
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