refactor: Lint
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6 changed files with 8 additions and 12 deletions
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@ -53,7 +53,7 @@ lemma coMetric_basis_expand : {η' | μ ν}ᵀ.tensor =
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rfl
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/-- Provides the explicit expansion of the co-metric tensor in terms of the basis elements, as
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a tensor tree.-/
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a tensor tree. -/
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lemma coMetric_basis_expand_tree : {η' | μ ν}ᵀ.tensor =
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(TensorTree.add (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 0))) <|
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TensorTree.add (smul (-1) (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 1)))) <|
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@ -33,7 +33,7 @@ import HepLean.Tensors.ComplexLorentz.Basic
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`{T | μ ν ⊗ T3 | μ σ}ᵀ` is `contr 0 1 _ (prodNode (tensorNode T1) (tensorNode T3))`.
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`{T | μ ν ⊗ T3 | μ ν }ᵀ` is
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`contr 0 0 _ (contr 0 1 _ (prodNode (tensorNode T1) (tensorNode T3)))`.
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- If `T4` is a tensor `S.F (OverColor.mk ![c2, c1])` then
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- If `T4` is a tensor `S.F (OverColor.mk ![c2, c1])` then
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`{T | μ ν + T4 | ν μ }ᵀ`is `addNode (tensorNode T) (perm _ (tensorNode T4))` where `_`
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is the permutation of the two indices of `T4`.
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`{T | μ ν = T4 | ν μ }ᵀ` is `(tensorNode T).tensor = (perm _ (tensorNode T4)).tensor` is the
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@ -42,8 +42,8 @@ import HepLean.Tensors.ComplexLorentz.Basic
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## Comments
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- In all of theses expressions `μ`, `ν` etc are free. It does not matter what they are called,
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Lean will elaborate them in the same way. I.e. `{T | μ ν ⊗ T3 | μ ν }ᵀ` is exactly the same
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to Lean as `{T | α β ⊗ T3 | α β }ᵀ`.
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Lean will elaborate them in the same way. I.e. `{T | μ ν ⊗ T3 | μ ν }ᵀ` is exactly the same
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to Lean as `{T | α β ⊗ T3 | α β }ᵀ`.
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- Note that compared to ordinary index notation, we do not rise or lower the indices.
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This is for two reasons: 1) It is difficult to make this general for all tensor species,
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2) It is a reduency in ordinary index notation, since the tensor `T` itself already tells you
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