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fix: Slow builds with tensors

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jstoobysmith 2024-11-03 08:41:55 +00:00
parent c9c9047a0c
commit e24fd5b40b
3 changed files with 56 additions and 51 deletions
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28
HepLean/Tensors/ComplexLorentz/PauliMatrices/Basic.lean
View file

@ -63,17 +63,18 @@ lemma tensorNode_pauliContr : {pauliContr | μ α β}ᵀ.tensor =
/-- The definitional tensor node relation for `pauliCo`. -/
lemma tensorNode_pauliCo : {pauliCo | μ α β}ᵀ.tensor =
{η' | μ ν ⊗ PauliMatrix.asConsTensor | ν α β}ᵀ.tensor := by
rfl
{η' | μ ν ⊗ pauliContr | ν α β}ᵀ.tensor := by
rw [pauliCo, tensorNode_tensor]
/-- The definitional tensor node relation for `pauliCoDown`. -/
lemma tensorNode_pauliCoDown : {pauliCoDown | μ α β}ᵀ.tensor =
{pauliCo | μ α β ⊗ εL' | α α' ⊗ εR' | β β'}ᵀ.tensor := by
rfl
rw [pauliCoDown, tensorNode_tensor]
/-- The definitional tensor node relation for `pauliContrDown`. -/
lemma tensorNode_pauliContrDown : {pauliContrDown | μ α β}ᵀ.tensor =
{pauliContr | μ α β ⊗ εL' | α α' ⊗ εR' | β β'}ᵀ.tensor := by
rw [pauliContr, tensorNode_tensor]
rfl
/-!
@ -200,10 +201,15 @@ lemma action_pauliCo (g : SL(2,ℂ)) : {g •ₐ pauliCo | μ α β}ᵀ.tensor =
conv =>
lhs
rw [action_tensor_eq <| tensorNode_pauliCo]
rw [action_tensor_eq <| contr_tensor_eq <| prod_tensor_eq_snd <| tensorNode_pauliContr]
rw [(contr_action _ _).symm]
rw [contr_tensor_eq <| (prod_action _ _ _).symm]
rw [contr_tensor_eq <| prod_tensor_eq_fst <| action_constTwoNode _ _]
rw [contr_tensor_eq <| prod_tensor_eq_snd <| action_constThreeNode _ _]
conv =>
rhs
rw [tensorNode_pauliCo]
rw [contr_tensor_eq <| prod_tensor_eq_snd <| tensorNode_pauliContr]
rfl
/-- The tensor `pauliCoDown` is invariant under the action of `SL(2,ℂ)`. -/
@ -219,9 +225,11 @@ lemma action_pauliCoDown (g : SL(2,ℂ)) : {g •ₐ pauliCoDown | μ α β}ᵀ.
rw [contr_tensor_eq <| prod_tensor_eq_fst <| contr_tensor_eq <| prod_tensor_eq_fst <|
action_pauliCo _]
rw [contr_tensor_eq <| prod_tensor_eq_fst <| contr_tensor_eq <| prod_tensor_eq_snd <|
action_constTwoNode _ _]
erw [contr_tensor_eq <| prod_tensor_eq_snd <| action_constTwoNode _ _]
rfl
action_altLeftMetric _]
rw [contr_tensor_eq <| prod_tensor_eq_snd <| action_altRightMetric _]
conv =>
rhs
rw [tensorNode_pauliCoDown]
/-- The tensor `pauliContrDown` is invariant under the action of `SL(2,ℂ)`. -/
lemma action_pauliContrDown (g : SL(2,ℂ)) : {g •ₐ pauliContrDown | μ α β}ᵀ.tensor =
@ -236,8 +244,10 @@ lemma action_pauliContrDown (g : SL(2,ℂ)) : {g •ₐ pauliContrDown | μ α
rw [contr_tensor_eq <| prod_tensor_eq_fst <| contr_tensor_eq <| prod_tensor_eq_fst <|
action_pauliContr _]
rw [contr_tensor_eq <| prod_tensor_eq_fst <| contr_tensor_eq <| prod_tensor_eq_snd <|
action_constTwoNode _ _]
erw [contr_tensor_eq <| prod_tensor_eq_snd <| action_constTwoNode _ _]
rfl
action_altLeftMetric _]
erw [contr_tensor_eq <| prod_tensor_eq_snd <| action_altRightMetric _]
conv =>
rhs
rw [tensorNode_pauliContrDown]
end complexLorentzTensor

27
HepLean/Tensors/ComplexLorentz/PauliMatrices/Basis.lean
View file

@ -458,15 +458,10 @@ lemma pauliMatrix_contr_down_2 :
conv =>
lhs
simp only [_root_.zero_smul, one_smul, _root_.smul_zero, _root_.add_zero, _root_.zero_add]
congr 1
· rw [basisVectorContrPauli]
congr 2
funext k
fin_cases k <;> rfl
· rw [basisVectorContrPauli]
congr 2
funext k
fin_cases k <;> rfl
rw [basisVectorContrPauli, basisVectorContrPauli]
congr 3
· decide
· decide
lemma pauliMatrix_contr_down_3 :
{(basisVector ![Color.down, Color.down] fun x => 3) | μ ν ⊗
@ -503,16 +498,10 @@ lemma pauliMatrix_contr_down_3 :
conv =>
lhs
simp only [_root_.zero_smul, one_smul, _root_.smul_zero, _root_.add_zero, _root_.zero_add]
congr 1
· rw [basisVectorContrPauli]
congr 1
funext k
fin_cases k <;> rfl
· rw [basisVectorContrPauli]
congr 1
congr 1
funext k
fin_cases k <;> rfl
rw [basisVectorContrPauli, basisVectorContrPauli]
congr 3
· decide
· decide
/-- The expansion of `pauliCo` in terms of a basis. -/
lemma pauliCo_basis_expand : pauliCo