refactor: basic golfing and renaming
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jstoobysmith
parent
dcfc4b1318
commit
bab9f10763
8 changed files with 177 additions and 188 deletions
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@ -9,15 +9,11 @@ import HepLean.Lorentz.ComplexTensor.PauliMatrices.Basic
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## Pauli matrices and the basis of complex Lorentz tensors
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-/
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open IndexNotation
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open CategoryTheory
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open MonoidalCategory
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open Matrix
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open MatrixGroups
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open Complex
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open TensorProduct
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open IndexNotation
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open CategoryTheory
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open TensorTree
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open OverColor.Discrete
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noncomputable section
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@ -342,40 +338,38 @@ lemma pauliMatrix_contr_down_0 :
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rw [basis_contr_pauliMatrix_basis_tree_expand_tensor]
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conv =>
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enter [1, 1, 1, 1, 1, 1, 1, 1]
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rw [contrBasisVectorMul_pos (by decide)]
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rw [contrBasisVectorMul_pos _]
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conv =>
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enter [1, 1, 1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_pos (by decide)]
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rw [contrBasisVectorMul_pos _]
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conv =>
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enter [1, 1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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enter [1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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enter [1, 1, 1, 1, 2, 2, 1]
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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enter [1, 1, 1, 2, 2, 1]
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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enter [1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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enter [1, 2, 2, 1]
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs
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simp only [_root_.zero_smul, one_smul, _root_.smul_zero, _root_.add_zero, _root_.zero_add]
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congr 1
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· rw [basisVectorContrPauli]
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congr 1
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funext k
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fin_cases k <;> rfl
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decide
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· rw [basisVectorContrPauli]
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congr 1
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funext k
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fin_cases k <;> rfl
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decide
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lemma pauliMatrix_contr_down_1 :
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{(basisVector ![Color.down, Color.down] fun _ => 1) | ν μ ⊗
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@ -386,29 +380,29 @@ lemma pauliMatrix_contr_down_1 :
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lhs
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rw [basis_contr_pauliMatrix_basis_tree_expand_tensor]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; lhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 1, 1, 1, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_pos (by decide)]
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enter [1, 1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_pos _]
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conv =>
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lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_pos (by decide)]
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enter [1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_pos _]
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conv =>
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lhs; lhs; lhs; lhs; rhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 1, 2, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; rhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 2, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; rhs; lhs;
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; rhs; rhs; lhs;
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 2, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs
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simp only [_root_.zero_smul, one_smul, _root_.smul_zero, _root_.add_zero, _root_.zero_add]
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@ -429,29 +423,29 @@ lemma pauliMatrix_contr_down_2 :
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lhs
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rw [basis_contr_pauliMatrix_basis_tree_expand_tensor]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; lhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 1, 1, 1, 1, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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enter [1, 1, 1, 1, 1, 1, 2, 1]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; rhs; rhs; lhs
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rw [contrBasisVectorMul_pos (by decide)]
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rw [contrBasisVectorMul_pos _]
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conv =>
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lhs; lhs; lhs; rhs; rhs; lhs
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rw [contrBasisVectorMul_pos (by decide)]
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rw [contrBasisVectorMul_pos _]
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conv =>
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lhs; lhs; rhs; lhs;
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; rhs; rhs; lhs;
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs
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simp only [_root_.zero_smul, one_smul, _root_.smul_zero, _root_.add_zero, _root_.zero_add]
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@ -470,28 +464,28 @@ lemma pauliMatrix_contr_down_3 :
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rw [basis_contr_pauliMatrix_basis_tree_expand_tensor]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; lhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; lhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; lhs; rhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; lhs; rhs; rhs; lhs
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rw [contrBasisVectorMul_neg (by decide)]
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rw [contrBasisVectorMul_neg (Nat.ne_of_beq_eq_false _)]
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conv =>
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lhs; lhs; rhs; lhs;
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rw [contrBasisVectorMul_pos (by decide)]
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rw [contrBasisVectorMul_pos _]
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conv =>
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lhs; rhs; rhs; lhs;
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rw [contrBasisVectorMul_pos (by decide)]
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rw [contrBasisVectorMul_pos _]
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conv =>
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lhs
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simp only [_root_.zero_smul, one_smul, _root_.smul_zero, _root_.add_zero, _root_.zero_add]
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@ -535,16 +529,16 @@ lemma pauliCo_basis_expand : pauliCo
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simp only [tensorNode_tensor, add_tensor, smul_tensor]
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simp only [Nat.succ_eq_add_one, Nat.reduceAdd, Fin.isValue, neg_smul, one_smul]
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conv =>
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lhs; lhs;
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enter [1, 1]
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rw [pauliMatrix_contr_down_0]
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conv =>
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lhs; rhs; lhs; rhs;
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enter [1, 2, 1, 1]
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rw [pauliMatrix_contr_down_1]
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conv =>
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lhs; rhs; rhs; lhs; rhs;
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enter [1, 2, 2, 1, 1]
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rw [pauliMatrix_contr_down_2]
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conv =>
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lhs; rhs; rhs; rhs; rhs;
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enter [1, 2, 2, 2, 1]
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rw [pauliMatrix_contr_down_3]
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simp only [neg_smul, one_smul]
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abel
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