feat: Add eval basis for complex Lorentz tensors

HepLean/SpaceTime/LorentzVector/Complex/Basic.lean

@@ -40,6 +40,10 @@ def complexCo : Rep ℂ SL(2, ℂ) := Rep.of CoℂModule.SL2CRep
 def complexContrBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexContr := Basis.ofEquivFun
   (Equiv.linearEquiv ℂ ContrℂModule.toFin13ℂFun)
 
+/-- The standard basis of complex contravariant Lorentz vectors indexed by `Fin 4`. -/
+def complexContrBasisFin4 : Basis (Fin 4) ℂ complexContr :=
+  Basis.reindex complexContrBasis finSumFinEquiv
+
 @[simp]
 lemma complexContrBasis_ρ_apply (M : SL(2,ℂ)) (i j : Fin 1 ⊕ Fin 3) :
     (LinearMap.toMatrix complexContrBasis complexContrBasis) (complexContr.ρ M) i j =
@@ -58,6 +62,10 @@ lemma complexContrBasis_ρ_val (M : SL(2,ℂ)) (v : complexContr) :
 def complexCoBasis : Basis (Fin 1 ⊕ Fin 3) ℂ complexCo := Basis.ofEquivFun
   (Equiv.linearEquiv ℂ CoℂModule.toFin13ℂFun)
 
+/-- The standard basis of complex covariant Lorentz vectors indexed by `Fin 4`. -/
+def complexCoBasisFin4 : Basis (Fin 4) ℂ complexCo :=
+  Basis.reindex complexCoBasis finSumFinEquiv
+
 @[simp]
 lemma complexCoBasis_ρ_apply (M : SL(2,ℂ)) (i j : Fin 1 ⊕ Fin 3) :
     (LinearMap.toMatrix complexCoBasis complexCoBasis) (complexCo.ρ M) i j =

HepLean/Tensors/ComplexLorentz/Basic.lean

@@ -135,7 +135,7 @@ def complexLorentzTensor : TensorSpecies where
     | Discrete.mk Color.downR => Fermion.rightAltRightUnit
     | Discrete.mk Color.up => Lorentz.coContrUnit
     | Discrete.mk Color.down => Lorentz.contrCoUnit
-  evalNo := fun c =>
+  repDim := fun c =>
     match c with
     | Color.upL => 2
     | Color.downL => 2
@@ -143,6 +143,14 @@ def complexLorentzTensor : TensorSpecies where
     | Color.downR => 2
     | Color.up => 4
     | Color.down => 4
+  basis := fun c =>
+    match c with
+    | Color.upL => Fermion.leftBasis
+    | Color.downL => Fermion.altLeftBasis
+    | Color.upR => Fermion.rightBasis
+    | Color.downR => Fermion.altRightBasis
+    | Color.up => Lorentz.complexContrBasisFin4
+    | Color.down => Lorentz.complexCoBasisFin4
   contr_tmul_symm := fun c =>
     match c with
     | Color.upL => Fermion.leftAltContraction_tmul_symm