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docs: More doc strings

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jstoobysmith 2024-11-12 05:49:43 +00:00
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4
HepLean/Lorentz/ComplexTensor/Basic.lean
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@ -199,6 +199,8 @@ namespace complexLorentzTensor
/-- Color for complex Lorentz tensors is decidable. -/
instance : DecidableEq complexLorentzTensor.C := complexLorentzTensor.instDecidableEqColor
/-- Contracting two basis elements gives `1` if the index for the basis elements is the same,
and `0` otherwise. Holds for any color of index. -/
lemma basis_contr (c : complexLorentzTensor.C) (i : Fin (complexLorentzTensor.repDim c))
(j : Fin (complexLorentzTensor.repDim (complexLorentzTensor.τ c))) :
complexLorentzTensor.castToField
@ -213,9 +215,11 @@ lemma basis_contr (c : complexLorentzTensor.C) (i : Fin (complexLorentzTensor.re
| Color.up => Lorentz.contrCoContraction_basis _ _
| Color.down => Lorentz.coContrContraction_basis _ _
/-- For any object in the over color category, with source `Fin n`, has a decidable source. -/
instance {n : ℕ} {c : Fin n → complexLorentzTensor.C} :
DecidableEq (OverColor.mk c).left := instDecidableEqFin n
/-- For any object in the over color category, with source `Fin n`, has a finite source. -/
instance {n : ℕ} {c : Fin n → complexLorentzTensor.C} :
Fintype (OverColor.mk c).left := Fin.fintype n

2
HepLean/Lorentz/RealVector/Basic.lean
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@ -30,6 +30,8 @@ open minkowskiMatrix
Lorentz vectors. In index notation these have an up index `ψⁱ`. -/
def Contr (d : ℕ) : Rep ℝ (LorentzGroup d) := Rep.of ContrMod.rep
/-- The representation of contrvariant Lorentz vectors forms a topological space, induced
by its equivalence to `Fin 1 ⊕ Fin d → ℝ`. -/
instance : TopologicalSpace (Contr d) := TopologicalSpace.induced
ContrMod.toFin1dℝEquiv (Pi.topologicalSpace)