/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license.
Authors: Joseph Tooby-Smith
-/
import HepLean.AnomalyCancellation.SMNu.Ordinary.Basic
import HepLean.AnomalyCancellation.SMNu.FamilyMaps
/-!
# Family Maps for SM with RHN (no hypercharge)

We give some propererties of the family maps for the SM with RHN, in particular, we
define family universal maps in the case of `LinSols`, `QuadSols`, and `Sols`.
-/
universe v u

namespace SMRHN
namespace SM

open SMνCharges
open SMνACCs
open BigOperators

variable {n : ℕ}

/-- The family universal maps on `LinSols`. -/
def familyUniversalLinear (n : ℕ) :
    (SM 1).LinSols →ₗ[ℚ] (SM n).LinSols where
  toFun S := chargeToLinear (familyUniversal n S.val)
    (by rw [familyUniversal_accGrav, gravSol S, mul_zero])
    (by rw [familyUniversal_accSU2, SU2Sol S, mul_zero])
    (by rw [familyUniversal_accSU3, SU3Sol S, mul_zero])
  map_add' S T := by
    apply ACCSystemLinear.LinSols.ext
    exact (familyUniversal n).map_add' _ _
  map_smul' a S := by
    apply ACCSystemLinear.LinSols.ext
    exact (familyUniversal n).map_smul' _ _

/-- The family universal maps on `QuadSols`. -/
def familyUniversalQuad (n : ℕ) :
    (SM 1).QuadSols → (SM n).QuadSols := fun S =>
  chargeToQuad (familyUniversal n S.val)
    (by rw [familyUniversal_accGrav, gravSol S.1, mul_zero])
    (by rw [familyUniversal_accSU2, SU2Sol S.1, mul_zero])
    (by rw [familyUniversal_accSU3, SU3Sol S.1, mul_zero])

/-- The family universal maps on `Sols`. -/
def familyUniversalAF (n : ℕ) :
    (SM 1).Sols → (SM n).Sols := fun S =>
  chargeToAF (familyUniversal n S.val)
    (by rw [familyUniversal_accGrav, gravSol S.1.1, mul_zero])
    (by rw [familyUniversal_accSU2, SU2Sol S.1.1, mul_zero])
    (by rw [familyUniversal_accSU3, SU3Sol S.1.1, mul_zero])
    (by rw [familyUniversal_accCube, cubeSol S, mul_zero])

end SM
end SMRHN