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refactor: Linting substrings

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jstoobysmith 2024-07-12 16:22:06 -04:00
parent cee38b7be8
commit ac1132c7ca
40 changed files with 133 additions and 132 deletions
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2
HepLean/AnomalyCancellation/MSSMNu/Basic.lean
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@ -76,7 +76,7 @@ def toSMSpecies (i : Fin 6) : MSSMCharges.Charges →ₗ[ℚ] MSSMSpecies.Charge
lemma toSMSpecies_toSpecies_inv (i : Fin 6) (f : (Fin 6 → Fin 3 → ℚ) × (Fin 2 → ℚ)) :
(toSMSpecies i) (toSpecies.symm f) = f.1 i := by
change (Prod.fst ∘ toSpecies ∘ toSpecies.symm ) _ i= f.1 i
change (Prod.fst ∘ toSpecies ∘ toSpecies.symm) _ i= f.1 i
simp
/-- The `Q` charges as a map `Fin 3 → ℚ`. -/

6
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/Basic.lean
View file

@ -56,7 +56,7 @@ def proj (T : MSSMACC.LinSols) : MSSMACC.AnomalyFreePerp :=
lemma proj_val (T : MSSMACC.LinSols) :
(proj T).val = (dot B₃.val T.val - dot Y₃.val T.val) • Y₃.val +
( (dot Y₃.val T.val - 2 * dot B₃.val T.val)) • B₃.val +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) • B₃.val +
dot Y₃.val B₃.val • T.val := by
rfl
@ -110,7 +110,7 @@ lemma quad_self_proj (T : MSSMACC.Sols) :
lemma quad_proj (T : MSSMACC.Sols) :
quadBiLin (proj T.1.1).val (proj T.1.1).val = 2 * dot Y₃.val B₃.val *
((dot B₃.val T.val - dot Y₃.val T.val) * quadBiLin Y₃.val T.val +
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * quadBiLin B₃.val T.val ) := by
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * quadBiLin B₃.val T.val) := by
nth_rewrite 1 [proj_val]
repeat rw [quadBiLin.map_add₁]
repeat rw [quadBiLin.map_smul₁]
@ -159,7 +159,7 @@ lemma cube_proj_proj_self (T : MSSMACC.Sols) :
cubeTriLin (proj T.1.1).val (proj T.1.1).val T.val =
2 * dot Y₃.val B₃.val *
((dot B₃.val T.val - dot Y₃.val T.val) * cubeTriLin T.val T.val Y₃.val +
( dot Y₃.val T.val- 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
(dot Y₃.val T.val - 2 * dot B₃.val T.val) * cubeTriLin T.val T.val B₃.val) := by
rw [proj_val]
rw [cubeTriLin.map_add₁, cubeTriLin.map_add₂]
erw [lineY₃B₃_doublePoint]

30
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/PlaneWithY3B3.lean
View file

@ -155,23 +155,23 @@ def α₁ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
(3 * cubeTriLin T.val T.val B₃.val * quadBiLin T.val T.val -
2 * cubeTriLin T.val T.val T.val * quadBiLin B₃.val T.val)
/-- A helper function to simplify following expressions. -/
def α₂ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
(2 * cubeTriLin T.val T.val T.val * quadBiLin Y₃.val T.val -
3 * cubeTriLin T.val T.val Y₃.val * quadBiLin T.val T.val)
/-- A helper function to simplify following expressions. -/
def α₂ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
(2 * cubeTriLin T.val T.val T.val * quadBiLin Y₃.val T.val -
3 * cubeTriLin T.val T.val Y₃.val * quadBiLin T.val T.val)
/-- A helper function to simplify following expressions. -/
def α₃ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
6 * ((cubeTriLin T.val T.val Y₃.val) * quadBiLin B₃.val T.val -
(cubeTriLin T.val T.val B₃.val) * quadBiLin Y₃.val T.val)
/-- A helper function to simplify following expressions. -/
def α₃ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
6 * ((cubeTriLin T.val T.val Y₃.val) * quadBiLin B₃.val T.val -
(cubeTriLin T.val T.val B₃.val) * quadBiLin Y₃.val T.val)
lemma lineQuad_cube (R : MSSMACC.AnomalyFreePerp) (c₁ c₂ c₃ : ℚ) :
accCube (lineQuad R c₁ c₂ c₃).val =
- 4 * ( c₁ * quadBiLin B₃.val R.val - c₂ * quadBiLin Y₃.val R.val) ^ 2 *
( α₁ R * c₁ + α₂ R * c₂ + α₃ R * c₃ ) := by
rw [lineQuad_val]
rw [planeY₃B₃_cubic, α₁, α₂, α₃]
ring
lemma lineQuad_cube (R : MSSMACC.AnomalyFreePerp) (c₁ c₂ c₃ : ℚ) :
accCube (lineQuad R c₁ c₂ c₃).val =
- 4 * (c₁ * quadBiLin B₃.val R.val - c₂ * quadBiLin Y₃.val R.val) ^ 2 *
(α₁ R * c₁ + α₂ R * c₂ + α₃ R * c₃) := by
rw [lineQuad_val]
rw [planeY₃B₃_cubic, α₁, α₂, α₃]
ring
/-- The line in the plane spanned by `Y₃`, `B₃` and `R` which is in the cubic. -/
def lineCube (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :

2
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/ToSols.lean
View file

@ -147,7 +147,7 @@ def InCubeSolProp (R : MSSMACC.Sols) : Prop :=
that solution satisfies `inCubeSolProp`. It appears in the definition of `inLineEqProj`. -/
def cubicCoeff (T : MSSMACC.Sols) : ℚ :=
3 * (dot Y₃.val B₃.val) ^ 3 * (cubeTriLin T.val T.val Y₃.val ^ 2 +
cubeTriLin T.val T.val B₃.val ^ 2 )
cubeTriLin T.val T.val B₃.val ^ 2)
lemma inCubeSolProp_iff_cubicCoeff_zero (T : MSSMACC.Sols) :
InCubeSolProp T ↔ cubicCoeff T = 0 := by

2
HepLean/AnomalyCancellation/MSSMNu/Permutations.lean
View file

@ -60,7 +60,7 @@ lemma chargeMap_toSpecies (f : PermGroup) (S : MSSMCharges.Charges) (j : Fin 6)
@[simp]
def repCharges : Representation ℚ PermGroup (MSSMCharges).Charges where
toFun f := chargeMap f⁻¹
map_mul' f g :=by
map_mul' f g := by
simp only [PermGroup, mul_inv_rev]
apply LinearMap.ext
intro S

9
HepLean/AnomalyCancellation/PureU1/Basic.lean
View file

@ -51,22 +51,19 @@ def accCubeTriLinSymm {n : ℕ} : TriLinearSymm (PureU1Charges n).Charges := Tri
rw [← Finset.sum_add_distrib]
apply Fintype.sum_congr
intro i
ring
)
ring)
(by
intro S L T
simp only [PureU1Charges_numberCharges]
apply Fintype.sum_congr
intro i
ring
)
ring)
(by
intro S L T
simp only [PureU1Charges_numberCharges]
apply Fintype.sum_congr
intro i
ring
)
ring)
/-- The cubic anomaly equation. -/
@[simp]

2
HepLean/AnomalyCancellation/PureU1/BasisLinear.lean
View file

@ -117,7 +117,7 @@ def coordinateMap : ((PureU1 n.succ).LinSols) ≃ₗ[ℚ] Fin n →₀ ℚ where
exact Rat.mul_zero (f k)
simp
/-- The basis of `LinSols`.-/
/-- The basis of `LinSols`. -/
noncomputable
def asBasis : Basis (Fin n) ℚ ((PureU1 n.succ).LinSols) where
repr := coordinateMap

2
HepLean/AnomalyCancellation/PureU1/ConstAbs.lean
View file

@ -191,7 +191,7 @@ lemma AFL_odd_noBoundary {A : (PureU1 (2 * n + 1)).LinSols} (h : ConstAbsSorted
lemma AFL_odd_zero {A : (PureU1 (2 * n + 1)).LinSols} (h : ConstAbsSorted A.val) :
A.val (0 : Fin (2 * n + 1)) = 0 := by
by_contra hn
exact (AFL_odd_noBoundary h hn ) (AFL_hasBoundary h hn)
exact (AFL_odd_noBoundary h hn) (AFL_hasBoundary h hn)
theorem AFL_odd (A : (PureU1 (2 * n + 1)).LinSols) (h : ConstAbsSorted A.val) :
A = 0 := by

2
HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean
View file

@ -689,7 +689,7 @@ lemma P!_in_span (f : Fin n → ℚ) : P! f ∈ Submodule.span ℚ (Set.range ba
use f
rfl
lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ )).LinSols) (j : Fin n) :
lemma smul_basis!AsCharges_in_span (S : (PureU1 (2 * n.succ)).LinSols) (j : Fin n) :
(S.val (δ!₂ j) - S.val (δ!₁ j)) • basis!AsCharges j ∈
Submodule.span ℚ (Set.range basis!AsCharges) := by
apply Submodule.smul_mem

8
HepLean/AnomalyCancellation/PureU1/Even/LineInCubic.lean
View file

@ -69,7 +69,7 @@ lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n.succ)).LinSols} (h : LineInCubic
/-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
def LineInCubicPerm (S : (PureU1 (2 * n.succ)).LinSols) : Prop :=
∀ (M : (FamilyPermutations (2 * n.succ)).group ),
∀ (M : (FamilyPermutations (2 * n.succ)).group),
LineInCubic ((FamilyPermutations (2 * n.succ)).linSolRep M S)
/-- If `lineInCubicPerm S` then `lineInCubic S`. -/
@ -104,7 +104,7 @@ lemma lineInCubicPerm_swap {S : (PureU1 (2 * n.succ)).LinSols}
rw [accCubeTriLinSymm.map_add₃, h1, accCubeTriLinSymm.map_smul₃] at h2
simpa using h2
lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ )).LinSols}
lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ)).LinSols}
(f : Fin n.succ.succ → ℚ) (g : Fin n.succ → ℚ) (hS : S.val = Pa f g) :
accCubeTriLinSymm (P f) (P f) (basis!AsCharges (Fin.last n)) =
- (S.val (δ!₂ (Fin.last n)) + S.val (δ!₁ (Fin.last n))) * (2 * S.val δ!₄ +
@ -114,12 +114,12 @@ lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ )).LinSols}
have h2 := Pa_δ!₁ f g (Fin.last n)
have h3 := Pa_δ!₂ f g (Fin.last n)
simp at h1 h2 h3
have hl : f (Fin.succ (Fin.last (n ))) = - Pa f g δ!₄ := by
have hl : f (Fin.succ (Fin.last n)) = - Pa f g δ!₄ := by
simp_all only [Fin.succ_last, neg_neg]
erw [hl] at h2
have hg : g (Fin.last n) = Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄ := by
linear_combination -(1 * h2)
have hll : f (Fin.castSucc (Fin.last (n ))) =
have hll : f (Fin.castSucc (Fin.last n)) =
- (Pa f g (δ!₂ (Fin.last n)) + Pa f g (δ!₁ (Fin.last n)) + Pa f g δ!₄) := by
linear_combination h3 - 1 * hg
rw [← hS] at hl hll

4
HepLean/AnomalyCancellation/PureU1/Even/Parameterization.lean
View file

@ -93,7 +93,7 @@ lemma genericCase_exists (S : (PureU1 (2 * n.succ)).Sols)
rw [hS'.1, hS'.2] at hC
exact hC' hC
/-- A proposition on a solution which is true if `accCubeTriLinSymm (P g, P g, P! f) = 0`.-/
/-- A proposition on a solution which is true if `accCubeTriLinSymm (P g, P g, P! f) = 0`. -/
def SpecialCase (S : (PureU1 (2 * n.succ)).Sols) : Prop :=
∀ (g : Fin n.succ → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f) ,
accCubeTriLinSymm (P g) (P g) (P! f) = 0
@ -125,7 +125,7 @@ theorem generic_case {S : (PureU1 (2 * n.succ)).Sols} (h : GenericCase S) :
rw [parameterization]
apply ACCSystem.Sols.ext
rw [parameterizationAsLinear_val]
change S.val = _ • ( _ • P g + _• P! f)
change S.val = _ • (_ • P g + _• P! f)
rw [anomalyFree_param _ _ hS]
rw [neg_neg, ← smul_add, smul_smul, inv_mul_cancel, one_smul]
exact hS

2
HepLean/AnomalyCancellation/PureU1/LineInPlaneCond.lean
View file

@ -52,7 +52,7 @@ lemma lineInPlaneCond_perm {S : (PureU1 (n)).LinSols} (hS : LineInPlaneCond S)
not_false_eq_true]
lemma lineInPlaneCond_eq_last' {S : (PureU1 (n.succ.succ)).LinSols} (hS : LineInPlaneCond S)
(h : ¬ (S.val ((Fin.last n).castSucc))^2 = (S.val ((Fin.last n).succ))^2 ) :
(h : ¬ (S.val ((Fin.last n).castSucc))^2 = (S.val ((Fin.last n).succ))^2) :
(2 - n) * S.val (Fin.last (n + 1)) =
- (2 - n)* S.val (Fin.castSucc (Fin.last n)) := by
erw [sq_eq_sq_iff_eq_or_eq_neg] at h

2
HepLean/AnomalyCancellation/PureU1/LowDim/Three.lean
View file

@ -43,7 +43,7 @@ lemma cube_for_linSol (S : (PureU1 3).LinSols) :
lemma three_sol_zero (S : (PureU1 3).Sols) : S.val (0 : Fin 3) = 0 ∨ S.val (1 : Fin 3) = 0
∨ S.val (2 : Fin 3) = 0 := (cube_for_linSol S.1.1).mpr S.cubicSol
/-- Given a `LinSol` with a charge equal to zero a `Sol`.-/
/-- Given a `LinSol` with a charge equal to zero a `Sol`. -/
def solOfLinear (S : (PureU1 3).LinSols)
(hS : S.val (0 : Fin 3) = 0 ∨ S.val (1 : Fin 3) = 0 ∨ S.val (2 : Fin 3) = 0) :
(PureU1 3).Sols :=

6
HepLean/AnomalyCancellation/PureU1/Odd/LineInCubic.lean
View file

@ -58,12 +58,12 @@ lemma line_in_cubic_P_P_P! {S : (PureU1 (2 * n + 1)).LinSols} (h : LineInCubic S
∀ (g : Fin n → ℚ) (f : Fin n → ℚ) (_ : S.val = P g + P! f),
accCubeTriLinSymm (P g) (P g) (P! f) = 0 := by
intro g f hS
linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1 ) -
(lineInCubic_expand h g f hS 1 2 ) / 6
linear_combination 2 / 3 * (lineInCubic_expand h g f hS 1 1) -
(lineInCubic_expand h g f hS 1 2) / 6
/-- We say a `LinSol` satisfies `lineInCubicPerm` if all its permutations satisfy `lineInCubic`. -/
def LineInCubicPerm (S : (PureU1 (2 * n + 1)).LinSols) : Prop :=
∀ (M : (FamilyPermutations (2 * n + 1)).group ),
∀ (M : (FamilyPermutations (2 * n + 1)).group),
LineInCubic ((FamilyPermutations (2 * n + 1)).linSolRep M S)
/-- If `lineInCubicPerm S` then `lineInCubic S`. -/

2
HepLean/AnomalyCancellation/PureU1/Odd/Parameterization.lean
View file

@ -124,7 +124,7 @@ theorem generic_case {S : (PureU1 (2 * n.succ + 1)).Sols} (h : GenericCase S) :
rw [parameterization]
apply ACCSystem.Sols.ext
rw [parameterizationAsLinear_val]
change S.val = _ • ( _ • P g + _• P! f)
change S.val = _ • (_ • P g + _• P! f)
rw [anomalyFree_param _ _ hS]
rw [neg_neg, ← smul_add, smul_smul, inv_mul_cancel, one_smul]
exact hS

18
HepLean/AnomalyCancellation/PureU1/Permutations.lean
View file

@ -51,7 +51,7 @@ open PureU1Charges in
@[simp]
def permCharges {n : ℕ} : Representation ℚ (PermGroup n) (PureU1 n).Charges where
toFun f := chargeMap f⁻¹
map_mul' f g :=by
map_mul' f g := by
simp only [PermGroup, mul_inv_rev]
apply LinearMap.ext
intro S
@ -214,7 +214,7 @@ lemma permTwo_fst : (permTwo hij hij').toFun i' = i := by
lemma permTwo_snd : (permTwo hij hij').toFun j' = j := by
rw [permTwo, permOfInjection]
have ht := Equiv.extendSubtype_apply_of_mem
((permTwoInj hij' ).toEquivRange.symm.trans
((permTwoInj hij').toEquivRange.symm.trans
(permTwoInj hij).toEquivRange) j' (permTwoInj_snd hij')
simp at ht
simp [ht, permTwoInj_snd_apply]
@ -303,16 +303,15 @@ lemma Prop_two (P : ℚ × ℚ → Prop) {S : (PureU1 n).LinSols}
{a b : Fin n} (hab : a ≠ b)
(h : ∀ (f : (FamilyPermutations n).group),
P ((((FamilyPermutations n).linSolRep f S).val a),
(((FamilyPermutations n).linSolRep f S).val b)
)) : ∀ (i j : Fin n) (_ : i ≠ j),
(((FamilyPermutations n).linSolRep f S).val b))) : ∀ (i j : Fin n) (_ : i ≠ j),
P (S.val i, S.val j) := by
intro i j hij
have h1 := h (permTwo hij hab ).symm
have h1 := h (permTwo hij hab).symm
rw [FamilyPermutations_anomalyFreeLinear_apply, FamilyPermutations_anomalyFreeLinear_apply] at h1
simp at h1
change P
(S.val ((permTwo hij hab ).toFun a),
S.val ((permTwo hij hab ).toFun b)) at h1
(S.val ((permTwo hij hab).toFun a),
S.val ((permTwo hij hab).toFun b)) at h1
erw [permTwo_fst,permTwo_snd] at h1
exact h1
@ -321,9 +320,8 @@ lemma Prop_three (P : ℚ × ℚ × ℚ → Prop) {S : (PureU1 n).LinSols}
(h : ∀ (f : (FamilyPermutations n).group),
P ((((FamilyPermutations n).linSolRep f S).val a),(
(((FamilyPermutations n).linSolRep f S).val b),
(((FamilyPermutations n).linSolRep f S).val c)
))) : ∀ (i j k : Fin n) (_ : i ≠ j) (_ : j ≠ k) (_ : i ≠ k),
P (S.val i, (S.val j, S.val k)) := by
(((FamilyPermutations n).linSolRep f S).val c)))) : ∀ (i j k : Fin n)
(_ : i ≠ j) (_ : j ≠ k) (_ : i ≠ k), P (S.val i, (S.val j, S.val k)) := by
intro i j k hij hjk hik
have h1 := h (permThree hij hjk hik hab hbc hac).symm
rw [FamilyPermutations_anomalyFreeLinear_apply, FamilyPermutations_anomalyFreeLinear_apply,

16
HepLean/AnomalyCancellation/SM/Basic.lean
View file

@ -54,9 +54,9 @@ lemma charges_eq_toSpecies_eq (S T : (SMCharges n).Charges) :
apply toSpeciesEquiv.injective
exact (Set.eqOn_univ (toSpeciesEquiv S) (toSpeciesEquiv T)).mp fun ⦃x⦄ _ => h x
lemma toSMSpecies_toSpecies_inv (i : Fin 5) (f : (Fin 5 → Fin n → ℚ) ) :
lemma toSMSpecies_toSpecies_inv (i : Fin 5) (f : Fin 5 → Fin n → ℚ) :
(toSpecies i) (toSpeciesEquiv.symm f) = f i := by
change (toSpeciesEquiv ∘ toSpeciesEquiv.symm ) _ i= f i
change (toSpeciesEquiv ∘ toSpeciesEquiv.symm) _ i= f i
simp
/-- The `Q` charges as a map `Fin n → ℚ`. -/
@ -272,8 +272,7 @@ def cubeTriLin : TriLinearSymm (SMCharges n).Charges := TriLinearSymm.mk₃
intro i
repeat erw [map_smul]
simp [HSMul.hSMul, SMul.smul]
ring
)
ring)
(by
intro S T R L
simp only
@ -282,22 +281,19 @@ def cubeTriLin : TriLinearSymm (SMCharges n).Charges := TriLinearSymm.mk₃
intro i
repeat erw [map_add]
simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue]
ring
)
ring)
(by
intro S T L
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
apply Fintype.sum_congr
intro i
ring
)
ring)
(by
intro S T L
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
apply Fintype.sum_congr
intro i
ring
)
ring)
/-- The cubic acc. -/
@[simp]

2
HepLean/AnomalyCancellation/SM/FamilyMaps.lean
View file

@ -100,7 +100,7 @@ def speciesFamilyUniversial (n : ℕ) :
/-- The embedding of the `1`-family charges into the `n`-family charges in
a universal manor. -/
def familyUniversal ( n : ℕ) : (SMCharges 1).Charges →ₗ[ℚ] (SMCharges n).Charges :=
def familyUniversal (n : ℕ) : (SMCharges 1).Charges →ₗ[ℚ] (SMCharges n).Charges :=
chargesMapOfSpeciesMap (speciesFamilyUniversial n)
end SM

7
HepLean/AnomalyCancellation/SM/NoGrav/One/LinearParameterization.lean
View file

@ -183,7 +183,8 @@ lemma grav (S : linearParameters) :
end linearParameters
/-- The parameters for solutions to the linear ACCs with the condition that Q and E are non-zero.-/
/-- The parameters for solutions to the linear ACCs with the condition that Q and E are
non-zero. -/
structure linearParametersQENeqZero where
/-- The parameter `x`. -/
x : ℚ
@ -291,7 +292,7 @@ lemma cubic_v_or_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection
exact h2 h
lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(hv : S.v = 0 ) : S.w = -1 := by
(hv : S.v = 0) : S.w = -1 := by
rw [S.cubic, hv] at h
simp at h
have h' : (S.w + 1) * (1 * S.w * S.w + (-1) * S.w + 1) = 0 := by
@ -309,7 +310,7 @@ lemma cubic_v_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.
exact eq_neg_of_add_eq_zero_left h'
lemma cube_w_zero (S : linearParametersQENeqZero) (h : accCube (bijection S).1.val = 0)
(hw : S.w = 0 ) : S.v = -1 := by
(hw : S.w = 0) : S.v = -1 := by
rw [S.cubic, hw] at h
simp at h
have h' : (S.v + 1) * (1 * S.v * S.v + (-1) * S.v + 1) = 0 := by

4
HepLean/AnomalyCancellation/SM/Permutations.lean
View file

@ -36,7 +36,7 @@ instance : Group (PermGroup n) := Pi.group
/-- The image of an element of `permGroup n` under the representation on charges. -/
@[simps!]
def chargeMap (f : PermGroup n) : (SMCharges n).Charges →ₗ[ℚ] (SMCharges n).Charges where
toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i )
toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i)
map_add' _ _ := rfl
map_smul' _ _ := rfl
@ -44,7 +44,7 @@ def chargeMap (f : PermGroup n) : (SMCharges n).Charges →ₗ[ℚ] (SMCharges n
@[simp]
def repCharges {n : ℕ} : Representation ℚ (PermGroup n) (SMCharges n).Charges where
toFun f := chargeMap f⁻¹
map_mul' f g :=by
map_mul' f g := by
simp only [PermGroup, mul_inv_rev]
apply LinearMap.ext
intro S

6
HepLean/AnomalyCancellation/SMNu/Basic.lean
View file

@ -31,7 +31,7 @@ namespace SMνCharges
variable {n : ℕ}
/-- An equivalence between `(SMνCharges n).charges` and `(Fin 6 → Fin n → ℚ)`
splitting the charges into species.-/
splitting the charges into species. -/
@[simps!]
def toSpeciesEquiv : (SMνCharges n).Charges ≃ (Fin 6 → Fin n → ℚ) :=
((Equiv.curry _ _ _).symm.trans ((@finProdFinEquiv 6 n).arrowCongr (Equiv.refl ℚ))).symm
@ -54,9 +54,9 @@ lemma charges_eq_toSpecies_eq (S T : (SMνCharges n).Charges) :
funext i
exact h i
lemma toSMSpecies_toSpecies_inv (i : Fin 6) (f : (Fin 6 → Fin n → ℚ) ) :
lemma toSMSpecies_toSpecies_inv (i : Fin 6) (f : Fin 6 → Fin n → ℚ) :
(toSpecies i) (toSpeciesEquiv.symm f) = f i := by
change (toSpeciesEquiv ∘ toSpeciesEquiv.symm ) _ i = f i
change (toSpeciesEquiv ∘ toSpeciesEquiv.symm) _ i = f i
simp
lemma toSpecies_one (S : (SMνCharges 1).Charges) (j : Fin 6) :

35
HepLean/AnomalyCancellation/SMNu/Ordinary/DimSevenPlane.lean
View file

@ -24,12 +24,11 @@ open BigOperators
namespace PlaneSeven
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₀ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₀ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 0, 0 => 1
| 0, 1 => - 1
| _, _ => 0
)
| _, _ => 0)
lemma B₀_cubic (S T : (SM 3).Charges) : cubeTriLin B₀ S T =
6 * (S (0 : Fin 18) * T (0 : Fin 18) - S (1 : Fin 18) * T (1 : Fin 18)) := by
@ -37,12 +36,11 @@ lemma B₀_cubic (S T : (SM 3).Charges) : cubeTriLin B₀ S T =
ring
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₁ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₁ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 1, 0 => 1
| 1, 1 => - 1
| _, _ => 0
)
| _, _ => 0)
lemma B₁_cubic (S T : (SM 3).Charges) : cubeTriLin B₁ S T =
3 * (S (3 : Fin 18) * T (3 : Fin 18) - S (4 : Fin 18) * T (4 : Fin 18)) := by
@ -50,12 +48,11 @@ lemma B₁_cubic (S T : (SM 3).Charges) : cubeTriLin B₁ S T =
ring
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₂ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₂ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 2, 0 => 1
| 2, 1 => - 1
| _, _ => 0
)
| _, _ => 0)
lemma B₂_cubic (S T : (SM 3).Charges) : cubeTriLin B₂ S T =
3 * (S (6 : Fin 18) * T (6 : Fin 18) - S (7 : Fin 18) * T (7 : Fin 18)) := by
@ -63,12 +60,11 @@ lemma B₂_cubic (S T : (SM 3).Charges) : cubeTriLin B₂ S T =
ring
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₃ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₃ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 3, 0 => 1
| 3, 1 => - 1
| _, _ => 0
)
| _, _ => 0)
lemma B₃_cubic (S T : (SM 3).Charges) : cubeTriLin B₃ S T =
2 * (S (9 : Fin 18) * T (9 : Fin 18) - S (10 : Fin 18) * T (10 : Fin 18)) := by
@ -77,12 +73,11 @@ lemma B₃_cubic (S T : (SM 3).Charges) : cubeTriLin B₃ S T =
rfl
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₄ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₄ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 4, 0 => 1
| 4, 1 => - 1
| _, _ => 0
)
| _, _ => 0)
lemma B₄_cubic (S T : (SM 3).Charges) : cubeTriLin B₄ S T =
(S (12 : Fin 18) * T (12 : Fin 18) - S (13 : Fin 18) * T (13 : Fin 18)) := by
@ -91,12 +86,11 @@ lemma B₄_cubic (S T : (SM 3).Charges) : cubeTriLin B₄ S T =
rfl
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₅ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₅ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 5, 0 => 1
| 5, 1 => - 1
| _, _ => 0
)
| _, _ => 0)
lemma B₅_cubic (S T : (SM 3).Charges) : cubeTriLin B₅ S T =
(S (15 : Fin 18) * T (15 : Fin 18) - S (16 : Fin 18) * T (16 : Fin 18)) := by
@ -105,12 +99,11 @@ lemma B₅_cubic (S T : (SM 3).Charges) : cubeTriLin B₅ S T =
rfl
/-- A charge assignment forming one of the basis elements of the plane. -/
def B₆ : (SM 3).Charges := toSpeciesEquiv.invFun ( fun s => fun i =>
def B₆ : (SM 3).Charges := toSpeciesEquiv.invFun (fun s => fun i =>
match s, i with
| 1, 2 => 1
| 2, 2 => -1
| _, _ => 0
)
| _, _ => 0)
lemma B₆_cubic (S T : (SM 3).Charges) : cubeTriLin B₆ S T =
3 * (S (5 : Fin 18) * T (5 : Fin 18) - S (8 : Fin 18) * T (8 : Fin 18)) := by

2
HepLean/AnomalyCancellation/SMNu/Permutations.lean
View file

@ -36,7 +36,7 @@ instance : Group (PermGroup n) := Pi.group
/-- The image of an element of `permGroup n` under the representation on charges. -/
@[simps!]
def chargeMap (f : PermGroup n) : (SMνCharges n).Charges →ₗ[ℚ] (SMνCharges n).Charges where
toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i )
toFun S := toSpeciesEquiv.symm (fun i => toSpecies i S ∘ f i)
map_add' _ _ := rfl
map_smul' _ _ := rfl