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fix: PlaneNonSols

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jstoobysmith 2024-11-02 08:15:34 +00:00
parent e6045e5f58
commit 32ca614942
3 changed files with 22 additions and 16 deletions
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21
HepLean/AnomalyCancellation/SMNu/PlusU1/PlaneNonSols.lean
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@ -75,7 +75,7 @@ def B : Fin 11 → (PlusU1 3).Charges := fun i =>
lemma Bi_Bj_quad {i j : Fin 11} (hi : i ≠ j) : quadBiLin (B i) (B j) = 0 := by
fin_cases i <;> fin_cases j
any_goals rfl
any_goals with_unfolding_all rfl
all_goals simp at hi
lemma Bi_sum_quad (i : Fin 11) (f : Fin 11 → ℚ) :
@ -92,7 +92,7 @@ def quadCoeff : Fin 11 → ℚ := ![1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]
lemma quadCoeff_eq_bilinear (i : Fin 11) : quadCoeff i = quadBiLin (B i) (B i) := by
fin_cases i
all_goals rfl
all_goals with_unfolding_all rfl
lemma on_accQuad (f : Fin 11 → ℚ) :
accQuad (∑ i, f i • B i) = ∑ i, quadCoeff i * (f i)^2 := by
@ -170,8 +170,9 @@ lemma isSolution_grav (f : Fin 11 → ℚ) (hS : (PlusU1 3).IsSolution (∑ i, f
have hx := isSolution_sum_part f hS
obtain ⟨S, hS'⟩ := hS
have hg := gravSol S.toLinSols
rw [hS', hx, accGrav.map_add, accGrav.map_smul, accGrav.map_smul, show accGrav B₉ = 3 by rfl,
show accGrav B₁₀ = 1 by rfl] at hg
rw [hS', hx, accGrav.map_add, accGrav.map_smul, accGrav.map_smul,
show accGrav B₉ = 3 by with_unfolding_all rfl,
show accGrav B₁₀ = 1 by with_unfolding_all rfl] at hg
simp only [Fin.isValue, smul_eq_mul, mul_one] at hg
linear_combination hg
@ -191,8 +192,10 @@ lemma isSolution_f9 (f : Fin 11 → ℚ) (hS : (PlusU1 3).IsSolution (∑ i, f i
erw [accCube.map_smul (- 3 * f 9) B₁₀] at hc
rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₁, cubeTriLin.map_smul₂, cubeTriLin.map_smul₂,
cubeTriLin.map_smul₃, cubeTriLin.map_smul₃] at hc
rw [show accCube B₉ = 9 by rfl, show accCube B₁₀ = 1 by rfl, show cubeTriLin B₉ B₉ B₁₀ = 0 by rfl,
show cubeTriLin B₁₀ B₁₀ B₉ = 0 by rfl] at hc
rw [show accCube B₉ = 9 by with_unfolding_all rfl,
show accCube B₁₀ = 1 by with_unfolding_all rfl,
show cubeTriLin B₉ B₉ B₁₀ = 0 by with_unfolding_all rfl,
show cubeTriLin B₁₀ B₁₀ B₉ = 0 by with_unfolding_all rfl] at hc
simp only [Fin.isValue, neg_mul, mul_one, mul_zero, add_zero] at hc
have h1 : f 9 ^ 3 * 9 + (-(3 * f 9)) ^ 3 = - 18 * f 9 ^ 3 := by ring
rw [h1] at hc
@ -201,7 +204,7 @@ lemma isSolution_f9 (f : Fin 11 → ℚ) (hS : (PlusU1 3).IsSolution (∑ i, f i
lemma isSolution_f10 (f : Fin 11 → ℚ) (hS : (PlusU1 3).IsSolution (∑ i, f i • B i)) :
f 10 = 0 := by
rw [isSolution_grav f hS, isSolution_f9 f hS]
rfl
with_unfolding_all rfl
lemma isSolution_f_zero (f : Fin 11 → ℚ) (hS : (PlusU1 3).IsSolution (∑ i, f i • B i))
(k : Fin 11) : f k = 0 := by
@ -225,7 +228,9 @@ lemma isSolution_only_if_zero (f : Fin 11 → ℚ) (hS : (PlusU1 3).IsSolution (
theorem basis_linear_independent : LinearIndependent ℚ B :=
Fintype.linearIndependent_iff.mpr fun f h ↦ isSolution_f_zero f
⟨chargeToAF 0 (by rfl) (by rfl) (by rfl) (by rfl) (by rfl) (by rfl), id (Eq.symm h)⟩
⟨chargeToAF 0 (by with_unfolding_all rfl) (by with_unfolding_all rfl)
(by with_unfolding_all rfl) (by with_unfolding_all rfl) (by with_unfolding_all rfl)
(by with_unfolding_all rfl), id (Eq.symm h)⟩
end ElevenPlane