DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: def of symmetric trilin function

Browse source
This commit is contained in:
jstoobysmith 2024-04-22 09:48:44 -04:00
parent 748bcb61ae
commit e36c61b331
24 changed files with 279 additions and 246 deletions
Download patch file Download diff file Expand all files Collapse all files

8
HepLean/AnomalyCancellation/SMNu/PlusU1/BMinusL.lean
View file

@ -91,7 +91,7 @@ lemma addQuad_zero (S : (PlusU1 n).QuadSols) (a : ℚ): addQuad S a 0 = a • S
rfl
lemma on_cubeTriLin (S : (PlusU1 n).charges) :
cubeTriLin ((BL n).val, (BL n).val, S) = 9 * accGrav S - 24 * accSU3 S := by
cubeTriLin (BL n).val (BL n).val S = 9 * accGrav S - 24 * accSU3 S := by
erw [familyUniversal_cubeTriLin']
rw [accGrav_decomp, accSU3_decomp]
simp only [Fin.isValue, BL₁_val, mul_one, SMνSpecies_numberCharges, toSpecies_apply, mul_neg,
@ -99,18 +99,18 @@ lemma on_cubeTriLin (S : (PlusU1 n).charges) :
ring
lemma on_cubeTriLin_AFL (S : (PlusU1 n).LinSols) :
cubeTriLin ((BL n).val, (BL n).val, S.val) = 0 := by
cubeTriLin (BL n).val (BL n).val S.val = 0 := by
rw [on_cubeTriLin]
rw [gravSol S, SU3Sol S]
simp
lemma add_AFL_cube (S : (PlusU1 n).LinSols) (a b : ℚ) :
accCube (a • S.val + b • (BL n).val) =
a ^ 2 * (a * accCube S.val + 3 * b * cubeTriLin (S.val, S.val, (BL n).val)) := by
a ^ 2 * (a * accCube S.val + 3 * b * cubeTriLin S.val S.val (BL n).val) := by
erw [TriLinearSymm.toCubic_add, cubeSol (b • (BL n)), accCube.map_smul]
repeat rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂, cubeTriLin.map_smul₃]
rw [on_cubeTriLin_AFL]
simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply, cubeTriLin_toFun, Fin.isValue,
simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply, Fin.isValue,
add_zero, BL_val, mul_zero]
ring

12
HepLean/AnomalyCancellation/SMNu/PlusU1/HyperCharge.lean
View file

@ -90,7 +90,7 @@ lemma addQuad_zero (S : (PlusU1 n).QuadSols) (a : ℚ): addQuad S a 0 = a • S
rfl
lemma on_cubeTriLin (S : (PlusU1 n).charges) :
cubeTriLin ((Y n).val, (Y n).val, S) = 6 * accYY S := by
cubeTriLin (Y n).val (Y n).val S = 6 * accYY S := by
erw [familyUniversal_cubeTriLin']
rw [accYY_decomp]
simp only [Fin.isValue, Y₁_val, mul_one, SMνSpecies_numberCharges, toSpecies_apply, mul_neg,
@ -98,13 +98,13 @@ lemma on_cubeTriLin (S : (PlusU1 n).charges) :
ring
lemma on_cubeTriLin_AFL (S : (PlusU1 n).LinSols) :
cubeTriLin ((Y n).val, (Y n).val, S.val) = 0 := by
cubeTriLin (Y n).val (Y n).val S.val = 0 := by
rw [on_cubeTriLin]
rw [YYsol S]
simp
lemma on_cubeTriLin' (S : (PlusU1 n).charges) :
cubeTriLin ((Y n).val, S, S) = 6 * accQuad S := by
cubeTriLin (Y n).val S S = 6 * accQuad S := by
erw [familyUniversal_cubeTriLin]
rw [accQuad_decomp]
simp only [Fin.isValue, Y₁_val, mul_one, SMνSpecies_numberCharges, toSpecies_apply, mul_neg,
@ -112,18 +112,18 @@ lemma on_cubeTriLin' (S : (PlusU1 n).charges) :
ring_nf
lemma on_cubeTriLin'_ALQ (S : (PlusU1 n).QuadSols) :
cubeTriLin ((Y n).val, S.val, S.val) = 0 := by
cubeTriLin (Y n).val S.val S.val = 0 := by
rw [on_cubeTriLin']
rw [quadSol S]
simp
lemma add_AFL_cube (S : (PlusU1 n).LinSols) (a b : ℚ) :
accCube (a • S.val + b • (Y n).val) =
a ^ 2 * (a * accCube S.val + 3 * b * cubeTriLin (S.val, S.val, (Y n).val)) := by
a ^ 2 * (a * accCube S.val + 3 * b * cubeTriLin S.val S.val (Y n).val) := by
erw [TriLinearSymm.toCubic_add, cubeSol (b • (Y n)), accCube.map_smul]
repeat rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂, cubeTriLin.map_smul₃]
rw [on_cubeTriLin_AFL]
simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply, cubeTriLin_toFun, Fin.isValue,
simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply, Fin.isValue,
add_zero, Y_val, mul_zero]
ring

4
HepLean/AnomalyCancellation/SMNu/PlusU1/PlaneNonSols.lean
View file

@ -204,8 +204,8 @@ lemma isSolution_f9 (f : Fin 11 → ℚ) (hS : (PlusU1 3).isSolution (∑ i, f i
cubeTriLin.map_smul₃, cubeTriLin.map_smul₃] at hc
rw [show accCube B₉ = 9 by rfl] at hc
rw [show accCube B₁₀ = 1 by rfl] at hc
rw [show cubeTriLin (B₉, B₉, B₁₀) = 0 by rfl] at hc
rw [show cubeTriLin (B₁₀, B₁₀, B₉) = 0 by rfl] at hc
rw [show cubeTriLin B₉ B₉ B₁₀ = 0 by rfl] at hc
rw [show cubeTriLin B₁₀ B₁₀ B₉ = 0 by rfl] at hc
simp at hc
have h1 : f 9 ^ 3 * 9 + (-(3 * f 9)) ^ 3 = - 18 * f 9 ^ 3 := by
ring

2
HepLean/AnomalyCancellation/SMNu/PlusU1/QuadSolToSol.lean
View file

@ -29,7 +29,7 @@ open BigOperators
variable {n : ℕ}
/-- A helper function for what follows. -/
@[simp]
def α₁ (S : (PlusU1 n).QuadSols) : ℚ := - 3 * cubeTriLin (S.val, S.val, (BL n).val)
def α₁ (S : (PlusU1 n).QuadSols) : ℚ := - 3 * cubeTriLin S.val S.val (BL n).val
/-- A helper function for what follows. -/
@[simp]