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refactor: def of symmetric trilin function

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jstoobysmith 2024-04-22 09:48:44 -04:00
parent 748bcb61ae
commit e36c61b331
24 changed files with 279 additions and 246 deletions
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12
HepLean/AnomalyCancellation/SMNu/PlusU1/HyperCharge.lean
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@ -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