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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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28
HepLean/AnomalyCancellation/SM/Basic.lean
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@ -262,13 +262,14 @@ lemma accQuad_ext {S T : (SMCharges n).charges}
/-- The trilinear function defining the cubic. -/
@[simps!]
def cubeTriLin : TriLinearSymm (SMCharges n).charges where
toFun S := ∑ i, (6 * ((Q S.1 i) * (Q S.2.1 i) * (Q S.2.2 i))
def cubeTriLin : TriLinearSymm (SMCharges n).charges := TriLinearSymm.mk₃
(fun S => ∑ i, (6 * ((Q S.1 i) * (Q S.2.1 i) * (Q S.2.2 i))
+ 3 * ((U S.1 i) * (U S.2.1 i) * (U S.2.2 i))
+ 3 * ((D S.1 i) * (D S.2.1 i) * (D S.2.2 i))
+ 2 * ((L S.1 i) * (L S.2.1 i) * (L S.2.2 i))
+ ((E S.1 i) * (E S.2.1 i) * (E S.2.2 i)))
map_smul₁' a S T R := by
+ ((E S.1 i) * (E S.2.1 i) * (E S.2.2 i))))
(by
intro a S T R
simp only
rw [Finset.mul_sum]
apply Fintype.sum_congr
@ -276,7 +277,9 @@ def cubeTriLin : TriLinearSymm (SMCharges n).charges where
repeat erw [map_smul]
simp [HSMul.hSMul, SMul.smul]
ring
map_add₁' S T R L := by
)
(by
intro S T R L
simp only
rw [← Finset.sum_add_distrib]
apply Fintype.sum_congr
@ -284,16 +287,21 @@ def cubeTriLin : TriLinearSymm (SMCharges n).charges where
repeat erw [map_add]
simp only [ACCSystemCharges.chargesAddCommMonoid_add, toSpecies_apply, Fin.isValue]
ring
swap₁' S T L := by
)
(by
intro S T L
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
apply Fintype.sum_congr
intro i
ring
swap₂' S T L := by
)
(by
intro S T L
simp only [SMSpecies_numberCharges, toSpecies_apply, Fin.isValue]
apply Fintype.sum_congr
intro i
ring
)
/-- The cubic acc. -/
@[simp]
@ -304,10 +312,8 @@ lemma accCube_ext {S T : (SMCharges n).charges}
(h : ∀ j, ∑ i, ((fun a => a^3) ∘ toSpecies j S) i =
∑ i, ((fun a => a^3) ∘ toSpecies j T) i) :
accCube S = accCube T := by
simp only [HomogeneousCubic, accCube, TriLinearSymm.toCubic_apply]
erw [← cubeTriLin.toFun_eq_coe]
rw [cubeTriLin]
simp only
simp only [HomogeneousCubic, accCube, cubeTriLin, TriLinearSymm.toCubic_apply,
TriLinearSymm.mk₃_toFun_apply_apply]
repeat erw [Finset.sum_add_distrib]
repeat erw [← Finset.mul_sum]
ring_nf