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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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14
HepLean/AnomalyCancellation/MSSMNu/LineY3B3.lean
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@ -54,8 +54,8 @@ lemma lineY₃B₃Charges_cubic (a b : ℚ) : accCube (lineY₃B₃Charges a b).
rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂, cubeTriLin.map_smul₃]
rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂, cubeTriLin.map_smul₃]
erw [Y₃.cubicSol, B₃.cubicSol]
rw [show cubeTriLin (Y₃.val, Y₃.val, B₃.val) = 0 by rfl]
rw [show cubeTriLin (B₃.val, B₃.val, Y₃.val) = 0 by rfl]
rw [show cubeTriLin Y₃.val Y₃.val B₃.val = 0 by rfl]
rw [show cubeTriLin B₃.val B₃.val Y₃.val = 0 by rfl]
simp
/-- The line through $Y_3$ and $B_3$ as `Sols`. -/
@ -63,9 +63,9 @@ def lineY₃B₃ (a b : ℚ) : MSSMACC.Sols :=
AnomalyFreeMk' (lineY₃B₃Charges a b) (lineY₃B₃Charges_quad a b) (lineY₃B₃Charges_cubic a b)
lemma doublePoint_Y₃_B₃ (R : MSSMACC.LinSols) :
cubeTriLin (Y₃.val, B₃.val, R.val) = 0 := by
rw [← TriLinearSymm.toFun_eq_coe]
simp only [cubeTriLin, cubeTriLinToFun, MSSMSpecies_numberCharges]
cubeTriLin Y₃.val B₃.val R.val = 0 := by
simp only [cubeTriLin, TriLinearSymm.mk₃_toFun_apply_apply, cubeTriLinToFun,
MSSMSpecies_numberCharges, Fin.isValue, Fin.reduceFinMk]
rw [Fin.sum_univ_three]
rw [B₃_val, Y₃_val]
rw [B₃AsCharge, Y₃AsCharge]
@ -83,8 +83,8 @@ lemma doublePoint_Y₃_B₃ (R : MSSMACC.LinSols) :
linear_combination -(12 * h2) + 9 * h1 + 3 * h3
lemma lineY₃B₃_doublePoint (R : MSSMACC.LinSols) (a b : ℚ) :
cubeTriLin ((lineY₃B₃ a b).val, (lineY₃B₃ a b).val, R.val) = 0 := by
change cubeTriLin (a • Y₃.val + b • B₃.val , a • Y₃.val + b • B₃.val, R.val ) = 0
cubeTriLin (lineY₃B₃ a b).val (lineY₃B₃ a b).val R.val = 0 := by
change cubeTriLin (a • Y₃.val + b • B₃.val) (a • Y₃.val + b • B₃.val) R.val = 0
rw [cubeTriLin.map_add₂, cubeTriLin.map_add₁, cubeTriLin.map_add₁]
repeat rw [cubeTriLin.map_smul₂, cubeTriLin.map_smul₁]
rw [doublePoint_B₃_B₃, doublePoint_Y₃_Y₃, doublePoint_Y₃_B₃]