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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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30
HepLean/AnomalyCancellation/MSSMNu/OrthogY3B3/PlaneWithY3B3.lean
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@ -115,8 +115,8 @@ lemma planeY₃B₃_quad (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) :
lemma planeY₃B₃_cubic (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) :
accCube (planeY₃B₃ R a b c).val = c ^ 2 *
(3 * a * cubeTriLin (R.val, R.val, Y₃.val)
+ 3 * b * cubeTriLin (R.val, R.val, B₃.val) + c * cubeTriLin (R.val, R.val, R.val) ) := by
(3 * a * cubeTriLin R.val R.val Y₃.val
+ 3 * b * cubeTriLin R.val R.val B₃.val + c * cubeTriLin R.val R.val R.val) := by
rw [planeY₃B₃_val]
erw [TriLinearSymm.toCubic_add]
erw [lineY₃B₃Charges_cubic]
@ -124,7 +124,7 @@ lemma planeY₃B₃_cubic (R : MSSMACC.AnomalyFreePerp) (a b c : ℚ) :
rw [cubeTriLin.toCubic.map_smul]
rw [cubeTriLin.map_smul₁, cubeTriLin.map_smul₂]
rw [cubeTriLin.map_add₃, cubeTriLin.map_smul₃, cubeTriLin.map_smul₃]
rw [show (TriLinearSymm.toCubic cubeTriLin) R.val = cubeTriLin (R.val, R.val, R.val) by rfl]
rw [show (TriLinearSymm.toCubic cubeTriLin) R.val = cubeTriLin R.val R.val R.val by rfl]
ring
/-- The line in the plane spanned by $Y_3$, $B_3$ and $R$ which is in the quadratic,
@ -163,18 +163,18 @@ lemma lineQuad_smul (R : MSSMACC.AnomalyFreePerp) (a b c d : ℚ) :
/-- A helper function to simplify following expressions. -/
def α₁ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
(3 * cubeTriLin (T.val, T.val, B₃.val) * quadBiLin T.val T.val -
2 * cubeTriLin (T.val, T.val, T.val) * quadBiLin B₃.val T.val)
(3 * cubeTriLin T.val T.val B₃.val * quadBiLin T.val T.val -
2 * cubeTriLin T.val T.val T.val * quadBiLin B₃.val T.val)
/-- A helper function to simplify following expressions. -/
def α₂ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
(2 * cubeTriLin (T.val, T.val, T.val) * quadBiLin Y₃.val T.val -
3 * cubeTriLin (T.val, T.val, Y₃.val) * quadBiLin T.val T.val)
(2 * cubeTriLin T.val T.val T.val * quadBiLin Y₃.val T.val -
3 * cubeTriLin T.val T.val Y₃.val * quadBiLin T.val T.val)
/-- A helper function to simplify following expressions. -/
def α₃ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
6 * ((cubeTriLin (T.val, T.val, Y₃.val)) * quadBiLin B₃.val T.val -
(cubeTriLin (T.val, T.val, B₃.val)) * quadBiLin Y₃.val T.val)
6 * ((cubeTriLin T.val T.val Y₃.val) * quadBiLin B₃.val T.val -
(cubeTriLin T.val T.val B₃.val) * quadBiLin Y₃.val T.val)
lemma lineQuad_cube (R : MSSMACC.AnomalyFreePerp) (c₁ c₂ c₃ : ℚ) :
accCube (lineQuad R c₁ c₂ c₃).val =
@ -188,9 +188,9 @@ def α₁ (T : MSSMACC.AnomalyFreePerp) : ℚ :=
def lineCube (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :
MSSMACC.LinSols :=
planeY₃B₃ R
(a₂ * cubeTriLin (R.val, R.val, R.val) - 3 * a₃ * cubeTriLin (R.val, R.val, B₃.val))
(3 * a₃ * cubeTriLin (R.val, R.val, Y₃.val) - a₁ * cubeTriLin (R.val, R.val, R.val))
(3 * (a₁ * cubeTriLin (R.val, R.val, B₃.val) - a₂ * cubeTriLin (R.val, R.val, Y₃.val)))
(a₂ * cubeTriLin R.val R.val R.val - 3 * a₃ * cubeTriLin R.val R.val B₃.val)
(3 * a₃ * cubeTriLin R.val R.val Y₃.val - a₁ * cubeTriLin R.val R.val R.val)
(3 * (a₁ * cubeTriLin R.val R.val B₃.val - a₂ * cubeTriLin R.val R.val Y₃.val))
lemma lineCube_smul (R : MSSMACC.AnomalyFreePerp) (a b c d : ℚ) :
@ -210,7 +210,7 @@ lemma lineCube_cube (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :
lemma lineCube_quad (R : MSSMACC.AnomalyFreePerp) (a₁ a₂ a₃ : ℚ) :
accQuad (lineCube R a₁ a₂ a₃).val =
3 * (a₁ * cubeTriLin (R.val, R.val, B₃.val) - a₂ * cubeTriLin (R.val, R.val, Y₃.val)) *
3 * (a₁ * cubeTriLin R.val R.val B₃.val - a₂ * cubeTriLin R.val R.val Y₃.val) *
(α₁ R * a₁ + α₂ R * a₂ + α₃ R * a₃) := by
erw [planeY₃B₃_quad]
rw [α₁, α₂, α₃]
@ -221,8 +221,8 @@ section proj
lemma α₃_proj (T : MSSMACC.Sols) : α₃ (proj T.1.1) =
6 * dot Y₃.val B₃.val ^ 3 * (
cubeTriLin (T.val, T.val, Y₃.val) * quadBiLin B₃.val T.val -
cubeTriLin (T.val, T.val, B₃.val) * quadBiLin Y₃.val T.val) := by
cubeTriLin T.val T.val Y₃.val * quadBiLin B₃.val T.val -
cubeTriLin T.val T.val B₃.val * quadBiLin Y₃.val T.val) := by
rw [α₃]
rw [cube_proj_proj_Y₃, cube_proj_proj_B₃, quad_B₃_proj, quad_Y₃_proj]
ring