Skip to content

Commit

Permalink
bump to nightly-2023-04-17-14
Browse files Browse the repository at this point in the history
  • Loading branch information
leanprover-community-bot committed Apr 17, 2023
1 parent ab6befd commit ce47306
Show file tree
Hide file tree
Showing 21 changed files with 656 additions and 572 deletions.
34 changes: 14 additions & 20 deletions Mathbin/Algebra/Lie/CartanMatrix.lean
Original file line number Diff line number Diff line change
Expand Up @@ -201,8 +201,7 @@ def Matrix.ToLieAlgebra :=

namespace CartanMatrix

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/-- The Cartan matrix of type e₆. See [bourbaki1968] plate V, page 277.
The corresponding Dynkin diagram is:
Expand All @@ -213,12 +212,11 @@ o --- o --- o --- o --- o
```
-/
def e₆ : Matrix (Fin 6) (Fin 6) ℤ :=
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
!![2, 0, -1, 0, 0, 0; 0, 2, 0, -1, 0, 0; -1, 0, 2, -1, 0, 0; 0, -1, -1, 2, -1, 0; 0, 0, 0, -1, 2,
-1; 0, 0, 0, 0, -1, 2]
#align cartan_matrix.E₆ CartanMatrix.e₆

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/-- The Cartan matrix of type e₇. See [bourbaki1968] plate VI, page 281.
The corresponding Dynkin diagram is:
Expand All @@ -229,12 +227,11 @@ o --- o --- o --- o --- o --- o
```
-/
def e₇ : Matrix (Fin 7) (Fin 7) ℤ :=
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
!![2, 0, -1, 0, 0, 0, 0; 0, 2, 0, -1, 0, 0, 0; -1, 0, 2, -1, 0, 0, 0; 0, -1, -1, 2, -1, 0, 0; 0,
0, 0, -1, 2, -1, 0; 0, 0, 0, 0, -1, 2, -1; 0, 0, 0, 0, 0, -1, 2]
#align cartan_matrix.E₇ CartanMatrix.e₇

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/-- The Cartan matrix of type e₈. See [bourbaki1968] plate VII, page 285.
The corresponding Dynkin diagram is:
Expand All @@ -245,12 +242,12 @@ o --- o --- o --- o --- o --- o --- o
```
-/
def e₈ : Matrix (Fin 8) (Fin 8) ℤ :=
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
!![2, 0, -1, 0, 0, 0, 0, 0; 0, 2, 0, -1, 0, 0, 0, 0; -1, 0, 2, -1, 0, 0, 0, 0; 0, -1, -1, 2, -1,
0, 0, 0; 0, 0, 0, -1, 2, -1, 0, 0; 0, 0, 0, 0, -1, 2, -1, 0; 0, 0, 0, 0, 0, -1, 2, -1; 0, 0, 0,
0, 0, 0, -1, 2]
#align cartan_matrix.E₈ CartanMatrix.e₈

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/-- The Cartan matrix of type f₄. See [bourbaki1968] plate VIII, page 288.
The corresponding Dynkin diagram is:
Expand All @@ -259,12 +256,10 @@ o --- o =>= o --- o
```
-/
def f₄ : Matrix (Fin 4) (Fin 4) ℤ :=
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
!![2, -1, 0, 0; -1, 2, -2, 0; 0, -1, 2, -1; 0, 0, -1, 2]
#align cartan_matrix.F₄ CartanMatrix.f₄

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/-- The Cartan matrix of type g₂. See [bourbaki1968] plate IX, page 290.
The corresponding Dynkin diagram is:
Expand All @@ -274,8 +269,7 @@ o ≡>≡ o
Actually we are using the transpose of Bourbaki's matrix. This is to make this matrix consistent
with `cartan_matrix.F₄`, in the sense that all non-zero values below the diagonal are -1. -/
def g₂ : Matrix (Fin 2) (Fin 2) ℤ :=
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
!![2, -3; -1, 2]
#align cartan_matrix.G₂ CartanMatrix.g₂

end CartanMatrix
Expand Down
12 changes: 4 additions & 8 deletions Mathbin/Analysis/SpecialFunctions/PolarCoord.lean
Original file line number Diff line number Diff line change
Expand Up @@ -101,13 +101,11 @@ def polarCoord : LocalHomeomorph (ℝ × ℝ) (ℝ × ℝ)
· exact complex.equiv_real_prod_clm.symm.continuous.continuous_on
#align polar_coord polarCoord

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem hasFderivAt_polarCoord_symm (p : ℝ × ℝ) :
HasFderivAt polarCoord.symm
(Matrix.toLin (Basis.finTwoProd ℝ) (Basis.finTwoProd ℝ)
expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation")).toContinuousLinearMap
!![cos p.2, -p.1 * sin p.2; sin p.2, p.1 * cos p.2]).toContinuousLinearMap
p :=
by
rw [Matrix.toLin_finTwoProd_toContinuousLinearMap]
Expand Down Expand Up @@ -137,16 +135,14 @@ theorem polarCoord_source_ae_eq_univ : polarCoord.source =ᵐ[volume] univ :=
exact le_antisymm ((measure_mono A).trans (le_of_eq B)) bot_le
#align polar_coord_source_ae_eq_univ polarCoord_source_ae_eq_univ

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem integral_comp_polarCoord_symm {E : Type _} [NormedAddCommGroup E] [NormedSpace ℝ E]
[CompleteSpace E] (f : ℝ × ℝ → E) :
(∫ p in polarCoord.target, p.1 • f (polarCoord.symm p)) = ∫ p, f p :=
by
set B : ℝ × ℝ → ℝ × ℝ →L[ℝ] ℝ × ℝ := fun p =>
(Matrix.toLin (Basis.finTwoProd ℝ) (Basis.finTwoProd ℝ)
expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation")).toContinuousLinearMap with
!![cos p.2, -p.1 * sin p.2; sin p.2, p.1 * cos p.2]).toContinuousLinearMap with
hB
have A : ∀ p ∈ polar_coord.symm.source, HasFderivAt polar_coord.symm (B p) p := fun p hp =>
hasFderivAt_polarCoord_symm p
Expand Down
7 changes: 2 additions & 5 deletions Mathbin/Data/Complex/Module.lean
Original file line number Diff line number Diff line change
Expand Up @@ -310,14 +310,11 @@ theorem conjAe_coe : ⇑conjAe = conj :=
rfl
#align complex.conj_ae_coe Complex.conjAe_coe

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/-- The matrix representation of `conj_ae`. -/
@[simp]
theorem toMatrix_conjAe :
LinearMap.toMatrix basisOneI basisOneI conjAe.toLinearMap =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
LinearMap.toMatrix basisOneI basisOneI conjAe.toLinearMap = !![1, 0; 0, -1] :=
by
ext (i j)
simp [LinearMap.toMatrix_apply]
Expand Down
71 changes: 24 additions & 47 deletions Mathbin/Data/Matrix/Notation.lean
Original file line number Diff line number Diff line change
Expand Up @@ -440,84 +440,61 @@ section One

variable [Zero α] [One α]

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
theorem one_fin_two :
(1 : Matrix (Fin 2) (Fin 2) α) =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem one_fin_two : (1 : Matrix (Fin 2) (Fin 2) α) = !![1, 0; 0, 1] :=
by
ext (i j)
fin_cases i <;> fin_cases j <;> rfl
#align matrix.one_fin_two Matrix.one_fin_two

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
theorem one_fin_three :
(1 : Matrix (Fin 3) (Fin 3) α) =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem one_fin_three : (1 : Matrix (Fin 3) (Fin 3) α) = !![1, 0, 0; 0, 1, 0; 0, 0, 1] :=
by
ext (i j)
fin_cases i <;> fin_cases j <;> rfl
#align matrix.one_fin_three Matrix.one_fin_three

end One

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
theorem eta_fin_two (A : Matrix (Fin 2) (Fin 2) α) :
A =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem eta_fin_two (A : Matrix (Fin 2) (Fin 2) α) : A = !![A 0 0, A 0 1; A 1 0, A 1 1] :=
by
ext (i j)
fin_cases i <;> fin_cases j <;> rfl
#align matrix.eta_fin_two Matrix.eta_fin_two

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem eta_fin_three (A : Matrix (Fin 3) (Fin 3) α) :
A =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
A = !![A 0 0, A 0 1, A 0 2; A 1 0, A 1 1, A 1 2; A 2 0, A 2 1, A 2 2] :=
by
ext (i j)
fin_cases i <;> fin_cases j <;> rfl
#align matrix.eta_fin_three Matrix.eta_fin_three

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem mul_fin_two [AddCommMonoid α] [Mul α] (a₁₁ a₁₂ a₂₁ a₂₂ b₁₁ b₁₂ b₂₁ b₂₂ : α) :
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
!![a₁₁, a₁₂; a₂₁, a₂₂] ⬝ !![b₁₁, b₁₂; b₂₁, b₂₂] =
!![a₁₁ * b₁₁ + a₁₂ * b₂₁, a₁₁ * b₁₂ + a₁₂ * b₂₂; a₂₁ * b₁₁ + a₂₂ * b₂₁,
a₂₁ * b₁₂ + a₂₂ * b₂₂] :=
by
ext (i j)
fin_cases i <;> fin_cases j <;> simp [Matrix.mul, dot_product, Fin.sum_univ_succ]
#align matrix.mul_fin_two Matrix.mul_fin_two

/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:207:4: warning: unsupported notation `«expr!![ » -/
/- ./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
/- ./././Mathport/Syntax/Translate/Tactic/Basic.lean:31:4: unsupported: too many args: matrix.notation ... #[[]] -/
theorem mul_fin_three [AddCommMonoid α] [Mul α]
(a₁₁ a₁₂ a₁₃ a₂₁ a₂₂ a₂₃ a₃₁ a₃₂ a₃₃ b₁₁ b₁₂ b₁₃ b₂₁ b₂₂ b₂₃ b₃₁ b₃₂ b₃₃ : α) :
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation"
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" =
«expr!![ »
"./././Mathport/Syntax/Translate/Expr.lean:387:14: unsupported user notation matrix.notation" :=
!![a₁₁, a₁₂, a₁₃; a₂₁, a₂₂, a₂₃; a₃₁, a₃₂, a₃₃] ⬝
!![b₁₁, b₁₂, b₁₃; b₂₁, b₂₂, b₂₃; b₃₁, b₃₂, b₃₃] =
!![a₁₁ * b₁₁ + a₁₂ * b₂₁ + a₁₃ * b₃₁, a₁₁ * b₁₂ + a₁₂ * b₂₂ + a₁₃ * b₃₂,
a₁₁ * b₁₃ + a₁₂ * b₂₃ + a₁₃ * b₃₃; a₂₁ * b₁₁ + a₂₂ * b₂₁ + a₂₃ * b₃₁,
a₂₁ * b₁₂ + a₂₂ * b₂₂ + a₂₃ * b₃₂, a₂₁ * b₁₃ + a₂₂ * b₂₃ + a₂₃ * b₃₃;
a₃₁ * b₁₁ + a₃₂ * b₂₁ + a₃₃ * b₃₁, a₃₁ * b₁₂ + a₃₂ * b₂₂ + a₃₃ * b₃₂,
a₃₁ * b₁₃ + a₃₂ * b₂₃ + a₃₃ * b₃₃] :=
by
ext (i j)
fin_cases i <;> fin_cases j <;> simp [Matrix.mul, dot_product, Fin.sum_univ_succ, ← add_assoc]
Expand Down
Loading

0 comments on commit ce47306

Please sign in to comment.