Update lun. 03 juil. 2023 11:14:04 CEST

Changes

93 changed files (+3459/-14090)

• MIL/C02_Basics/S01_Calculating.lean
  • @@ -1,7 +1,7 @@
    - -- An example. - import Mathlib.Tactic + import Mathlib.Data.Real.Basic import Mathlib.Data.Real.Basic + -- An example. example (a b c : ℝ) : a * b * c = b * (a * c) := by rw [mul_comm a b] rw [mul_assoc b a c]
  • @@ -46,7 +46,7 @@ example (a b c d e f : ℝ) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c *
    section - variable (a b c d e f : ℝ) + variable (a b c d e f g : ℝ) example (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by rw [h', ← mul_assoc, h, mul_assoc]
  • @@ -64,6 +64,7 @@ variable (a b c : ℝ)
    #check mul_assoc c a b #check mul_comm a #check mul_comm + #check @mul_comm end
• MIL/C02_Basics/S02_Proving_Identities_in_Algebraic_Structures.lean
  • @@ -40,8 +40,8 @@ theorem add_zero (a : R) : a + 0 = a := by rw [add_comm, zero_add]
    theorem add_right_neg (a : R) : a + -a = 0 := by rw [add_comm, add_left_neg] - #check MyRing.add_zero - #check add_zero + #check @MyRing.add_zero + #check @add_zero end MyRing
• MIL/C02_Basics/S03_Using_Theorems_and_Lemmas.lean
  • @@ -74,7 +74,7 @@ example (h : 1 ≤ a) (h' : b ≤ c) : 2 + a + exp b ≤ 3 * a + exp c := by
    #check (add_pos : 0 < a → 0 < b → 0 < a + b) #check (add_pos_of_pos_of_nonneg : 0 < a → 0 ≤ b → 0 < a + b) #check (exp_pos : ∀ a, 0 < exp a) - #check add_le_add_left + #check @add_le_add_left example (h : a ≤ b) : exp a ≤ exp b := by rw [exp_le_exp]
• MIL/C02_Basics/S04_More_on_Order_and_Divisibility.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C02S04
• MIL/C02_Basics/S05_Proving_Facts_about_Algebraic_Structures.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.MetricSpace.Basic section
• MIL/C02_Basics/solutions/Solutions_S01_Calculating.lean
  • @@ -1,3 +1,6 @@
    + import Mathlib.Data.Real.Basic + import Mathlib.Data.Real.Basic + example (a b c : ℝ) : c * b * a = b * (a * c) := by rw [mul_comm c b] rw [mul_assoc b c a]
• MIL/C02_Basics/solutions/Solutions_S04_More_on_Order_and_Divisibility.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C02S04
• MIL/C02_Basics/solutions/Solutions_S05_Proving_Facts_about_Algebraic_Structures.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.MetricSpace.Basic section
• MIL/C03_Logic/S01_Implication_and_the_Universal_Quantifier.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S01
  • @@ -77,7 +76,7 @@ end
    section variable {α : Type _} {R : Type _} [OrderedCancelAddCommMonoid R] - #check add_le_add + #check @add_le_add def FnUb' (f : α → R) (a : R) : Prop := ∀ x, f x ≤ a
• MIL/C03_Logic/S02_The_Existential_Quantifier.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S02
• MIL/C03_Logic/S03_Negation.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S03
• MIL/C03_Logic/S04_Conjunction_and_Bi-implication.lean
  • @@ -1,6 +1,6 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic import Mathlib.Data.Nat.Prime + import Mathlib.Tactic.NormNum namespace C03S04 example {x y : ℝ} (h₀ : x ≤ y) (h₁ : ¬y ≤ x) : x ≤ y ∧ x ≠ y := by
• MIL/C03_Logic/S05_Disjunction.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S05
• MIL/C03_Logic/S06_Sequences_and_Convergence.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S06
• MIL/C03_Logic/solutions/Solutions_S01_Implication_and_the_Universal_Quantifier.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S01
• MIL/C03_Logic/solutions/Solutions_S02_The_Existential_Quantifier.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S02
• MIL/C03_Logic/solutions/Solutions_S03_Negation.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S03
• MIL/C03_Logic/solutions/Solutions_S04_Conjunction_and_Bi-implication.lean
  • @@ -1,6 +1,6 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic import Mathlib.Data.Nat.Prime + import Mathlib.Tactic.NormNum namespace C03S04 example {m n : ℕ} (h : m ∣ n ∧ m ≠ n) : m ∣ n ∧ ¬n ∣ m := by
• MIL/C03_Logic/solutions/Solutions_S05_Disjunction.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S05
• MIL/C03_Logic/solutions/Solutions_S06_Sequences_and_Convergence.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C03S06
• MIL/C04_Sets_and_Functions/S02_Functions.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Set.Lattice import Mathlib.Data.Set.Function import Mathlib.Analysis.SpecialFunctions.Log.Basic
• MIL/C04_Sets_and_Functions/solutions/Solutions_S02_Functions.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Set.Lattice import Mathlib.Data.Set.Function import Mathlib.Analysis.SpecialFunctions.Log.Basic
• MIL/C05_Number_Theory/S01_Irrational_Roots.lean
  • @@ -1,6 +1,7 @@
    - import Mathlib.Tactic import Mathlib.Data.Nat.Factorization.Basic import Mathlib.Data.Nat.Prime + import Mathlib.Tactic.NormNum.GCD + import Mathlib.Tactic.NormNum.Prime #print Nat.coprime
  • @@ -15,7 +16,7 @@ example : Nat.coprime 12 7 := by norm_num
    example : Nat.gcd 12 8 = 4 := by norm_num - #check Nat.prime_def_lt + #check @Nat.prime_def_lt example (p : ℕ) (prime_p : Nat.Prime p) : 2 ≤ p ∧ ∀ m : ℕ, m < p → m ∣ p → m = 1 := by rwa [Nat.prime_def_lt] at prime_p
  • @@ -34,7 +35,7 @@ example : Nat.Prime 2 :=
    example : Nat.Prime 3 := Nat.prime_three - #check Nat.Prime.dvd_mul + #check @Nat.Prime.dvd_mul #check Nat.Prime.dvd_mul Nat.prime_two #check Nat.prime_two.dvd_mul
• MIL/C05_Number_Theory/S03_Infinitely_Many_Primes.lean
  • @@ -1,6 +1,7 @@
    import Mathlib.Data.Nat.Prime import Mathlib.Algebra.BigOperators.Order import Mathlib.Tactic + import Mathlib.Tactic.IntervalCases open BigOperators
• MIL/C05_Number_Theory/solutions/Solutions_S01_Irrational_Roots.lean
  • @@ -1,6 +1,7 @@
    - import Mathlib.Tactic import Mathlib.Data.Nat.Factorization.Basic import Mathlib.Data.Nat.Prime + import Mathlib.Tactic.NormNum.GCD + import Mathlib.Tactic.NormNum.Prime theorem even_of_even_sqr {m : ℕ} (h : 2 ∣ m ^ 2) : 2 ∣ m := by rw [pow_two, Nat.prime_two.dvd_mul] at h
• MIL/C05_Number_Theory/solutions/Solutions_S03_Infinitely_Many_Primes.lean
  • @@ -1,6 +1,7 @@
    import Mathlib.Data.Nat.Prime import Mathlib.Algebra.BigOperators.Order import Mathlib.Tactic + import Mathlib.Tactic.IntervalCases open BigOperators
• MIL/C06_Abstract_Algebra/S01_Structures.lean (new)
  • @@ -0,0 +1,227 @@
    + import Mathlib.Algebra.BigOperators.Ring + import Mathlib.Data.Real.Basic + + noncomputable section + + @[ext] + structure Point where + x : ℝ + y : ℝ + z : ℝ + + #check Point.ext + + example (a b : Point) (hx : a.x = b.x) (hy : a.y = b.y) (hz : a.z = b.z) : a = b := by + ext + repeat' assumption + + def myPoint1 : Point where + x := 2 + y := -1 + z := 4 + + def myPoint2 : Point := + ⟨2, -1, 4⟩ + + def myPoint3 := + Point.mk 2 (-1) 4 + + structure Point' where build :: + x : ℝ + y : ℝ + z : ℝ + + #check Point'.build 2 (-1) 4 + + namespace Point + + def add (a b : Point) : Point := + ⟨a.x + b.x, a.y + b.y, a.z + b.z⟩ + + def add' (a b : Point) : Point where + x := a.x + b.x + y := a.y + b.y + z := a.z + b.z + + #check add myPoint1 myPoint2 + + #check myPoint1.add myPoint2 + + end Point + + #check Point.add myPoint1 myPoint2 + + #check myPoint1.add myPoint2 + + namespace Point + + protected theorem add_comm (a b : Point) : add a b = add b a := by + rw [add, add] + ext <;> dsimp + repeat' apply add_comm + + example (a b : Point) : add a b = add b a := by simp [add, add_comm] + + theorem add_x (a b : Point) : (a.add b).x = a.x + b.x := + rfl + + def addAlt : Point → Point → Point + | Point.mk x₁ y₁ z₁, Point.mk x₂ y₂ z₂ => ⟨x₁ + x₂, y₁ + y₂, z₁ + z₂⟩ + + def addAlt' : Point → Point → Point + | ⟨x₁, y₁, z₁⟩, ⟨x₂, y₂, z₂⟩ => ⟨x₁ + x₂, y₁ + y₂, z₁ + z₂⟩ + + theorem addAlt_x (a b : Point) : (a.addAlt b).x = a.x + b.x := by + cases a + cases b + rfl + + theorem addAlt_comm (a b : Point) : addAlt a b = addAlt b a := by + rcases a with ⟨xa, ya, za⟩ + rcases b with ⟨xb, yb, zb⟩ + rw [addAlt, addAlt] + ext <;> dsimp + apply add_comm + repeat' apply add_comm + + example (a b : Point) : addAlt a b = addAlt b a := by + rcases a with ⟨xa, ya, za⟩ + rcases b with ⟨xb, yb, zb⟩ + simp [addAlt, add_comm] + + example : ∀ a b : Point, addAlt a b = addAlt b a := by + rintro ⟨xa, ya, za⟩ ⟨xb, yb, zb⟩ + simp [addAlt, add_comm] + + example : ∀ a b : Point, add a b = add b a := fun ⟨xa, ya, za⟩ ⟨xb, yb, zb⟩ => by + simp [add, add_comm] + + protected theorem add_assoc (a b c : Point) : (a.add b).add c = a.add (b.add c) := by + sorry + def smul (r : ℝ) (a : Point) : Point := + sorry + theorem smul_distrib (r : ℝ) (a b : Point) : (smul r a).add (smul r b) = smul r (a.add b) := by + sorry + end Point + + structure StandardTwoSimplex where + x : ℝ + y : ℝ + z : ℝ + x_nonneg : 0 ≤ x + y_nonneg : 0 ≤ y + z_nonneg : 0 ≤ z + sum_eq : x + y + z = 1 + + namespace StandardTwoSimplex + + def swapXy (a : StandardTwoSimplex) : StandardTwoSimplex + where + x := a.y + y := a.x + z := a.z + x_nonneg := a.y_nonneg + y_nonneg := a.x_nonneg + z_nonneg := a.z_nonneg + sum_eq := by rw [add_comm a.y a.x, a.sum_eq] + + noncomputable section + + def midpoint (a b : StandardTwoSimplex) : StandardTwoSimplex + where + x := (a.x + b.x) / 2 + y := (a.y + b.y) / 2 + z := (a.z + b.z) / 2 + x_nonneg := div_nonneg (add_nonneg a.x_nonneg b.x_nonneg) (by norm_num) + y_nonneg := div_nonneg (add_nonneg a.y_nonneg b.y_nonneg) (by norm_num) + z_nonneg := div_nonneg (add_nonneg a.z_nonneg b.z_nonneg) (by norm_num) + sum_eq := by field_simp; linarith [a.sum_eq, b.sum_eq] + + def weightedAverage (lambda : Real) (lambda_nonneg : 0 ≤ lambda) (lambda_le : lambda ≤ 1) + (a b : StandardTwoSimplex) : StandardTwoSimplex + where + sorry + end + + end StandardTwoSimplex + + open BigOperators + + structure StandardSimplex (n : ℕ) where + V : Fin n → ℝ + NonNeg : ∀ i : Fin n, 0 ≤ V i + sum_eq_one : (∑ i, V i) = 1 + + namespace StandardSimplex + + def midpoint (n : ℕ) (a b : StandardSimplex n) : StandardSimplex n + where + V i := (a.V i + b.V i) / 2 + NonNeg := by + intro i + apply div_nonneg + · linarith [a.NonNeg i, b.NonNeg i] + norm_num + sum_eq_one := by + simp [div_eq_mul_inv, ← Finset.sum_mul, Finset.sum_add_distrib, a.sum_eq_one, b.sum_eq_one] + field_simp + + end StandardSimplex + + structure IsLinear (f : ℝ → ℝ) where + is_additive : ∀ x y, f (x + y) = f x + f y + preserves_mul : ∀ x c, f (c * x) = c * f x + + section + + variable (f : ℝ → ℝ) (linf : IsLinear f) + + #check linf.is_additive + + #check linf.preserves_mul + + end + + def Point'' := + ℝ × ℝ × ℝ + + def IsLinear' (f : ℝ → ℝ) := + (∀ x y, f (x + y) = f x + f y) ∧ ∀ x c, f (c * x) = c * f x + + def PReal := + { y : ℝ // 0 < y } + + section + + variable (x : PReal) + + #check x.val + + #check x.property + + #check x.1 + + #check x.2 + + end + + def StandardTwoSimplex' := + { p : ℝ × ℝ × ℝ // 0 ≤ p.1 ∧ 0 ≤ p.2.1 ∧ 0 ≤ p.2.2 ∧ p.1 + p.2.1 + p.2.2 = 1 } + + def StandardSimplex' (n : ℕ) := + { v : Fin n → ℝ // (∀ i : Fin n, 0 ≤ v i) ∧ (∑ i, v i) = 1 } + + def StdSimplex := Σ n : ℕ, StandardSimplex n + + section + + variable (s : StdSimplex) + + #check s.fst + #check s.snd + + #check s.1 + #check s.2 + + end +
• MIL/C06_Abstract_Algebra/S02_Algebraic_Structures.lean (new)
  • @@ -0,0 +1,172 @@
    + import Mathlib.Data.Real.Basic + + structure Group₁ (α : Type _) where + mul : α → α → α + one : α + inv : α → α + mul_assoc : ∀ x y z : α, mul (mul x y) z = mul x (mul y z) + mul_one : ∀ x : α, mul x one = x + one_mul : ∀ x : α, mul one x = x + mul_left_inv : ∀ x : α, mul (inv x) x = one + + structure Group₁Cat where + α : Type _ + str : Group₁ α + + section + + variable (α β γ : Type _) + variable (f : α ≃ β) (g : β ≃ γ) + + #check Equiv α β + #check (f.toFun : α → β) + #check (f.invFun : β → α) + #check (f.right_inv : ∀ x : β, f (f.invFun x) = x) + #check (f.left_inv : ∀ x : α, f.invFun (f x) = x) + #check (Equiv.refl α : α ≃ α) + #check (f.symm : β ≃ α) + #check (f.trans g : α ≃ γ) + + example (x : α) : (f.trans g).toFun x = g.toFun (f.toFun x) := + rfl + + example (x : α) : (f.trans g) x = g (f x) := + rfl + + example : (f.trans g : α → γ) = g ∘ f := + rfl + + end + + example (α : Type _) : Equiv.Perm α = (α ≃ α) := + rfl + + def permGroup {α : Type _} : Group₁ (Equiv.Perm α) + where + mul f g := Equiv.trans g f + one := Equiv.refl α + inv := Equiv.symm + mul_assoc f g h := (Equiv.trans_assoc _ _ _).symm + one_mul := Equiv.trans_refl + mul_one := Equiv.refl_trans + mul_left_inv := Equiv.self_trans_symm + + structure AddGroup₁ (α : Type _) where + (add : α → α → α) + -- fill in the rest + @[ext] + structure Point where + x : ℝ + y : ℝ + z : ℝ + + namespace Point + + def add (a b : Point) : Point := + ⟨a.x + b.x, a.y + b.y, a.z + b.z⟩ + + def neg (a : point) : point := sorry + + def zero : point := sorry + + def add_group_point : add_group₁ point := sorry + end Point + + section + + variable {α : Type _} (f g : Equiv.Perm α) (n : ℕ) + + #check f * g + #check mul_assoc f g g⁻¹ + + -- group power, defined for any group + #check g ^ n + + example : f * g * g⁻¹ = f := by rw [mul_assoc, mul_right_inv, mul_one] + + example : f * g * g⁻¹ = f := + mul_inv_cancel_right f g + + example {α : Type _} (f g : Equiv.Perm α) : g.symm.trans (g.trans f) = f := + mul_inv_cancel_right f g + + end + + class Group₂ (α : Type _) where + mul : α → α → α + one : α + inv : α → α + mul_assoc : ∀ x y z : α, mul (mul x y) z = mul x (mul y z) + mul_one : ∀ x : α, mul x one = x + one_mul : ∀ x : α, mul one x = x + mul_left_inv : ∀ x : α, mul (inv x) x = one + + instance {α : Type _} : Group₂ (Equiv.Perm α) where + mul f g := Equiv.trans g f + one := Equiv.refl α + inv := Equiv.symm + mul_assoc f g h := (Equiv.trans_assoc _ _ _).symm + one_mul := Equiv.trans_refl + mul_one := Equiv.refl_trans + mul_left_inv := Equiv.self_trans_symm + + #check @Group₂.mul + + def mySquare {α : Type _} [Group₂ α] (x : α) := + Group₂.mul x x + + #check @mySquare + + section + variable {β : Type _} (f g : Equiv.Perm β) + + example : Group₂.mul f g = g.trans f := + rfl + + example : mySquare f = f.trans f := + rfl + + end + + instance : Inhabited Point where default := ⟨0, 0, 0⟩ + + #check (default : Point) + + example : ([] : List Point).headI = default := + rfl + + instance : Add Point where add := Point.add + + section + variable (x y : Point) + + #check x + y + + example : x + y = Point.add x y := + rfl + + end + + instance hasMulGroup₂ {α : Type _} [Group₂ α] : Mul α := + ⟨Group₂.mul⟩ + + instance hasOneGroup₂ {α : Type _} [Group₂ α] : One α := + ⟨Group₂.one⟩ + + instance hasInvGroup₂ {α : Type _} [Group₂ α] : Inv α := + ⟨Group₂.inv⟩ + + section + + variable {α : Type _} (f g : Equiv.Perm α) + + #check f * 1 * g⁻¹ + + def foo : f * 1 * g⁻¹ = g.symm.trans ((Equiv.refl α).trans f) := + rfl + + end + + class AddGroup₂ (α : Type _) where + add : α → α → α + -- fill in the rest
• MIL/C06_Abstract_Algebra/S03_Building_the_Gaussian_Integers.lean (new)
  • @@ -0,0 +1,271 @@
    + import Mathlib.Data.Int.Basic + import Mathlib.Algebra.EuclideanDomain.Basic + import Mathlib.RingTheory.PrincipalIdealDomain + import Mathlib.Tactic + + @[ext] + structure gaussInt where + re : ℤ + im : ℤ + + namespace gaussInt + + instance : Zero gaussInt := + ⟨⟨0, 0⟩⟩ + + instance : One gaussInt := + ⟨⟨1, 0⟩⟩ + + instance : Add gaussInt := + ⟨fun x y => ⟨x.re + y.re, x.im + y.im⟩⟩ + + instance : Neg gaussInt := + ⟨fun x => ⟨-x.re, -x.im⟩⟩ + + instance : Mul gaussInt := + ⟨fun x y => ⟨x.re * y.re - x.im * y.im, x.re * y.im + x.im * y.re⟩⟩ + + theorem zero_def : (0 : gaussInt) = ⟨0, 0⟩ := + rfl + + theorem one_def : (1 : gaussInt) = ⟨1, 0⟩ := + rfl + + theorem add_def (x y : gaussInt) : x + y = ⟨x.re + y.re, x.im + y.im⟩ := + rfl + + theorem neg_def (x : gaussInt) : -x = ⟨-x.re, -x.im⟩ := + rfl + + theorem mul_def (x y : gaussInt) : x * y = ⟨x.re * y.re - x.im * y.im, x.re * y.im + x.im * y.re⟩ := + rfl + + @[simp] + theorem zero_re : (0 : gaussInt).re = 0 := + rfl + + @[simp] + theorem zero_im : (0 : gaussInt).im = 0 := + rfl + + @[simp] + theorem one_re : (1 : gaussInt).re = 1 := + rfl + + @[simp] + theorem one_im : (1 : gaussInt).im = 0 := + rfl + + @[simp] + theorem add_re (x y : gaussInt) : (x + y).re = x.re + y.re := + rfl + + @[simp] + theorem add_im (x y : gaussInt) : (x + y).im = x.im + y.im := + rfl + + @[simp] + theorem neg_re (x : gaussInt) : (-x).re = -x.re := + rfl + + @[simp] + theorem neg_im (x : gaussInt) : (-x).im = -x.im := + rfl + + @[simp] + theorem mul_re (x y : gaussInt) : (x * y).re = x.re * y.re - x.im * y.im := + rfl + + @[simp] + theorem mul_im (x y : gaussInt) : (x * y).im = x.re * y.im + x.im * y.re := + rfl + + instance instCommRing : CommRing gaussInt where + zero := 0 + one := 1 + add := (· + ·) + neg x := -x + mul := (· * ·) + add_assoc := by + intros + ext <;> simp <;> ring + zero_add := by + intros + ext <;> simp + add_zero := by + intros + ext <;> simp + add_left_neg := by + intros + ext <;> simp + add_comm := by + intros + ext <;> simp <;> ring + mul_assoc := by + intros + ext <;> simp <;> ring + one_mul := by + intros + ext <;> simp + mul_one := by + intros + ext <;> simp + left_distrib := by + intros + ext <;> simp <;> ring + right_distrib := by + intros + ext <;> simp <;> ring + mul_comm := by + intros + ext <;> simp <;> ring + zero_mul := sorry + mul_zero := sorry + + instance : Nontrivial gaussInt := by + use 0, 1 + rw [Ne, gaussInt.ext_iff] + simp + + end gaussInt + + example (a b : ℤ) : a = b * (a / b) + a % b := + Eq.symm <| Int.ediv_add_emod a b + + example (a b : ℤ) : b ≠ 0 → 0 ≤ a % b := + Int.emod_nonneg a + + example (a b : ℤ) : b ≠ 0 → a % b < |b| := + Int.emod_lt a + + namespace Int + + def div' (a b : ℤ) := + (a + b / 2) / b + + def mod' (a b : ℤ) := + (a + b / 2) % b - b / 2 + + theorem div'_add_mod' (a b : ℤ) : b * div' a b + mod' a b = a := by + rw [div', mod'] + linarith [Int.ediv_add_emod (a + b / 2) b] + + theorem abs_mod'_le (a b : ℤ) (h : 0 < b) : |mod' a b| ≤ b / 2 := by + rw [mod', abs_le] + constructor + · linarith [Int.emod_nonneg (a + b / 2) h.ne'] + have := Int.emod_lt_of_pos (a + b / 2) h + have := Int.ediv_add_emod b 2 + have := Int.emod_lt_of_pos b zero_lt_two + revert this; intro this -- FIXME, this should not be needed + linarith + + theorem mod'_eq (a b : ℤ) : mod' a b = a - b * div' a b := by linarith [div'_add_mod' a b] + + end Int + + theorem sq_add_sq_eq_zero {α : Type _} [LinearOrderedRing α] (x y : α) : + x ^ 2 + y ^ 2 = 0 ↔ x = 0 ∧ y = 0 := by + sorry + namespace gaussInt + + def norm (x : gaussInt) := + x.re ^ 2 + x.im ^ 2 + + @[simp] + theorem norm_nonneg (x : gaussInt) : 0 ≤ norm x := by + sorry + theorem norm_eq_zero (x : gaussInt) : norm x = 0 ↔ x = 0 := by + sorry + theorem norm_pos (x : gaussInt) : 0 < norm x ↔ x ≠ 0 := by + sorry + theorem norm_mul (x y : gaussInt) : norm (x * y) = norm x * norm y := by + sorry + def conj (x : gaussInt) : gaussInt := + ⟨x.re, -x.im⟩ + + @[simp] + theorem conj_re (x : gaussInt) : (conj x).re = x.re := + rfl + + @[simp] + theorem conj_im (x : gaussInt) : (conj x).im = -x.im := + rfl + + theorem norm_conj (x : gaussInt) : norm (conj x) = norm x := by simp [norm] + + instance : Div gaussInt := + ⟨fun x y => ⟨Int.div' (x * conj y).re (norm y), Int.div' (x * conj y).im (norm y)⟩⟩ + + instance : Mod gaussInt := + ⟨fun x y => x - y * (x / y)⟩ + + theorem div_def (x y : gaussInt) : + x / y = ⟨Int.div' (x * conj y).re (norm y), Int.div' (x * conj y).im (norm y)⟩ := + rfl + + theorem mod_def (x y : gaussInt) : x % y = x - y * (x / y) := + rfl + + theorem norm_mod_lt (x : gaussInt) {y : gaussInt} (hy : y ≠ 0) : (x % y).norm < y.norm := by + have norm_y_pos : 0 < norm y := by rwa [norm_pos] + have : x % y * conj y = ⟨Int.mod' (x * conj y).re (norm y), Int.mod' (x * conj y).im (norm y)⟩ := by + rw [mod_def, sub_mul, Int.mod'_eq, Int.mod'_eq, sub_eq_add_neg, div_def, norm] + ext <;> simp <;> ring + have : norm (x % y) * norm y ≤ norm y / 2 * norm y := by + conv => + lhs + rw [← norm_conj y, ← norm_mul, this, norm] + simp + trans 2 * (y.norm / 2) ^ 2 + · rw [two_mul] + apply add_le_add <;> + · rw [sq_le_sq] + apply le_trans (Int.abs_mod'_le _ _ norm_y_pos) + apply le_abs_self + rw [pow_two, ← mul_assoc, mul_comm, mul_comm (2 : ℤ)] + apply mul_le_mul_of_nonneg_left + · apply Int.ediv_mul_le + norm_num + apply Int.ediv_nonneg (norm_nonneg y) + norm_num + have : norm (x % y) ≤ norm y / 2 := le_of_mul_le_mul_right this norm_y_pos + apply lt_of_le_of_lt this + apply Int.ediv_lt_of_lt_mul + · norm_num + linarith + + theorem coe_natAbs_norm (x : gaussInt) : (x.norm.natAbs : ℤ) = x.norm := + Int.natAbs_of_nonneg (norm_nonneg _) + + theorem natAbs_norm_mod_lt (x y : gaussInt) (hy : y ≠ 0) : (x % y).norm.natAbs < y.norm.natAbs := by + apply Int.ofNat_lt.1 + simp only [Int.coe_natAbs, abs_of_nonneg, norm_nonneg] + apply norm_mod_lt x hy + + theorem not_norm_mul_left_lt_norm (x : gaussInt) {y : gaussInt} (hy : y ≠ 0) : + ¬(norm (x * y)).natAbs < (norm x).natAbs := by + apply not_lt_of_ge + rw [norm_mul, Int.natAbs_mul] + apply le_mul_of_one_le_right (Nat.zero_le _) + apply Int.ofNat_le.1 + rw [coe_natAbs_norm] + exact Int.add_one_le_of_lt ((norm_pos _).mpr hy) + + instance : EuclideanDomain gaussInt := + { gaussInt.instCommRing with + quotient := (· / ·) + remainder := (· % ·) + quotient_mul_add_remainder_eq := fun x y => by simp only; rw [mod_def, add_comm, sub_add_cancel] + quotient_zero := fun x => by + simp [div_def, norm, Int.div'] + rfl + r := Measure (Int.natAbs ∘ norm) + r_wellFounded := (measure (Int.natAbs ∘ norm)).2 + remainder_lt := natAbs_norm_mod_lt + mul_left_not_lt := not_norm_mul_left_lt_norm } + + example (x : gaussInt) : Irreducible x ↔ Prime x := + PrincipalIdealRing.irreducible_iff_prime + + end gaussInt
• MIL/C06_Abstract_Algebra/solutions/Solutions_S01_Structures.lean (new)
  • @@ -0,0 +1,96 @@
    + import Mathlib.Algebra.BigOperators.Ring + import Mathlib.Data.Real.Basic + + noncomputable section + + @[ext] + structure Point where + x : ℝ + y : ℝ + z : ℝ + + namespace Point + + def add (a b : Point) : Point := + ⟨a.x + b.x, a.y + b.y, a.z + b.z⟩ + + protected theorem add_assoc (a b c : Point) : (a.add b).add c = a.add (b.add c) := by + simp [add, add_assoc] + + def smul (r : ℝ) (a : Point) : Point := + ⟨r * a.x, r * a.y, r * a.z⟩ + + theorem smul_distrib (r : ℝ) (a b : Point) : (smul r a).add (smul r b) = smul r (a.add b) := by + simp [add, smul, mul_add] + + end Point + + structure StandardTwoSimplex where + x : ℝ + y : ℝ + z : ℝ + x_nonneg : 0 ≤ x + y_nonneg : 0 ≤ y + z_nonneg : 0 ≤ z + sum_eq : x + y + z = 1 + + namespace StandardTwoSimplex + + noncomputable section + + def weightedAverage (lambda : Real) (lambda_nonneg : 0 ≤ lambda) (lambda_le : lambda ≤ 1) + (a b : StandardTwoSimplex) : StandardTwoSimplex + where + x := lambda * a.x + (1 - lambda) * b.x + y := lambda * a.y + (1 - lambda) * b.y + z := lambda * a.z + (1 - lambda) * b.z + x_nonneg := add_nonneg (mul_nonneg lambda_nonneg a.x_nonneg) (mul_nonneg (by linarith) b.x_nonneg) + y_nonneg := add_nonneg (mul_nonneg lambda_nonneg a.y_nonneg) (mul_nonneg (by linarith) b.y_nonneg) + z_nonneg := add_nonneg (mul_nonneg lambda_nonneg a.z_nonneg) (mul_nonneg (by linarith) b.z_nonneg) + sum_eq := by + trans (a.x + a.y + a.z) * lambda + (b.x + b.y + b.z) * (1 - lambda) + · ring + simp [a.sum_eq, b.sum_eq] + + end + + end StandardTwoSimplex + + open BigOperators + + structure StandardSimplex (n : ℕ) where + V : Fin n → ℝ + NonNeg : ∀ i : Fin n, 0 ≤ V i + sum_eq_one : (∑ i, V i) = 1 + + namespace StandardSimplex + + def midpoint (n : ℕ) (a b : StandardSimplex n) : StandardSimplex n + where + V i := (a.V i + b.V i) / 2 + NonNeg := by + intro i + apply div_nonneg + · linarith [a.NonNeg i, b.NonNeg i] + norm_num + sum_eq_one := by + simp [div_eq_mul_inv, ← Finset.sum_mul, Finset.sum_add_distrib, a.sum_eq_one, b.sum_eq_one] + field_simp + + end StandardSimplex + + namespace StandardSimplex + + def weightedAverage {n : ℕ} (lambda : Real) (lambda_nonneg : 0 ≤ lambda) (lambda_le : lambda ≤ 1) + (a b : StandardSimplex n) : StandardSimplex n + where + V i := lambda * a.V i + (1 - lambda) * b.V i + NonNeg i := + add_nonneg (mul_nonneg lambda_nonneg (a.NonNeg i)) (mul_nonneg (by linarith) (b.NonNeg i)) + sum_eq_one := by + trans (lambda * ∑ i, a.V i) + (1 - lambda) * ∑ i, b.V i + · rw [Finset.sum_add_distrib, Finset.mul_sum, Finset.mul_sum] + simp [a.sum_eq_one, b.sum_eq_one] + + end StandardSimplex +
• MIL/C06_Abstract_Algebra/solutions/Solutions_S02_Algebraic_Structures.lean (new)
  • @@ -0,0 +1,73 @@
    + import Mathlib.Data.Real.Basic + + structure AddGroup₁ (α : Type _) where + add : α → α → α + zero : α + neg : α → α + add_assoc : ∀ x y z : α, add (add x y) z = add x (add y z) + add_zero : ∀ x : α, add x zero = x + zero_add : ∀ x : α, add x zero = x + add_left_neg : ∀ x : α, add (neg x) x = zero + + @[ext] + structure Point where + x : ℝ + y : ℝ + z : ℝ + + namespace Point + + def add (a b : Point) : Point := + ⟨a.x + b.x, a.y + b.y, a.z + b.z⟩ + + def neg (a : Point) : Point := + ⟨-a.x, -a.y, -a.z⟩ + + def zero : Point := + ⟨0, 0, 0⟩ + + def addGroupPoint : AddGroup₁ Point where + add := Point.add + zero := Point.zero + neg := Point.neg + add_assoc := by simp [Point.add, add_assoc] + add_zero := by simp [Point.add, Point.zero] + zero_add := by simp [Point.add, Point.zero] + add_left_neg := by simp [Point.add, Point.neg, Point.zero] + + end Point + + class AddGroup₂ (α : Type _) where + add : α → α → α + zero : α + neg : α → α + add_assoc : ∀ x y z : α, add (add x y) z = add x (add y z) + add_zero : ∀ x : α, add x zero = x + zero_add : ∀ x : α, add x zero = x + add_left_neg : ∀ x : α, add (neg x) x = zero + + instance hasAddAddGroup₂ {α : Type _} [AddGroup₂ α] : Add α := + ⟨AddGroup₂.add⟩ + + instance hasZeroAddGroup₂ {α : Type _} [AddGroup₂ α] : Zero α := + ⟨AddGroup₂.zero⟩ + + instance hasNegAddGroup₂ {α : Type _} [AddGroup₂ α] : Neg α := + ⟨AddGroup₂.neg⟩ + + instance : AddGroup₂ Point where + add := Point.add + zero := Point.zero + neg := Point.neg + add_assoc := by simp [Point.add, add_assoc] + add_zero := by simp [Point.add, Point.zero] + zero_add := by simp [Point.add, Point.zero] + add_left_neg := by simp [Point.add, Point.neg, Point.zero] + + section + variable (x y : Point) + + #check x + -y + 0 + + end +
• MIL/C06_Abstract_Algebra/solutions/Solutions_S03_Building_the_Gaussian_Integers.lean (new)
  • @@ -0,0 +1,285 @@
    + import Mathlib.Data.Int.Basic + import Mathlib.Algebra.EuclideanDomain.Basic + import Mathlib.RingTheory.PrincipalIdealDomain + import Mathlib.Tactic + + @[ext] + structure gaussInt where + re : ℤ + im : ℤ + + namespace gaussInt + + instance : Zero gaussInt := + ⟨⟨0, 0⟩⟩ + + instance : One gaussInt := + ⟨⟨1, 0⟩⟩ + + instance : Add gaussInt := + ⟨fun x y => ⟨x.re + y.re, x.im + y.im⟩⟩ + + instance : Neg gaussInt := + ⟨fun x => ⟨-x.re, -x.im⟩⟩ + + instance : Mul gaussInt := + ⟨fun x y => ⟨x.re * y.re - x.im * y.im, x.re * y.im + x.im * y.re⟩⟩ + + theorem zero_def : (0 : gaussInt) = ⟨0, 0⟩ := + rfl + + theorem one_def : (1 : gaussInt) = ⟨1, 0⟩ := + rfl + + theorem add_def (x y : gaussInt) : x + y = ⟨x.re + y.re, x.im + y.im⟩ := + rfl + + theorem neg_def (x : gaussInt) : -x = ⟨-x.re, -x.im⟩ := + rfl + + theorem mul_def (x y : gaussInt) : x * y = ⟨x.re * y.re - x.im * y.im, x.re * y.im + x.im * y.re⟩ := + rfl + + @[simp] + theorem zero_re : (0 : gaussInt).re = 0 := + rfl + + @[simp] + theorem zero_im : (0 : gaussInt).im = 0 := + rfl + + @[simp] + theorem one_re : (1 : gaussInt).re = 1 := + rfl + + @[simp] + theorem one_im : (1 : gaussInt).im = 0 := + rfl + + @[simp] + theorem add_re (x y : gaussInt) : (x + y).re = x.re + y.re := + rfl + + @[simp] + theorem add_im (x y : gaussInt) : (x + y).im = x.im + y.im := + rfl + + @[simp] + theorem neg_re (x : gaussInt) : (-x).re = -x.re := + rfl + + @[simp] + theorem neg_im (x : gaussInt) : (-x).im = -x.im := + rfl + + @[simp] + theorem mul_re (x y : gaussInt) : (x * y).re = x.re * y.re - x.im * y.im := + rfl + + @[simp] + theorem mul_im (x y : gaussInt) : (x * y).im = x.re * y.im + x.im * y.re := + rfl + + instance instCommRing : CommRing gaussInt where + zero := 0 + one := 1 + add := (· + ·) + neg x := -x + mul := (· * ·) + add_assoc := by + intros + ext <;> simp <;> ring + zero_add := by + intros + ext <;> simp + add_zero := by + intros + ext <;> simp + add_left_neg := by + intros + ext <;> simp + add_comm := by + intros + ext <;> simp <;> ring + mul_assoc := by + intros + ext <;> simp <;> ring + one_mul := by + intros + ext <;> simp + mul_one := by + intros + ext <;> simp + left_distrib := by + intros + ext <;> simp <;> ring + right_distrib := by + intros + ext <;> simp <;> ring + mul_comm := by + intros + ext <;> simp <;> ring + zero_mul := sorry + mul_zero := sorry + + instance : Nontrivial gaussInt := by + use 0, 1 + rw [Ne, gaussInt.ext_iff] + simp + + end gaussInt + + namespace Int + + def div' (a b : ℤ) := + (a + b / 2) / b + + def mod' (a b : ℤ) := + (a + b / 2) % b - b / 2 + + theorem div'_add_mod' (a b : ℤ) : b * div' a b + mod' a b = a := by + rw [div', mod'] + linarith [Int.ediv_add_emod (a + b / 2) b] + + theorem abs_mod'_le (a b : ℤ) (h : 0 < b) : abs (mod' a b) ≤ b / 2 := by + rw [mod', abs_le] + constructor + · linarith [Int.emod_nonneg (a + b / 2) h.ne'] + have := Int.emod_lt_of_pos (a + b / 2) h + have := Int.ediv_add_emod b 2 + have := Int.emod_lt_of_pos b zero_lt_two + revert this; intro this -- FIXME, this should not be needed + linarith + + theorem mod'_eq (a b : ℤ) : mod' a b = a - b * div' a b := by linarith [div'_add_mod' a b] + + end Int + + private theorem aux {α : Type _} [LinearOrderedRing α] {x y : α} (h : x ^ 2 + y ^ 2 = 0) : x = 0 := + haveI h' : x ^ 2 = 0 := by + apply le_antisymm _ (sq_nonneg x) + rw [← h] + apply le_add_of_nonneg_right (sq_nonneg y) + pow_eq_zero h' + + theorem sq_add_sq_eq_zero {α : Type _} [LinearOrderedRing α] (x y : α) : + x ^ 2 + y ^ 2 = 0 ↔ x = 0 ∧ y = 0 := by + constructor + · intro h + constructor + · exact aux h + rw [add_comm] at h + exact aux h + rintro ⟨rfl, rfl⟩ + norm_num + + namespace gaussInt + + def norm (x : gaussInt) := + x.re ^ 2 + x.im ^ 2 + + @[simp] + theorem norm_nonneg (x : gaussInt) : 0 ≤ norm x := by + apply add_nonneg <;> + apply sq_nonneg + + theorem norm_eq_zero (x : gaussInt) : norm x = 0 ↔ x = 0 := by + rw [norm, sq_add_sq_eq_zero, gaussInt.ext_iff] + rfl + + theorem norm_pos (x : gaussInt) : 0 < norm x ↔ x ≠ 0 := by + rw [lt_iff_le_and_ne, ne_comm, Ne, norm_eq_zero] + simp [norm_nonneg] + + theorem norm_mul (x y : gaussInt) : norm (x * y) = norm x * norm y := by + simp [norm] + ring + + def conj (x : gaussInt) : gaussInt := + ⟨x.re, -x.im⟩ + + @[simp] + theorem conj_re (x : gaussInt) : (conj x).re = x.re := + rfl + + @[simp] + theorem conj_im (x : gaussInt) : (conj x).im = -x.im := + rfl + + theorem norm_conj (x : gaussInt) : norm (conj x) = norm x := by simp [norm] + + instance : Div gaussInt := + ⟨fun x y => ⟨Int.div' (x * conj y).re (norm y), Int.div' (x * conj y).im (norm y)⟩⟩ + + instance : Mod gaussInt := + ⟨fun x y => x - y * (x / y)⟩ + + theorem div_def (x y : gaussInt) : + x / y = ⟨Int.div' (x * conj y).re (norm y), Int.div' (x * conj y).im (norm y)⟩ := + rfl + + theorem mod_def (x y : gaussInt) : x % y = x - y * (x / y) := + rfl + + theorem norm_mod_lt (x : gaussInt) {y : gaussInt} (hy : y ≠ 0) : (x % y).norm < y.norm := by + have norm_y_pos : 0 < norm y := by rwa [norm_pos] + have : x % y * conj y = ⟨Int.mod' (x * conj y).re (norm y), Int.mod' (x * conj y).im (norm y)⟩ := by + rw [mod_def, sub_mul, Int.mod'_eq, Int.mod'_eq, sub_eq_add_neg, div_def, norm] + ext <;> simp <;> ring + have : norm (x % y) * norm y ≤ norm y / 2 * norm y := by + conv => + lhs + rw [← norm_conj y, ← norm_mul, this, norm] + simp + trans 2 * (y.norm / 2) ^ 2 + · rw [two_mul] + apply add_le_add <;> + · rw [sq_le_sq] + apply le_trans (Int.abs_mod'_le _ _ norm_y_pos) + apply le_abs_self + rw [pow_two, ← mul_assoc, mul_comm, mul_comm (2 : ℤ)] + apply mul_le_mul_of_nonneg_left + · apply Int.ediv_mul_le + norm_num + apply Int.ediv_nonneg (norm_nonneg y) + norm_num + have : norm (x % y) ≤ norm y / 2 := le_of_mul_le_mul_right this norm_y_pos + apply lt_of_le_of_lt this + apply Int.ediv_lt_of_lt_mul + · norm_num + linarith + + theorem coe_natAbs_norm (x : gaussInt) : (x.norm.natAbs : ℤ) = x.norm := + Int.natAbs_of_nonneg (norm_nonneg _) + + theorem natAbs_norm_mod_lt (x y : gaussInt) (hy : y ≠ 0) : (x % y).norm.natAbs < y.norm.natAbs := by + apply Int.ofNat_lt.1 + simp only [Int.coe_natAbs, abs_of_nonneg, norm_nonneg] + apply norm_mod_lt x hy + + theorem not_norm_mul_left_lt_norm (x : gaussInt) {y : gaussInt} (hy : y ≠ 0) : + ¬(norm (x * y)).natAbs < (norm x).natAbs := by + apply not_lt_of_ge + rw [norm_mul, Int.natAbs_mul] + apply le_mul_of_one_le_right (Nat.zero_le _) + apply Int.ofNat_le.1 + rw [coe_natAbs_norm] + exact Int.add_one_le_of_lt ((norm_pos _).mpr hy) + + instance : EuclideanDomain gaussInt := + { gaussInt.instCommRing with + quotient := (· / ·) + remainder := (· % ·) + quotient_mul_add_remainder_eq := fun x y => by simp only; rw [mod_def, add_comm, sub_add_cancel] + quotient_zero := fun x => by + simp [div_def, norm, Int.div'] + rfl + r := Measure (Int.natAbs ∘ norm) + r_wellFounded := (measure (Int.natAbs ∘ norm)).2 + remainder_lt := natAbs_norm_mod_lt + mul_left_not_lt := not_norm_mul_left_lt_norm } + + example (x : gaussInt) : Irreducible x ↔ Prime x := + PrincipalIdealRing.irreducible_iff_prime + + end gaussInt
• MIL/C06_Structures/S01_Structures.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C06_Structures/S02_Algebraic_Structures.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C06S02
  • @@ -111,12 +110,12 @@ instance {α : Type _} : Group₂ (Equiv.Perm α) where
    mul_one := Equiv.refl_trans mul_left_inv := Equiv.self_trans_symm - #check Group₂.mul + #check @Group₂.mul def mySquare {α : Type _} [Group₂ α] (x : α) := Group₂.mul x x - #check mySquare + #check @mySquare section variable {β : Type _} (f g : Equiv.Perm β)
• MIL/C06_Structures/solutions/Solutions_S01_Structures.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C06_Structures/solutions/Solutions_S02_Algebraic_Structures.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Data.Real.Basic namespace C06S02
• MIL/C07_Hierarchies/S01_Basics.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C07_Hierarchies/S02_Morphisms.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real
• MIL/C07_Hierarchies/S03_Subobjects.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.GroupTheory.QuotientGroup
• MIL/C07_Hierarchies/solutions/Solutions_S01_Basics.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Algebra.BigOperators.Ring import Mathlib.Data.Real.Basic
• MIL/C07_Hierarchies/solutions/Solutions_S02_Morphisms.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real
• MIL/C07_Hierarchies/solutions/Solutions_S03_Subobjects.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.GroupTheory.QuotientGroup
• MIL/C07_Topology/S01_Filters.lean (new)
  • @@ -0,0 +1,110 @@
    + import Mathlib.Topology.Instances.Real + + open Set Filter Topology + + def principal {α : Type _} (s : Set α) : Filter α + where + sets := { t | s ⊆ t } + univ_sets := sorry + sets_of_superset := sorry + inter_sets := sorry + + example : Filter ℕ := + { sets := { s | ∃ a, ∀ b, a ≤ b → b ∈ s } + univ_sets := sorry + sets_of_superset := sorry + inter_sets := sorry } + + def Tendsto₁ {X Y : Type _} (f : X → Y) (F : Filter X) (G : Filter Y) := + ∀ V ∈ G, f ⁻¹' V ∈ F + + def Tendsto₂ {X Y : Type _} (f : X → Y) (F : Filter X) (G : Filter Y) := + map f F ≤ G + + example {X Y : Type _} (f : X → Y) (F : Filter X) (G : Filter Y) : + Tendsto₂ f F G ↔ Tendsto₁ f F G := + Iff.rfl + + #check (@Filter.map_mono : ∀ {α β} {m : α → β}, Monotone (map m)) + + #check + (@Filter.map_map : + ∀ {α β γ} {f : Filter α} {m : α → β} {m' : β → γ}, map m' (map m f) = map (m' ∘ m) f) + + example {X Y Z : Type _} {F : Filter X} {G : Filter Y} {H : Filter Z} {f : X → Y} {g : Y → Z} + (hf : Tendsto₁ f F G) (hg : Tendsto₁ g G H) : Tendsto₁ (g ∘ f) F H := + sorry + + variable (f : ℝ → ℝ) (x₀ y₀ : ℝ) + + #check comap ((↑) : ℚ → ℝ) (𝓝 x₀) + + #check Tendsto (f ∘ (↑)) (comap ((↑) : ℚ → ℝ) (𝓝 x₀)) (𝓝 y₀) + + section + + variable {α β γ : Type _} (F : Filter α) {m : γ → β} {n : β → α} + + #check (comap_comap : comap m (comap n F) = comap (n ∘ m) F) + + end + + example : 𝓝 (x₀, y₀) = 𝓝 x₀ ×ᶠ 𝓝 y₀ := + nhds_prod_eq + + #check le_inf_iff + + example (f : ℕ → ℝ × ℝ) (x₀ y₀ : ℝ) : + Tendsto f atTop (𝓝 (x₀, y₀)) ↔ + Tendsto (Prod.fst ∘ f) atTop (𝓝 x₀) ∧ Tendsto (Prod.snd ∘ f) atTop (𝓝 y₀) := + sorry + + example (x₀ : ℝ) : HasBasis (𝓝 x₀) (fun ε : ℝ => 0 < ε) fun ε => Ioo (x₀ - ε) (x₀ + ε) := + nhds_basis_Ioo_pos x₀ + + example (u : ℕ → ℝ) (x₀ : ℝ) : + Tendsto u atTop (𝓝 x₀) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, u n ∈ Ioo (x₀ - ε) (x₀ + ε) := by + have : atTop.HasBasis (fun n : ℕ => True) Ici := atTop_basis + rw [this.tendsto_iff (nhds_basis_Ioo_pos x₀)] + simp + + example (P Q : ℕ → Prop) (hP : ∀ᶠ n in atTop, P n) (hQ : ∀ᶠ n in atTop, Q n) : + ∀ᶠ n in atTop, P n ∧ Q n := + hP.and hQ + + example (u v : ℕ → ℝ) (h : ∀ᶠ n in atTop, u n = v n) (x₀ : ℝ) : + Tendsto u atTop (𝓝 x₀) ↔ Tendsto v atTop (𝓝 x₀) := + tendsto_congr' h + + example (u v : ℕ → ℝ) (h : u =ᶠ[atTop] v) (x₀ : ℝ) : + Tendsto u atTop (𝓝 x₀) ↔ Tendsto v atTop (𝓝 x₀) := + tendsto_congr' h + + #check @eventually_of_forall + + #check @Eventually.mono + + #check @Eventually.and + + example (P Q R : ℕ → Prop) (hP : ∀ᶠ n in atTop, P n) (hQ : ∀ᶠ n in atTop, Q n) + (hR : ∀ᶠ n in atTop, P n ∧ Q n → R n) : ∀ᶠ n in atTop, R n := by + apply (hP.and (hQ.and hR)).mono + rintro n ⟨h, h', h''⟩ + exact h'' ⟨h, h'⟩ + + example (P Q R : ℕ → Prop) (hP : ∀ᶠ n in atTop, P n) (hQ : ∀ᶠ n in atTop, Q n) + (hR : ∀ᶠ n in atTop, P n ∧ Q n → R n) : ∀ᶠ n in atTop, R n := by + filter_upwards [hP, hQ, hR] + intro n h h' h'' + exact h'' ⟨h, h'⟩ + + #check mem_closure_iff_clusterPt + + #check le_principal_iff + + #check neBot_of_le + + example (u : ℕ → ℝ) (M : Set ℝ) (x : ℝ) (hux : Tendsto u atTop (𝓝 x)) + (huM : ∀ᶠ n in atTop, u n ∈ M) : x ∈ closure M := + sorry +
• MIL/C07_Topology/S02_Metric_Spaces.lean (new)
  • @@ -0,0 +1,200 @@
    + import Mathlib.Topology.Instances.Real + import Mathlib.Analysis.NormedSpace.BanachSteinhaus + + open Set Filter + + open Topology Filter + + variable {X : Type _} [MetricSpace X] (a b c : X) + + #check (dist a b : ℝ) + + #check (dist_nonneg : 0 ≤ dist a b) + + #check (dist_eq_zero : dist a b = 0 ↔ a = b) + + #check (dist_comm a b : dist a b = dist b a) + + #check (dist_triangle a b c : dist a c ≤ dist a b + dist b c) + + -- Note the next three lines are not quoted, their purpose is to make sure those things don't get renamed while we're looking elsewhere. + #check EMetricSpace + + #check PseudoMetricSpace + + #check PseudoEMetricSpace + + example {u : ℕ → X} {a : X} : Tendsto u atTop (𝓝 a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, dist (u n) a < ε := + Metric.tendsto_atTop + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} : + Continuous f ↔ ∀ x : X, ∀ ε > 0, ∃ δ > 0, ∀ x', dist x' x < δ → dist (f x') (f x) < ε := + Metric.continuous_iff + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := by continuity + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := + continuous_dist.comp ((hf.comp continuous_fst).prod_mk (hf.comp continuous_snd)) + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := by + apply Continuous.dist + exact hf.comp continuous_fst + exact hf.comp continuous_snd + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := + (hf.comp continuous_fst).dist (hf.comp continuous_snd) + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := + hf.fst'.dist hf.snd' + + example {f : ℝ → X} (hf : Continuous f) : Continuous fun x : ℝ => f (x ^ 2 + x) := + sorry + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] (f : X → Y) (a : X) : + ContinuousAt f a ↔ ∀ ε > 0, ∃ δ > 0, ∀ {x}, dist x a < δ → dist (f x) (f a) < ε := + Metric.continuousAt_iff + + variable (r : ℝ) + + example : Metric.ball a r = { b | dist b a < r } := + rfl + + example : Metric.closedBall a r = { b | dist b a ≤ r } := + rfl + + example (hr : 0 < r) : a ∈ Metric.ball a r := + Metric.mem_ball_self hr + + example (hr : 0 ≤ r) : a ∈ Metric.closedBall a r := + Metric.mem_closedBall_self hr + + example (s : Set X) : IsOpen s ↔ ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s := + Metric.isOpen_iff + + example {s : Set X} : IsClosed s ↔ IsOpen (sᶜ) := + isOpen_compl_iff.symm + + example {s : Set X} (hs : IsClosed s) {u : ℕ → X} (hu : Tendsto u atTop (𝓝 a)) + (hus : ∀ n, u n ∈ s) : a ∈ s := + hs.mem_of_tendsto hu (eventually_of_forall hus) + + example {s : Set X} : a ∈ closure s ↔ ∀ ε > 0, ∃ b ∈ s, a ∈ Metric.ball b ε := + Metric.mem_closure_iff + + example {u : ℕ → X} (hu : Tendsto u atTop (𝓝 a)) {s : Set X} (hs : ∀ n, u n ∈ s) : a ∈ closure s := + sorry + + example {x : X} {s : Set X} : s ∈ 𝓝 x ↔ ∃ ε > 0, Metric.ball x ε ⊆ s := + Metric.nhds_basis_ball.mem_iff + + example {x : X} {s : Set X} : s ∈ 𝓝 x ↔ ∃ ε > 0, Metric.closedBall x ε ⊆ s := + Metric.nhds_basis_closedBall.mem_iff + + example : IsCompact (Set.Icc 0 1 : Set ℝ) := + isCompact_Icc + + example {s : Set X} (hs : IsCompact s) {u : ℕ → X} (hu : ∀ n, u n ∈ s) : + ∃ a ∈ s, ∃ φ : ℕ → ℕ, StrictMono φ ∧ Tendsto (u ∘ φ) atTop (𝓝 a) := + hs.tendsto_subseq hu + + example {s : Set X} (hs : IsCompact s) (hs' : s.Nonempty) {f : X → ℝ} (hfs : ContinuousOn f s) : + ∃ x ∈ s, ∀ y ∈ s, f x ≤ f y := + hs.exists_forall_le hs' hfs + + example {s : Set X} (hs : IsCompact s) (hs' : s.Nonempty) {f : X → ℝ} (hfs : ContinuousOn f s) : + ∃ x ∈ s, ∀ y ∈ s, f y ≤ f x := + hs.exists_forall_ge hs' hfs + + example {s : Set X} (hs : IsCompact s) : IsClosed s := + hs.IsClosed + + example {X : Type _} [MetricSpace X] [CompactSpace X] : IsCompact (univ : Set X) := + isCompact_univ + + #check IsCompact.isClosed + + example {X : Type _} [MetricSpace X] {Y : Type _} [MetricSpace Y] {f : X → Y} : + UniformContinuous f ↔ ∀ ε > 0, ∃ δ > 0, ∀ {a b : X}, dist a b < δ → dist (f a) (f b) < ε := + Metric.uniformContinuous_iff + + example {X : Type _} [MetricSpace X] [CompactSpace X] {Y : Type _} [MetricSpace Y] {f : X → Y} + (hf : Continuous f) : UniformContinuous f := + sorry + + example (u : ℕ → X) : CauchySeq u ↔ ∀ ε > 0, ∃ N : ℕ, ∀ m ≥ N, ∀ n ≥ N, dist (u m) (u n) < ε := + Metric.cauchySeq_iff + + example (u : ℕ → X) : CauchySeq u ↔ ∀ ε > 0, ∃ N : ℕ, ∀ n ≥ N, dist (u n) (u N) < ε := + Metric.cauchySeq_iff' + + example [CompleteSpace X] (u : ℕ → X) (hu : CauchySeq u) : ∃ x, Tendsto u atTop (𝓝 x) := + cauchySeq_tendsto_of_complete hu + + open BigOperators + + open Finset + + theorem cauchySeq_of_le_geometric_two' {u : ℕ → X} + (hu : ∀ n : ℕ, dist (u n) (u (n + 1)) ≤ (1 / 2) ^ n) : CauchySeq u := by + rw [Metric.cauchySeq_iff'] + intro ε ε_pos + obtain ⟨N, hN⟩ : ∃ N : ℕ, 1 / 2 ^ N * 2 < ε := by sorry + use N + intro n hn + obtain ⟨k, rfl : n = N + k⟩ := le_iff_exists_add.mp hn + calc + dist (u (N + k)) (u N) = dist (u (N + 0)) (u (N + k)) := sorry + _ ≤ ∑ i in range k, dist (u (N + i)) (u (N + (i + 1))) := sorry + _ ≤ ∑ i in range k, (1 / 2 : ℝ) ^ (N + i) := sorry + _ = 1 / 2 ^ N * ∑ i in range k, (1 / 2) ^ i := sorry + _ ≤ 1 / 2 ^ N * 2 := sorry + _ < ε := sorry + + + open Metric + + example [CompleteSpace X] (f : ℕ → Set X) (ho : ∀ n, IsOpen (f n)) (hd : ∀ n, Dense (f n)) : + Dense (⋂ n, f n) := by + let B : ℕ → ℝ := fun n => (1 / 2) ^ n + have Bpos : ∀ n, 0 < B n + sorry + /- Translate the density assumption into two functions `center` and `radius` associating + to any n, x, δ, δpos a center and a positive radius such that + `closed_ball center radius` is included both in `f n` and in `closed_ball x δ`. + We can also require `radius ≤ (1/2)^(n+1)`, to ensure we get a Cauchy sequence later. -/ + have : + ∀ (n : ℕ) (x : X), + ∀ δ > 0, ∃ y : X, ∃ r > 0, r ≤ B (n + 1) ∧ closed_ball y r ⊆ closed_ball x δ ∩ f n := + by sorry + choose! center radius Hpos HB Hball using this + intro x + rw [mem_closure_iff_nhds_basis nhds_basis_closed_ball] + intro ε εpos + /- `ε` is positive. We have to find a point in the ball of radius `ε` around `x` belonging to all + `f n`. For this, we construct inductively a sequence `F n = (c n, r n)` such that the closed ball + `closed_ball (c n) (r n)` is included in the previous ball and in `f n`, and such that + `r n` is small enough to ensure that `c n` is a Cauchy sequence. Then `c n` converges to a + limit which belongs to all the `f n`. -/ + let F : ℕ → X × ℝ := fun n => + Nat.recOn n (Prod.mk x (min ε (B 0))) fun n p => Prod.mk (center n p.1 p.2) (radius n p.1 p.2) + let c : ℕ → X := fun n => (F n).1 + let r : ℕ → ℝ := fun n => (F n).2 + have rpos : ∀ n, 0 < r n := by sorry + have rB : ∀ n, r n ≤ B n := by sorry + have incl : ∀ n, closed_ball (c (n + 1)) (r (n + 1)) ⊆ closed_ball (c n) (r n) ∩ f n := by sorry + have cdist : ∀ n, dist (c n) (c (n + 1)) ≤ B n := by sorry + have : CauchySeq c := cauchySeq_of_le_geometric_two' cdist + -- as the sequence `c n` is Cauchy in a complete space, it converges to a limit `y`. + rcases cauchySeq_tendsto_of_complete this with ⟨y, ylim⟩ + -- this point `y` will be the desired point. We will check that it belongs to all + -- `f n` and to `ball x ε`. + use y + have I : ∀ n, ∀ m ≥ n, closed_ball (c m) (r m) ⊆ closed_ball (c n) (r n) := by sorry + have yball : ∀ n, y ∈ closed_ball (c n) (r n) := by sorry + sorry +
• MIL/C07_Topology/S03_Topological_Spaces.lean (new)
  • @@ -0,0 +1,151 @@
    + import Mathlib.Topology.Instances.Real + import Mathlib.Analysis.NormedSpace.BanachSteinhaus + + open Set Filter + + open Topology Filter + + section + + variable {X : Type _} [TopologicalSpace X] + + example : IsOpen (univ : Set X) := + isOpen_univ + + example : IsOpen (∅ : Set X) := + isOpen_empty + + example {ι : Type _} {s : ι → Set X} (hs : ∀ i, IsOpen <| s i) : IsOpen (⋃ i, s i) := + isOpen_iUnion hs + + example {ι : Type _} [Fintype ι] {s : ι → Set X} (hs : ∀ i, IsOpen <| s i) : IsOpen (⋂ i, s i) := + isOpen_iInter hs + + variable {Y : Type _} [TopologicalSpace Y] + + example {f : X → Y} : Continuous f ↔ ∀ s, IsOpen s → IsOpen (f ⁻¹' s) := + continuous_def + + example {f : X → Y} {x : X} : ContinuousAt f x ↔ map f (𝓝 x) ≤ 𝓝 (f x) := + Iff.rfl + + example {f : X → Y} {x : X} : ContinuousAt f x ↔ ∀ U ∈ 𝓝 (f x), ∀ᶠ x in 𝓝 x, f x ∈ U := + Iff.rfl + + example {x : X} {s : Set X} : s ∈ 𝓝 x ↔ ∃ t, t ⊆ s ∧ IsOpen t ∧ x ∈ t := + mem_nhds_iff + + example (x : X) : pure x ≤ 𝓝 x := + pure_le_nhds x + + example (x : X) (P : X → Prop) (h : ∀ᶠ y in 𝓝 x, P y) : P x := + pure_le_nhds x h + + example {P : X → Prop} {x : X} (h : ∀ᶠ y in 𝓝 x, P y) : ∀ᶠ y in 𝓝 x, ∀ᶠ z in 𝓝 y, P z := + eventually_eventually_nhds.mpr h + + #check TopologicalSpace.mkOfNhds + + #check TopologicalSpace.nhds_mkOfNhds + + example {α : Type _} (n : α → Filter α) (H₀ : ∀ a, pure a ≤ n a) + (H : ∀ a : α, ∀ p : α → Prop, (∀ᶠ x in n a, p x) → ∀ᶠ y in n a, ∀ᶠ x in n y, p x) : + ∀ a, ∀ s ∈ n a, ∃ t ∈ n a, t ⊆ s ∧ ∀ a' ∈ t, s ∈ n a' := + sorry + + end + + -- BOTH. + variable {X Y : Type _} + + example (f : X → Y) : TopologicalSpace X → TopologicalSpace Y := + TopologicalSpace.coinduced f + + example (f : X → Y) : TopologicalSpace Y → TopologicalSpace X := + TopologicalSpace.induced f + + example (f : X → Y) (T_X : TopologicalSpace X) (T_Y : TopologicalSpace Y) : + TopologicalSpace.coinduced f T_X ≤ T_Y ↔ T_X ≤ TopologicalSpace.induced f T_Y := + coinduced_le_iff_le_induced + + #check coinduced_compose + + #check induced_compose + + example {T T' : TopologicalSpace X} : T ≤ T' ↔ ∀ s, T'.IsOpen s → T.IsOpen s := + Iff.rfl + + example (T_X : TopologicalSpace X) (T_Y : TopologicalSpace Y) (f : X → Y) : + Continuous f ↔ TopologicalSpace.coinduced f T_X ≤ T_Y := + continuous_iff_coinduced_le + + example {Z : Type _} (f : X → Y) (T_X : TopologicalSpace X) (T_Z : TopologicalSpace Z) (g : Y → Z) : + @Continuous Y Z (TopologicalSpace.coinduced f T_X) T_Z g ↔ @Continuous X Z T_X T_Z (g ∘ f) := by + rw [continuous_iff_coinduced_le, coinduced_compose, continuous_iff_coinduced_le] + + example (ι : Type _) (X : ι → Type _) (T_X : ∀ i, TopologicalSpace <| X i) : + (Pi.topologicalSpace : TopologicalSpace (∀ i, X i)) = + ⨅ i, TopologicalSpace.induced (fun x => x i) (T_X i) := + rfl + + example [TopologicalSpace X] [T2Space X] {u : ℕ → X} {a b : X} (ha : Tendsto u atTop (𝓝 a)) + (hb : Tendsto u atTop (𝓝 b)) : a = b := + tendsto_nhds_unique ha hb + + example [TopologicalSpace X] [RegularSpace X] (a : X) : + (𝓝 a).HasBasis (fun s : Set X => s ∈ 𝓝 a ∧ IsClosed s) id := + closed_nhds_basis a + + example [TopologicalSpace X] {x : X} : (𝓝 x).HasBasis (fun t : Set X => t ∈ 𝓝 x ∧ IsOpen t) id := + nhds_basis_opens' x + + theorem aux {X Y A : Type _} [TopologicalSpace X] {c : A → X} {f : A → Y} {x : X} {F : Filter Y} + (h : Tendsto f (comap c (𝓝 x)) F) {V' : Set Y} (V'_in : V' ∈ F) : + ∃ V ∈ 𝓝 x, IsOpen V ∧ c ⁻¹' V ⊆ f ⁻¹' V' := + sorry + + example [TopologicalSpace X] [TopologicalSpace Y] [RegularSpace Y] {A : Set X} + (hA : ∀ x, x ∈ closure A) {f : A → Y} (f_cont : Continuous f) + (hf : ∀ x : X, ∃ c : Y, Tendsto f (comap (↑) <| 𝓝 x) <| 𝓝 c) : + ∃ φ : X → Y, Continuous φ ∧ ∀ a : A, φ a = f a := + sorry + + #check @HasBasis.tendsto_right_iff + + example [TopologicalSpace X] [TopologicalSpace.FirstCountableTopology X] {s : Set X} {a : X} : + a ∈ closure s ↔ ∃ u : ℕ → X, (∀ n, u n ∈ s) ∧ Tendsto u atTop (𝓝 a) := + mem_closure_iff_seq_limit + + variable [TopologicalSpace X] + + example {F : Filter X} {x : X} : ClusterPt x F ↔ NeBot (𝓝 x ⊓ F) := + Iff.rfl + + example {s : Set X} : IsCompact s ↔ ∀ (F : Filter X) [NeBot F], F ≤ 𝓟 s → ∃ a ∈ s, ClusterPt a F := + Iff.rfl + + example [TopologicalSpace.FirstCountableTopology X] {s : Set X} {u : ℕ → X} (hs : IsCompact s) + (hu : ∀ n, u n ∈ s) : ∃ a ∈ s, ∃ φ : ℕ → ℕ, StrictMono φ ∧ Tendsto (u ∘ φ) atTop (𝓝 a) := + hs.tendsto_subseq hu + + variable [TopologicalSpace Y] + + example {x : X} {F : Filter X} {G : Filter Y} (H : ClusterPt x F) {f : X → Y} + (hfx : ContinuousAt f x) (hf : Tendsto f F G) : ClusterPt (f x) G := + ClusterPt.map H hfx hf + + example [TopologicalSpace Y] {f : X → Y} (hf : Continuous f) {s : Set X} (hs : IsCompact s) : + IsCompact (f '' s) := by + intro F F_ne F_le + have map_eq : map f (𝓟 s ⊓ comap f F) = 𝓟 (f '' s) ⊓ F := by sorry + have Hne : (𝓟 s ⊓ comap f F).NeBot := by sorry + have Hle : 𝓟 s ⊓ comap f F ≤ 𝓟 s := inf_le_left + sorry + + example {ι : Type _} {s : Set X} (hs : IsCompact s) (U : ι → Set X) (hUo : ∀ i, IsOpen (U i)) + (hsU : s ⊆ ⋃ i, U i) : ∃ t : Finset ι, s ⊆ ⋃ i ∈ t, U i := + hs.elim_finite_subcover U hUo hsU + + example [CompactSpace X] : IsCompact (univ : Set X) := + isCompact_univ +
• MIL/C07_Topology/solutions/Solutions_S01_Filters.lean (new)
  • @@ -0,0 +1,72 @@
    + import Mathlib.Topology.Instances.Real + + open Set Filter Topology + + -- In the next example we could use `tauto` in each proof instead of knowing the lemmas + example {α : Type _} (s : Set α) : Filter α := + { sets := { t | s ⊆ t } + univ_sets := subset_univ s + sets_of_superset := fun hU hUV => Subset.trans hU hUV + inter_sets := fun hU hV => subset_inter hU hV } + + example : Filter ℕ := + { sets := { s | ∃ a, ∀ b, a ≤ b → b ∈ s } + univ_sets := by + use 42 + simp + sets_of_superset := by + rintro U V ⟨N, hN⟩ hUV + use N + tauto + inter_sets := by + rintro U V ⟨N, hN⟩ ⟨N', hN'⟩ + use max N N' + intro b hb + rw [max_le_iff] at hb + constructor <;> tauto } + + def Tendsto₁ {X Y : Type _} (f : X → Y) (F : Filter X) (G : Filter Y) := + ∀ V ∈ G, f ⁻¹' V ∈ F + + example {X Y Z : Type _} {F : Filter X} {G : Filter Y} {H : Filter Z} {f : X → Y} {g : Y → Z} + (hf : Tendsto₁ f F G) (hg : Tendsto₁ g G H) : Tendsto₁ (g ∘ f) F H := + calc + map (g ∘ f) F = map g (map f F) := by rw [map_map] + _ ≤ map g G := (map_mono hf) + _ ≤ H := hg + + + example {X Y Z : Type _} {F : Filter X} {G : Filter Y} {H : Filter Z} {f : X → Y} {g : Y → Z} + (hf : Tendsto₁ f F G) (hg : Tendsto₁ g G H) : Tendsto₁ (g ∘ f) F H := by + intro V hV + rw [preimage_comp] + apply hf + apply hg + exact hV + + example (f : ℕ → ℝ × ℝ) (x₀ y₀ : ℝ) : + Tendsto f atTop (𝓝 (x₀, y₀)) ↔ + Tendsto (Prod.fst ∘ f) atTop (𝓝 x₀) ∧ Tendsto (Prod.snd ∘ f) atTop (𝓝 y₀) := + calc + Tendsto f atTop (𝓝 (x₀, y₀)) ↔ map f atTop ≤ 𝓝 (x₀, y₀) := Iff.rfl + _ ↔ map f atTop ≤ 𝓝 x₀ ×ᶠ 𝓝 y₀ := by rw [nhds_prod_eq] + _ ↔ map f atTop ≤ comap Prod.fst (𝓝 x₀) ⊓ comap Prod.snd (𝓝 y₀) := Iff.rfl + _ ↔ map f atTop ≤ comap Prod.fst (𝓝 x₀) ∧ map f atTop ≤ comap Prod.snd (𝓝 y₀) := le_inf_iff + _ ↔ map Prod.fst (map f atTop) ≤ 𝓝 x₀ ∧ map Prod.snd (map f atTop) ≤ 𝓝 y₀ := by + rw [← map_le_iff_le_comap, ← map_le_iff_le_comap] + _ ↔ map (Prod.fst ∘ f) atTop ≤ 𝓝 x₀ ∧ map (Prod.snd ∘ f) atTop ≤ 𝓝 y₀ := by + rw [map_map, map_map] + + + -- an alternative solution + example (f : ℕ → ℝ × ℝ) (x₀ y₀ : ℝ) : + Tendsto f atTop (𝓝 (x₀, y₀)) ↔ + Tendsto (Prod.fst ∘ f) atTop (𝓝 x₀) ∧ Tendsto (Prod.snd ∘ f) atTop (𝓝 y₀) := by + rw [nhds_prod_eq] + unfold Tendsto Filter.prod + rw [le_inf_iff, ← map_le_iff_le_comap, map_map, ← map_le_iff_le_comap, map_map] + + example (u : ℕ → ℝ) (M : Set ℝ) (x : ℝ) (hux : Tendsto u atTop (𝓝 x)) + (huM : ∀ᶠ n in atTop, u n ∈ M) : x ∈ closure M := + mem_closure_iff_clusterPt.mpr (neBot_of_le <| le_inf hux <| le_principal_iff.mpr huM) +
• MIL/C07_Topology/solutions/Solutions_S02_Metric_Spaces.lean (new)
  • @@ -0,0 +1,365 @@
    + import Mathlib.Topology.Instances.Real + import Mathlib.Analysis.NormedSpace.BanachSteinhaus + + open Set Filter + + open Topology Filter + + variable {X : Type _} [MetricSpace X] (a b c : X) + + #check (dist a b : ℝ) + + #check (dist_nonneg : 0 ≤ dist a b) + + #check (dist_eq_zero : dist a b = 0 ↔ a = b) + + #check (dist_comm a b : dist a b = dist b a) + + #check (dist_triangle a b c : dist a c ≤ dist a b + dist b c) + + -- Note the next three lines are not quoted, their purpose is to make sure those things don't get renamed while we're looking elsewhere. + #check EMetricSpace + + #check PseudoMetricSpace + + #check PseudoEMetricSpace + + example {u : ℕ → X} {a : X} : Tendsto u atTop (𝓝 a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, dist (u n) a < ε := + Metric.tendsto_atTop + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} : + Continuous f ↔ ∀ x : X, ∀ ε > 0, ∃ δ > 0, ∀ x', dist x' x < δ → dist (f x') (f x) < ε := + Metric.continuous_iff + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := by continuity + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := + continuous_dist.comp ((hf.comp continuous_fst).prod_mk (hf.comp continuous_snd)) + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := by + apply Continuous.dist + exact hf.comp continuous_fst + exact hf.comp continuous_snd + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := + (hf.comp continuous_fst).dist (hf.comp continuous_snd) + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] {f : X → Y} (hf : Continuous f) : + Continuous fun p : X × X => dist (f p.1) (f p.2) := + hf.fst'.dist hf.snd' + + example {f : ℝ → X} (hf : Continuous f) : Continuous fun x : ℝ => f (x ^ 2 + x) := + sorry + + example {f : ℝ → X} (hf : Continuous f) : Continuous fun x : ℝ => f (x ^ 2 + x) := + hf.comp <| (continuous_pow 2).add continuous_id + + example {X Y : Type _} [MetricSpace X] [MetricSpace Y] (f : X → Y) (a : X) : + ContinuousAt f a ↔ ∀ ε > 0, ∃ δ > 0, ∀ {x}, dist x a < δ → dist (f x) (f a) < ε := + Metric.continuousAt_iff + + variable (r : ℝ) + + example : Metric.ball a r = { b | dist b a < r } := + rfl + + example : Metric.closedBall a r = { b | dist b a ≤ r } := + rfl + + example (hr : 0 < r) : a ∈ Metric.ball a r := + Metric.mem_ball_self hr + + example (hr : 0 ≤ r) : a ∈ Metric.closedBall a r := + Metric.mem_closedBall_self hr + + example (s : Set X) : IsOpen s ↔ ∀ x ∈ s, ∃ ε > 0, Metric.ball x ε ⊆ s := + Metric.isOpen_iff + + example {s : Set X} : IsClosed s ↔ IsOpen (sᶜ) := + isOpen_compl_iff.symm + + example {s : Set X} (hs : IsClosed s) {u : ℕ → X} (hu : Tendsto u atTop (𝓝 a)) + (hus : ∀ n, u n ∈ s) : a ∈ s := + hs.mem_of_tendsto hu (eventually_of_forall hus) + + example {s : Set X} : a ∈ closure s ↔ ∀ ε > 0, ∃ b ∈ s, a ∈ Metric.ball b ε := + Metric.mem_closure_iff + + example {u : ℕ → X} (hu : Tendsto u atTop (𝓝 a)) {s : Set X} (hs : ∀ n, u n ∈ s) : a ∈ closure s := + sorry + + example {u : ℕ → X} (hu : Tendsto u atTop (𝓝 a)) {s : Set X} (hs : ∀ n, u n ∈ s) : a ∈ closure s := by + rw [Metric.tendsto_atTop] at hu + rw [Metric.mem_closure_iff] + intro ε ε_pos + rcases hu ε ε_pos with ⟨N, hN⟩ + refine' ⟨u N, hs _, _⟩ + rw [dist_comm] + exact hN N le_rfl + + example {x : X} {s : Set X} : s ∈ 𝓝 x ↔ ∃ ε > 0, Metric.ball x ε ⊆ s := + Metric.nhds_basis_ball.mem_iff + + example {x : X} {s : Set X} : s ∈ 𝓝 x ↔ ∃ ε > 0, Metric.closedBall x ε ⊆ s := + Metric.nhds_basis_closedBall.mem_iff + + example : IsCompact (Set.Icc 0 1 : Set ℝ) := + isCompact_Icc + + example {s : Set X} (hs : IsCompact s) {u : ℕ → X} (hu : ∀ n, u n ∈ s) : + ∃ a ∈ s, ∃ φ : ℕ → ℕ, StrictMono φ ∧ Tendsto (u ∘ φ) atTop (𝓝 a) := + hs.tendsto_subseq hu + + example {s : Set X} (hs : IsCompact s) (hs' : s.Nonempty) {f : X → ℝ} (hfs : ContinuousOn f s) : + ∃ x ∈ s, ∀ y ∈ s, f x ≤ f y := + hs.exists_forall_le hs' hfs + + example {s : Set X} (hs : IsCompact s) (hs' : s.Nonempty) {f : X → ℝ} (hfs : ContinuousOn f s) : + ∃ x ∈ s, ∀ y ∈ s, f y ≤ f x := + hs.exists_forall_ge hs' hfs + + example {s : Set X} (hs : IsCompact s) : IsClosed s := + hs.IsClosed + + example {X : Type _} [MetricSpace X] [CompactSpace X] : IsCompact (univ : Set X) := + isCompact_univ + + #check IsCompact.isClosed + + example {X : Type _} [MetricSpace X] {Y : Type _} [MetricSpace Y] {f : X → Y} : + UniformContinuous f ↔ ∀ ε > 0, ∃ δ > 0, ∀ {a b : X}, dist a b < δ → dist (f a) (f b) < ε := + Metric.uniformContinuous_iff + + example {X : Type _} [MetricSpace X] [CompactSpace X] {Y : Type _} [MetricSpace Y] {f : X → Y} + (hf : Continuous f) : UniformContinuous f := + sorry + + example {X : Type _} [MetricSpace X] [CompactSpace X] {Y : Type _} [MetricSpace Y] {f : X → Y} + (hf : Continuous f) : UniformContinuous f := by + rw [Metric.uniformContinuous_iff] + intro ε ε_pos + let φ : X × X → ℝ := fun p => dist (f p.1) (f p.2) + have φ_cont : Continuous φ := hf.fst'.dist hf.snd' + let K := { p : X × X | ε ≤ φ p } + have K_closed : IsClosed K := isClosed_le continuous_const φ_cont + have K_cpct : IsCompact K := K_closed.is_compact + cases' eq_empty_or_nonempty K with hK hK + · use 1, by norm_num + intro x y hxy + have : (x, y) ∉ K := by simp [hK] + simpa [K] + · rcases K_cpct.exists_forall_le hK continuous_dist.continuous_on with ⟨⟨x₀, x₁⟩, xx_in, H⟩ + use dist x₀ x₁ + constructor + · change _ < _ + rw [dist_pos] + intro h + have : ε ≤ 0 := by simpa [*] using xx_in + linarith + · intro x x' + contrapose! + intro hxx' + exact H (x, x') hxx' + + example (u : ℕ → X) : CauchySeq u ↔ ∀ ε > 0, ∃ N : ℕ, ∀ m ≥ N, ∀ n ≥ N, dist (u m) (u n) < ε := + Metric.cauchySeq_iff + + example (u : ℕ → X) : CauchySeq u ↔ ∀ ε > 0, ∃ N : ℕ, ∀ n ≥ N, dist (u n) (u N) < ε := + Metric.cauchySeq_iff' + + example [CompleteSpace X] (u : ℕ → X) (hu : CauchySeq u) : ∃ x, Tendsto u atTop (𝓝 x) := + cauchySeq_tendsto_of_complete hu + + open BigOperators + + open Finset + + theorem cauchySeq_of_le_geometric_two' {u : ℕ → X} + (hu : ∀ n : ℕ, dist (u n) (u (n + 1)) ≤ (1 / 2) ^ n) : CauchySeq u := by + rw [Metric.cauchySeq_iff'] + intro ε ε_pos + obtain ⟨N, hN⟩ : ∃ N : ℕ, 1 / 2 ^ N * 2 < ε := by sorry + use N + intro n hn + obtain ⟨k, rfl : n = N + k⟩ := le_iff_exists_add.mp hn + calc + dist (u (N + k)) (u N) = dist (u (N + 0)) (u (N + k)) := sorry + _ ≤ ∑ i in range k, dist (u (N + i)) (u (N + (i + 1))) := sorry + _ ≤ ∑ i in range k, (1 / 2 : ℝ) ^ (N + i) := sorry + _ = 1 / 2 ^ N * ∑ i in range k, (1 / 2) ^ i := sorry + _ ≤ 1 / 2 ^ N * 2 := sorry + _ < ε := sorry + + + example {u : ℕ → X} (hu : ∀ n : ℕ, dist (u n) (u (n + 1)) ≤ (1 / 2) ^ n) : CauchySeq u := by + rw [Metric.cauchySeq_iff'] + intro ε ε_pos + obtain ⟨N, hN⟩ : ∃ N : ℕ, 1 / 2 ^ N * 2 < ε := by + have : Tendsto (fun N : ℕ => (1 / 2 ^ N * 2 : ℝ)) atTop (𝓝 0) := by + rw [← MulZeroClass.zero_mul (2 : ℝ)] + apply Tendsto.mul + simp_rw [← one_div_pow (2 : ℝ)] + apply tendsto_pow_atTop_nhds_0_of_lt_1 <;> linarith + exact tendsto_const_nhds + rcases(atTop_basis.tendsto_iff (nhds_basis_Ioo_pos (0 : ℝ))).mp this ε ε_pos with ⟨N, H, hN⟩ + exact ⟨N, by simpa using (hN N le_rfl).2⟩ + use N + intro n hn + obtain ⟨k, rfl : n = N + k⟩ := le_iff_exists_add.mp hn + calc + dist (u (N + k)) (u N) = dist (u (N + 0)) (u (N + k)) := by rw [dist_comm, add_zero] + _ ≤ ∑ i in range k, dist (u (N + i)) (u (N + (i + 1))) := + (dist_le_range_sum_dist (fun i => u (N + i)) k) + _ ≤ ∑ i in range k, (1 / 2 : ℝ) ^ (N + i) := (sum_le_sum fun i hi => hu <| N + i) + _ = 1 / 2 ^ N * ∑ i in range k, (1 / 2) ^ i := by simp_rw [← one_div_pow, pow_add, ← mul_sum] + _ ≤ 1 / 2 ^ N * 2 := + (mul_le_mul_of_nonneg_left (sum_geometric_two_le _) + (one_div_nonneg.mpr (pow_nonneg (zero_le_two : (0 : ℝ) ≤ 2) _))) + _ < ε := hN + + + open Metric + + example [CompleteSpace X] (f : ℕ → Set X) (ho : ∀ n, IsOpen (f n)) (hd : ∀ n, Dense (f n)) : + Dense (⋂ n, f n) := by + let B : ℕ → ℝ := fun n => (1 / 2) ^ n + have Bpos : ∀ n, 0 < B n + sorry + /- Translate the density assumption into two functions `center` and `radius` associating + to any n, x, δ, δpos a center and a positive radius such that + `closed_ball center radius` is included both in `f n` and in `closed_ball x δ`. + We can also require `radius ≤ (1/2)^(n+1)`, to ensure we get a Cauchy sequence later. -/ + have : + ∀ (n : ℕ) (x : X), + ∀ δ > 0, ∃ y : X, ∃ r > 0, r ≤ B (n + 1) ∧ closed_ball y r ⊆ closed_ball x δ ∩ f n := + by sorry + choose! center radius Hpos HB Hball using this + intro x + rw [mem_closure_iff_nhds_basis nhds_basis_closed_ball] + intro ε εpos + /- `ε` is positive. We have to find a point in the ball of radius `ε` around `x` belonging to all + `f n`. For this, we construct inductively a sequence `F n = (c n, r n)` such that the closed ball + `closed_ball (c n) (r n)` is included in the previous ball and in `f n`, and such that + `r n` is small enough to ensure that `c n` is a Cauchy sequence. Then `c n` converges to a + limit which belongs to all the `f n`. -/ + let F : ℕ → X × ℝ := fun n => + Nat.recOn n (Prod.mk x (min ε (B 0))) fun n p => Prod.mk (center n p.1 p.2) (radius n p.1 p.2) + let c : ℕ → X := fun n => (F n).1 + let r : ℕ → ℝ := fun n => (F n).2 + have rpos : ∀ n, 0 < r n := by sorry + have rB : ∀ n, r n ≤ B n := by sorry + have incl : ∀ n, closed_ball (c (n + 1)) (r (n + 1)) ⊆ closed_ball (c n) (r n) ∩ f n := by sorry + have cdist : ∀ n, dist (c n) (c (n + 1)) ≤ B n := by sorry + have : CauchySeq c := cauchySeq_of_le_geometric_two' cdist + -- as the sequence `c n` is Cauchy in a complete space, it converges to a limit `y`. + rcases cauchySeq_tendsto_of_complete this with ⟨y, ylim⟩ + -- this point `y` will be the desired point. We will check that it belongs to all + -- `f n` and to `ball x ε`. + use y + have I : ∀ n, ∀ m ≥ n, closed_ball (c m) (r m) ⊆ closed_ball (c n) (r n) := by sorry + have yball : ∀ n, y ∈ closed_ball (c n) (r n) := by sorry + sorry + + example [CompleteSpace X] (f : ℕ → Set X) (ho : ∀ n, IsOpen (f n)) (hd : ∀ n, Dense (f n)) : + Dense (⋂ n, f n) := by + let B : ℕ → ℝ := fun n => (1 / 2) ^ n + have Bpos : ∀ n, 0 < B n := fun n => pow_pos sorry n + /- Translate the density assumption into two functions `center` and `radius` associating + to any n, x, δ, δpos a center and a positive radius such that + `closed_ball center radius` is included both in `f n` and in `closed_ball x δ`. + We can also require `radius ≤ (1/2)^(n+1)`, to ensure we get a Cauchy sequence later. -/ + have : + ∀ (n : ℕ) (x : X), + ∀ δ > 0, ∃ y : X, ∃ r > 0, r ≤ B (n + 1) ∧ closed_ball y r ⊆ closed_ball x δ ∩ f n := by + intro n x δ δpos + have : x ∈ closure (f n) := hd n x + rcases Metric.mem_closure_iff.1 this (δ / 2) (half_pos δpos) with ⟨y, ys, xy⟩ + rw [dist_comm] at xy + obtain ⟨r, rpos, hr⟩ : ∃ r > 0, closed_ball y r ⊆ f n := + nhds_basis_closed_ball.mem_iff.1 (isOpen_iff_mem_nhds.1 (ho n) y ys) + refine' ⟨y, min (min (δ / 2) r) (B (n + 1)), _, _, fun z hz => ⟨_, _⟩⟩ + show 0 < min (min (δ / 2) r) (B (n + 1)) + exact lt_min (lt_min (half_pos δpos) rpos) (Bpos (n + 1)) + show min (min (δ / 2) r) (B (n + 1)) ≤ B (n + 1) + exact min_le_right _ _ + show z ∈ closed_ball x δ + exact + calc + dist z x ≤ dist z y + dist y x := dist_triangle _ _ _ + _ ≤ min (min (δ / 2) r) (B (n + 1)) + δ / 2 := (add_le_add hz xy.le) + _ ≤ δ / 2 + δ / 2 := (add_le_add_right ((min_le_left _ _).trans (min_le_left _ _)) _) + _ = δ := add_halves δ + + show z ∈ f n + exact + hr + (calc + dist z y ≤ min (min (δ / 2) r) (B (n + 1)) := hz + _ ≤ r := (min_le_left _ _).trans (min_le_right _ _) + ) + choose! center radius Hpos HB Hball using this + refine' fun x => (mem_closure_iff_nhds_basis nhds_basis_closed_ball).2 fun ε εpos => _ + /- `ε` is positive. We have to find a point in the ball of radius `ε` around `x` belonging to all + `f n`. For this, we construct inductively a sequence `F n = (c n, r n)` such that the closed ball + `closed_ball (c n) (r n)` is included in the previous ball and in `f n`, and such that + `r n` is small enough to ensure that `c n` is a Cauchy sequence. Then `c n` converges to a + limit which belongs to all the `f n`. -/ + let F : ℕ → X × ℝ := fun n => + Nat.recOn n (Prod.mk x (min ε (B 0))) fun n p => Prod.mk (center n p.1 p.2) (radius n p.1 p.2) + let c : ℕ → X := fun n => (F n).1 + let r : ℕ → ℝ := fun n => (F n).2 + have rpos : ∀ n, 0 < r n := by + intro n + induction' n with n hn + exact lt_min εpos (Bpos 0) + exact Hpos n (c n) (r n) hn + have rB : ∀ n, r n ≤ B n := by + intro n + induction' n with n hn + exact min_le_right _ _ + exact HB n (c n) (r n) (rpos n) + have incl : ∀ n, closed_ball (c (n + 1)) (r (n + 1)) ⊆ closed_ball (c n) (r n) ∩ f n := fun n => + Hball n (c n) (r n) (rpos n) + have cdist : ∀ n, dist (c n) (c (n + 1)) ≤ B n := by + intro n + rw [dist_comm] + have A : c (n + 1) ∈ closed_ball (c (n + 1)) (r (n + 1)) := + mem_closed_ball_self (rpos <| n + 1).le + have I := + calc + closed_ball (c (n + 1)) (r (n + 1)) ⊆ closed_ball (c n) (r n) := + (incl n).trans (inter_subset_left _ _) + _ ⊆ closed_ball (c n) (B n) := closed_ball_subset_closed_ball (rB n) + + exact I A + have : CauchySeq c := cauchySeq_of_le_geometric_two' cdist + -- as the sequence `c n` is Cauchy in a complete space, it converges to a limit `y`. + rcases cauchySeq_tendsto_of_complete this with ⟨y, ylim⟩ + -- this point `y` will be the desired point. We will check that it belongs to all + -- `f n` and to `ball x ε`. + use y + have I : ∀ n, ∀ m ≥ n, closed_ball (c m) (r m) ⊆ closed_ball (c n) (r n) := by + intro n + refine' Nat.le_induction _ fun m hnm h => _ + · exact Subset.rfl + · exact (incl m).trans ((Set.inter_subset_left _ _).trans h) + have yball : ∀ n, y ∈ closed_ball (c n) (r n) := by + intro n + refine' is_closed_ball.mem_of_tendsto ylim _ + refine' (Filter.eventually_ge_atTop n).mono fun m hm => _ + exact I n m hm (mem_closed_ball_self (rpos _).le) + constructor + · suffices ∀ n, y ∈ f n by rwa [Set.mem_iInter] + intro n + have : closed_ball (c (n + 1)) (r (n + 1)) ⊆ f n := + Subset.trans (incl n) (inter_subset_right _ _) + exact this (yball (n + 1)) + calc + dist y x ≤ r 0 := yball 0 + _ ≤ ε := min_le_left _ _ + +
• MIL/C07_Topology/solutions/Solutions_S03_Topological_Spaces.lean (new)
  • @@ -0,0 +1,202 @@
    + import Mathlib.Topology.Instances.Real + import Mathlib.Analysis.NormedSpace.BanachSteinhaus + + open Set Filter + + open Topology Filter + + section + + variable {X : Type _} [TopologicalSpace X] + + example : IsOpen (univ : Set X) := + isOpen_univ + + example : IsOpen (∅ : Set X) := + isOpen_empty + + example {ι : Type _} {s : ι → Set X} (hs : ∀ i, IsOpen <| s i) : IsOpen (⋃ i, s i) := + isOpen_iUnion hs + + example {ι : Type _} [Fintype ι] {s : ι → Set X} (hs : ∀ i, IsOpen <| s i) : IsOpen (⋂ i, s i) := + isOpen_iInter hs + + variable {Y : Type _} [TopologicalSpace Y] + + example {f : X → Y} : Continuous f ↔ ∀ s, IsOpen s → IsOpen (f ⁻¹' s) := + continuous_def + + example {f : X → Y} {x : X} : ContinuousAt f x ↔ map f (𝓝 x) ≤ 𝓝 (f x) := + Iff.rfl + + example {f : X → Y} {x : X} : ContinuousAt f x ↔ ∀ U ∈ 𝓝 (f x), ∀ᶠ x in 𝓝 x, f x ∈ U := + Iff.rfl + + example {x : X} {s : Set X} : s ∈ 𝓝 x ↔ ∃ t, t ⊆ s ∧ IsOpen t ∧ x ∈ t := + mem_nhds_iff + + example (x : X) : pure x ≤ 𝓝 x := + pure_le_nhds x + + example (x : X) (P : X → Prop) (h : ∀ᶠ y in 𝓝 x, P y) : P x := + pure_le_nhds x h + + example {P : X → Prop} {x : X} (h : ∀ᶠ y in 𝓝 x, P y) : ∀ᶠ y in 𝓝 x, ∀ᶠ z in 𝓝 y, P z := + eventually_eventually_nhds.mpr h + + #check TopologicalSpace.mkOfNhds + + #check TopologicalSpace.nhds_mkOfNhds + + example {α : Type _} (n : α → Filter α) (H₀ : ∀ a, pure a ≤ n a) + (H : ∀ a : α, ∀ p : α → Prop, (∀ᶠ x in n a, p x) → ∀ᶠ y in n a, ∀ᶠ x in n y, p x) : + ∀ a, ∀ s ∈ n a, ∃ t ∈ n a, t ⊆ s ∧ ∀ a' ∈ t, s ∈ n a' := + sorry + + example {α : Type _} (n : α → Filter α) (H₀ : ∀ a, pure a ≤ n a) + (H : ∀ a : α, ∀ p : α → Prop, (∀ᶠ x in n a, p x) → ∀ᶠ y in n a, ∀ᶠ x in n y, p x) : + ∀ a, ∀ s ∈ n a, ∃ t ∈ n a, t ⊆ s ∧ ∀ a' ∈ t, s ∈ n a' := by + intro a s s_in + refine' ⟨{ y | s ∈ n y }, H a (fun x => x ∈ s) s_in, _, by tauto⟩ + rintro y (hy : s ∈ n y) + exact H₀ y hy + + end + + -- BOTH. + variable {X Y : Type _} + + example (f : X → Y) : TopologicalSpace X → TopologicalSpace Y := + TopologicalSpace.coinduced f + + example (f : X → Y) : TopologicalSpace Y → TopologicalSpace X := + TopologicalSpace.induced f + + example (f : X → Y) (T_X : TopologicalSpace X) (T_Y : TopologicalSpace Y) : + TopologicalSpace.coinduced f T_X ≤ T_Y ↔ T_X ≤ TopologicalSpace.induced f T_Y := + coinduced_le_iff_le_induced + + #check coinduced_compose + + #check induced_compose + + example {T T' : TopologicalSpace X} : T ≤ T' ↔ ∀ s, T'.IsOpen s → T.IsOpen s := + Iff.rfl + + example (T_X : TopologicalSpace X) (T_Y : TopologicalSpace Y) (f : X → Y) : + Continuous f ↔ TopologicalSpace.coinduced f T_X ≤ T_Y := + continuous_iff_coinduced_le + + example {Z : Type _} (f : X → Y) (T_X : TopologicalSpace X) (T_Z : TopologicalSpace Z) (g : Y → Z) : + @Continuous Y Z (TopologicalSpace.coinduced f T_X) T_Z g ↔ @Continuous X Z T_X T_Z (g ∘ f) := by + rw [continuous_iff_coinduced_le, coinduced_compose, continuous_iff_coinduced_le] + + example (ι : Type _) (X : ι → Type _) (T_X : ∀ i, TopologicalSpace <| X i) : + (Pi.topologicalSpace : TopologicalSpace (∀ i, X i)) = + ⨅ i, TopologicalSpace.induced (fun x => x i) (T_X i) := + rfl + + example [TopologicalSpace X] [T2Space X] {u : ℕ → X} {a b : X} (ha : Tendsto u atTop (𝓝 a)) + (hb : Tendsto u atTop (𝓝 b)) : a = b := + tendsto_nhds_unique ha hb + + example [TopologicalSpace X] [RegularSpace X] (a : X) : + (𝓝 a).HasBasis (fun s : Set X => s ∈ 𝓝 a ∧ IsClosed s) id := + closed_nhds_basis a + + example [TopologicalSpace X] {x : X} : (𝓝 x).HasBasis (fun t : Set X => t ∈ 𝓝 x ∧ IsOpen t) id := + nhds_basis_opens' x + + theorem aux {X Y A : Type _} [TopologicalSpace X] {c : A → X} {f : A → Y} {x : X} {F : Filter Y} + (h : Tendsto f (comap c (𝓝 x)) F) {V' : Set Y} (V'_in : V' ∈ F) : + ∃ V ∈ 𝓝 x, IsOpen V ∧ c ⁻¹' V ⊆ f ⁻¹' V' := + sorry + + example {X Y A : Type _} [TopologicalSpace X] {c : A → X} {f : A → Y} {x : X} {F : Filter Y} + (h : Tendsto f (comap c (𝓝 x)) F) {V' : Set Y} (V'_in : V' ∈ F) : + ∃ V ∈ 𝓝 x, IsOpen V ∧ c ⁻¹' V ⊆ f ⁻¹' V' := by + simpa [and_assoc] using ((nhds_basis_opens' x).comap c).tendsto_left_iff.mp h V' V'_in + + example [TopologicalSpace X] [TopologicalSpace Y] [RegularSpace Y] {A : Set X} + (hA : ∀ x, x ∈ closure A) {f : A → Y} (f_cont : Continuous f) + (hf : ∀ x : X, ∃ c : Y, Tendsto f (comap (↑) <| 𝓝 x) <| 𝓝 c) : + ∃ φ : X → Y, Continuous φ ∧ ∀ a : A, φ a = f a := + sorry + + #check @HasBasis.tendsto_right_iff + + example [TopologicalSpace X] [TopologicalSpace Y] [T3Space Y] {A : Set X} (hA : ∀ x, x ∈ closure A) + {f : A → Y} (f_cont : Continuous f) + (hf : ∀ x : X, ∃ c : Y, Tendsto f (comap (↑) <| 𝓝 x) <| 𝓝 c) : + ∃ φ : X → Y, Continuous φ ∧ ∀ a : A, φ a = f a := by + choose φ hφ using hf + use φ + constructor + · rw [continuous_iff_continuousAt] + intro x + suffices ∀ V' ∈ 𝓝 (φ x), IsClosed V' → φ ⁻¹' V' ∈ 𝓝 x by + simp [ContinuousAt, (closed_nhds_basis _).tendsto_right_iff] + intro V' V'_in V'_closed + obtain ⟨V, V_in, V_op, hV⟩ : ∃ V ∈ 𝓝 x, IsOpen V ∧ (↑) ⁻¹' V ⊆ f ⁻¹' V' := aux (hφ x) V'_in + suffices : ∀ y ∈ V, φ y ∈ V' + exact mem_of_superset V_in this + intro y y_in + have hVx : V ∈ 𝓝 y := V_op.mem_nhds y_in + haveI : (comap ((↑) : A → X) (𝓝 y)).NeBot := by simpa [mem_closure_iff_comap_neBot] using hA y + apply V'_closed.mem_of_tendsto (hφ y) + exact mem_of_superset (preimage_mem_comap hVx) hV + · intro a + have lim : Tendsto f (𝓝 a) (𝓝 <| φ a) := by simpa [nhds_induced] using hφ a + exact tendsto_nhds_unique limUnder f_cont.continuousAt + + example [TopologicalSpace X] [TopologicalSpace.FirstCountableTopology X] {s : Set X} {a : X} : + a ∈ closure s ↔ ∃ u : ℕ → X, (∀ n, u n ∈ s) ∧ Tendsto u atTop (𝓝 a) := + mem_closure_iff_seq_limit + + variable [TopologicalSpace X] + + example {F : Filter X} {x : X} : ClusterPt x F ↔ NeBot (𝓝 x ⊓ F) := + Iff.rfl + + example {s : Set X} : IsCompact s ↔ ∀ (F : Filter X) [NeBot F], F ≤ 𝓟 s → ∃ a ∈ s, ClusterPt a F := + Iff.rfl + + example [TopologicalSpace.FirstCountableTopology X] {s : Set X} {u : ℕ → X} (hs : IsCompact s) + (hu : ∀ n, u n ∈ s) : ∃ a ∈ s, ∃ φ : ℕ → ℕ, StrictMono φ ∧ Tendsto (u ∘ φ) atTop (𝓝 a) := + hs.tendsto_subseq hu + + variable [TopologicalSpace Y] + + example {x : X} {F : Filter X} {G : Filter Y} (H : ClusterPt x F) {f : X → Y} + (hfx : ContinuousAt f x) (hf : Tendsto f F G) : ClusterPt (f x) G := + ClusterPt.map H hfx hf + + example [TopologicalSpace Y] {f : X → Y} (hf : Continuous f) {s : Set X} (hs : IsCompact s) : + IsCompact (f '' s) := by + intro F F_ne F_le + have map_eq : map f (𝓟 s ⊓ comap f F) = 𝓟 (f '' s) ⊓ F := by sorry + have Hne : (𝓟 s ⊓ comap f F).NeBot := by sorry + have Hle : 𝓟 s ⊓ comap f F ≤ 𝓟 s := inf_le_left + sorry + + example [TopologicalSpace Y] {f : X → Y} (hf : Continuous f) {s : Set X} (hs : IsCompact s) : + IsCompact (f '' s) := by + intro F F_ne F_le + have map_eq : map f (𝓟 s ⊓ comap f F) = 𝓟 (f '' s) ⊓ F := by rw [Filter.push_pull, map_principal] + have Hne : (𝓟 s ⊓ comap f F).NeBot := by + apply NeBot.of_map + rwa [map_eq, inf_of_le_right F_le] + have Hle : 𝓟 s ⊓ comap f F ≤ 𝓟 s := inf_le_left + rcases hs Hle with ⟨x, x_in, hx⟩ + refine' ⟨f x, mem_image_of_mem f x_in, _⟩ + apply hx.map hf.continuousAt + rw [Tendsto, map_eq] + exact inf_le_right + + example {ι : Type _} {s : Set X} (hs : IsCompact s) (U : ι → Set X) (hUo : ∀ i, IsOpen (U i)) + (hsU : s ⊆ ⋃ i, U i) : ∃ t : Finset ι, s ⊆ ⋃ i ∈ t, U i := + hs.elim_finite_subcover U hUo hsU + + example [CompactSpace X] : IsCompact (univ : Set X) := + isCompact_univ +
• MIL/C08_Topology/S01_Filters.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real open Set Filter Topology
  • @@ -80,9 +79,9 @@ example (u v : ℕ → ℝ) (h : u =ᶠ[atTop] v) (x₀ : ℝ) :
    Tendsto u atTop (𝓝 x₀) ↔ Tendsto v atTop (𝓝 x₀) := tendsto_congr' h - #check eventually_of_forall - #check Eventually.mono - #check Eventually.and + #check @eventually_of_forall + #check @Eventually.mono + #check @Eventually.and example (P Q R : ℕ → Prop) (hP : ∀ᶠ n in atTop, P n) (hQ : ∀ᶠ n in atTop, Q n) (hR : ∀ᶠ n in atTop, P n ∧ Q n → R n) : ∀ᶠ n in atTop, R n := by
• MIL/C08_Topology/S02_Metric_Spaces.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
• MIL/C08_Topology/S03_Topological_Spaces.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
  • @@ -113,7 +112,7 @@ example [TopologicalSpace X] [TopologicalSpace Y] [RegularSpace Y] {A : Set X}
    ∃ φ : X → Y, Continuous φ ∧ ∀ a : A, φ a = f a := sorry - #check HasBasis.tendsto_right_iff + #check @HasBasis.tendsto_right_iff example [TopologicalSpace X] [TopologicalSpace.FirstCountableTopology X] {s : Set X} {a : X} :
• MIL/C08_Topology/solutions/Solutions_S01_Filters.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real open Set Filter Topology
• MIL/C08_Topology/solutions/Solutions_S02_Metric_Spaces.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
• MIL/C08_Topology/solutions/Solutions_S03_Topological_Spaces.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Topology.Instances.Real import Mathlib.Analysis.NormedSpace.BanachSteinhaus
  • @@ -127,7 +126,7 @@ example [TopologicalSpace X] [TopologicalSpace Y] [RegularSpace Y] {A : Set X}
    ∃ φ : X → Y, Continuous φ ∧ ∀ a : A, φ a = f a := sorry - #check HasBasis.tendsto_right_iff + #check @HasBasis.tendsto_right_iff example [TopologicalSpace X] [TopologicalSpace Y] [T3Space Y] {A : Set X} (hA : ∀ x, x ∈ closure A) {f : A → Y} (f_cont : Continuous f)
• MIL/C09_Differential_Calculus/S01_Elementary_Differential_Calculus.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv import Mathlib.Analysis.Calculus.MeanValue
  • @@ -28,8 +27,6 @@ example {f g : ℝ → ℝ} {x : ℝ} (hf : DifferentiableAt ℝ f x) (hg : Diff
    example {f : ℝ → ℝ} {a : ℝ} (h : IsLocalMin f a) : deriv f a = 0 := h.deriv_eq_zero - open Set - example {f : ℝ → ℝ} {a b : ℝ} (hab : a < b) (hfc : ContinuousOn f (Icc a b)) (hfI : f a = f b) : ∃ c ∈ Ioo a b, deriv f c = 0 := exists_deriv_eq_zero f hab hfc hfI
• MIL/C09_Differential_Calculus/S02_Differential_Calculus_in_Normed_Spaces.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.NormedSpace.BanachSteinhaus import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Calculus.Inverse
  • @@ -114,6 +113,8 @@ end
    open Asymptotics + open Asymptotics + example {α : Type _} {E : Type _} [NormedGroup E] {F : Type _} [NormedGroup F] (c : ℝ) (l : Filter α) (f : α → E) (g : α → F) : IsBigOWith c l f g ↔ ∀ᶠ x in l, ‖f x‖ ≤ c * ‖g x‖ := isBigOWith_iff
  • @@ -132,8 +133,6 @@ example {α : Type _} {E : Type _} [NormedAddCommGroup E] (l : Filter α) (f g :
    section - open Topology - variable {𝕜 : Type _} [NontriviallyNormedField 𝕜] {E : Type _} [NormedAddCommGroup E] [NormedSpace 𝕜 E] {F : Type _} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
  • @@ -172,7 +171,7 @@ example (hf : HasStrictFDerivAt f (f' : E →L[𝕜] F) a) :
    ∀ᶠ x in 𝓝 (f a), f (hf.localInverse f f' a x) = x := hf.eventually_right_inverse - example {f : E → F} {f' : E ≃L[𝕜] F} {a : E} + example [CompleteSpace E] {f : E → F} {f' : E ≃L[𝕜] F} {a : E} (hf : HasStrictFDerivAt f (f' : E →L[𝕜] F) a) : HasStrictFDerivAt (HasStrictFDerivAt.localInverse f f' a hf) (f'.symm : F →L[𝕜] E) (f a) := HasStrictFDerivAt.to_localInverse hf
• MIL/C09_Differential_Calculus/solutions/Solutions_S01_Elementary_Differential_Calculus.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv import Mathlib.Analysis.Calculus.MeanValue
• MIL/C09_Differential_Calculus/solutions/Solutions_S02_Differential_Calculus_in_Normed_Spaces.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.NormedSpace.BanachSteinhaus import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Calculus.Inverse
• MIL/C10_Integration_and_Measure_Theory/S01_Elementary_Integration.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.MeasureTheory.Integral.IntervalIntegral import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.Analysis.Convolution
• MIL/C10_Integration_and_Measure_Theory/S02_Measure_Theory.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• MIL/C10_Integration_and_Measure_Theory/S03_Integration.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
  • @@ -25,8 +24,6 @@ example {f g : α → E} (hf : Integrable f μ) (hg : Integrable g μ) :
    example {s : Set α} (c : E) : (∫ x in s, c ∂μ) = (μ s).toReal • c := set_integral_const c - open Filter - example {F : ℕ → α → E} {f : α → E} (bound : α → ℝ) (hmeas : ∀ n, AEStronglyMeasurable (F n) μ) (hint : Integrable bound μ) (hbound : ∀ n, ∀ᵐ a ∂μ, ‖F n a‖ ≤ bound a) (hlim : ∀ᵐ a ∂μ, Tendsto (fun n : ℕ ↦ F n a) atTop (𝓝 (f a))) :
• MIL/C10_Integration_and_Measure_Theory/solutions/Solutions_S01_Elementary_Integration.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.MeasureTheory.Integral.IntervalIntegral import Mathlib.Analysis.SpecialFunctions.Integrals import Mathlib.Analysis.Convolution
• MIL/C10_Integration_and_Measure_Theory/solutions/Solutions_S02_Measure_Theory.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• MIL/C10_Integration_and_Measure_Theory/solutions/Solutions_S03_Integration.lean
  • @@ -1,4 +1,3 @@
    - import Mathlib.Tactic import Mathlib.Analysis.NormedSpace.FiniteDimension import Mathlib.Analysis.Convolution import Mathlib.MeasureTheory.Function.Jacobian
• html/.buildinfo
  • @@ -1,4 +1,4 @@
    # Sphinx build info version 1 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. - config: 803b947a09f3db5a52c6c529e3761a53 + config: dfa3c760a9c309561b2de03685612f6b tags: 645f666f9bcd5a90fca523b33c5a78b7
• html/C01_Introduction.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>1. Introduction &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
  • @@ -12,10 +13,11 @@
    <script src="_static/js/html5shiv.min.js"></script> <![endif]--> - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> <script src="_static/jquery.js"></script> - <script src="_static/underscore.js"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js"></script> + <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> <script src="_static/doctools.js"></script> + <script src="_static/sphinx_highlight.js"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" />
  • @@ -28,11 +30,15 @@
    <nav data-toggle="wy-nav-shift" class="wy-nav-side"> <div class="wy-side-scroll"> <div class="wy-side-nav-search" > - <a href="index.html" class="icon icon-home"> Mathematics in Lean + + + + <a href="index.html" class="icon icon-home"> + Mathematics in Lean </a> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> - <input type="text" name="q" placeholder="Search docs" /> + <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form>
  • @@ -71,8 +77,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">1. </span>Introduction</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">1. </span>Introduction</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C01_Introduction.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -82,10 +88,10 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="introduction"> - <span id="id1"></span><h1><span class="section-number">1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">&#61633;</a></h1> - <div class="section" id="getting-started"> - <h2><span class="section-number">1.1. </span>Getting Started<a class="headerlink" href="#getting-started" title="Permalink to this headline">&#61633;</a></h2> + <section id="introduction"> + <span id="id1"></span><h1><span class="section-number">1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">&#61633;</a></h1> + <section id="getting-started"> + <h2><span class="section-number">1.1. </span>Getting Started<a class="headerlink" href="#getting-started" title="Permalink to this heading">&#61633;</a></h2> <p>The goal of this book is to teach you to formalize mathematics using the Lean 4 interactive proof assistant. It assumes that you know some mathematics, but it does not require much.
  • @@ -157,9 +163,9 @@ Lean is about <em>doing</em> mathematics interactively, not just reading about i
    Working through the exercises is central to the experience. You can always compare your solutions to the ones in the <code class="docutils literal notranslate"><span class="pre">solutions</span></code> folder associated with each section.</p> - </div> - <div class="section" id="overview"> - <h2><span class="section-number">1.2. </span>Overview<a class="headerlink" href="#overview" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="overview"> + <h2><span class="section-number">1.2. </span>Overview<a class="headerlink" href="#overview" title="Permalink to this heading">&#61633;</a></h2> <p>Put simply, Lean is a tool for building complex expressions in a formal language known as <em>dependent type theory</em>.</p> <p id="index-0">Every expression has a <em>type</em>, and you can use the <cite>#check</cite> command to
  • @@ -327,8 +333,8 @@ Giovanni Mascellani, Hunter Monroe, Pietro Monticone, Bartosz Piotrowski,
    and Guilherme Silva. Our work has been partially supported by the Hoskinson Center for Formal Mathematics.</p> - </div> - </div> + </section> + </section> </div>
• html/C02_Basics.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>2. Basics &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
  • @@ -12,10 +13,11 @@
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  • @@ -86,14 +92,14 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="basics"> - <span id="id1"></span><h1><span class="section-number">2. </span>Basics<a class="headerlink" href="#basics" title="Permalink to this headline">&#61633;</a></h1> + <section id="basics"> + <span id="id1"></span><h1><span class="section-number">2. </span>Basics<a class="headerlink" href="#basics" title="Permalink to this heading">&#61633;</a></h1> <p>This chapter is designed to introduce you to the nuts and bolts of mathematical reasoning in Lean: calculating, applying lemmas and theorems, and reasoning about generic structures.</p> - <div class="section" id="calculating"> - <h2><span class="section-number">2.1. </span>Calculating<a class="headerlink" href="#calculating" title="Permalink to this headline">&#61633;</a></h2> + <section id="calculating"> + <h2><span class="section-number">2.1. </span>Calculating<a class="headerlink" href="#calculating" title="Permalink to this heading">&#61633;</a></h2> <p>We generally learn to carry out mathematical calculations without thinking of them as proofs. But when we justify each step in a calculation,
  • @@ -115,10 +121,7 @@ so the left-hand side of <code class="docutils literal notranslate"><span class=
    However, it is generally good style to be mindful of Lean&#8217;s notational conventions and leave out parentheses when Lean does as well.</p> <p>Let&#8217;s try out <code class="docutils literal notranslate"><span class="pre">rw</span></code>.</p> - <div class="highlight-lean notranslate" id="index-1"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="n">Mathlib.Tactic</span> - <span class="kn">import</span> <span class="n">Mathlib.Data.Real.Basic</span> - - <span class="kd">example</span> <span class="o">(</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">)</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">*</span> <span class="n">b</span> <span class="bp">*</span> <span class="n">c</span> <span class="bp">=</span> <span class="n">b</span> <span class="bp">*</span> <span class="o">(</span><span class="n">a</span> <span class="bp">*</span> <span class="n">c</span><span class="o">)</span> <span class="o">:=</span> <span class="kd">by</span> + <div class="highlight-lean notranslate" id="index-1"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">(</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">)</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">*</span> <span class="n">b</span> <span class="bp">*</span> <span class="n">c</span> <span class="bp">=</span> <span class="n">b</span> <span class="bp">*</span> <span class="o">(</span><span class="n">a</span> <span class="bp">*</span> <span class="n">c</span><span class="o">)</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">rw</span> <span class="o">[</span><span class="n">mul_comm</span> <span class="n">a</span> <span class="n">b</span><span class="o">]</span> <span class="n">rw</span> <span class="o">[</span><span class="n">mul_assoc</span> <span class="n">b</span> <span class="n">a</span> <span class="n">c</span><span class="o">]</span> </pre></div>
  • @@ -232,7 +235,7 @@ by listing the relevant identities separated by commas inside the square bracket
    a comma in any list of rewrites.</p> <p>Another trick is that we can declare variables once and for all outside an example or theorem. Lean then includes them automatically.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">variable</span> <span class="o">(</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span> <span class="n">e</span> <span class="n">f</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">)</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">variable</span> <span class="o">(</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span> <span class="n">e</span> <span class="n">f</span> <span class="n">g</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">)</span> <span class="kd">example</span> <span class="o">(</span><span class="n">h</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">*</span> <span class="n">b</span> <span class="bp">=</span> <span class="n">c</span> <span class="bp">*</span> <span class="n">d</span><span class="o">)</span> <span class="o">(</span><span class="n">h&#39;</span> <span class="o">:</span> <span class="n">e</span> <span class="bp">=</span> <span class="n">f</span><span class="o">)</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">*</span> <span class="o">(</span><span class="n">b</span> <span class="bp">*</span> <span class="n">e</span><span class="o">)</span> <span class="bp">=</span> <span class="n">c</span> <span class="bp">*</span> <span class="o">(</span><span class="n">d</span> <span class="bp">*</span> <span class="n">f</span><span class="o">)</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">rw</span> <span class="o">[</span><span class="n">h&#39;</span><span class="o">,</span> <span class="bp">&#8592;</span> <span class="n">mul_assoc</span><span class="o">,</span> <span class="n">h</span><span class="o">,</span> <span class="n">mul_assoc</span><span class="o">]</span>
  • @@ -255,6 +258,7 @@ command to determine the type of an expression:</p>
    <span class="k">#check</span> <span class="n">mul_assoc</span> <span class="n">c</span> <span class="n">a</span> <span class="n">b</span> <span class="k">#check</span> <span class="n">mul_comm</span> <span class="n">a</span> <span class="k">#check</span> <span class="n">mul_comm</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">mul_comm</span> <span class="kd">end</span> </pre></div>
  • @@ -386,9 +390,9 @@ occurrence of <code class="docutils literal notranslate"><span class="pre">a</sp
    <span class="n">rw</span> <span class="o">[</span><span class="n">add_mul</span><span class="o">]</span> </pre></div> </div> - </div> - <div class="section" id="proving-identities-in-algebraic-structures"> - <span id="id2"></span><h2><span class="section-number">2.2. </span>Proving Identities in Algebraic Structures<a class="headerlink" href="#proving-identities-in-algebraic-structures" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="proving-identities-in-algebraic-structures"> + <span id="id2"></span><h2><span class="section-number">2.2. </span>Proving Identities in Algebraic Structures<a class="headerlink" href="#proving-identities-in-algebraic-structures" title="Permalink to this heading">&#61633;</a></h2> <p id="index-7">Mathematically, a ring consists of a collection of objects, <span class="math notranslate nohighlight">\(R\)</span>, operations <span class="math notranslate nohighlight">\(+\)</span> <span class="math notranslate nohighlight">\(\times\)</span>, and constants <span class="math notranslate nohighlight">\(0\)</span> and <span class="math notranslate nohighlight">\(1\)</span>, and an operation <span class="math notranslate nohighlight">\(x \mapsto -x\)</span> such that:</p>
  • @@ -494,8 +498,8 @@ as ring axioms, because they follow from the other axioms.</p>
    <span class="kd">theorem</span> <span class="n">add_right_neg</span> <span class="o">(</span><span class="n">a</span> <span class="o">:</span> <span class="n">R</span><span class="o">)</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">+</span> <span class="bp">-</span><span class="n">a</span> <span class="bp">=</span> <span class="mi">0</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">rw</span> <span class="o">[</span><span class="n">add_comm</span><span class="o">,</span> <span class="n">add_left_neg</span><span class="o">]</span> - <span class="k">#check</span> <span class="n">MyRing.add_zero</span> - <span class="k">#check</span> <span class="n">add_zero</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">MyRing.add_zero</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">add_zero</span> <span class="kd">end</span> <span class="n">MyRing</span> </pre></div>
  • @@ -707,9 +711,9 @@ It may seem odd that the algebraic structures are called
    <cite>noncomm_ring</cite> and <cite>ring</cite>. This is partly for historical reasons, but also for the convenience of using a shorter name for the tactic that deals with commutative rings, since it is used more often.</p> - </div> - <div class="section" id="using-theorems-and-lemmas"> - <span id="id3"></span><h2><span class="section-number">2.3. </span>Using Theorems and Lemmas<a class="headerlink" href="#using-theorems-and-lemmas" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="using-theorems-and-lemmas"> + <span id="id3"></span><h2><span class="section-number">2.3. </span>Using Theorems and Lemmas<a class="headerlink" href="#using-theorems-and-lemmas" title="Permalink to this heading">&#61633;</a></h2> <p id="index-15">Rewriting is great for proving equations, but what about other sorts of theorems? For example, how can we prove an inequality,
  • @@ -833,7 +837,7 @@ inequalities on the real numbers.</p>
    <span class="k">#check</span> <span class="o">(</span><span class="n">add_pos</span> <span class="o">:</span> <span class="mi">0</span> <span class="bp">&lt;</span> <span class="n">a</span> <span class="bp">&#8594;</span> <span class="mi">0</span> <span class="bp">&lt;</span> <span class="n">b</span> <span class="bp">&#8594;</span> <span class="mi">0</span> <span class="bp">&lt;</span> <span class="n">a</span> <span class="bp">+</span> <span class="n">b</span><span class="o">)</span> <span class="k">#check</span> <span class="o">(</span><span class="n">add_pos_of_pos_of_nonneg</span> <span class="o">:</span> <span class="mi">0</span> <span class="bp">&lt;</span> <span class="n">a</span> <span class="bp">&#8594;</span> <span class="mi">0</span> <span class="bp">&#8804;</span> <span class="n">b</span> <span class="bp">&#8594;</span> <span class="mi">0</span> <span class="bp">&lt;</span> <span class="n">a</span> <span class="bp">+</span> <span class="n">b</span><span class="o">)</span> <span class="k">#check</span> <span class="o">(</span><span class="n">exp_pos</span> <span class="o">:</span> <span class="bp">&#8704;</span> <span class="n">a</span><span class="o">,</span> <span class="mi">0</span> <span class="bp">&lt;</span> <span class="n">exp</span> <span class="n">a</span><span class="o">)</span> - <span class="k">#check</span> <span class="n">add_le_add_left</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">add_le_add_left</span> </pre></div> </div> <p>Some of the theorems, <code class="docutils literal notranslate"><span class="pre">exp_le_exp</span></code>, <code class="docutils literal notranslate"><span class="pre">exp_lt_exp</span></code>, and <code class="docutils literal notranslate"><span class="pre">log_le_log</span></code>
  • @@ -974,9 +978,9 @@ following theorem. You can use the theorem <code class="docutils literal notrans
    </div> <p>If you managed to solve this, congratulations! You are well on your way to becoming a master formalizer.</p> - </div> - <div class="section" id="more-examples-using-apply-and-rw"> - <span id="more-on-order-and-divisibility"></span><h2><span class="section-number">2.4. </span>More examples using apply and rw<a class="headerlink" href="#more-examples-using-apply-and-rw" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="more-examples-using-apply-and-rw"> + <span id="more-on-order-and-divisibility"></span><h2><span class="section-number">2.4. </span>More examples using apply and rw<a class="headerlink" href="#more-examples-using-apply-and-rw" title="Permalink to this heading">&#61633;</a></h2> <p id="index-20">The <code class="docutils literal notranslate"><span class="pre">min</span></code> function on the real numbers is uniquely characterized by the following three facts:</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="o">(</span><span class="n">min_le_left</span> <span class="n">a</span> <span class="n">b</span> <span class="o">:</span> <span class="n">min</span> <span class="n">a</span> <span class="n">b</span> <span class="bp">&#8804;</span> <span class="n">a</span><span class="o">)</span>
  • @@ -1183,9 +1187,9 @@ theorem and the version <code class="docutils literal notranslate"><span class="
    the one specifically for the natural numbers. You can use <code class="docutils literal notranslate"><span class="pre">_root_.dvd_antisymm</span></code> to specify the generic one; either one will work.</p> - </div> - <div class="section" id="proving-facts-about-algebraic-structures"> - <span id="id4"></span><h2><span class="section-number">2.5. </span>Proving Facts about Algebraic Structures<a class="headerlink" href="#proving-facts-about-algebraic-structures" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="proving-facts-about-algebraic-structures"> + <span id="id4"></span><h2><span class="section-number">2.5. </span>Proving Facts about Algebraic Structures<a class="headerlink" href="#proving-facts-about-algebraic-structures" title="Permalink to this heading">&#61633;</a></h2> <p id="index-26">In <a class="reference internal" href="#proving-identities-in-algebraic-structures"><span class="std std-numref">Section 2.2</span></a>, we saw that many common identities governing the real numbers hold in more general classes of algebraic structures,
  • @@ -1398,8 +1402,8 @@ always nonnegative:</p>
    </div> <p>We recommend making use of the theorem <code class="docutils literal notranslate"><span class="pre">nonneg_of_mul_nonneg_left</span></code>. As you may have guessed, this theorem is called <code class="docutils literal notranslate"><span class="pre">dist_nonneg</span></code> in mathlib.</p> - </div> - </div> + </section> + </section> </div>
• html/C03_Logic.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>3. Logic &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
  • @@ -12,10 +13,11 @@
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  • @@ -29,11 +31,15 @@
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  • @@ -76,8 +82,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">3. </span>Logic</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">3. </span>Logic</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C03_Logic.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -87,8 +93,8 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="logic"> - <span id="id1"></span><h1><span class="section-number">3. </span>Logic<a class="headerlink" href="#logic" title="Permalink to this headline">&#61633;</a></h1> + <section id="logic"> + <span id="id1"></span><h1><span class="section-number">3. </span>Logic<a class="headerlink" href="#logic" title="Permalink to this heading">&#61633;</a></h1> <p>In the last chapter, we dealt with equations, inequalities, and basic mathematical statements like &#8220;<span class="math notranslate nohighlight">\(x\)</span> divides <span class="math notranslate nohighlight">\(y\)</span>.&#8221;
  • @@ -98,8 +104,8 @@ using logical terms like &#8220;and,&#8221; &#8220;or,&#8221; &#8220;not,&#8221;
    &#8220;if &#8230; then,&#8221; &#8220;every,&#8221; and &#8220;some.&#8221; In this chapter, we show you how to work with statements that are built up in this way.</p> - <div class="section" id="implication-and-the-universal-quantifier"> - <span id="id2"></span><h2><span class="section-number">3.1. </span>Implication and the Universal Quantifier<a class="headerlink" href="#implication-and-the-universal-quantifier" title="Permalink to this headline">&#61633;</a></h2> + <section id="implication-and-the-universal-quantifier"> + <span id="id2"></span><h2><span class="section-number">3.1. </span>Implication and the Universal Quantifier<a class="headerlink" href="#implication-and-the-universal-quantifier" title="Permalink to this heading">&#61633;</a></h2> <p>Consider the statement after the <code class="docutils literal notranslate"><span class="pre">#check</span></code>:</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="bp">&#8704;</span> <span class="n">x</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">,</span> <span class="mi">0</span> <span class="bp">&#8804;</span> <span class="n">x</span> <span class="bp">&#8594;</span> <span class="bp">|</span><span class="n">x</span><span class="bp">|</span> <span class="bp">=</span> <span class="n">x</span> </pre></div>
  • @@ -281,7 +287,7 @@ So if we prove the theorem <code class="docutils literal notranslate"><span clas
    it will apply in all these instances.</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">variable</span> <span class="o">{</span><span class="n">&#945;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">{</span><span class="n">R</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">OrderedCancelAddCommMonoid</span> <span class="n">R</span><span class="o">]</span> - <span class="k">#check</span> <span class="n">add_le_add</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">add_le_add</span> <span class="kd">def</span> <span class="n">FnUb&#39;</span> <span class="o">(</span><span class="n">f</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">R</span><span class="o">)</span> <span class="o">(</span><span class="n">a</span> <span class="o">:</span> <span class="n">R</span><span class="o">)</span> <span class="o">:</span> <span class="kt">Prop</span> <span class="o">:=</span> <span class="bp">&#8704;</span> <span class="n">x</span><span class="o">,</span> <span class="n">f</span> <span class="n">x</span> <span class="bp">&#8804;</span> <span class="n">a</span>
  • @@ -487,9 +493,9 @@ a lemma name.</p>
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="the-existential-quantifier"> - <span id="id3"></span><h2><span class="section-number">3.2. </span>The Existential Quantifier<a class="headerlink" href="#the-existential-quantifier" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="the-existential-quantifier"> + <span id="id3"></span><h2><span class="section-number">3.2. </span>The Existential Quantifier<a class="headerlink" href="#the-existential-quantifier" title="Permalink to this heading">&#61633;</a></h2> <p>The existential quantifier, which can be entered as <code class="docutils literal notranslate"><span class="pre">\ex</span></code> in VS Code, is used to represent the phrase &#8220;there exists.&#8221; The formal expression <code class="docutils literal notranslate"><span class="pre">&#8707;</span> <span class="pre">x</span> <span class="pre">:</span> <span class="pre">&#8477;,</span> <span class="pre">2</span> <span class="pre">&lt;</span> <span class="pre">x</span> <span class="pre">&#8743;</span> <span class="pre">x</span> <span class="pre">&lt;</span> <span class="pre">3</span></code> in Lean says
  • @@ -757,9 +763,9 @@ the composition of surjective functions is surjective.</p>
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="negation"> - <span id="id4"></span><h2><span class="section-number">3.3. </span>Negation<a class="headerlink" href="#negation" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="negation"> + <span id="id4"></span><h2><span class="section-number">3.3. </span>Negation<a class="headerlink" href="#negation" title="Permalink to this heading">&#61633;</a></h2> <p>The symbol <code class="docutils literal notranslate"><span class="pre">&#172;</span></code> is meant to express negation, so <code class="docutils literal notranslate"><span class="pre">&#172;</span> <span class="pre">x</span> <span class="pre">&lt;</span> <span class="pre">y</span></code> says that <code class="docutils literal notranslate"><span class="pre">x</span></code> is not less than <code class="docutils literal notranslate"><span class="pre">y</span></code>, <code class="docutils literal notranslate"><span class="pre">&#172;</span> <span class="pre">x</span> <span class="pre">=</span> <span class="pre">y</span></code> (or, equivalently, <code class="docutils literal notranslate"><span class="pre">x</span> <span class="pre">&#8800;</span> <span class="pre">y</span></code>) says that
  • @@ -1024,9 +1030,9 @@ Finally, the <code class="docutils literal notranslate"><span class="pre">contra
    by finding a contradiction in the hypotheses, such as a pair of the form <code class="docutils literal notranslate"><span class="pre">h</span> <span class="pre">:</span> <span class="pre">P</span></code> and <code class="docutils literal notranslate"><span class="pre">h'</span> <span class="pre">:</span> <span class="pre">&#172;</span> <span class="pre">P</span></code>. Of course, in this example, <code class="docutils literal notranslate"><span class="pre">linarith</span></code> also works.</p> - </div> - <div class="section" id="conjunction-and-bi-implication"> - <span id="conjunction-and-biimplication"></span><h2><span class="section-number">3.4. </span>Conjunction and Bi-implication<a class="headerlink" href="#conjunction-and-bi-implication" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="conjunction-and-bi-implication"> + <span id="conjunction-and-biimplication"></span><h2><span class="section-number">3.4. </span>Conjunction and Bi-implication<a class="headerlink" href="#conjunction-and-bi-implication" title="Permalink to this heading">&#61633;</a></h2> <p id="index-18">You have already seen that the conjunction symbol, <code class="docutils literal notranslate"><span class="pre">&#8743;</span></code>, is used to express &#8220;and.&#8221; The <code class="docutils literal notranslate"><span class="pre">constructor</span></code> tactic allows you to prove a statement of
  • @@ -1256,9 +1262,9 @@ to be instantiated to different values.</p>
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="disjunction"> - <span id="id5"></span><h2><span class="section-number">3.5. </span>Disjunction<a class="headerlink" href="#disjunction" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="disjunction"> + <span id="id5"></span><h2><span class="section-number">3.5. </span>Disjunction<a class="headerlink" href="#disjunction" title="Permalink to this heading">&#61633;</a></h2> <p id="index-21">The canonical way to prove a disjunction <code class="docutils literal notranslate"><span class="pre">A</span> <span class="pre">&#8744;</span> <span class="pre">B</span></code> is to prove <code class="docutils literal notranslate"><span class="pre">A</span></code> or to prove <code class="docutils literal notranslate"><span class="pre">B</span></code>. The <code class="docutils literal notranslate"><span class="pre">left</span></code> tactic chooses <code class="docutils literal notranslate"><span class="pre">A</span></code>,
  • @@ -1451,9 +1457,9 @@ using <code class="docutils literal notranslate"><span class="pre">by_cases</spa
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="sequences-and-convergence"> - <span id="id6"></span><h2><span class="section-number">3.6. </span>Sequences and Convergence<a class="headerlink" href="#sequences-and-convergence" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="sequences-and-convergence"> + <span id="id6"></span><h2><span class="section-number">3.6. </span>Sequences and Convergence<a class="headerlink" href="#sequences-and-convergence" title="Permalink to this heading">&#61633;</a></h2> <p>We now have enough skills at our disposal to do some real mathematics. In Lean, we can represent a sequence <span class="math notranslate nohighlight">\(s_0, s_1, s_2, \ldots\)</span> of real numbers as a function <code class="docutils literal notranslate"><span class="pre">s</span> <span class="pre">:</span> <span class="pre">&#8469;</span> <span class="pre">&#8594;</span> <span class="pre">&#8477;</span></code>.
  • @@ -1688,8 +1694,8 @@ for dealing with convergence in vastly more general terms,
    not only abstracting away particular features of the domain and codomain, but also abstracting over different types of convergence.</p> - </div> - </div> + </section> + </section> </div>
• html/C04_Sets_and_Functions.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>4. Sets and Functions &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
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  • @@ -29,11 +31,15 @@
    <nav data-toggle="wy-nav-shift" class="wy-nav-side"> <div class="wy-side-scroll"> <div class="wy-side-nav-search" > - <a href="index.html" class="icon icon-home"> Mathematics in Lean + + + + <a href="index.html" class="icon icon-home"> + Mathematics in Lean </a> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> - <input type="text" name="q" placeholder="Search docs" /> + <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form>
  • @@ -73,8 +79,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">4. </span>Sets and Functions</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">4. </span>Sets and Functions</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C04_Sets_and_Functions.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -84,8 +90,8 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="sets-and-functions"> - <span id="id1"></span><h1><span class="section-number">4. </span>Sets and Functions<a class="headerlink" href="#sets-and-functions" title="Permalink to this headline">&#61633;</a></h1> + <section id="sets-and-functions"> + <span id="id1"></span><h1><span class="section-number">4. </span>Sets and Functions<a class="headerlink" href="#sets-and-functions" title="Permalink to this heading">&#61633;</a></h1> <p>The vocabulary of sets, relations, and functions provides a uniform language for carrying out constructions in all the branches of mathematics.
  • @@ -117,8 +123,8 @@ such as a set natural numbers or a set of functions
    from real numbers to real numbers. The distinction between types and set takes some getting used to, but this chapter will take you through the essentials.</p> - <div class="section" id="sets"> - <span id="id2"></span><h2><span class="section-number">4.1. </span>Sets<a class="headerlink" href="#sets" title="Permalink to this headline">&#61633;</a></h2> + <section id="sets"> + <span id="id2"></span><h2><span class="section-number">4.1. </span>Sets<a class="headerlink" href="#sets" title="Permalink to this heading">&#61633;</a></h2> <p id="index-0">If <code class="docutils literal notranslate"><span class="pre">&#945;</span></code> is any type, the type <code class="docutils literal notranslate"><span class="pre">Set</span> <span class="pre">&#945;</span></code> consists of sets of elements of <code class="docutils literal notranslate"><span class="pre">&#945;</span></code>. This type supports the usual set-theoretic operations and relations.
  • @@ -559,9 +565,9 @@ and intersection.</p>
    </div> <p>In the library, these identities are called <code class="docutils literal notranslate"><span class="pre">sUnion_eq_biUnion</span></code> and <code class="docutils literal notranslate"><span class="pre">sInter_eq_biInter</span></code>.</p> - </div> - <div class="section" id="functions"> - <span id="id3"></span><h2><span class="section-number">4.2. </span>Functions<a class="headerlink" href="#functions" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="functions"> + <span id="id3"></span><h2><span class="section-number">4.2. </span>Functions<a class="headerlink" href="#functions" title="Permalink to this heading">&#61633;</a></h2> <p>If <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">:</span> <span class="pre">&#945;</span> <span class="pre">&#8594;</span> <span class="pre">&#946;</span></code> is a function and <code class="docutils literal notranslate"><span class="pre">p</span></code> is a set of elements of type <code class="docutils literal notranslate"><span class="pre">&#946;</span></code>, the library defines <code class="docutils literal notranslate"><span class="pre">preimage</span> <span class="pre">f</span> <span class="pre">p</span></code>, written <code class="docutils literal notranslate"><span class="pre">f</span> <span class="pre">&#8315;&#185;'</span> <span class="pre">p</span></code>,
  • @@ -886,9 +892,9 @@ and then fill in the two lines that are missing.</p>
    <span class="n">contradiction</span> </pre></div> </div> - </div> - <div class="section" id="the-schroder-bernstein-theorem"> - <span id="the-schroeder-bernstein-theorem"></span><h2><span class="section-number">4.3. </span>The Schr&#246;der-Bernstein Theorem<a class="headerlink" href="#the-schroder-bernstein-theorem" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="the-schroder-bernstein-theorem"> + <span id="the-schroeder-bernstein-theorem"></span><h2><span class="section-number">4.3. </span>The Schr&#246;der-Bernstein Theorem<a class="headerlink" href="#the-schroder-bernstein-theorem" title="Permalink to this heading">&#61633;</a></h2> <p>We close this chapter with an elementary but nontrivial theorem of set theory. Let <span class="math notranslate nohighlight">\(\alpha\)</span> and <span class="math notranslate nohighlight">\(\beta\)</span> be sets. (In our formalization, they will actually be types.)
  • @@ -1147,8 +1153,8 @@ and the proof uses the fact that <code class="docutils literal notranslate"><spa
    <span class="o">&#10216;</span><span class="n">sbFun</span> <span class="n">f</span> <span class="n">g</span><span class="o">,</span> <span class="n">sb_injective</span> <span class="n">f</span> <span class="n">g</span> <span class="n">hf</span> <span class="n">hg</span><span class="o">,</span> <span class="n">sb_surjective</span> <span class="n">f</span> <span class="n">g</span> <span class="n">hf</span> <span class="n">hg</span><span class="o">&#10217;</span> </pre></div> </div> - </div> - </div> + </section> + </section> </div>
• html/C05_Number_Theory.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>5. Elementary Number Theory &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
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  • @@ -29,11 +31,15 @@
    <nav data-toggle="wy-nav-shift" class="wy-nav-side"> <div class="wy-side-scroll"> <div class="wy-side-nav-search" > - <a href="index.html" class="icon icon-home"> Mathematics in Lean + + + + <a href="index.html" class="icon icon-home"> + Mathematics in Lean </a> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> - <input type="text" name="q" placeholder="Search docs" /> + <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form>
  • @@ -73,8 +79,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">5. </span>Elementary Number Theory</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">5. </span>Elementary Number Theory</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C05_Number_Theory.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -84,15 +90,15 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="elementary-number-theory"> - <span id="number-theory"></span><h1><span class="section-number">5. </span>Elementary Number Theory<a class="headerlink" href="#elementary-number-theory" title="Permalink to this headline">&#61633;</a></h1> + <section id="elementary-number-theory"> + <span id="number-theory"></span><h1><span class="section-number">5. </span>Elementary Number Theory<a class="headerlink" href="#elementary-number-theory" title="Permalink to this heading">&#61633;</a></h1> <p>In this chapter, we show you how to formalize some elementary results in number theory. As we deal with more substantive mathematical content, the proofs will get longer and more involved, building on the skills you have already mastered.</p> - <div class="section" id="irrational-roots"> - <span id="section-irrational-roots"></span><h2><span class="section-number">5.1. </span>Irrational Roots<a class="headerlink" href="#irrational-roots" title="Permalink to this headline">&#61633;</a></h2> + <section id="irrational-roots"> + <span id="section-irrational-roots"></span><h2><span class="section-number">5.1. </span>Irrational Roots<a class="headerlink" href="#irrational-roots" title="Permalink to this heading">&#61633;</a></h2> <p>Let&#8217;s start with a fact known to the ancient greeks, namely, that the square root of 2 is irrational. If we suppose otherwise,
  • @@ -145,7 +151,7 @@ to the natural numbers.</p>
    <p>We also need the notion of a prime number, <code class="docutils literal notranslate"><span class="pre">Nat.Prime</span></code>. The theorem <code class="docutils literal notranslate"><span class="pre">Nat.prime_def_lt</span></code> provides one familiar characterization, and <code class="docutils literal notranslate"><span class="pre">Nat.Prime.eq_one_or_self_of_dvd</span></code> provides another.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="n">Nat.prime_def_lt</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="bp">@</span><span class="n">Nat.prime_def_lt</span> <span class="kd">example</span> <span class="o">(</span><span class="n">p</span> <span class="o">:</span> <span class="n">&#8469;</span><span class="o">)</span> <span class="o">(</span><span class="n">prime_p</span> <span class="o">:</span> <span class="n">Nat.Prime</span> <span class="n">p</span><span class="o">)</span> <span class="o">:</span> <span class="mi">2</span> <span class="bp">&#8804;</span> <span class="n">p</span> <span class="bp">&#8743;</span> <span class="bp">&#8704;</span> <span class="n">m</span> <span class="o">:</span> <span class="n">&#8469;</span><span class="o">,</span> <span class="n">m</span> <span class="bp">&lt;</span> <span class="n">p</span> <span class="bp">&#8594;</span> <span class="n">m</span> <span class="bp">&#8739;</span> <span class="n">p</span> <span class="bp">&#8594;</span> <span class="n">m</span> <span class="bp">=</span> <span class="mi">1</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">rwa</span> <span class="o">[</span><span class="n">Nat.prime_def_lt</span><span class="o">]</span> <span class="n">at</span> <span class="n">prime_p</span>
  • @@ -180,7 +186,7 @@ if the square of a number is even, then that number is even as well.
    Mathlib defines the predicate <code class="docutils literal notranslate"><span class="pre">Even</span></code> in <code class="docutils literal notranslate"><span class="pre">Data.Nat.Parity</span></code>, but for reasons that will become clear below, we will simply use <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">&#8739;</span> <span class="pre">m</span></code> to express that <code class="docutils literal notranslate"><span class="pre">m</span></code> is even.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="n">Nat.Prime.dvd_mul</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="bp">@</span><span class="n">Nat.Prime.dvd_mul</span> <span class="k">#check</span> <span class="n">Nat.Prime.dvd_mul</span> <span class="n">Nat.prime_two</span> <span class="k">#check</span> <span class="n">Nat.prime_two.dvd_mul</span>
  • @@ -391,9 +397,9 @@ and that it takes values in the extended natural numbers <code class="docutils l
    which adds the value infinity to the natural numbers. In the next chapter, we will begin to develop the means to appreciate the way that Lean supports this sort of generality.</p> - </div> - <div class="section" id="induction-and-recursion"> - <span id="section-induction-and-recursion"></span><h2><span class="section-number">5.2. </span>Induction and Recursion<a class="headerlink" href="#induction-and-recursion" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="induction-and-recursion"> + <span id="section-induction-and-recursion"></span><h2><span class="section-number">5.2. </span>Induction and Recursion<a class="headerlink" href="#induction-and-recursion" title="Permalink to this heading">&#61633;</a></h2> <p>The set of natural numbers <span class="math notranslate nohighlight">\(\mathbb{N} = \{ 0, 1, 2, \ldots \}\)</span> is not only fundamentally important in its own right, but also a plays a central role in the construction of new mathematical objects.
  • @@ -696,9 +702,9 @@ The function <code class="docutils literal notranslate"><span class="pre">pred</
    <span class="kd">end</span> <span class="n">MyNat</span> </pre></div> </div> - </div> - <div class="section" id="infinitely-many-primes"> - <span id="section-infinitely-many-primes"></span><h2><span class="section-number">5.3. </span>Infinitely Many Primes<a class="headerlink" href="#infinitely-many-primes" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="infinitely-many-primes"> + <span id="section-infinitely-many-primes"></span><h2><span class="section-number">5.3. </span>Infinitely Many Primes<a class="headerlink" href="#infinitely-many-primes" title="Permalink to this heading">&#61633;</a></h2> <p>Let us continue our exploration of induction and recursion with another mathematical standard: a proof that there are infinitely many primes. One way to formulate this is as the statement that
  • @@ -1138,8 +1144,8 @@ along the way.</p>
    </div> <p>If you managed to complete the proof, congratulations! This has been a serious feat of formalization.</p> - </div> - </div> + </section> + </section> </div>
• html/C06_Structures.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>6. Structures &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
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    <script src="_static/js/html5shiv.min.js"></script> <![endif]--> - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> <script src="_static/jquery.js"></script> - <script src="_static/underscore.js"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js"></script> + <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> <script src="_static/doctools.js"></script> + <script src="_static/sphinx_highlight.js"></script> <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" />
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    <nav data-toggle="wy-nav-shift" class="wy-nav-side"> <div class="wy-side-scroll"> <div class="wy-side-nav-search" > - <a href="index.html" class="icon icon-home"> Mathematics in Lean + + + + <a href="index.html" class="icon icon-home"> + Mathematics in Lean </a> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> - <input type="text" name="q" placeholder="Search docs" /> + <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form>
  • @@ -73,8 +79,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">6. </span>Structures</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">6. </span>Structures</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C06_Structures.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -84,8 +90,8 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="structures"> - <span id="id1"></span><h1><span class="section-number">6. </span>Structures<a class="headerlink" href="#structures" title="Permalink to this headline">&#61633;</a></h1> + <section id="structures"> + <span id="id1"></span><h1><span class="section-number">6. </span>Structures<a class="headerlink" href="#structures" title="Permalink to this heading">&#61633;</a></h1> <p>Modern mathematics makes essential use of algebraic structures, which encapsulate patterns that can be instantiated in
  • @@ -104,8 +110,8 @@ It will also show you how to define and use
    algebraic structures on your own.</p> <p>For more technical detail, you can consult <a class="reference external" href="https://leanprover.github.io/theorem_proving_in_lean/">Theorem Proving in Lean</a>, and a paper by Anne Baanen, <a class="reference external" href="https://arxiv.org/abs/2202.01629">Use and abuse of instance parameters in the Lean mathematical library</a>.</p> - <div class="section" id="defining-structures"> - <span id="section-structures"></span><h2><span class="section-number">6.1. </span>Defining structures<a class="headerlink" href="#defining-structures" title="Permalink to this headline">&#61633;</a></h2> + <section id="defining-structures"> + <span id="section-structures"></span><h2><span class="section-number">6.1. </span>Defining structures<a class="headerlink" href="#defining-structures" title="Permalink to this heading">&#61633;</a></h2> <p>In the broadest sense of the term, a <em>structure</em> is a specification of a collection of data, possibly with constraints that the data is required to satisfy.
  • @@ -482,9 +488,9 @@ as long as we redefine the old accessors in terms of the new definition.
    Moreover, as we are about to see, Lean provides support for weaving structures together into a rich, interconnected hierarchy, and for managing the interactions between them.</p> - </div> - <div class="section" id="algebraic-structures"> - <span id="section-algebraic-structures"></span><h2><span class="section-number">6.2. </span>Algebraic Structures<a class="headerlink" href="#algebraic-structures" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="algebraic-structures"> + <span id="section-algebraic-structures"></span><h2><span class="section-number">6.2. </span>Algebraic Structures<a class="headerlink" href="#algebraic-structures" title="Permalink to this heading">&#61633;</a></h2> <p>To clarify what we mean by the phrase <em>algebraic structure</em>, it will help to consider some examples.</p> <ol class="arabic simple">
  • @@ -879,12 +885,12 @@ without troubling us with the details.</p>
    </pre></div> </div> <p>The following illustrates their use.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="n">Group&#8322;.mul</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="bp">@</span><span class="n">Group&#8322;.mul</span> <span class="kd">def</span> <span class="n">mySquare</span> <span class="o">{</span><span class="n">&#945;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">Group&#8322;</span> <span class="n">&#945;</span><span class="o">]</span> <span class="o">(</span><span class="n">x</span> <span class="o">:</span> <span class="n">&#945;</span><span class="o">)</span> <span class="o">:=</span> <span class="n">Group&#8322;.mul</span> <span class="n">x</span> <span class="n">x</span> - <span class="k">#check</span> <span class="n">mySquare</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">mySquare</span> <span class="kn">section</span> <span class="kd">variable</span> <span class="o">{</span><span class="n">&#946;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">(</span><span class="n">f</span> <span class="n">g</span> <span class="o">:</span> <span class="n">Equiv.Perm</span> <span class="n">&#946;</span><span class="o">)</span>
  • @@ -1031,9 +1037,9 @@ because it configures automation that invisibly governs the interpretation of
    the expressions we type. When used wisely, however, class inference is a powerful tool. It is what makes algebraic reasoning possible in Lean.</p> - </div> - <div class="section" id="building-the-gaussian-integers"> - <span id="section-building-the-gaussian-integers"></span><h2><span class="section-number">6.3. </span>Building the Gaussian Integers<a class="headerlink" href="#building-the-gaussian-integers" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="building-the-gaussian-integers"> + <span id="section-building-the-gaussian-integers"></span><h2><span class="section-number">6.3. </span>Building the Gaussian Integers<a class="headerlink" href="#building-the-gaussian-integers" title="Permalink to this heading">&#61633;</a></h2> <p>We will now illustrate the use of the algebraic hierarchy in Lean by building an important mathematical object, the <em>Gaussian integers</em>, and showing that it is a Euclidean domain. In other words, according to
  • @@ -1527,8 +1533,8 @@ the notions of being prime and being irreducible coincide.</p>
    <span class="n">PrincipalIdealRing.irreducible_iff_prime</span> </pre></div> </div> - </div> - </div> + </section> + </section> </div>
• html/C07_Hierarchies.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>7. Hierarchies &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
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    <nav data-toggle="wy-nav-shift" class="wy-nav-side"> <div class="wy-side-scroll"> <div class="wy-side-nav-search" > - <a href="index.html" class="icon icon-home"> Mathematics in Lean + + + + <a href="index.html" class="icon icon-home"> + Mathematics in Lean </a> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> - <input type="text" name="q" placeholder="Search docs" /> + <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form>
  • @@ -72,8 +78,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">7. </span>Hierarchies</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">7. </span>Hierarchies</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C07_Hierarchies.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -83,8 +89,8 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <div class="section" id="hierarchies"> - <span id="id1"></span><h1><span class="section-number">7. </span>Hierarchies<a class="headerlink" href="#hierarchies" title="Permalink to this headline">&#61633;</a></h1> + <section id="hierarchies"> + <span id="id1"></span><h1><span class="section-number">7. </span>Hierarchies<a class="headerlink" href="#hierarchies" title="Permalink to this heading">&#61633;</a></h1> <p>We have seen in <a class="reference internal" href="C06_Structures.html#structures"><span class="std std-numref">Chapter 6</span></a> how to define the class of groups and build instances of this class, and then how to build an instance of the commutative ring class. But of course there is a hierarchy here: a
  • @@ -100,8 +106,8 @@ the following chapters and come back here for a second reading.</p>
    so we will used indices to distinguish our version. For instance we will have <code class="docutils literal notranslate"><span class="pre">Ring&#8321;</span></code> as our version of <code class="docutils literal notranslate"><span class="pre">Ring</span></code>. Since we will gradually explain more powerful ways of formalizing structures, those indices will sometimes grow beyond one.</p> - <div class="section" id="basics"> - <span id="section-hierarchies-basics"></span><h2><span class="section-number">7.1. </span>Basics<a class="headerlink" href="#basics" title="Permalink to this headline">&#61633;</a></h2> + <section id="basics"> + <span id="section-hierarchies-basics"></span><h2><span class="section-number">7.1. </span>Basics<a class="headerlink" href="#basics" title="Permalink to this heading">&#61633;</a></h2> <p>At the very bottom of all hierarchies in Lean, we find data-carrying classes. The following class records that the given type <code class="docutils literal notranslate"><span class="pre">&#945;</span></code> is endowed with a distinguished element called <code class="docutils literal notranslate"><span class="pre">one</span></code>. At this stage, it has no property at all.</p>
  • @@ -484,7 +490,7 @@ type <code class="docutils literal notranslate"><span class="pre">&#946;</span><
    </pre></div> </div> <p>There is something interesting going on here. While it isn&#8217;t too surprising that the - ring structure on <code class="docutils literal notranslate"><span class="pre">R</span></code> is a parameter in this definition, you probably expected <code class="docutils literal notranslate"><span class="pre">AddCommGroup&#8323;</span> <span class="pre">M</span></code> + ring structure on <code class="docutils literal notranslate"><span class="pre">R</span></code> is a parameter in this definition, you probably expected <code class="docutils literal notranslate"><span class="pre">AddCommGroup3</span> <span class="pre">M</span></code> to be part of the <code class="docutils literal notranslate"><span class="pre">extends</span></code> clause just as <code class="docutils literal notranslate"><span class="pre">SMul&#8323;</span> <span class="pre">R</span> <span class="pre">M</span></code> is. Trying to do that would lead to a mysterious sounding error message: <code class="docutils literal notranslate"><span class="pre">cannot</span> <span class="pre">find</span> <span class="pre">synthesization</span> <span class="pre">order</span> <span class="pre">for</span> <span class="pre">instance</span> <span class="pre">Module&#8321;.toAddCommGroup&#8323;</span> <span class="pre">with</span> <span class="pre">type</span> <span class="pre">(R</span> <span class="pre">:</span> <span class="pre">Type)</span> <span class="pre">&#8594;</span> <span class="pre">[inst</span> <span class="pre">:</span> <span class="pre">Ring&#8323;</span> <span class="pre">R]</span> <span class="pre">&#8594;</span> <span class="pre">{M</span> <span class="pre">:</span> <span class="pre">Type}</span> <span class="pre">&#8594;</span> <span class="pre">[self</span> <span class="pre">:</span> <span class="pre">Module&#8321;</span> <span class="pre">R</span> <span class="pre">M]</span> <span class="pre">&#8594;</span> <span class="pre">AddCommGroup&#8323;</span> <span class="pre">M</span>
  • @@ -626,9 +632,9 @@ to incorporate a type class <code class="docutils literal notranslate"><span cla
    that every preorder comes with a <code class="docutils literal notranslate"><span class="pre">&lt;&#8321;</span></code> which has a default value built from <code class="docutils literal notranslate"><span class="pre">&#8804;&#8321;</span></code> and a <code class="docutils literal notranslate"><span class="pre">Prop</span></code>-valued field asserting the natural relation between those two comparison operators. -/</p> - </div> - <div class="section" id="morphisms"> - <span id="section-hierarchies-morphisms"></span><h2><span class="section-number">7.2. </span>Morphisms<a class="headerlink" href="#morphisms" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="morphisms"> + <span id="section-hierarchies-morphisms"></span><h2><span class="section-number">7.2. </span>Morphisms<a class="headerlink" href="#morphisms" title="Permalink to this heading">&#61633;</a></h2> <p>So far in this chapter, we discussed how to create a hierarchy of mathematical structures. But defining structures is not really completed until we have morphisms. There are two main approaches here. The most obvious one is to define a predicate on functions.</p>
  • @@ -830,9 +836,9 @@ definitions below.</p>
    <span class="o">:=</span> <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="sub-objects"> - <span id="section-hierarchies-subobjects"></span><h2><span class="section-number">7.3. </span>Sub-objects<a class="headerlink" href="#sub-objects" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="sub-objects"> + <span id="section-hierarchies-subobjects"></span><h2><span class="section-number">7.3. </span>Sub-objects<a class="headerlink" href="#sub-objects" title="Permalink to this heading">&#61633;</a></h2> <p>After defining some algebraic structure and its morphisms, the next step is to consider sets that inherit this algebraic structure, for instance subgroups or subrings. This largely overlaps our previous topic. Indeed a set in <code class="docutils literal notranslate"><span class="pre">X</span></code> is implemented as a function from
  • @@ -938,9 +944,7 @@ convenient notation are built and code duplication is avoided in Mathlib. Here t
    is the <code class="docutils literal notranslate"><span class="pre">HasQuotient</span></code> class which allows notations like <code class="docutils literal notranslate"><span class="pre">M</span> <span class="pre">&#10744;</span> <span class="pre">N</span></code>. Beware the quotient symbol <code class="docutils literal notranslate"><span class="pre">&#10744;</span></code> is a special unicode character, not a regular ASCII division symbol.</p> <p>As an example, we will build the quotient of a commutative monoid by a submonoid, leave proofs - to you. In the last example, you can use <code class="docutils literal notranslate"><span class="pre">Setoid.refl</span></code> but it won&#8217;t automatically pick up - the relevant <code class="docutils literal notranslate"><span class="pre">Setoid</span></code> structure. You can fix this issue by providing all arguments using - the <code class="docutils literal notranslate"><span class="pre">&#64;</span></code> syntax, as in <code class="docutils literal notranslate"><span class="pre">&#64;Setoid.refl</span> <span class="pre">M</span> <span class="pre">N.Setoid</span></code>.</p> + to you.</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">def</span> <span class="n">Submonoid.Setoid</span> <span class="o">[</span><span class="n">CommMonoid</span> <span class="n">M</span><span class="o">]</span> <span class="o">(</span><span class="n">N</span> <span class="o">:</span> <span class="n">Submonoid</span> <span class="n">M</span><span class="o">)</span> <span class="o">:</span> <span class="n">Setoid</span> <span class="n">M</span> <span class="n">where</span> <span class="n">r</span> <span class="o">:=</span> <span class="k">fun</span> <span class="n">x</span> <span class="n">y</span> <span class="bp">&#8614;</span> <span class="bp">&#8707;</span> <span class="n">w</span> <span class="bp">&#8712;</span> <span class="n">N</span><span class="o">,</span> <span class="bp">&#8707;</span> <span class="n">z</span> <span class="bp">&#8712;</span> <span class="n">N</span><span class="o">,</span> <span class="n">x</span><span class="bp">*</span><span class="n">w</span> <span class="bp">=</span> <span class="n">y</span><span class="bp">*</span><span class="n">z</span> <span class="n">iseqv</span> <span class="o">:=</span> <span class="o">{</span>
  • @@ -968,8 +972,8 @@ the <code class="docutils literal notranslate"><span class="pre">&#64;</span></c
    <span class="gr">sorry</span> </pre></div> </div> - </div> - </div> + </section> + </section> </div>
• html/C08_Topology.html
  • @@ -1,7 +1,8 @@
    <!DOCTYPE html> <html class="writer-html5" lang="en" > <head> - <meta charset="utf-8" /> + <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>8. Topology &mdash; Mathematics in Lean 0.1 documentation</title> <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
  • @@ -12,10 +13,11 @@
    <script src="_static/js/html5shiv.min.js"></script> <![endif]--> - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> <script src="_static/jquery.js"></script> - <script src="_static/underscore.js"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js"></script> + <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> <script src="_static/doctools.js"></script> + <script src="_static/sphinx_highlight.js"></script> <script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" />
  • @@ -29,11 +31,15 @@
    <nav data-toggle="wy-nav-shift" class="wy-nav-side"> <div class="wy-side-scroll"> <div class="wy-side-nav-search" > - <a href="index.html" class="icon icon-home"> Mathematics in Lean + + + + <a href="index.html" class="icon icon-home"> + Mathematics in Lean </a> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> - <input type="text" name="q" placeholder="Search docs" /> + <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form>
  • @@ -85,8 +91,8 @@
    <div class="rst-content"> <div role="navigation" aria-label="Page navigation"> <ul class="wy-breadcrumbs"> - <li><a href="index.html" class="icon icon-home"></a> &raquo;</li> - <li><span class="section-number">8. </span>Topology</li> + <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li> + <li class="breadcrumb-item active"><span class="section-number">8. </span>Topology</li> <li class="wy-breadcrumbs-aside"> <a href="_sources/C08_Topology.rst.txt" rel="nofollow"> View page source</a> </li>
  • @@ -96,8 +102,8 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <span class="target" id="topology"></span><div class="section" id="index-0"> - <span id="id1"></span><h1><span class="section-number">8. </span>Topology<a class="headerlink" href="#index-0" title="Permalink to this headline">&#61633;</a></h1> + <span class="target" id="topology"></span><section id="index-0"> + <span id="id1"></span><h1><span class="section-number">8. </span>Topology<a class="headerlink" href="#index-0" title="Permalink to this heading">&#61633;</a></h1> <p>Calculus is based on the concept of a function, which is used to model quantities that depend on one another. For example, it is common to study quantities that change over time.
  • @@ -164,8 +170,8 @@ and simply note that the rest can be proved &#8220;in the same way.&#8221;
    Formalizing mathematics requires making the relevant notion of &#8220;sameness&#8221; fully explicit, and that is exactly what Bourbaki&#8217;s theory of filters manages to do.</p> - <div class="section" id="filters"> - <span id="index-1"></span><span id="id2"></span><h2><span class="section-number">8.1. </span>Filters<a class="headerlink" href="#filters" title="Permalink to this headline">&#61633;</a></h2> + <section id="filters"> + <span id="index-1"></span><span id="id2"></span><h2><span class="section-number">8.1. </span>Filters<a class="headerlink" href="#filters" title="Permalink to this heading">&#61633;</a></h2> <p>A <em>filter</em> on a type <code class="docutils literal notranslate"><span class="pre">X</span></code> is a collection of sets of <code class="docutils literal notranslate"><span class="pre">X</span></code> that satisfies three conditions that we will spell out below. The notion supports two related ideas:</p>
  • @@ -465,9 +471,9 @@ Given <code class="docutils literal notranslate"><span class="pre">F</span> <spa
    <li><p>the condition <code class="docutils literal notranslate"><span class="pre">U</span> <span class="pre">&#8712;</span> <span class="pre">F</span> <span class="pre">&#8594;</span> <span class="pre">U</span> <span class="pre">&#8838;</span> <span class="pre">V</span> <span class="pre">&#8594;</span> <span class="pre">V</span> <span class="pre">&#8712;</span> <span class="pre">F</span></code> ensures <code class="docutils literal notranslate"><span class="pre">(&#8704;&#7584;</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">F,</span> <span class="pre">P</span> <span class="pre">x)</span> <span class="pre">&#8594;</span> <span class="pre">(&#8704;</span> <span class="pre">x,</span> <span class="pre">P</span> <span class="pre">x</span> <span class="pre">&#8594;</span> <span class="pre">Q</span> <span class="pre">x)</span> <span class="pre">&#8594;</span> <span class="pre">&#8704;&#7584;</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">F,</span> <span class="pre">Q</span> <span class="pre">x</span></code>, and</p></li> <li><p>the condition <code class="docutils literal notranslate"><span class="pre">U</span> <span class="pre">&#8712;</span> <span class="pre">F</span> <span class="pre">&#8594;</span> <span class="pre">V</span> <span class="pre">&#8712;</span> <span class="pre">F</span> <span class="pre">&#8594;</span> <span class="pre">U</span> <span class="pre">&#8745;</span> <span class="pre">V</span> <span class="pre">&#8712;</span> <span class="pre">F</span></code> ensures <code class="docutils literal notranslate"><span class="pre">(&#8704;&#7584;</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">F,</span> <span class="pre">P</span> <span class="pre">x)</span> <span class="pre">&#8594;</span> <span class="pre">(&#8704;&#7584;</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">F,</span> <span class="pre">Q</span> <span class="pre">x)</span> <span class="pre">&#8594;</span> <span class="pre">&#8704;&#7584;</span> <span class="pre">x</span> <span class="pre">in</span> <span class="pre">F,</span> <span class="pre">P</span> <span class="pre">x</span> <span class="pre">&#8743;</span> <span class="pre">Q</span> <span class="pre">x</span></code>.</p></li> </ul> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="n">eventually_of_forall</span> - <span class="k">#check</span> <span class="n">Eventually.mono</span> - <span class="k">#check</span> <span class="n">Eventually.and</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="k">#check</span> <span class="bp">@</span><span class="n">eventually_of_forall</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">Eventually.mono</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">Eventually.and</span> </pre></div> </div> <p>The second item, corresponding to <code class="docutils literal notranslate"><span class="pre">eventually.mono</span></code>, supports nice ways
  • @@ -518,9 +524,9 @@ by definition, the assumption <code class="docutils literal notranslate"><span c
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="metric-spaces"> - <span id="index-2"></span><span id="id3"></span><h2><span class="section-number">8.2. </span>Metric spaces<a class="headerlink" href="#metric-spaces" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="metric-spaces"> + <span id="index-2"></span><span id="id3"></span><h2><span class="section-number">8.2. </span>Metric spaces<a class="headerlink" href="#metric-spaces" title="Permalink to this heading">&#61633;</a></h2> <p>Examples in the previous section focus on sequences of real numbers. In this section we will go up a bit in generality and focus on metric spaces. A metric space is a type <code class="docutils literal notranslate"><span class="pre">X</span></code> equipped with a distance function <code class="docutils literal notranslate"><span class="pre">dist</span> <span class="pre">:</span> <span class="pre">X</span> <span class="pre">&#8594;</span> <span class="pre">X</span> <span class="pre">&#8594;</span> <span class="pre">&#8477;</span></code> which is a generalization of the function <code class="docutils literal notranslate"><span class="pre">fun</span> <span class="pre">x</span> <span class="pre">y</span> <span class="pre">&#8614;</span> <span class="pre">|x</span> <span class="pre">-</span> <span class="pre">y|</span></code> from the case where <code class="docutils literal notranslate"><span class="pre">X</span> <span class="pre">=</span> <span class="pre">&#8477;</span></code>.</p>
  • @@ -538,8 +544,8 @@ the function <code class="docutils literal notranslate"><span class="pre">fun</s
    They are called <code class="docutils literal notranslate"><span class="pre">EMetricSpace</span></code>, <code class="docutils literal notranslate"><span class="pre">PseudoMetricSpace</span></code> and <code class="docutils literal notranslate"><span class="pre">PseudoEMetricSpace</span></code> respectively (here &#8220;e&#8221; stands for &#8220;extended&#8221;).</p> <p>Note that our journey from <code class="docutils literal notranslate"><span class="pre">&#8477;</span></code> to metric spaces jumped over the special case of normed spaces that also require linear algebra and will be explained as part of the calculus chapter.</p> - <div class="section" id="convergence-and-continuity"> - <h3><span class="section-number">8.2.1. </span>Convergence and continuity<a class="headerlink" href="#convergence-and-continuity" title="Permalink to this headline">&#61633;</a></h3> + <section id="convergence-and-continuity"> + <h3><span class="section-number">8.2.1. </span>Convergence and continuity<a class="headerlink" href="#convergence-and-continuity" title="Permalink to this heading">&#61633;</a></h3> <p>Using distance functions, we can already define convergent sequences and continuous functions between metric spaces. They are actually defined in a more general setting covered in the next section, but we have lemmas recasting the definition is terms of distances.</p>
  • @@ -626,9 +632,9 @@ and get our final proof, now bordering obfuscation.</p>
    <span class="n">Metric.continuousAt_iff</span> </pre></div> </div> - </div> - <div class="section" id="balls-open-sets-and-closed-sets"> - <h3><span class="section-number">8.2.2. </span>Balls, open sets and closed sets<a class="headerlink" href="#balls-open-sets-and-closed-sets" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="balls-open-sets-and-closed-sets"> + <h3><span class="section-number">8.2.2. </span>Balls, open sets and closed sets<a class="headerlink" href="#balls-open-sets-and-closed-sets" title="Permalink to this heading">&#61633;</a></h3> <p>Once we have a distance function, the most important geometric definitions are (open) balls and closed balls.</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">variable</span> <span class="o">(</span><span class="n">r</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">)</span>
  • @@ -683,9 +689,9 @@ argument so we can invoke <code class="docutils literal notranslate"><span class
    <span class="n">Metric.nhds_basis_closedBall.mem_iff</span> </pre></div> </div> - </div> - <div class="section" id="compactness"> - <h3><span class="section-number">8.2.3. </span>Compactness<a class="headerlink" href="#compactness" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="compactness"> + <h3><span class="section-number">8.2.3. </span>Compactness<a class="headerlink" href="#compactness" title="Permalink to this heading">&#61633;</a></h3> <p>Compactness is an important topological notion. It distinguishes subsets of a metric space that enjoy the same kind of properties as segments in reals compared to other intervals:</p> <ul class="simple">
  • @@ -726,9 +732,9 @@ are deduced from more general versions, some of which will be discussed in later
    </pre></div> </div> <p>In a compact metric space any closed set is compact, this is <code class="docutils literal notranslate"><span class="pre">IsCompact.isClosed</span></code>.</p> - </div> - <div class="section" id="uniformly-continuous-functions"> - <h3><span class="section-number">8.2.4. </span>Uniformly continuous functions<a class="headerlink" href="#uniformly-continuous-functions" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="uniformly-continuous-functions"> + <h3><span class="section-number">8.2.4. </span>Uniformly continuous functions<a class="headerlink" href="#uniformly-continuous-functions" title="Permalink to this heading">&#61633;</a></h3> <p>We now turn to uniformity notions on metric spaces : uniformly continuous functions, Cauchy sequences and completeness. Again those are defined in a more general context but we have lemmas in the metric name space to access their elementary definitions. We start with uniform continuity.</p>
  • @@ -757,9 +763,9 @@ of the distance function on <code class="docutils literal notranslate"><span cla
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="completeness"> - <h3><span class="section-number">8.2.5. </span>Completeness<a class="headerlink" href="#completeness" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="completeness"> + <h3><span class="section-number">8.2.5. </span>Completeness<a class="headerlink" href="#completeness" title="Permalink to this heading">&#61633;</a></h3> <p>A Cauchy sequence in a metric space is a sequence whose terms get closer and closer to each other. There are a couple of equivalent ways to state that idea. In particular converging sequences are Cauchy. The converse is true only in so-called <em>complete</em>
  • @@ -848,12 +854,12 @@ define something inductively in the middle of a proof using <code class="docutil
    <span class="gr">sorry</span> </pre></div> </div> - </div> - </div> - <div class="section" id="topological-spaces"> - <span id="index-4"></span><span id="id4"></span><h2><span class="section-number">8.3. </span>Topological spaces<a class="headerlink" href="#topological-spaces" title="Permalink to this headline">&#61633;</a></h2> - <div class="section" id="fundamentals"> - <h3><span class="section-number">8.3.1. </span>Fundamentals<a class="headerlink" href="#fundamentals" title="Permalink to this headline">&#61633;</a></h3> + </section> + </section> + <section id="topological-spaces"> + <span id="index-4"></span><span id="id4"></span><h2><span class="section-number">8.3. </span>Topological spaces<a class="headerlink" href="#topological-spaces" title="Permalink to this heading">&#61633;</a></h2> + <section id="fundamentals"> + <h3><span class="section-number">8.3.1. </span>Fundamentals<a class="headerlink" href="#fundamentals" title="Permalink to this heading">&#61633;</a></h3> <p>We now go up in generality and introduce topological spaces. We will review the two main ways to define topological spaces and then explain how the category of topological spaces is much better behaved than the category of metric spaces. Note that we won&#8217;t be using mathlib category theory here, only having
  • @@ -1040,9 +1046,9 @@ Let us explore that constraint &#8220;on paper&#8221; using notation <span class
    </div> <p>This ends our tour of how mathlib thinks that topological spaces fix defects of the theory of metric spaces by being a more functorial theory and having a complete lattice structure for any fixed type.</p> - </div> - <div class="section" id="separation-and-countability"> - <h3><span class="section-number">8.3.2. </span>Separation and countability<a class="headerlink" href="#separation-and-countability" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="separation-and-countability"> + <h3><span class="section-number">8.3.2. </span>Separation and countability<a class="headerlink" href="#separation-and-countability" title="Permalink to this heading">&#61633;</a></h3> <p>We saw that the category of topological spaces have very nice properties. The price to pay for this is existence of rather pathological topological spaces. There are a number of assumptions you can make on a topological space to ensure its behavior
  • @@ -1117,7 +1123,7 @@ together with the fact that <code class="docutils literal notranslate"><span cla
    <span class="bp">&#8707;</span> <span class="n">&#966;</span> <span class="o">:</span> <span class="n">X</span> <span class="bp">&#8594;</span> <span class="n">Y</span><span class="o">,</span> <span class="n">Continuous</span> <span class="n">&#966;</span> <span class="bp">&#8743;</span> <span class="bp">&#8704;</span> <span class="n">a</span> <span class="o">:</span> <span class="n">A</span><span class="o">,</span> <span class="n">&#966;</span> <span class="n">a</span> <span class="bp">=</span> <span class="n">f</span> <span class="n">a</span> <span class="o">:=</span> <span class="gr">sorry</span> - <span class="k">#check</span> <span class="n">HasBasis.tendsto_right_iff</span> + <span class="k">#check</span> <span class="bp">@</span><span class="n">HasBasis.tendsto_right_iff</span> </pre></div> </div> <p>In addition to separation property, the main kind of assumption you can make on a topological
  • @@ -1130,9 +1136,9 @@ of sets can be understood using sequences.</p>
    <span class="n">mem_closure_iff_seq_limit</span> </pre></div> </div> - </div> - <div class="section" id="id5"> - <h3><span class="section-number">8.3.3. </span>Compactness<a class="headerlink" href="#id5" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="id5"> + <h3><span class="section-number">8.3.3. </span>Compactness<a class="headerlink" href="#id5" title="Permalink to this heading">&#61633;</a></h3> <p>Let us now discuss how compactness is defined for topological spaces. As usual there are several ways to think about it and mathlib goes for the filter version.</p> <p>We first need to define cluster points of filters. Given a filter <code class="docutils literal notranslate"><span class="pre">F</span></code> on a topological space <code class="docutils literal notranslate"><span class="pre">X</span></code>,
  • @@ -1193,9 +1199,9 @@ cover <code class="docutils literal notranslate"><span class="pre">s</span></cod
    <span class="n">isCompact_univ</span> </pre></div> </div> - </div> - </div> - </div> + </section> + </section> + </section> </div>
• html/C09_Differential_Calculus.html
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    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <span class="target" id="differential-calculus"></span><div class="section" id="index-0"> - <span id="id1"></span><h1><span class="section-number">9. </span>Differential Calculus<a class="headerlink" href="#index-0" title="Permalink to this headline">&#61633;</a></h1> + <span class="target" id="differential-calculus"></span><section id="index-0"> + <span id="id1"></span><h1><span class="section-number">9. </span>Differential Calculus<a class="headerlink" href="#index-0" title="Permalink to this heading">&#61633;</a></h1> <p>We now consider the formalization of notions from <em>analysis</em>, starting with differentiation in this chapter and turning integration and measure theory in the next.
  • @@ -99,8 +105,8 @@ setting of functions from the real numbers to the real numbers,
    which is familiar from any introductory calculus class. In <a class="reference internal" href="#normed-spaces"><span class="std std-numref">Section 9.2</span></a>, we then consider the notion of a derivative in a much broader setting.</p> - <div class="section" id="elementary-differential-calculus"> - <span id="index-1"></span><span id="id2"></span><h2><span class="section-number">9.1. </span>Elementary Differential Calculus<a class="headerlink" href="#elementary-differential-calculus" title="Permalink to this headline">&#61633;</a></h2> + <section id="elementary-differential-calculus"> + <span id="index-1"></span><span id="id2"></span><h2><span class="section-number">9.1. </span>Elementary Differential Calculus<a class="headerlink" href="#elementary-differential-calculus" title="Permalink to this heading">&#61633;</a></h2> <p>Let <code class="docutils literal notranslate"><span class="pre">f</span></code> be a function from the reals to the reals. There is a difference between talking about the derivative of <code class="docutils literal notranslate"><span class="pre">f</span></code> at a single point and talking about the derivative function.
  • @@ -154,9 +160,7 @@ definition of <code class="docutils literal notranslate"><span class="pre">deriv
    </div> <p>We can eve state Rolle&#8217;s theorem without any differentiability assumptions, which seems even weirder.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kn">open</span> <span class="n">Set</span> - - <span class="kd">example</span> <span class="o">{</span><span class="n">f</span> <span class="o">:</span> <span class="n">&#8477;</span> <span class="bp">&#8594;</span> <span class="n">&#8477;</span><span class="o">}</span> <span class="o">{</span><span class="n">a</span> <span class="n">b</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">}</span> <span class="o">(</span><span class="n">hab</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">&lt;</span> <span class="n">b</span><span class="o">)</span> <span class="o">(</span><span class="n">hfc</span> <span class="o">:</span> <span class="n">ContinuousOn</span> <span class="n">f</span> <span class="o">(</span><span class="n">Icc</span> <span class="n">a</span> <span class="n">b</span><span class="o">))</span> <span class="o">(</span><span class="n">hfI</span> <span class="o">:</span> <span class="n">f</span> <span class="n">a</span> <span class="bp">=</span> <span class="n">f</span> <span class="n">b</span><span class="o">)</span> <span class="o">:</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">{</span><span class="n">f</span> <span class="o">:</span> <span class="n">&#8477;</span> <span class="bp">&#8594;</span> <span class="n">&#8477;</span><span class="o">}</span> <span class="o">{</span><span class="n">a</span> <span class="n">b</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">}</span> <span class="o">(</span><span class="n">hab</span> <span class="o">:</span> <span class="n">a</span> <span class="bp">&lt;</span> <span class="n">b</span><span class="o">)</span> <span class="o">(</span><span class="n">hfc</span> <span class="o">:</span> <span class="n">ContinuousOn</span> <span class="n">f</span> <span class="o">(</span><span class="n">Icc</span> <span class="n">a</span> <span class="n">b</span><span class="o">))</span> <span class="o">(</span><span class="n">hfI</span> <span class="o">:</span> <span class="n">f</span> <span class="n">a</span> <span class="bp">=</span> <span class="n">f</span> <span class="n">b</span><span class="o">)</span> <span class="o">:</span> <span class="bp">&#8707;</span> <span class="n">c</span> <span class="bp">&#8712;</span> <span class="n">Ioo</span> <span class="n">a</span> <span class="n">b</span><span class="o">,</span> <span class="n">deriv</span> <span class="n">f</span> <span class="n">c</span> <span class="bp">=</span> <span class="mi">0</span> <span class="o">:=</span> <span class="n">exists_deriv_eq_zero</span> <span class="n">f</span> <span class="n">hab</span> <span class="n">hfc</span> <span class="n">hfI</span> </pre></div>
  • @@ -173,11 +177,11 @@ seems even weirder.</p>
    <span class="kd">example</span> <span class="o">:</span> <span class="n">deriv</span> <span class="n">sin</span> <span class="n">&#960;</span> <span class="bp">=</span> <span class="bp">-</span><span class="mi">1</span> <span class="o">:=</span> <span class="kd">by</span> <span class="n">simp</span> </pre></div> </div> - </div> - <div class="section" id="differential-calculus-in-normed-spaces"> - <span id="normed-spaces"></span><span id="index-2"></span><h2><span class="section-number">9.2. </span>Differential Calculus in Normed Spaces<a class="headerlink" href="#differential-calculus-in-normed-spaces" title="Permalink to this headline">&#61633;</a></h2> - <div class="section" id="id3"> - <h3><span class="section-number">9.2.1. </span>Normed spaces<a class="headerlink" href="#id3" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="differential-calculus-in-normed-spaces"> + <span id="normed-spaces"></span><span id="index-2"></span><h2><span class="section-number">9.2. </span>Differential Calculus in Normed Spaces<a class="headerlink" href="#differential-calculus-in-normed-spaces" title="Permalink to this heading">&#61633;</a></h2> + <section id="id3"> + <h3><span class="section-number">9.2.1. </span>Normed spaces<a class="headerlink" href="#id3" title="Permalink to this heading">&#61633;</a></h3> <p>Differentiation can be generalized beyond <code class="docutils literal notranslate"><span class="pre">&#8477;</span></code> using the notion of a <em>normed vector space</em>, which encapsulates both direction and distance. We start with the notion of a <em>normed group</em>, which as an additive commutative
  • @@ -240,9 +244,9 @@ complete as long as the field itself is complete.</p>
    <span class="n">FiniteDimensional.complete</span> <span class="bp">&#120156;</span> <span class="n">E</span> </pre></div> </div> - </div> - <div class="section" id="continuous-linear-maps"> - <h3><span class="section-number">9.2.2. </span>Continuous linear maps<a class="headerlink" href="#continuous-linear-maps" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="continuous-linear-maps"> + <h3><span class="section-number">9.2.2. </span>Continuous linear maps<a class="headerlink" href="#continuous-linear-maps" title="Permalink to this heading">&#61633;</a></h3> <p>We now turn to the morphisms in the category of normed spaces, namely, continuous linear maps. In mathlib, the type of <code class="docutils literal notranslate"><span class="pre">&#120156;</span></code>-linear continuous maps between normed spaces
  • @@ -322,9 +326,9 @@ Minor ingredients include <code class="docutils literal notranslate"><span class
    <span class="gr">sorry</span> </pre></div> </div> - </div> - <div class="section" id="asymptotic-comparisons"> - <h3><span class="section-number">9.2.3. </span>Asymptotic comparisons<a class="headerlink" href="#asymptotic-comparisons" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="asymptotic-comparisons"> + <h3><span class="section-number">9.2.3. </span>Asymptotic comparisons<a class="headerlink" href="#asymptotic-comparisons" title="Permalink to this heading">&#61633;</a></h3> <p>Defining differentiability also requires asymptotic comparisons. Mathlib has an extensive library covering the big O and little o relations, whose definitions are shown below.
  • @@ -333,6 +337,8 @@ notation.
    Here we will only use little o to define differentiability.</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kn">open</span> <span class="n">Asymptotics</span> + <span class="kn">open</span> <span class="n">Asymptotics</span> + <span class="kd">example</span> <span class="o">{</span><span class="n">&#945;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">{</span><span class="n">E</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NormedGroup</span> <span class="n">E</span><span class="o">]</span> <span class="o">{</span><span class="n">F</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NormedGroup</span> <span class="n">F</span><span class="o">]</span> <span class="o">(</span><span class="n">c</span> <span class="o">:</span> <span class="n">&#8477;</span><span class="o">)</span> <span class="o">(</span><span class="n">l</span> <span class="o">:</span> <span class="n">Filter</span> <span class="n">&#945;</span><span class="o">)</span> <span class="o">(</span><span class="n">f</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">E</span><span class="o">)</span> <span class="o">(</span><span class="n">g</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">F</span><span class="o">)</span> <span class="o">:</span> <span class="n">IsBigOWith</span> <span class="n">c</span> <span class="n">l</span> <span class="n">f</span> <span class="n">g</span> <span class="bp">&#8596;</span> <span class="bp">&#8704;&#7584;</span> <span class="n">x</span> <span class="k">in</span> <span class="n">l</span><span class="o">,</span> <span class="bp">&#8214;</span><span class="n">f</span> <span class="n">x</span><span class="bp">&#8214;</span> <span class="bp">&#8804;</span> <span class="n">c</span> <span class="bp">*</span> <span class="bp">&#8214;</span><span class="n">g</span> <span class="n">x</span><span class="bp">&#8214;</span> <span class="o">:=</span> <span class="n">isBigOWith_iff</span>
  • @@ -350,17 +356,15 @@ Here we will only use little o to define differentiability.</p>
    <span class="n">Iff.rfl</span> </pre></div> </div> - </div> - <div class="section" id="differentiability"> - <h3><span class="section-number">9.2.4. </span>Differentiability<a class="headerlink" href="#differentiability" title="Permalink to this headline">&#61633;</a></h3> + </section> + <section id="differentiability"> + <h3><span class="section-number">9.2.4. </span>Differentiability<a class="headerlink" href="#differentiability" title="Permalink to this heading">&#61633;</a></h3> <p>We are now ready to discuss differentiable functions between normed spaces. In analogy the elementary one-dimensional, mathlib defines a predicate <code class="docutils literal notranslate"><span class="pre">has_fderiv_at</span></code> and a function <code class="docutils literal notranslate"><span class="pre">fderiv</span></code>. Here the letter &#8220;f&#8221; stands for <em>Fr&#233;chet</em>.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kn">open</span> <span class="n">Topology</span> - - <span class="kd">variable</span> <span class="o">{</span><span class="bp">&#120156;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NontriviallyNormedField</span> <span class="bp">&#120156;</span><span class="o">]</span> <span class="o">{</span><span class="n">E</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NormedAddCommGroup</span> <span class="n">E</span><span class="o">]</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">variable</span> <span class="o">{</span><span class="bp">&#120156;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NontriviallyNormedField</span> <span class="bp">&#120156;</span><span class="o">]</span> <span class="o">{</span><span class="n">E</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NormedAddCommGroup</span> <span class="n">E</span><span class="o">]</span> <span class="o">[</span><span class="n">NormedSpace</span> <span class="bp">&#120156;</span> <span class="n">E</span><span class="o">]</span> <span class="o">{</span><span class="n">F</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">NormedAddCommGroup</span> <span class="n">F</span><span class="o">]</span> <span class="o">[</span><span class="n">NormedSpace</span> <span class="bp">&#120156;</span> <span class="n">F</span><span class="o">]</span> <span class="kd">example</span> <span class="o">(</span><span class="n">f</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8594;</span> <span class="n">F</span><span class="o">)</span> <span class="o">(</span><span class="n">f&#39;</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8594;</span><span class="n">L</span><span class="o">[</span><span class="bp">&#120156;</span><span class="o">]</span> <span class="n">F</span><span class="o">)</span> <span class="o">(</span><span class="n">x&#8320;</span> <span class="o">:</span> <span class="n">E</span><span class="o">)</span> <span class="o">:</span>
  • @@ -421,7 +425,7 @@ from the left and from the right, and that it is strictly differentiable.</p>
    <span class="bp">&#8704;&#7584;</span> <span class="n">x</span> <span class="k">in</span> <span class="bp">&#120029;</span> <span class="o">(</span><span class="n">f</span> <span class="n">a</span><span class="o">),</span> <span class="n">f</span> <span class="o">(</span><span class="n">hf.localInverse</span> <span class="n">f</span> <span class="n">f&#39;</span> <span class="n">a</span> <span class="n">x</span><span class="o">)</span> <span class="bp">=</span> <span class="n">x</span> <span class="o">:=</span> <span class="n">hf.eventually_right_inverse</span> - <span class="kd">example</span> <span class="o">{</span><span class="n">f</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8594;</span> <span class="n">F</span><span class="o">}</span> <span class="o">{</span><span class="n">f&#39;</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8771;</span><span class="n">L</span><span class="o">[</span><span class="bp">&#120156;</span><span class="o">]</span> <span class="n">F</span><span class="o">}</span> <span class="o">{</span><span class="n">a</span> <span class="o">:</span> <span class="n">E</span><span class="o">}</span> + <span class="kd">example</span> <span class="o">[</span><span class="n">CompleteSpace</span> <span class="n">E</span><span class="o">]</span> <span class="o">{</span><span class="n">f</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8594;</span> <span class="n">F</span><span class="o">}</span> <span class="o">{</span><span class="n">f&#39;</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8771;</span><span class="n">L</span><span class="o">[</span><span class="bp">&#120156;</span><span class="o">]</span> <span class="n">F</span><span class="o">}</span> <span class="o">{</span><span class="n">a</span> <span class="o">:</span> <span class="n">E</span><span class="o">}</span> <span class="o">(</span><span class="n">hf</span> <span class="o">:</span> <span class="n">HasStrictFDerivAt</span> <span class="n">f</span> <span class="o">(</span><span class="n">f&#39;</span> <span class="o">:</span> <span class="n">E</span> <span class="bp">&#8594;</span><span class="n">L</span><span class="o">[</span><span class="bp">&#120156;</span><span class="o">]</span> <span class="n">F</span><span class="o">)</span> <span class="n">a</span><span class="o">)</span> <span class="o">:</span> <span class="n">HasStrictFDerivAt</span> <span class="o">(</span><span class="n">HasStrictFDerivAt.localInverse</span> <span class="n">f</span> <span class="n">f&#39;</span> <span class="n">a</span> <span class="n">hf</span><span class="o">)</span> <span class="o">(</span><span class="n">f&#39;.symm</span> <span class="o">:</span> <span class="n">F</span> <span class="bp">&#8594;</span><span class="n">L</span><span class="o">[</span><span class="bp">&#120156;</span><span class="o">]</span> <span class="n">E</span><span class="o">)</span> <span class="o">(</span><span class="n">f</span> <span class="n">a</span><span class="o">)</span> <span class="o">:=</span> <span class="n">HasStrictFDerivAt.to_localInverse</span> <span class="n">hf</span>
  • @@ -435,9 +439,9 @@ For example, you may want to use one-sided derivatives in the
    one-dimensional setting. The means to do so are found in mathlib in a more general context; see <code class="docutils literal notranslate"><span class="pre">HasFDerivWithinAt</span></code> or the even more general <code class="docutils literal notranslate"><span class="pre">HasFDerivAtFilter</span></code>.</p> - </div> - </div> - </div> + </section> + </section> + </section> </div>
• html/C10_Integration_and_Measure_Theory.html
  • @@ -1,7 +1,8 @@
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  • @@ -12,10 +13,11 @@
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  • @@ -29,11 +31,15 @@
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  • @@ -73,8 +79,8 @@
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  • @@ -84,10 +90,10 @@
    <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article"> <div itemprop="articleBody"> - <span class="target" id="integration-and-measure-theory"></span><div class="section" id="index-0"> - <span id="id1"></span><h1><span class="section-number">10. </span>Integration and Measure Theory<a class="headerlink" href="#index-0" title="Permalink to this headline">&#61633;</a></h1> - <div class="section" id="elementary-integration"> - <span id="index-1"></span><span id="id2"></span><h2><span class="section-number">10.1. </span>Elementary Integration<a class="headerlink" href="#elementary-integration" title="Permalink to this headline">&#61633;</a></h2> + <span class="target" id="integration-and-measure-theory"></span><section id="index-0"> + <span id="id1"></span><h1><span class="section-number">10. </span>Integration and Measure Theory<a class="headerlink" href="#index-0" title="Permalink to this heading">&#61633;</a></h1> + <section id="elementary-integration"> + <span id="index-1"></span><span id="id2"></span><h2><span class="section-number">10.1. </span>Elementary Integration<a class="headerlink" href="#elementary-integration" title="Permalink to this heading">&#61633;</a></h2> <p>We first focus on integration of functions on finite intervals in <code class="docutils literal notranslate"><span class="pre">&#8477;</span></code>. We can integrate elementary functions.</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kn">open</span> <span class="n">MeasureTheory</span> <span class="n">intervalIntegral</span>
  • @@ -124,9 +130,9 @@ which are not shown here, are not equivalent.)</p>
    <span class="n">rfl</span> </pre></div> </div> - </div> - <div class="section" id="measure-theory"> - <span id="index-2"></span><span id="id3"></span><h2><span class="section-number">10.2. </span>Measure Theory<a class="headerlink" href="#measure-theory" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="measure-theory"> + <span id="index-2"></span><span id="id3"></span><h2><span class="section-number">10.2. </span>Measure Theory<a class="headerlink" href="#measure-theory" title="Permalink to this heading">&#61633;</a></h2> <p>The general context for integration in mathlib is measure theory. Even the elementary integrals of the previous section are in fact Bochner integrals. Bochner integration is a generalization of Lebesgue integration where the target space can be any Banach space,
  • @@ -134,14 +140,14 @@ not necessarily finite dimensional.</p>
    <p>The first component in the development of measure theory is the notion of a <span class="math notranslate nohighlight">\(\sigma\)</span>-algebra of sets, which are called the <em>measurable</em> sets. - The type class <code class="docutils literal notranslate"><span class="pre">MeasurableSpace</span></code> serves to equip a type with such a structure. + The type class <code class="docutils literal notranslate"><span class="pre">measurable_space</span></code> serves to equip a type with such a structure. The sets <code class="docutils literal notranslate"><span class="pre">empty</span></code> and <code class="docutils literal notranslate"><span class="pre">univ</span></code> are measurable, the complement of a measurable set is measurable, and a countable union or intersection of measurable sets is measurable. - Note that these axioms are redundant; if you <code class="docutils literal notranslate"><span class="pre">#print</span> <span class="pre">MeasurableSpace</span></code>, + Note that these axioms are redundant; if you <code class="docutils literal notranslate"><span class="pre">#print</span> <span class="pre">measurable_space</span></code>, you will see the ones that mathlib uses. As the examples below show, countability assumptions can be expressed using the - <code class="docutils literal notranslate"><span class="pre">Encodable</span></code> type class.</p> + <code class="docutils literal notranslate"><span class="pre">encodable</span></code> type class.</p> <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">variable</span> <span class="o">{</span><span class="n">&#945;</span> <span class="o">:</span> <span class="kt">Type</span> <span class="n">_</span><span class="o">}</span> <span class="o">[</span><span class="n">MeasurableSpace</span> <span class="n">&#945;</span><span class="o">]</span> <span class="kd">example</span> <span class="o">:</span> <span class="n">MeasurableSet</span> <span class="o">(</span><span class="bp">&#8709;</span> <span class="o">:</span> <span class="n">Set</span> <span class="n">&#945;</span><span class="o">)</span> <span class="o">:=</span>
  • @@ -201,9 +207,9 @@ almost everywhere.</p>
    <span class="n">Iff.rfl</span> </pre></div> </div> - </div> - <div class="section" id="integration"> - <span id="id4"></span><h2><span class="section-number">10.3. </span>Integration<a class="headerlink" href="#integration" title="Permalink to this headline">&#61633;</a></h2> + </section> + <section id="integration"> + <span id="id4"></span><h2><span class="section-number">10.3. </span>Integration<a class="headerlink" href="#integration" title="Permalink to this heading">&#61633;</a></h2> <p>Now that we have measurable spaces and measures we can consider integrals. As explained above, mathlib uses a very general notion of integration that allows any Banach space as the target.
  • @@ -234,9 +240,7 @@ So in all cases we have the following lemma.</p>
    <p>We now quickly explain how to access the most important theorems in integration theory, starting with the dominated convergence theorem. There are several versions in mathlib, and here we only show the most basic one.</p> - <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kn">open</span> <span class="n">Filter</span> - - <span class="kd">example</span> <span class="o">{</span><span class="n">F</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8594;</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">E</span><span class="o">}</span> <span class="o">{</span><span class="n">f</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">E</span><span class="o">}</span> <span class="o">(</span><span class="n">bound</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">&#8477;</span><span class="o">)</span> <span class="o">(</span><span class="n">hmeas</span> <span class="o">:</span> <span class="bp">&#8704;</span> <span class="n">n</span><span class="o">,</span> <span class="n">AEStronglyMeasurable</span> <span class="o">(</span><span class="n">F</span> <span class="n">n</span><span class="o">)</span> <span class="n">&#956;</span><span class="o">)</span> + <div class="highlight-lean notranslate"><div class="highlight"><pre><span></span><span class="kd">example</span> <span class="o">{</span><span class="n">F</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8594;</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">E</span><span class="o">}</span> <span class="o">{</span><span class="n">f</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">E</span><span class="o">}</span> <span class="o">(</span><span class="n">bound</span> <span class="o">:</span> <span class="n">&#945;</span> <span class="bp">&#8594;</span> <span class="n">&#8477;</span><span class="o">)</span> <span class="o">(</span><span class="n">hmeas</span> <span class="o">:</span> <span class="bp">&#8704;</span> <span class="n">n</span><span class="o">,</span> <span class="n">AEStronglyMeasurable</span> <span class="o">(</span><span class="n">F</span> <span class="n">n</span><span class="o">)</span> <span class="n">&#956;</span><span class="o">)</span> <span class="o">(</span><span class="n">hint</span> <span class="o">:</span> <span class="n">Integrable</span> <span class="n">bound</span> <span class="n">&#956;</span><span class="o">)</span> <span class="o">(</span><span class="n">hbound</span> <span class="o">:</span> <span class="bp">&#8704;</span> <span class="n">n</span><span class="o">,</span> <span class="bp">&#8704;&#7504;</span> <span class="n">a</span> <span class="bp">&#8706;</span><span class="n">&#956;</span><span class="o">,</span> <span class="bp">&#8214;</span><span class="n">F</span> <span class="n">n</span> <span class="n">a</span><span class="bp">&#8214;</span> <span class="bp">&#8804;</span> <span class="n">bound</span> <span class="n">a</span><span class="o">)</span> <span class="o">(</span><span class="n">hlim</span> <span class="o">:</span> <span class="bp">&#8704;&#7504;</span> <span class="n">a</span> <span class="bp">&#8706;</span><span class="n">&#956;</span><span class="o">,</span> <span class="n">Tendsto</span> <span class="o">(</span><span class="k">fun</span> <span class="n">n</span> <span class="o">:</span> <span class="n">&#8469;</span> <span class="bp">&#8614;</span> <span class="n">F</span> <span class="n">n</span> <span class="n">a</span><span class="o">)</span> <span class="n">atTop</span> <span class="o">(</span><span class="bp">&#120029;</span> <span class="o">(</span><span class="n">f</span> <span class="n">a</span><span class="o">)))</span> <span class="o">:</span> <span class="n">Tendsto</span> <span class="o">(</span><span class="k">fun</span> <span class="n">n</span> <span class="bp">&#8614;</span> <span class="bp">&#8747;</span> <span class="n">a</span><span class="o">,</span> <span class="n">F</span> <span class="n">n</span> <span class="n">a</span> <span class="bp">&#8706;</span><span class="n">&#956;</span><span class="o">)</span> <span class="n">atTop</span> <span class="o">(</span><span class="bp">&#120029;</span> <span class="o">(</span><span class="bp">&#8747;</span> <span class="n">a</span><span class="o">,</span> <span class="n">f</span> <span class="n">a</span> <span class="bp">&#8706;</span><span class="n">&#956;</span><span class="o">))</span> <span class="o">:=</span>
  • @@ -278,8 +282,8 @@ gives finite mass to compact sets, and give positive mass to open sets.</p>
    <span class="n">integral_image_eq_integral_abs_det_fderiv_smul</span> <span class="n">&#956;</span> <span class="n">hs</span> <span class="n">hf</span> <span class="n">h_inj</span> <span class="n">g</span> </pre></div> </div> - </div> - </div> + </section> + </section> </div>
• html/_static/_sphinx_javascript_frameworks_compat.js (new)
  • @@ -0,0 +1,123 @@
    + /* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + + /** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ + jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); + }; + + /** + * small helper function to urlencode strings + */ + jQuery.urlencode = encodeURIComponent; + + /** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ + jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; + }; + + /** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ + jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; + }; + + /* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ + if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; + }
• html/_static/basic.css
  • @@ -4,7 +4,7 @@
    * * Sphinx stylesheet -- basic theme. * - * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */
  • @@ -222,7 +222,7 @@ table.modindextable td {
    /* -- general body styles --------------------------------------------------- */ div.body { - min-width: 450px; + min-width: 360px; max-width: 800px; }
  • @@ -237,16 +237,6 @@ a.headerlink {
    visibility: hidden; } - a.brackets:before, - span.brackets > a:before{ - content: "["; - } - - a.brackets:after, - span.brackets > a:after { - content: "]"; - } - h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink,
  • @@ -335,12 +325,16 @@ p.sidebar-title {
    font-weight: bold; } + nav.contents, + aside.topic, div.admonition, div.topic, blockquote { clear: left; } /* -- topics ---------------------------------------------------------------- */ + nav.contents, + aside.topic, div.topic { border: 1px solid #ccc; padding: 7px;
  • @@ -379,6 +373,8 @@ div.body p.centered {
    div.sidebar > :last-child, aside.sidebar > :last-child, + nav.contents > :last-child, + aside.topic > :last-child, div.topic > :last-child, div.admonition > :last-child { margin-bottom: 0;
  • @@ -386,6 +382,8 @@ div.admonition > :last-child {
    div.sidebar::after, aside.sidebar::after, + nav.contents::after, + aside.topic::after, div.topic::after, div.admonition::after, blockquote::after {
  • @@ -428,10 +426,6 @@ table.docutils td, table.docutils th {
    border-bottom: 1px solid #aaa; } - table.footnote td, table.footnote th { - border: 0 !important; - } - th { text-align: left; padding-right: 5px;
  • @@ -615,19 +609,26 @@ ul.simple p {
    margin-bottom: 0; } - dl.footnote > dt, - dl.citation > dt { + aside.footnote > span, + div.citation > span { float: left; - margin-right: 0.5em; } - - dl.footnote > dd, - dl.citation > dd { + aside.footnote > span:last-of-type, + div.citation > span:last-of-type { + padding-right: 0.5em; + } + aside.footnote > p { + margin-left: 2em; + } + div.citation > p { + margin-left: 4em; + } + aside.footnote > p:last-of-type, + div.citation > p:last-of-type { margin-bottom: 0em; } - - dl.footnote > dd:after, - dl.citation > dd:after { + aside.footnote > p:last-of-type:after, + div.citation > p:last-of-type:after { content: ""; clear: both; }
  • @@ -644,10 +645,6 @@ dl.field-list > dt {
    padding-right: 5px; } - dl.field-list > dt:after { - content: ":"; - } - dl.field-list > dd { padding-left: 0.5em; margin-top: 0em;
• html/_static/css/badge_only.css
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• html/_static/css/theme.css
  • @@ -1,4 +1,4 @@
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• html/_static/doctools.js
  • @@ -2,325 +2,155 @@
    * doctools.js * ~~~~~~~~~~~ * - * Sphinx JavaScript utilities for all documentation. + * Base JavaScript utilities for all Sphinx HTML documentation. * - * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ - - /** - * select a different prefix for underscore - */ - $u = _.noConflict(); - - /** - * make the code below compatible with browsers without - * an installed firebug like debugger - if (!window.console || !console.firebug) { - var names = ["log", "debug", "info", "warn", "error", "assert", "dir", - "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", - "profile", "profileEnd"]; - window.console = {}; - for (var i = 0; i < names.length; ++i) - window.console[names[i]] = function() {}; - } - */ - - /** - * small helper function to urldecode strings - * - * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL - */ - jQuery.urldecode = function(x) { - if (!x) { - return x - } - return decodeURIComponent(x.replace(/\+/g, ' ')); - }; - - /** - * small helper function to urlencode strings - */ - jQuery.urlencode = encodeURIComponent; - - /** - * This function returns the parsed url parameters of the - * current request. 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rv:([\w.]+)|)/.exec(ua) || - []; - - return { - browser: match[ 1 ] || "", - version: match[ 2 ] || "0" - }; - }; - jQuery.browser = {}; - jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; - } - /** * Small JavaScript module for the documentation. */ - var Documentation = { - - init : function() { - this.fixFirefoxAnchorBug(); - this.highlightSearchWords(); - this.initIndexTable(); - if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { - this.initOnKeyListeners(); - } + const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); }, /** * i18n support */ - TRANSLATIONS : {}, - PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, - LOCALE : 'unknown', + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", // gettext and ngettext don't access this so that the functions // can safely bound to a different name (_ = Documentation.gettext) - gettext : function(string) { - var translated = Documentation.TRANSLATIONS[string]; - if (typeof translated === 'undefined') - return string; - return (typeof translated === 'string') ? translated : translated[0]; + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } }, - ngettext : function(singular, plural, n) { - var translated = Documentation.TRANSLATIONS[singular]; - if (typeof translated === 'undefined') - return (n == 1) ? singular : plural; - return translated[Documentation.PLURALEXPR(n)]; + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; }, - addTranslations : function(catalog) { - for (var key in catalog.messages) - this.TRANSLATIONS[key] = catalog.messages[key]; - this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); - this.LOCALE = catalog.locale; + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; }, /** - * add context elements like header anchor links + * helper function to focus on search bar */ - addContextElements : function() { - $('div[id] > :header:first').each(function() { - $('<a class="headerlink">\u00B6</a>'). - attr('href', '#' + this.id). - attr('title', _('Permalink to this headline')). - appendTo(this); - }); - $('dt[id]').each(function() { - $('<a class="headerlink">\u00B6</a>'). - attr('href', '#' + this.id). - attr('title', _('Permalink to this definition')). - appendTo(this); - }); + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); }, /** - * workaround a firefox stupidity - * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + * Initialise the domain index toggle buttons */ - fixFirefoxAnchorBug : function() { - if (document.location.hash && $.browser.mozilla) - window.setTimeout(function() { - document.location.href += ''; - }, 10); - }, - - /** - * highlight the search words provided in the url in the text - */ - highlightSearchWords : function() { - var params = $.getQueryParameters(); - var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; - if (terms.length) { - var body = $('div.body'); - if (!body.length) { - body = $('body'); + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); } - window.setTimeout(function() { - $.each(terms, function() { - body.highlightText(this.toLowerCase(), 'highlighted'); - }); - }, 10); - $('<p class="highlight-link"><a href="javascript:Documentation.' + - 'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>') - .appendTo($('#searchbox')); - } - }, - - /** - * init the domain index toggle buttons - */ - initIndexTable : function() { - var togglers = $('img.toggler').click(function() { - var src = $(this).attr('src'); - var idnum = $(this).attr('id').substr(7); - $('tr.cg-' + idnum).toggle(); - if (src.substr(-9) === 'minus.png') - $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); - else - $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); - }).css('display', ''); - if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { - togglers.click(); - } - }, + }; - /** - * helper function to hide the search marks again - */ - hideSearchWords : function() { - $('#searchbox .highlight-link').fadeOut(300); - $('span.highlighted').removeClass('highlighted'); - var url = new URL(window.location); - url.searchParams.delete('highlight'); - window.history.replaceState({}, '', url); + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); }, - /** - * make the url absolute - */ - makeURL : function(relativeURL) { - return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; - }, - - /** - * get the current relative url - */ - getCurrentURL : function() { - var path = document.location.pathname; - var parts = path.split(/\//); - $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { - if (this === '..') - parts.pop(); - }); - var url = parts.join('/'); - return path.substring(url.lastIndexOf('/') + 1, path.length - 1); - }, - - initOnKeyListeners: function() { - $(document).keydown(function(event) { - var activeElementType = document.activeElement.tagName; - // don't navigate when in search box, textarea, dropdown or button - if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' - && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey - && !event.shiftKey) { - switch (event.keyCode) { - case 37: // left - var prevHref = $('link[rel="prev"]').prop('href'); - if (prevHref) { - window.location.href = prevHref; - return false; + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); } break; - case 39: // right - var nextHref = $('link[rel="next"]').prop('href'); - if (nextHref) { - window.location.href = nextHref; - return false; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); } break; } } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } }); - } + }, }; // quick alias for translations - _ = Documentation.gettext; + const _ = Documentation.gettext; - $(document).ready(function() { - Documentation.init(); - }); + _ready(Documentation.init);
• html/_static/documentation_options.js
  • @@ -1,12 +1,14 @@
    var DOCUMENTATION_OPTIONS = { URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), VERSION: '0.1', - LANGUAGE: 'None', + LANGUAGE: 'en', COLLAPSE_INDEX: false, BUILDER: 'html', FILE_SUFFIX: '.html', LINK_SUFFIX: '.html', HAS_SOURCE: true, SOURCELINK_SUFFIX: '.txt', - NAVIGATION_WITH_KEYS: false + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, };
• html/_static/jquery-3.5.1.js (deleted)
  • @@ -1,10872 +0,0 @@
    - /*! - * jQuery JavaScript Library v3.5.1 - * https://jquery.com/ - * - * Includes Sizzle.js - * https://sizzlejs.com/ - * - * Copyright JS Foundation and other contributors - * Released under the MIT license - * https://jquery.org/license - * - * Date: 2020-05-04T22:49Z - */ - ( function( global, factory ) { - - "use strict"; - - if ( typeof module === "object" && typeof module.exports === "object" ) { - - // For CommonJS and CommonJS-like environments where a proper `window` - // is present, execute the factory and get jQuery. - // For environments that do not have a `window` with a `document` - // (such as Node.js), expose a factory as module.exports. - // This accentuates the need for the creation of a real `window`. - // e.g. var jQuery = require("jquery")(window); - // See ticket #14549 for more info. - module.exports = global.document ? - factory( global, true ) : - function( w ) { - if ( !w.document ) { - throw new Error( "jQuery requires a window with a document" ); - } - return factory( w ); - }; - } else { - factory( global ); - } - - // Pass this if window is not defined yet - } )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { - - // Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 - // throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode - // arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common - // enough that all such attempts are guarded in a try block. - "use strict"; - - var arr = []; - - var getProto = Object.getPrototypeOf; - - var slice = arr.slice; - - var flat = arr.flat ? function( array ) { - return arr.flat.call( array ); - } : function( array ) { - return arr.concat.apply( [], array ); - }; - - - var push = arr.push; - - var indexOf = arr.indexOf; - - var class2type = {}; - - var toString = class2type.toString; - - var hasOwn = class2type.hasOwnProperty; - - var fnToString = hasOwn.toString; - - var ObjectFunctionString = fnToString.call( Object ); - - var support = {}; - - var isFunction = function isFunction( obj ) { - - // Support: Chrome <=57, Firefox <=52 - // In some browsers, typeof returns "function" for HTML <object> elements - // (i.e., `typeof document.createElement( "object" ) === "function"`). - // We don't want to classify *any* DOM node as a function. - return typeof obj === "function" && typeof obj.nodeType !== "number"; - }; - - - var isWindow = function isWindow( obj ) { - return obj != null && obj === obj.window; - }; - - - var document = window.document; - - - - var preservedScriptAttributes = { - type: true, - src: true, - nonce: true, - noModule: true - }; - - function DOMEval( code, node, doc ) { - doc = doc || document; - - var i, val, - script = doc.createElement( "script" ); - - script.text = code; - if ( node ) { - for ( i in preservedScriptAttributes ) { - - // Support: Firefox 64+, Edge 18+ - // Some browsers don't support the "nonce" property on scripts. - // On the other hand, just using `getAttribute` is not enough as - // the `nonce` attribute is reset to an empty string whenever it - // becomes browsing-context connected. - // See https://github.com/whatwg/html/issues/2369 - // See https://html.spec.whatwg.org/#nonce-attributes - // The `node.getAttribute` check was added for the sake of - // `jQuery.globalEval` so that it can fake a nonce-containing node - // via an object. - val = node[ i ] || node.getAttribute && node.getAttribute( i ); - if ( val ) { - script.setAttribute( i, val ); - } - } - } - doc.head.appendChild( script ).parentNode.removeChild( script ); - } - - - function toType( obj ) { - if ( obj == null ) { - return obj + ""; - } - - // Support: Android <=2.3 only (functionish RegExp) - return typeof obj === "object" || typeof obj === "function" ? - class2type[ toString.call( obj ) ] || "object" : - typeof obj; - } - /* global Symbol */ - // Defining this global in .eslintrc.json would create a danger of using the global - // unguarded in another place, it seems safer to define global only for this module - - - - var - version = "3.5.1", - - // Define a local copy of jQuery - jQuery = function( selector, context ) { - - // The jQuery object is actually just the init constructor 'enhanced' - // Need init if jQuery is called (just allow error to be thrown if not included) - return new jQuery.fn.init( selector, context ); - }; - - jQuery.fn = jQuery.prototype = { - - // The current version of jQuery being used - jquery: version, - - constructor: jQuery, - - // The default length of a jQuery object is 0 - length: 0, - - toArray: function() { - return slice.call( this ); - }, - - // Get the Nth element in the matched element set OR - // Get the whole matched element set as a clean array - get: function( num ) { - - // Return all the elements in a clean array - if ( num == null ) { - return slice.call( this ); - } - - // Return just the one element from the set - return num < 0 ? this[ num + this.length ] : this[ num ]; - }, - - // Take an array of elements and push it onto the stack - // (returning the new matched element set) - pushStack: function( elems ) { - - // Build a new jQuery matched element set - var ret = jQuery.merge( this.constructor(), elems ); - - // Add the old object onto the stack (as a reference) - ret.prevObject = this; - - // Return the newly-formed element set - return ret; - }, - - // Execute a callback for every element in the matched set. - each: function( callback ) { - return jQuery.each( this, callback ); - }, - - map: function( callback ) { - return this.pushStack( jQuery.map( this, function( elem, i ) { - return callback.call( elem, i, elem ); - } ) ); - }, - - slice: function() { - return this.pushStack( slice.apply( this, arguments ) ); - }, - - first: function() { - return this.eq( 0 ); - }, - - last: function() { - return this.eq( -1 ); - }, - - even: function() { - return this.pushStack( jQuery.grep( this, function( _elem, i ) { - return ( i + 1 ) % 2; - } ) ); - }, - - odd: function() { - return this.pushStack( jQuery.grep( this, function( _elem, i ) { - return i % 2; - } ) ); - }, - - eq: function( i ) { - var len = this.length, - j = +i + ( i < 0 ? len : 0 ); - return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); - }, - - end: function() { - return this.prevObject || this.constructor(); - }, - - // For internal use only. - // Behaves like an Array's method, not like a jQuery method. - push: push, - sort: arr.sort, - splice: arr.splice - }; - - jQuery.extend = jQuery.fn.extend = function() { - var options, name, src, copy, copyIsArray, clone, - target = arguments[ 0 ] || {}, - i = 1, - length = arguments.length, - deep = false; - - // Handle a deep copy situation - if ( typeof target === "boolean" ) { - deep = target; - - // Skip the boolean and the target - target = arguments[ i ] || {}; - i++; - } - - // Handle case when target is a string or something (possible in deep copy) - if ( typeof target !== "object" && !isFunction( target ) ) { - target = {}; - } - - // Extend jQuery itself if only one argument is passed - if ( i === length ) { - target = this; - i--; - } - - for ( ; i < length; i++ ) { - - // Only deal with non-null/undefined values - if ( ( options = arguments[ i ] ) != null ) { - - // Extend the base object - for ( name in options ) { - copy = options[ name ]; - - // Prevent Object.prototype pollution - // Prevent never-ending loop - if ( name === "__proto__" || target === copy ) { - continue; - } - - // Recurse if we're merging plain objects or arrays - if ( deep && copy && ( jQuery.isPlainObject( copy ) || - ( copyIsArray = Array.isArray( copy ) ) ) ) { - src = target[ name ]; - - // Ensure proper type for the source value - if ( copyIsArray && !Array.isArray( src ) ) { - clone = []; - } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { - clone = {}; - } else { - clone = src; - } - copyIsArray = false; - - // Never move original objects, clone them - target[ name ] = jQuery.extend( deep, clone, copy ); - - // Don't bring in undefined values - } else if ( copy !== undefined ) { - target[ name ] = copy; - } - } - } - } - - // Return the modified object - return target; - }; - - jQuery.extend( { - - // Unique for each copy of jQuery on the page - expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), - - // Assume jQuery is ready without the ready module - isReady: true, - - error: function( msg ) { - throw new Error( msg ); - }, - - noop: function() {}, - - isPlainObject: function( obj ) { - var proto, Ctor; - - // Detect obvious negatives - // Use toString instead of jQuery.type to catch host objects - if ( !obj || toString.call( obj ) !== "[object Object]" ) { - return false; - } - - proto = getProto( obj ); - - // Objects with no prototype (e.g., `Object.create( null )`) are plain - if ( !proto ) { - return true; - } - - // Objects with prototype are plain iff they were constructed by a global Object function - Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; - return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; - }, - - isEmptyObject: function( obj ) { - var name; - - for ( name in obj ) { - return false; - } - return true; - }, - - // Evaluates a script in a provided context; falls back to the global one - // if not specified. - globalEval: function( code, options, doc ) { - DOMEval( code, { nonce: options && options.nonce }, doc ); - }, - - each: function( obj, callback ) { - var length, i = 0; - - if ( isArrayLike( obj ) ) { - length = obj.length; - for ( ; i < length; i++ ) { - if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { - break; - } - } - } else { - for ( i in obj ) { - if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { - break; - } - } - } - - return obj; - }, - - // results is for internal usage only - makeArray: function( arr, results ) { - var ret = results || []; - - if ( arr != null ) { - if ( isArrayLike( Object( arr ) ) ) { - jQuery.merge( ret, - typeof arr === "string" ? - [ arr ] : arr - ); - } else { - push.call( ret, arr ); - } - } - - return ret; - }, - - inArray: function( elem, arr, i ) { - return arr == null ? -1 : indexOf.call( arr, elem, i ); - }, - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - merge: function( first, second ) { - var len = +second.length, - j = 0, - i = first.length; - - for ( ; j < len; j++ ) { - first[ i++ ] = second[ j ]; - } - - first.length = i; - - return first; - }, - - grep: function( elems, callback, invert ) { - var callbackInverse, - matches = [], - i = 0, - length = elems.length, - callbackExpect = !invert; - - // Go through the array, only saving the items - // that pass the validator function - for ( ; i < length; i++ ) { - callbackInverse = !callback( elems[ i ], i ); - if ( callbackInverse !== callbackExpect ) { - matches.push( elems[ i ] ); - } - } - - return matches; - }, - - // arg is for internal usage only - map: function( elems, callback, arg ) { - var length, value, - i = 0, - ret = []; - - // Go through the array, translating each of the items to their new values - if ( isArrayLike( elems ) ) { - length = elems.length; - for ( ; i < length; i++ ) { - value = callback( elems[ i ], i, arg ); - - if ( value != null ) { - ret.push( value ); - } - } - - // Go through every key on the object, - } else { - for ( i in elems ) { - value = callback( elems[ i ], i, arg ); - - if ( value != null ) { - ret.push( value ); - } - } - } - - // Flatten any nested arrays - return flat( ret ); - }, - - // A global GUID counter for objects - guid: 1, - - // jQuery.support is not used in Core but other projects attach their - // properties to it so it needs to exist. - support: support - } ); - - if ( typeof Symbol === "function" ) { - jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; - } - - // Populate the class2type map - jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), - function( _i, name ) { - class2type[ "[object " + name + "]" ] = name.toLowerCase(); - } ); - - function isArrayLike( obj ) { - - // Support: real iOS 8.2 only (not reproducible in simulator) - // `in` check used to prevent JIT error (gh-2145) - // hasOwn isn't used here due to false negatives - // regarding Nodelist length in IE - var length = !!obj && "length" in obj && obj.length, - type = toType( obj ); - - if ( isFunction( obj ) || isWindow( obj ) ) { - return false; - } - - return type === "array" || length === 0 || - typeof length === "number" && length > 0 && ( length - 1 ) in obj; - } - var Sizzle = - /*! - * Sizzle CSS Selector Engine v2.3.5 - * https://sizzlejs.com/ - * - * Copyright JS Foundation and other contributors - * Released under the MIT license - * https://js.foundation/ - * - * Date: 2020-03-14 - */ - ( function( window ) { - var i, - support, - Expr, - getText, - isXML, - tokenize, - compile, - select, - outermostContext, - sortInput, - hasDuplicate, - - // Local document vars - setDocument, - document, - docElem, - documentIsHTML, - rbuggyQSA, - rbuggyMatches, - matches, - contains, - - // Instance-specific data - expando = "sizzle" + 1 * new Date(), - preferredDoc = window.document, - dirruns = 0, - done = 0, - classCache = createCache(), - tokenCache = createCache(), - compilerCache = createCache(), - nonnativeSelectorCache = createCache(), - sortOrder = function( a, b ) { - if ( a === b ) { - hasDuplicate = true; - } - return 0; - }, - - // Instance methods - hasOwn = ( {} ).hasOwnProperty, - arr = [], - pop = arr.pop, - pushNative = arr.push, - push = arr.push, - slice = arr.slice, - - // Use a stripped-down indexOf as it's faster than native - // https://jsperf.com/thor-indexof-vs-for/5 - indexOf = function( list, elem ) { - var i = 0, - len = list.length; - for ( ; i < len; i++ ) { - if ( list[ i ] === elem ) { - return i; - } - } - return -1; - }, - - booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + - "ismap|loop|multiple|open|readonly|required|scoped", - - // Regular expressions - - // http://www.w3.org/TR/css3-selectors/#whitespace - whitespace = "[\\x20\\t\\r\\n\\f]", - - // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram - identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + - "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", - - // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors - attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + - - // Operator (capture 2) - "*([*^$|!~]?=)" + whitespace + - - // "Attribute values must be CSS identifiers [capture 5] - // or strings [capture 3 or capture 4]" - "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + - whitespace + "*\\]", - - pseudos = ":(" + identifier + ")(?:\\((" + - - // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: - // 1. quoted (capture 3; capture 4 or capture 5) - "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + - - // 2. simple (capture 6) - "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + - - // 3. anything else (capture 2) - ".*" + - ")\\)|)", - - // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter - rwhitespace = new RegExp( whitespace + "+", "g" ), - rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + - whitespace + "+$", "g" ), - - rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), - rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + - "*" ), - rdescend = new RegExp( whitespace + "|>" ), - - rpseudo = new RegExp( pseudos ), - ridentifier = new RegExp( "^" + identifier + "$" ), - - matchExpr = { - "ID": new RegExp( "^#(" + identifier + ")" ), - "CLASS": new RegExp( "^\\.(" + identifier + ")" ), - "TAG": new RegExp( "^(" + identifier + "|[*])" ), - "ATTR": new RegExp( "^" + attributes ), - "PSEUDO": new RegExp( "^" + pseudos ), - "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + - whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + - whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), - "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), - - // For use in libraries implementing .is() - // We use this for POS matching in `select` - "needsContext": new RegExp( "^" + whitespace + - "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + - "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) - }, - - rhtml = /HTML$/i, - rinputs = /^(?:input|select|textarea|button)$/i, - rheader = /^h\d$/i, - - rnative = /^[^{]+\{\s*\[native \w/, - - // Easily-parseable/retrievable ID or TAG or CLASS selectors - rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, - - rsibling = /[+~]/, - - // CSS escapes - // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters - runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), - funescape = function( escape, nonHex ) { - var high = "0x" + escape.slice( 1 ) - 0x10000; - - return nonHex ? - - // Strip the backslash prefix from a non-hex escape sequence - nonHex : - - // Replace a hexadecimal escape sequence with the encoded Unicode code point - // Support: IE <=11+ - // For values outside the Basic Multilingual Plane (BMP), manually construct a - // surrogate pair - high < 0 ? - String.fromCharCode( high + 0x10000 ) : - String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); - }, - - // CSS string/identifier serialization - // https://drafts.csswg.org/cssom/#common-serializing-idioms - rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, - fcssescape = function( ch, asCodePoint ) { - if ( asCodePoint ) { - - // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER - if ( ch === "\0" ) { - return "\uFFFD"; - } - - // Control characters and (dependent upon position) numbers get escaped as code points - return ch.slice( 0, -1 ) + "\\" + - ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; - } - - // Other potentially-special ASCII characters get backslash-escaped - return "\\" + ch; - }, - - // Used for iframes - // See setDocument() - // Removing the function wrapper causes a "Permission Denied" - // error in IE - unloadHandler = function() { - setDocument(); - }, - - inDisabledFieldset = addCombinator( - function( elem ) { - return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; - }, - { dir: "parentNode", next: "legend" } - ); - - // Optimize for push.apply( _, NodeList ) - try { - push.apply( - ( arr = slice.call( preferredDoc.childNodes ) ), - preferredDoc.childNodes - ); - - // Support: Android<4.0 - // Detect silently failing push.apply - // eslint-disable-next-line no-unused-expressions - arr[ preferredDoc.childNodes.length ].nodeType; - } catch ( e ) { - push = { apply: arr.length ? - - // Leverage slice if possible - function( target, els ) { - pushNative.apply( target, slice.call( els ) ); - } : - - // Support: IE<9 - // Otherwise append directly - function( target, els ) { - var j = target.length, - i = 0; - - // Can't trust NodeList.length - while ( ( target[ j++ ] = els[ i++ ] ) ) {} - target.length = j - 1; - } - }; - } - - function Sizzle( selector, context, results, seed ) { - var m, i, elem, nid, match, groups, newSelector, - newContext = context && context.ownerDocument, - - // nodeType defaults to 9, since context defaults to document - nodeType = context ? context.nodeType : 9; - - results = results || []; - - // Return early from calls with invalid selector or context - if ( typeof selector !== "string" || !selector || - nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { - - return results; - } - - // Try to shortcut find operations (as opposed to filters) in HTML documents - if ( !seed ) { - setDocument( context ); - context = context || document; - - if ( documentIsHTML ) { - - // If the selector is sufficiently simple, try using a "get*By*" DOM method - // (excepting DocumentFragment context, where the methods don't exist) - if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { - - // ID selector - if ( ( m = match[ 1 ] ) ) { - - // Document context - if ( nodeType === 9 ) { - if ( ( elem = context.getElementById( m ) ) ) { - - // Support: IE, Opera, Webkit - // TODO: identify versions - // getElementById can match elements by name instead of ID - if ( elem.id === m ) { - results.push( elem ); - return results; - } - } else { - return results; - } - - // Element context - } else { - - // Support: IE, Opera, Webkit - // TODO: identify versions - // getElementById can match elements by name instead of ID - if ( newContext && ( elem = newContext.getElementById( m ) ) && - contains( context, elem ) && - elem.id === m ) { - - results.push( elem ); - return results; - } - } - - // Type selector - } else if ( match[ 2 ] ) { - push.apply( results, context.getElementsByTagName( selector ) ); - return results; - - // Class selector - } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && - context.getElementsByClassName ) { - - push.apply( results, context.getElementsByClassName( m ) ); - return results; - } - } - - // Take advantage of querySelectorAll - if ( support.qsa && - !nonnativeSelectorCache[ selector + " " ] && - ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && - - // Support: IE 8 only - // Exclude object elements - ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { - - newSelector = selector; - newContext = context; - - // qSA considers elements outside a scoping root when evaluating child or - // descendant combinators, which is not what we want. - // In such cases, we work around the behavior by prefixing every selector in the - // list with an ID selector referencing the scope context. - // The technique has to be used as well when a leading combinator is used - // as such selectors are not recognized by querySelectorAll. - // Thanks to Andrew Dupont for this technique. - if ( nodeType === 1 && - ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { - - // Expand context for sibling selectors - newContext = rsibling.test( selector ) && testContext( context.parentNode ) || - context; - - // We can use :scope instead of the ID hack if the browser - // supports it & if we're not changing the context. - if ( newContext !== context || !support.scope ) { - - // Capture the context ID, setting it first if necessary - if ( ( nid = context.getAttribute( "id" ) ) ) { - nid = nid.replace( rcssescape, fcssescape ); - } else { - context.setAttribute( "id", ( nid = expando ) ); - } - } - - // Prefix every selector in the list - groups = tokenize( selector ); - i = groups.length; - while ( i-- ) { - groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + - toSelector( groups[ i ] ); - } - newSelector = groups.join( "," ); - } - - try { - push.apply( results, - newContext.querySelectorAll( newSelector ) - ); - return results; - } catch ( qsaError ) { - nonnativeSelectorCache( selector, true ); - } finally { - if ( nid === expando ) { - context.removeAttribute( "id" ); - } - } - } - } - } - - // All others - return select( selector.replace( rtrim, "$1" ), context, results, seed ); - } - - /** - * Create key-value caches of limited size - * @returns {function(string, object)} Returns the Object data after storing it on itself with - * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) - * deleting the oldest entry - */ - function createCache() { - var keys = []; - - function cache( key, value ) { - - // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) - if ( keys.push( key + " " ) > Expr.cacheLength ) { - - // Only keep the most recent entries - delete cache[ keys.shift() ]; - } - return ( cache[ key + " " ] = value ); - } - return cache; - } - - /** - * Mark a function for special use by Sizzle - * @param {Function} fn The function to mark - */ - function markFunction( fn ) { - fn[ expando ] = true; - return fn; - } - - /** - * Support testing using an element - * @param {Function} fn Passed the created element and returns a boolean result - */ - function assert( fn ) { - var el = document.createElement( "fieldset" ); - - try { - return !!fn( el ); - } catch ( e ) { - return false; - } finally { - - // Remove from its parent by default - if ( el.parentNode ) { - el.parentNode.removeChild( el ); - } - - // release memory in IE - el = null; - } - } - - /** - * Adds the same handler for all of the specified attrs - * @param {String} attrs Pipe-separated list of attributes - * @param {Function} handler The method that will be applied - */ - function addHandle( attrs, handler ) { - var arr = attrs.split( "|" ), - i = arr.length; - - while ( i-- ) { - Expr.attrHandle[ arr[ i ] ] = handler; - } - } - - /** - * Checks document order of two siblings - * @param {Element} a - * @param {Element} b - * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b - */ - function siblingCheck( a, b ) { - var cur = b && a, - diff = cur && a.nodeType === 1 && b.nodeType === 1 && - a.sourceIndex - b.sourceIndex; - - // Use IE sourceIndex if available on both nodes - if ( diff ) { - return diff; - } - - // Check if b follows a - if ( cur ) { - while ( ( cur = cur.nextSibling ) ) { - if ( cur === b ) { - return -1; - } - } - } - - return a ? 1 : -1; - } - - /** - * Returns a function to use in pseudos for input types - * @param {String} type - */ - function createInputPseudo( type ) { - return function( elem ) { - var name = elem.nodeName.toLowerCase(); - return name === "input" && elem.type === type; - }; - } - - /** - * Returns a function to use in pseudos for buttons - * @param {String} type - */ - function createButtonPseudo( type ) { - return function( elem ) { - var name = elem.nodeName.toLowerCase(); - return ( name === "input" || name === "button" ) && elem.type === type; - }; - } - - /** - * Returns a function to use in pseudos for :enabled/:disabled - * @param {Boolean} disabled true for :disabled; false for :enabled - */ - function createDisabledPseudo( disabled ) { - - // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable - return function( elem ) { - - // Only certain elements can match :enabled or :disabled - // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled - // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled - if ( "form" in elem ) { - - // Check for inherited disabledness on relevant non-disabled elements: - // * listed form-associated elements in a disabled fieldset - // https://html.spec.whatwg.org/multipage/forms.html#category-listed - // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled - // * option elements in a disabled optgroup - // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled - // All such elements have a "form" property. - if ( elem.parentNode && elem.disabled === false ) { - - // Option elements defer to a parent optgroup if present - if ( "label" in elem ) { - if ( "label" in elem.parentNode ) { - return elem.parentNode.disabled === disabled; - } else { - return elem.disabled === disabled; - } - } - - // Support: IE 6 - 11 - // Use the isDisabled shortcut property to check for disabled fieldset ancestors - return elem.isDisabled === disabled || - - // Where there is no isDisabled, check manually - /* jshint -W018 */ - elem.isDisabled !== !disabled && - inDisabledFieldset( elem ) === disabled; - } - - return elem.disabled === disabled; - - // Try to winnow out elements that can't be disabled before trusting the disabled property. - // Some victims get caught in our net (label, legend, menu, track), but it shouldn't - // even exist on them, let alone have a boolean value. - } else if ( "label" in elem ) { - return elem.disabled === disabled; - } - - // Remaining elements are neither :enabled nor :disabled - return false; - }; - } - - /** - * Returns a function to use in pseudos for positionals - * @param {Function} fn - */ - function createPositionalPseudo( fn ) { - return markFunction( function( argument ) { - argument = +argument; - return markFunction( function( seed, matches ) { - var j, - matchIndexes = fn( [], seed.length, argument ), - i = matchIndexes.length; - - // Match elements found at the specified indexes - while ( i-- ) { - if ( seed[ ( j = matchIndexes[ i ] ) ] ) { - seed[ j ] = !( matches[ j ] = seed[ j ] ); - } - } - } ); - } ); - } - - /** - * Checks a node for validity as a Sizzle context - * @param {Element|Object=} context - * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value - */ - function testContext( context ) { - return context && typeof context.getElementsByTagName !== "undefined" && context; - } - - // Expose support vars for convenience - support = Sizzle.support = {}; - - /** - * Detects XML nodes - * @param {Element|Object} elem An element or a document - * @returns {Boolean} True iff elem is a non-HTML XML node - */ - isXML = Sizzle.isXML = function( elem ) { - var namespace = elem.namespaceURI, - docElem = ( elem.ownerDocument || elem ).documentElement; - - // Support: IE <=8 - // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes - // https://bugs.jquery.com/ticket/4833 - return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); - }; - - /** - * Sets document-related variables once based on the current document - * @param {Element|Object} [doc] An element or document object to use to set the document - * @returns {Object} Returns the current document - */ - setDocument = Sizzle.setDocument = function( node ) { - var hasCompare, subWindow, - doc = node ? node.ownerDocument || node : preferredDoc; - - // Return early if doc is invalid or already selected - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { - return document; - } - - // Update global variables - document = doc; - docElem = document.documentElement; - documentIsHTML = !isXML( document ); - - // Support: IE 9 - 11+, Edge 12 - 18+ - // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( preferredDoc != document && - ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { - - // Support: IE 11, Edge - if ( subWindow.addEventListener ) { - subWindow.addEventListener( "unload", unloadHandler, false ); - - // Support: IE 9 - 10 only - } else if ( subWindow.attachEvent ) { - subWindow.attachEvent( "onunload", unloadHandler ); - } - } - - // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, - // Safari 4 - 5 only, Opera <=11.6 - 12.x only - // IE/Edge & older browsers don't support the :scope pseudo-class. - // Support: Safari 6.0 only - // Safari 6.0 supports :scope but it's an alias of :root there. - support.scope = assert( function( el ) { - docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); - return typeof el.querySelectorAll !== "undefined" && - !el.querySelectorAll( ":scope fieldset div" ).length; - } ); - - /* Attributes - ---------------------------------------------------------------------- */ - - // Support: IE<8 - // Verify that getAttribute really returns attributes and not properties - // (excepting IE8 booleans) - support.attributes = assert( function( el ) { - el.className = "i"; - return !el.getAttribute( "className" ); - } ); - - /* getElement(s)By* - ---------------------------------------------------------------------- */ - - // Check if getElementsByTagName("*") returns only elements - support.getElementsByTagName = assert( function( el ) { - el.appendChild( document.createComment( "" ) ); - return !el.getElementsByTagName( "*" ).length; - } ); - - // Support: IE<9 - support.getElementsByClassName = rnative.test( document.getElementsByClassName ); - - // Support: IE<10 - // Check if getElementById returns elements by name - // The broken getElementById methods don't pick up programmatically-set names, - // so use a roundabout getElementsByName test - support.getById = assert( function( el ) { - docElem.appendChild( el ).id = expando; - return !document.getElementsByName || !document.getElementsByName( expando ).length; - } ); - - // ID filter and find - if ( support.getById ) { - Expr.filter[ "ID" ] = function( id ) { - var attrId = id.replace( runescape, funescape ); - return function( elem ) { - return elem.getAttribute( "id" ) === attrId; - }; - }; - Expr.find[ "ID" ] = function( id, context ) { - if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { - var elem = context.getElementById( id ); - return elem ? [ elem ] : []; - } - }; - } else { - Expr.filter[ "ID" ] = function( id ) { - var attrId = id.replace( runescape, funescape ); - return function( elem ) { - var node = typeof elem.getAttributeNode !== "undefined" && - elem.getAttributeNode( "id" ); - return node && node.value === attrId; - }; - }; - - // Support: IE 6 - 7 only - // getElementById is not reliable as a find shortcut - Expr.find[ "ID" ] = function( id, context ) { - if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { - var node, i, elems, - elem = context.getElementById( id ); - - if ( elem ) { - - // Verify the id attribute - node = elem.getAttributeNode( "id" ); - if ( node && node.value === id ) { - return [ elem ]; - } - - // Fall back on getElementsByName - elems = context.getElementsByName( id ); - i = 0; - while ( ( elem = elems[ i++ ] ) ) { - node = elem.getAttributeNode( "id" ); - if ( node && node.value === id ) { - return [ elem ]; - } - } - } - - return []; - } - }; - } - - // Tag - Expr.find[ "TAG" ] = support.getElementsByTagName ? - function( tag, context ) { - if ( typeof context.getElementsByTagName !== "undefined" ) { - return context.getElementsByTagName( tag ); - - // DocumentFragment nodes don't have gEBTN - } else if ( support.qsa ) { - return context.querySelectorAll( tag ); - } - } : - - function( tag, context ) { - var elem, - tmp = [], - i = 0, - - // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too - results = context.getElementsByTagName( tag ); - - // Filter out possible comments - if ( tag === "*" ) { - while ( ( elem = results[ i++ ] ) ) { - if ( elem.nodeType === 1 ) { - tmp.push( elem ); - } - } - - return tmp; - } - return results; - }; - - // Class - Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { - if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { - return context.getElementsByClassName( className ); - } - }; - - /* QSA/matchesSelector - ---------------------------------------------------------------------- */ - - // QSA and matchesSelector support - - // matchesSelector(:active) reports false when true (IE9/Opera 11.5) - rbuggyMatches = []; - - // qSa(:focus) reports false when true (Chrome 21) - // We allow this because of a bug in IE8/9 that throws an error - // whenever `document.activeElement` is accessed on an iframe - // So, we allow :focus to pass through QSA all the time to avoid the IE error - // See https://bugs.jquery.com/ticket/13378 - rbuggyQSA = []; - - if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { - - // Build QSA regex - // Regex strategy adopted from Diego Perini - assert( function( el ) { - - var input; - - // Select is set to empty string on purpose - // This is to test IE's treatment of not explicitly - // setting a boolean content attribute, - // since its presence should be enough - // https://bugs.jquery.com/ticket/12359 - docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" + - "<select id='" + expando + "-\r\\' msallowcapture=''>" + - "<option selected=''></option></select>"; - - // Support: IE8, Opera 11-12.16 - // Nothing should be selected when empty strings follow ^= or $= or *= - // The test attribute must be unknown in Opera but "safe" for WinRT - // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section - if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { - rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); - } - - // Support: IE8 - // Boolean attributes and "value" are not treated correctly - if ( !el.querySelectorAll( "[selected]" ).length ) { - rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); - } - - // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ - if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { - rbuggyQSA.push( "~=" ); - } - - // Support: IE 11+, Edge 15 - 18+ - // IE 11/Edge don't find elements on a `[name='']` query in some cases. - // Adding a temporary attribute to the document before the selection works - // around the issue. - // Interestingly, IE 10 & older don't seem to have the issue. - input = document.createElement( "input" ); - input.setAttribute( "name", "" ); - el.appendChild( input ); - if ( !el.querySelectorAll( "[name='']" ).length ) { - rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + - whitespace + "*(?:''|\"\")" ); - } - - // Webkit/Opera - :checked should return selected option elements - // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked - // IE8 throws error here and will not see later tests - if ( !el.querySelectorAll( ":checked" ).length ) { - rbuggyQSA.push( ":checked" ); - } - - // Support: Safari 8+, iOS 8+ - // https://bugs.webkit.org/show_bug.cgi?id=136851 - // In-page `selector#id sibling-combinator selector` fails - if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { - rbuggyQSA.push( ".#.+[+~]" ); - } - - // Support: Firefox <=3.6 - 5 only - // Old Firefox doesn't throw on a badly-escaped identifier. - el.querySelectorAll( "\\\f" ); - rbuggyQSA.push( "[\\r\\n\\f]" ); - } ); - - assert( function( el ) { - el.innerHTML = "<a href='' disabled='disabled'></a>" + - "<select disabled='disabled'><option/></select>"; - - // Support: Windows 8 Native Apps - // The type and name attributes are restricted during .innerHTML assignment - var input = document.createElement( "input" ); - input.setAttribute( "type", "hidden" ); - el.appendChild( input ).setAttribute( "name", "D" ); - - // Support: IE8 - // Enforce case-sensitivity of name attribute - if ( el.querySelectorAll( "[name=d]" ).length ) { - rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); - } - - // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) - // IE8 throws error here and will not see later tests - if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { - rbuggyQSA.push( ":enabled", ":disabled" ); - } - - // Support: IE9-11+ - // IE's :disabled selector does not pick up the children of disabled fieldsets - docElem.appendChild( el ).disabled = true; - if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { - rbuggyQSA.push( ":enabled", ":disabled" ); - } - - // Support: Opera 10 - 11 only - // Opera 10-11 does not throw on post-comma invalid pseudos - el.querySelectorAll( "*,:x" ); - rbuggyQSA.push( ",.*:" ); - } ); - } - - if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || - docElem.webkitMatchesSelector || - docElem.mozMatchesSelector || - docElem.oMatchesSelector || - docElem.msMatchesSelector ) ) ) ) { - - assert( function( el ) { - - // Check to see if it's possible to do matchesSelector - // on a disconnected node (IE 9) - support.disconnectedMatch = matches.call( el, "*" ); - - // This should fail with an exception - // Gecko does not error, returns false instead - matches.call( el, "[s!='']:x" ); - rbuggyMatches.push( "!=", pseudos ); - } ); - } - - rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); - rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); - - /* Contains - ---------------------------------------------------------------------- */ - hasCompare = rnative.test( docElem.compareDocumentPosition ); - - // Element contains another - // Purposefully self-exclusive - // As in, an element does not contain itself - contains = hasCompare || rnative.test( docElem.contains ) ? - function( a, b ) { - var adown = a.nodeType === 9 ? a.documentElement : a, - bup = b && b.parentNode; - return a === bup || !!( bup && bup.nodeType === 1 && ( - adown.contains ? - adown.contains( bup ) : - a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 - ) ); - } : - function( a, b ) { - if ( b ) { - while ( ( b = b.parentNode ) ) { - if ( b === a ) { - return true; - } - } - } - return false; - }; - - /* Sorting - ---------------------------------------------------------------------- */ - - // Document order sorting - sortOrder = hasCompare ? - function( a, b ) { - - // Flag for duplicate removal - if ( a === b ) { - hasDuplicate = true; - return 0; - } - - // Sort on method existence if only one input has compareDocumentPosition - var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; - if ( compare ) { - return compare; - } - - // Calculate position if both inputs belong to the same document - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? - a.compareDocumentPosition( b ) : - - // Otherwise we know they are disconnected - 1; - - // Disconnected nodes - if ( compare & 1 || - ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { - - // Choose the first element that is related to our preferred document - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( a == document || a.ownerDocument == preferredDoc && - contains( preferredDoc, a ) ) { - return -1; - } - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( b == document || b.ownerDocument == preferredDoc && - contains( preferredDoc, b ) ) { - return 1; - } - - // Maintain original order - return sortInput ? - ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : - 0; - } - - return compare & 4 ? -1 : 1; - } : - function( a, b ) { - - // Exit early if the nodes are identical - if ( a === b ) { - hasDuplicate = true; - return 0; - } - - var cur, - i = 0, - aup = a.parentNode, - bup = b.parentNode, - ap = [ a ], - bp = [ b ]; - - // Parentless nodes are either documents or disconnected - if ( !aup || !bup ) { - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - /* eslint-disable eqeqeq */ - return a == document ? -1 : - b == document ? 1 : - /* eslint-enable eqeqeq */ - aup ? -1 : - bup ? 1 : - sortInput ? - ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : - 0; - - // If the nodes are siblings, we can do a quick check - } else if ( aup === bup ) { - return siblingCheck( a, b ); - } - - // Otherwise we need full lists of their ancestors for comparison - cur = a; - while ( ( cur = cur.parentNode ) ) { - ap.unshift( cur ); - } - cur = b; - while ( ( cur = cur.parentNode ) ) { - bp.unshift( cur ); - } - - // Walk down the tree looking for a discrepancy - while ( ap[ i ] === bp[ i ] ) { - i++; - } - - return i ? - - // Do a sibling check if the nodes have a common ancestor - siblingCheck( ap[ i ], bp[ i ] ) : - - // Otherwise nodes in our document sort first - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - /* eslint-disable eqeqeq */ - ap[ i ] == preferredDoc ? -1 : - bp[ i ] == preferredDoc ? 1 : - /* eslint-enable eqeqeq */ - 0; - }; - - return document; - }; - - Sizzle.matches = function( expr, elements ) { - return Sizzle( expr, null, null, elements ); - }; - - Sizzle.matchesSelector = function( elem, expr ) { - setDocument( elem ); - - if ( support.matchesSelector && documentIsHTML && - !nonnativeSelectorCache[ expr + " " ] && - ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && - ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { - - try { - var ret = matches.call( elem, expr ); - - // IE 9's matchesSelector returns false on disconnected nodes - if ( ret || support.disconnectedMatch || - - // As well, disconnected nodes are said to be in a document - // fragment in IE 9 - elem.document && elem.document.nodeType !== 11 ) { - return ret; - } - } catch ( e ) { - nonnativeSelectorCache( expr, true ); - } - } - - return Sizzle( expr, document, null, [ elem ] ).length > 0; - }; - - Sizzle.contains = function( context, elem ) { - - // Set document vars if needed - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( ( context.ownerDocument || context ) != document ) { - setDocument( context ); - } - return contains( context, elem ); - }; - - Sizzle.attr = function( elem, name ) { - - // Set document vars if needed - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( ( elem.ownerDocument || elem ) != document ) { - setDocument( elem ); - } - - var fn = Expr.attrHandle[ name.toLowerCase() ], - - // Don't get fooled by Object.prototype properties (jQuery #13807) - val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? - fn( elem, name, !documentIsHTML ) : - undefined; - - return val !== undefined ? - val : - support.attributes || !documentIsHTML ? - elem.getAttribute( name ) : - ( val = elem.getAttributeNode( name ) ) && val.specified ? - val.value : - null; - }; - - Sizzle.escape = function( sel ) { - return ( sel + "" ).replace( rcssescape, fcssescape ); - }; - - Sizzle.error = function( msg ) { - throw new Error( "Syntax error, unrecognized expression: " + msg ); - }; - - /** - * Document sorting and removing duplicates - * @param {ArrayLike} results - */ - Sizzle.uniqueSort = function( results ) { - var elem, - duplicates = [], - j = 0, - i = 0; - - // Unless we *know* we can detect duplicates, assume their presence - hasDuplicate = !support.detectDuplicates; - sortInput = !support.sortStable && results.slice( 0 ); - results.sort( sortOrder ); - - if ( hasDuplicate ) { - while ( ( elem = results[ i++ ] ) ) { - if ( elem === results[ i ] ) { - j = duplicates.push( i ); - } - } - while ( j-- ) { - results.splice( duplicates[ j ], 1 ); - } - } - - // Clear input after sorting to release objects - // See https://github.com/jquery/sizzle/pull/225 - sortInput = null; - - return results; - }; - - /** - * Utility function for retrieving the text value of an array of DOM nodes - * @param {Array|Element} elem - */ - getText = Sizzle.getText = function( elem ) { - var node, - ret = "", - i = 0, - nodeType = elem.nodeType; - - if ( !nodeType ) { - - // If no nodeType, this is expected to be an array - while ( ( node = elem[ i++ ] ) ) { - - // Do not traverse comment nodes - ret += getText( node ); - } - } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { - - // Use textContent for elements - // innerText usage removed for consistency of new lines (jQuery #11153) - if ( typeof elem.textContent === "string" ) { - return elem.textContent; - } else { - - // Traverse its children - for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { - ret += getText( elem ); - } - } - } else if ( nodeType === 3 || nodeType === 4 ) { - return elem.nodeValue; - } - - // Do not include comment or processing instruction nodes - - return ret; - }; - - Expr = Sizzle.selectors = { - - // Can be adjusted by the user - cacheLength: 50, - - createPseudo: markFunction, - - match: matchExpr, - - attrHandle: {}, - - find: {}, - - relative: { - ">": { dir: "parentNode", first: true }, - " ": { dir: "parentNode" }, - "+": { dir: "previousSibling", first: true }, - "~": { dir: "previousSibling" } - }, - - preFilter: { - "ATTR": function( match ) { - match[ 1 ] = match[ 1 ].replace( runescape, funescape ); - - // Move the given value to match[3] whether quoted or unquoted - match[ 3 ] = ( match[ 3 ] || match[ 4 ] || - match[ 5 ] || "" ).replace( runescape, funescape ); - - if ( match[ 2 ] === "~=" ) { - match[ 3 ] = " " + match[ 3 ] + " "; - } - - return match.slice( 0, 4 ); - }, - - "CHILD": function( match ) { - - /* matches from matchExpr["CHILD"] - 1 type (only|nth|...) - 2 what (child|of-type) - 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) - 4 xn-component of xn+y argument ([+-]?\d*n|) - 5 sign of xn-component - 6 x of xn-component - 7 sign of y-component - 8 y of y-component - */ - match[ 1 ] = match[ 1 ].toLowerCase(); - - if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { - - // nth-* requires argument - if ( !match[ 3 ] ) { - Sizzle.error( match[ 0 ] ); - } - - // numeric x and y parameters for Expr.filter.CHILD - // remember that false/true cast respectively to 0/1 - match[ 4 ] = +( match[ 4 ] ? - match[ 5 ] + ( match[ 6 ] || 1 ) : - 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); - match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); - - // other types prohibit arguments - } else if ( match[ 3 ] ) { - Sizzle.error( match[ 0 ] ); - } - - return match; - }, - - "PSEUDO": function( match ) { - var excess, - unquoted = !match[ 6 ] && match[ 2 ]; - - if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { - return null; - } - - // Accept quoted arguments as-is - if ( match[ 3 ] ) { - match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; - - // Strip excess characters from unquoted arguments - } else if ( unquoted && rpseudo.test( unquoted ) && - - // Get excess from tokenize (recursively) - ( excess = tokenize( unquoted, true ) ) && - - // advance to the next closing parenthesis - ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { - - // excess is a negative index - match[ 0 ] = match[ 0 ].slice( 0, excess ); - match[ 2 ] = unquoted.slice( 0, excess ); - } - - // Return only captures needed by the pseudo filter method (type and argument) - return match.slice( 0, 3 ); - } - }, - - filter: { - - "TAG": function( nodeNameSelector ) { - var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); - return nodeNameSelector === "*" ? - function() { - return true; - } : - function( elem ) { - return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; - }; - }, - - "CLASS": function( className ) { - var pattern = classCache[ className + " " ]; - - return pattern || - ( pattern = new RegExp( "(^|" + whitespace + - ")" + className + "(" + whitespace + "|$)" ) ) && classCache( - className, function( elem ) { - return pattern.test( - typeof elem.className === "string" && elem.className || - typeof elem.getAttribute !== "undefined" && - elem.getAttribute( "class" ) || - "" - ); - } ); - }, - - "ATTR": function( name, operator, check ) { - return function( elem ) { - var result = Sizzle.attr( elem, name ); - - if ( result == null ) { - return operator === "!="; - } - if ( !operator ) { - return true; - } - - result += ""; - - /* eslint-disable max-len */ - - return operator === "=" ? result === check : - operator === "!=" ? result !== check : - operator === "^=" ? check && result.indexOf( check ) === 0 : - operator === "*=" ? check && result.indexOf( check ) > -1 : - operator === "$=" ? check && result.slice( -check.length ) === check : - operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : - operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : - false; - /* eslint-enable max-len */ - - }; - }, - - "CHILD": function( type, what, _argument, first, last ) { - var simple = type.slice( 0, 3 ) !== "nth", - forward = type.slice( -4 ) !== "last", - ofType = what === "of-type"; - - return first === 1 && last === 0 ? - - // Shortcut for :nth-*(n) - function( elem ) { - return !!elem.parentNode; - } : - - function( elem, _context, xml ) { - var cache, uniqueCache, outerCache, node, nodeIndex, start, - dir = simple !== forward ? "nextSibling" : "previousSibling", - parent = elem.parentNode, - name = ofType && elem.nodeName.toLowerCase(), - useCache = !xml && !ofType, - diff = false; - - if ( parent ) { - - // :(first|last|only)-(child|of-type) - if ( simple ) { - while ( dir ) { - node = elem; - while ( ( node = node[ dir ] ) ) { - if ( ofType ? - node.nodeName.toLowerCase() === name : - node.nodeType === 1 ) { - - return false; - } - } - - // Reverse direction for :only-* (if we haven't yet done so) - start = dir = type === "only" && !start && "nextSibling"; - } - return true; - } - - start = [ forward ? parent.firstChild : parent.lastChild ]; - - // non-xml :nth-child(...) stores cache data on `parent` - if ( forward && useCache ) { - - // Seek `elem` from a previously-cached index - - // ...in a gzip-friendly way - node = parent; - outerCache = node[ expando ] || ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - cache = uniqueCache[ type ] || []; - nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; - diff = nodeIndex && cache[ 2 ]; - node = nodeIndex && parent.childNodes[ nodeIndex ]; - - while ( ( node = ++nodeIndex && node && node[ dir ] || - - // Fallback to seeking `elem` from the start - ( diff = nodeIndex = 0 ) || start.pop() ) ) { - - // When found, cache indexes on `parent` and break - if ( node.nodeType === 1 && ++diff && node === elem ) { - uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; - break; - } - } - - } else { - - // Use previously-cached element index if available - if ( useCache ) { - - // ...in a gzip-friendly way - node = elem; - outerCache = node[ expando ] || ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - cache = uniqueCache[ type ] || []; - nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; - diff = nodeIndex; - } - - // xml :nth-child(...) - // or :nth-last-child(...) or :nth(-last)?-of-type(...) - if ( diff === false ) { - - // Use the same loop as above to seek `elem` from the start - while ( ( node = ++nodeIndex && node && node[ dir ] || - ( diff = nodeIndex = 0 ) || start.pop() ) ) { - - if ( ( ofType ? - node.nodeName.toLowerCase() === name : - node.nodeType === 1 ) && - ++diff ) { - - // Cache the index of each encountered element - if ( useCache ) { - outerCache = node[ expando ] || - ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - uniqueCache[ type ] = [ dirruns, diff ]; - } - - if ( node === elem ) { - break; - } - } - } - } - } - - // Incorporate the offset, then check against cycle size - diff -= last; - return diff === first || ( diff % first === 0 && diff / first >= 0 ); - } - }; - }, - - "PSEUDO": function( pseudo, argument ) { - - // pseudo-class names are case-insensitive - // http://www.w3.org/TR/selectors/#pseudo-classes - // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters - // Remember that setFilters inherits from pseudos - var args, - fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || - Sizzle.error( "unsupported pseudo: " + pseudo ); - - // The user may use createPseudo to indicate that - // arguments are needed to create the filter function - // just as Sizzle does - if ( fn[ expando ] ) { - return fn( argument ); - } - - // But maintain support for old signatures - if ( fn.length > 1 ) { - args = [ pseudo, pseudo, "", argument ]; - return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? - markFunction( function( seed, matches ) { - var idx, - matched = fn( seed, argument ), - i = matched.length; - while ( i-- ) { - idx = indexOf( seed, matched[ i ] ); - seed[ idx ] = !( matches[ idx ] = matched[ i ] ); - } - } ) : - function( elem ) { - return fn( elem, 0, args ); - }; - } - - return fn; - } - }, - - pseudos: { - - // Potentially complex pseudos - "not": markFunction( function( selector ) { - - // Trim the selector passed to compile - // to avoid treating leading and trailing - // spaces as combinators - var input = [], - results = [], - matcher = compile( selector.replace( rtrim, "$1" ) ); - - return matcher[ expando ] ? - markFunction( function( seed, matches, _context, xml ) { - var elem, - unmatched = matcher( seed, null, xml, [] ), - i = seed.length; - - // Match elements unmatched by `matcher` - while ( i-- ) { - if ( ( elem = unmatched[ i ] ) ) { - seed[ i ] = !( matches[ i ] = elem ); - } - } - } ) : - function( elem, _context, xml ) { - input[ 0 ] = elem; - matcher( input, null, xml, results ); - - // Don't keep the element (issue #299) - input[ 0 ] = null; - return !results.pop(); - }; - } ), - - "has": markFunction( function( selector ) { - return function( elem ) { - return Sizzle( selector, elem ).length > 0; - }; - } ), - - "contains": markFunction( function( text ) { - text = text.replace( runescape, funescape ); - return function( elem ) { - return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; - }; - } ), - - // "Whether an element is represented by a :lang() selector - // is based solely on the element's language value - // being equal to the identifier C, - // or beginning with the identifier C immediately followed by "-". - // The matching of C against the element's language value is performed case-insensitively. - // The identifier C does not have to be a valid language name." - // http://www.w3.org/TR/selectors/#lang-pseudo - "lang": markFunction( function( lang ) { - - // lang value must be a valid identifier - if ( !ridentifier.test( lang || "" ) ) { - Sizzle.error( "unsupported lang: " + lang ); - } - lang = lang.replace( runescape, funescape ).toLowerCase(); - return function( elem ) { - var elemLang; - do { - if ( ( elemLang = documentIsHTML ? - elem.lang : - elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { - - elemLang = elemLang.toLowerCase(); - return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; - } - } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); - return false; - }; - } ), - - // Miscellaneous - "target": function( elem ) { - var hash = window.location && window.location.hash; - return hash && hash.slice( 1 ) === elem.id; - }, - - "root": function( elem ) { - return elem === docElem; - }, - - "focus": function( elem ) { - return elem === document.activeElement && - ( !document.hasFocus || document.hasFocus() ) && - !!( elem.type || elem.href || ~elem.tabIndex ); - }, - - // Boolean properties - "enabled": createDisabledPseudo( false ), - "disabled": createDisabledPseudo( true ), - - "checked": function( elem ) { - - // In CSS3, :checked should return both checked and selected elements - // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked - var nodeName = elem.nodeName.toLowerCase(); - return ( nodeName === "input" && !!elem.checked ) || - ( nodeName === "option" && !!elem.selected ); - }, - - "selected": function( elem ) { - - // Accessing this property makes selected-by-default - // options in Safari work properly - if ( elem.parentNode ) { - // eslint-disable-next-line no-unused-expressions - elem.parentNode.selectedIndex; - } - - return elem.selected === true; - }, - - // Contents - "empty": function( elem ) { - - // http://www.w3.org/TR/selectors/#empty-pseudo - // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), - // but not by others (comment: 8; processing instruction: 7; etc.) - // nodeType < 6 works because attributes (2) do not appear as children - for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { - if ( elem.nodeType < 6 ) { - return false; - } - } - return true; - }, - - "parent": function( elem ) { - return !Expr.pseudos[ "empty" ]( elem ); - }, - - // Element/input types - "header": function( elem ) { - return rheader.test( elem.nodeName ); - }, - - "input": function( elem ) { - return rinputs.test( elem.nodeName ); - }, - - "button": function( elem ) { - var name = elem.nodeName.toLowerCase(); - return name === "input" && elem.type === "button" || name === "button"; - }, - - "text": function( elem ) { - var attr; - return elem.nodeName.toLowerCase() === "input" && - elem.type === "text" && - - // Support: IE<8 - // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" - ( ( attr = elem.getAttribute( "type" ) ) == null || - attr.toLowerCase() === "text" ); - }, - - // Position-in-collection - "first": createPositionalPseudo( function() { - return [ 0 ]; - } ), - - "last": createPositionalPseudo( function( _matchIndexes, length ) { - return [ length - 1 ]; - } ), - - "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { - return [ argument < 0 ? argument + length : argument ]; - } ), - - "even": createPositionalPseudo( function( matchIndexes, length ) { - var i = 0; - for ( ; i < length; i += 2 ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "odd": createPositionalPseudo( function( matchIndexes, length ) { - var i = 1; - for ( ; i < length; i += 2 ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { - var i = argument < 0 ? - argument + length : - argument > length ? - length : - argument; - for ( ; --i >= 0; ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { - var i = argument < 0 ? argument + length : argument; - for ( ; ++i < length; ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ) - } - }; - - Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; - - // Add button/input type pseudos - for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { - Expr.pseudos[ i ] = createInputPseudo( i ); - } - for ( i in { submit: true, reset: true } ) { - Expr.pseudos[ i ] = createButtonPseudo( i ); - } - - // Easy API for creating new setFilters - function setFilters() {} - setFilters.prototype = Expr.filters = Expr.pseudos; - Expr.setFilters = new setFilters(); - - tokenize = Sizzle.tokenize = function( selector, parseOnly ) { - var matched, match, tokens, type, - soFar, groups, preFilters, - cached = tokenCache[ selector + " " ]; - - if ( cached ) { - return parseOnly ? 0 : cached.slice( 0 ); - } - - soFar = selector; - groups = []; - preFilters = Expr.preFilter; - - while ( soFar ) { - - // Comma and first run - if ( !matched || ( match = rcomma.exec( soFar ) ) ) { - if ( match ) { - - // Don't consume trailing commas as valid - soFar = soFar.slice( match[ 0 ].length ) || soFar; - } - groups.push( ( tokens = [] ) ); - } - - matched = false; - - // Combinators - if ( ( match = rcombinators.exec( soFar ) ) ) { - matched = match.shift(); - tokens.push( { - value: matched, - - // Cast descendant combinators to space - type: match[ 0 ].replace( rtrim, " " ) - } ); - soFar = soFar.slice( matched.length ); - } - - // Filters - for ( type in Expr.filter ) { - if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || - ( match = preFilters[ type ]( match ) ) ) ) { - matched = match.shift(); - tokens.push( { - value: matched, - type: type, - matches: match - } ); - soFar = soFar.slice( matched.length ); - } - } - - if ( !matched ) { - break; - } - } - - // Return the length of the invalid excess - // if we're just parsing - // Otherwise, throw an error or return tokens - return parseOnly ? - soFar.length : - soFar ? - Sizzle.error( selector ) : - - // Cache the tokens - tokenCache( selector, groups ).slice( 0 ); - }; - - function toSelector( tokens ) { - var i = 0, - len = tokens.length, - selector = ""; - for ( ; i < len; i++ ) { - selector += tokens[ i ].value; - } - return selector; - } - - function addCombinator( matcher, combinator, base ) { - var dir = combinator.dir, - skip = combinator.next, - key = skip || dir, - checkNonElements = base && key === "parentNode", - doneName = done++; - - return combinator.first ? - - // Check against closest ancestor/preceding element - function( elem, context, xml ) { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - return matcher( elem, context, xml ); - } - } - return false; - } : - - // Check against all ancestor/preceding elements - function( elem, context, xml ) { - var oldCache, uniqueCache, outerCache, - newCache = [ dirruns, doneName ]; - - // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching - if ( xml ) { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - if ( matcher( elem, context, xml ) ) { - return true; - } - } - } - } else { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - outerCache = elem[ expando ] || ( elem[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ elem.uniqueID ] || - ( outerCache[ elem.uniqueID ] = {} ); - - if ( skip && skip === elem.nodeName.toLowerCase() ) { - elem = elem[ dir ] || elem; - } else if ( ( oldCache = uniqueCache[ key ] ) && - oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { - - // Assign to newCache so results back-propagate to previous elements - return ( newCache[ 2 ] = oldCache[ 2 ] ); - } else { - - // Reuse newcache so results back-propagate to previous elements - uniqueCache[ key ] = newCache; - - // A match means we're done; a fail means we have to keep checking - if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { - return true; - } - } - } - } - } - return false; - }; - } - - function elementMatcher( matchers ) { - return matchers.length > 1 ? - function( elem, context, xml ) { - var i = matchers.length; - while ( i-- ) { - if ( !matchers[ i ]( elem, context, xml ) ) { - return false; - } - } - return true; - } : - matchers[ 0 ]; - } - - function multipleContexts( selector, contexts, results ) { - var i = 0, - len = contexts.length; - for ( ; i < len; i++ ) { - Sizzle( selector, contexts[ i ], results ); - } - return results; - } - - function condense( unmatched, map, filter, context, xml ) { - var elem, - newUnmatched = [], - i = 0, - len = unmatched.length, - mapped = map != null; - - for ( ; i < len; i++ ) { - if ( ( elem = unmatched[ i ] ) ) { - if ( !filter || filter( elem, context, xml ) ) { - newUnmatched.push( elem ); - if ( mapped ) { - map.push( i ); - } - } - } - } - - return newUnmatched; - } - - function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { - if ( postFilter && !postFilter[ expando ] ) { - postFilter = setMatcher( postFilter ); - } - if ( postFinder && !postFinder[ expando ] ) { - postFinder = setMatcher( postFinder, postSelector ); - } - return markFunction( function( seed, results, context, xml ) { - var temp, i, elem, - preMap = [], - postMap = [], - preexisting = results.length, - - // Get initial elements from seed or context - elems = seed || multipleContexts( - selector || "*", - context.nodeType ? [ context ] : context, - [] - ), - - // Prefilter to get matcher input, preserving a map for seed-results synchronization - matcherIn = preFilter && ( seed || !selector ) ? - condense( elems, preMap, preFilter, context, xml ) : - elems, - - matcherOut = matcher ? - - // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, - postFinder || ( seed ? preFilter : preexisting || postFilter ) ? - - // ...intermediate processing is necessary - [] : - - // ...otherwise use results directly - results : - matcherIn; - - // Find primary matches - if ( matcher ) { - matcher( matcherIn, matcherOut, context, xml ); - } - - // Apply postFilter - if ( postFilter ) { - temp = condense( matcherOut, postMap ); - postFilter( temp, [], context, xml ); - - // Un-match failing elements by moving them back to matcherIn - i = temp.length; - while ( i-- ) { - if ( ( elem = temp[ i ] ) ) { - matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); - } - } - } - - if ( seed ) { - if ( postFinder || preFilter ) { - if ( postFinder ) { - - // Get the final matcherOut by condensing this intermediate into postFinder contexts - temp = []; - i = matcherOut.length; - while ( i-- ) { - if ( ( elem = matcherOut[ i ] ) ) { - - // Restore matcherIn since elem is not yet a final match - temp.push( ( matcherIn[ i ] = elem ) ); - } - } - postFinder( null, ( matcherOut = [] ), temp, xml ); - } - - // Move matched elements from seed to results to keep them synchronized - i = matcherOut.length; - while ( i-- ) { - if ( ( elem = matcherOut[ i ] ) && - ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { - - seed[ temp ] = !( results[ temp ] = elem ); - } - } - } - - // Add elements to results, through postFinder if defined - } else { - matcherOut = condense( - matcherOut === results ? - matcherOut.splice( preexisting, matcherOut.length ) : - matcherOut - ); - if ( postFinder ) { - postFinder( null, results, matcherOut, xml ); - } else { - push.apply( results, matcherOut ); - } - } - } ); - } - - function matcherFromTokens( tokens ) { - var checkContext, matcher, j, - len = tokens.length, - leadingRelative = Expr.relative[ tokens[ 0 ].type ], - implicitRelative = leadingRelative || Expr.relative[ " " ], - i = leadingRelative ? 1 : 0, - - // The foundational matcher ensures that elements are reachable from top-level context(s) - matchContext = addCombinator( function( elem ) { - return elem === checkContext; - }, implicitRelative, true ), - matchAnyContext = addCombinator( function( elem ) { - return indexOf( checkContext, elem ) > -1; - }, implicitRelative, true ), - matchers = [ function( elem, context, xml ) { - var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( - ( checkContext = context ).nodeType ? - matchContext( elem, context, xml ) : - matchAnyContext( elem, context, xml ) ); - - // Avoid hanging onto element (issue #299) - checkContext = null; - return ret; - } ]; - - for ( ; i < len; i++ ) { - if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { - matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; - } else { - matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); - - // Return special upon seeing a positional matcher - if ( matcher[ expando ] ) { - - // Find the next relative operator (if any) for proper handling - j = ++i; - for ( ; j < len; j++ ) { - if ( Expr.relative[ tokens[ j ].type ] ) { - break; - } - } - return setMatcher( - i > 1 && elementMatcher( matchers ), - i > 1 && toSelector( - - // If the preceding token was a descendant combinator, insert an implicit any-element `*` - tokens - .slice( 0, i - 1 ) - .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) - ).replace( rtrim, "$1" ), - matcher, - i < j && matcherFromTokens( tokens.slice( i, j ) ), - j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), - j < len && toSelector( tokens ) - ); - } - matchers.push( matcher ); - } - } - - return elementMatcher( matchers ); - } - - function matcherFromGroupMatchers( elementMatchers, setMatchers ) { - var bySet = setMatchers.length > 0, - byElement = elementMatchers.length > 0, - superMatcher = function( seed, context, xml, results, outermost ) { - var elem, j, matcher, - matchedCount = 0, - i = "0", - unmatched = seed && [], - setMatched = [], - contextBackup = outermostContext, - - // We must always have either seed elements or outermost context - elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), - - // Use integer dirruns iff this is the outermost matcher - dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), - len = elems.length; - - if ( outermost ) { - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - outermostContext = context == document || context || outermost; - } - - // Add elements passing elementMatchers directly to results - // Support: IE<9, Safari - // Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id - for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { - if ( byElement && elem ) { - j = 0; - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( !context && elem.ownerDocument != document ) { - setDocument( elem ); - xml = !documentIsHTML; - } - while ( ( matcher = elementMatchers[ j++ ] ) ) { - if ( matcher( elem, context || document, xml ) ) { - results.push( elem ); - break; - } - } - if ( outermost ) { - dirruns = dirrunsUnique; - } - } - - // Track unmatched elements for set filters - if ( bySet ) { - - // They will have gone through all possible matchers - if ( ( elem = !matcher && elem ) ) { - matchedCount--; - } - - // Lengthen the array for every element, matched or not - if ( seed ) { - unmatched.push( elem ); - } - } - } - - // `i` is now the count of elements visited above, and adding it to `matchedCount` - // makes the latter nonnegative. - matchedCount += i; - - // Apply set filters to unmatched elements - // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` - // equals `i`), unless we didn't visit _any_ elements in the above loop because we have - // no element matchers and no seed. - // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that - // case, which will result in a "00" `matchedCount` that differs from `i` but is also - // numerically zero. - if ( bySet && i !== matchedCount ) { - j = 0; - while ( ( matcher = setMatchers[ j++ ] ) ) { - matcher( unmatched, setMatched, context, xml ); - } - - if ( seed ) { - - // Reintegrate element matches to eliminate the need for sorting - if ( matchedCount > 0 ) { - while ( i-- ) { - if ( !( unmatched[ i ] || setMatched[ i ] ) ) { - setMatched[ i ] = pop.call( results ); - } - } - } - - // Discard index placeholder values to get only actual matches - setMatched = condense( setMatched ); - } - - // Add matches to results - push.apply( results, setMatched ); - - // Seedless set matches succeeding multiple successful matchers stipulate sorting - if ( outermost && !seed && setMatched.length > 0 && - ( matchedCount + setMatchers.length ) > 1 ) { - - Sizzle.uniqueSort( results ); - } - } - - // Override manipulation of globals by nested matchers - if ( outermost ) { - dirruns = dirrunsUnique; - outermostContext = contextBackup; - } - - return unmatched; - }; - - return bySet ? - markFunction( superMatcher ) : - superMatcher; - } - - compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { - var i, - setMatchers = [], - elementMatchers = [], - cached = compilerCache[ selector + " " ]; - - if ( !cached ) { - - // Generate a function of recursive functions that can be used to check each element - if ( !match ) { - match = tokenize( selector ); - } - i = match.length; - while ( i-- ) { - cached = matcherFromTokens( match[ i ] ); - if ( cached[ expando ] ) { - setMatchers.push( cached ); - } else { - elementMatchers.push( cached ); - } - } - - // Cache the compiled function - cached = compilerCache( - selector, - matcherFromGroupMatchers( elementMatchers, setMatchers ) - ); - - // Save selector and tokenization - cached.selector = selector; - } - return cached; - }; - - /** - * A low-level selection function that works with Sizzle's compiled - * selector functions - * @param {String|Function} selector A selector or a pre-compiled - * selector function built with Sizzle.compile - * @param {Element} context - * @param {Array} [results] - * @param {Array} [seed] A set of elements to match against - */ - select = Sizzle.select = function( selector, context, results, seed ) { - var i, tokens, token, type, find, - compiled = typeof selector === "function" && selector, - match = !seed && tokenize( ( selector = compiled.selector || selector ) ); - - results = results || []; - - // Try to minimize operations if there is only one selector in the list and no seed - // (the latter of which guarantees us context) - if ( match.length === 1 ) { - - // Reduce context if the leading compound selector is an ID - tokens = match[ 0 ] = match[ 0 ].slice( 0 ); - if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && - context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { - - context = ( Expr.find[ "ID" ]( token.matches[ 0 ] - .replace( runescape, funescape ), context ) || [] )[ 0 ]; - if ( !context ) { - return results; - - // Precompiled matchers will still verify ancestry, so step up a level - } else if ( compiled ) { - context = context.parentNode; - } - - selector = selector.slice( tokens.shift().value.length ); - } - - // Fetch a seed set for right-to-left matching - i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; - while ( i-- ) { - token = tokens[ i ]; - - // Abort if we hit a combinator - if ( Expr.relative[ ( type = token.type ) ] ) { - break; - } - if ( ( find = Expr.find[ type ] ) ) { - - // Search, expanding context for leading sibling combinators - if ( ( seed = find( - token.matches[ 0 ].replace( runescape, funescape ), - rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || - context - ) ) ) { - - // If seed is empty or no tokens remain, we can return early - tokens.splice( i, 1 ); - selector = seed.length && toSelector( tokens ); - if ( !selector ) { - push.apply( results, seed ); - return results; - } - - break; - } - } - } - } - - // Compile and execute a filtering function if one is not provided - // Provide `match` to avoid retokenization if we modified the selector above - ( compiled || compile( selector, match ) )( - seed, - context, - !documentIsHTML, - results, - !context || rsibling.test( selector ) && testContext( context.parentNode ) || context - ); - return results; - }; - - // One-time assignments - - // Sort stability - support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; - - // Support: Chrome 14-35+ - // Always assume duplicates if they aren't passed to the comparison function - support.detectDuplicates = !!hasDuplicate; - - // Initialize against the default document - setDocument(); - - // Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) - // Detached nodes confoundingly follow *each other* - support.sortDetached = assert( function( el ) { - - // Should return 1, but returns 4 (following) - return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; - } ); - - // Support: IE<8 - // Prevent attribute/property "interpolation" - // https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx - if ( !assert( function( el ) { - el.innerHTML = "<a href='#'></a>"; - return el.firstChild.getAttribute( "href" ) === "#"; - } ) ) { - addHandle( "type|href|height|width", function( elem, name, isXML ) { - if ( !isXML ) { - return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); - } - } ); - } - - // Support: IE<9 - // Use defaultValue in place of getAttribute("value") - if ( !support.attributes || !assert( function( el ) { - el.innerHTML = "<input/>"; - el.firstChild.setAttribute( "value", "" ); - return el.firstChild.getAttribute( "value" ) === ""; - } ) ) { - addHandle( "value", function( elem, _name, isXML ) { - if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { - return elem.defaultValue; - } - } ); - } - - // Support: IE<9 - // Use getAttributeNode to fetch booleans when getAttribute lies - if ( !assert( function( el ) { - return el.getAttribute( "disabled" ) == null; - } ) ) { - addHandle( booleans, function( elem, name, isXML ) { - var val; - if ( !isXML ) { - return elem[ name ] === true ? name.toLowerCase() : - ( val = elem.getAttributeNode( name ) ) && val.specified ? - val.value : - null; - } - } ); - } - - return Sizzle; - - } )( window ); - - - - jQuery.find = Sizzle; - jQuery.expr = Sizzle.selectors; - - // Deprecated - jQuery.expr[ ":" ] = jQuery.expr.pseudos; - jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; - jQuery.text = Sizzle.getText; - jQuery.isXMLDoc = Sizzle.isXML; - jQuery.contains = Sizzle.contains; - jQuery.escapeSelector = Sizzle.escape; - - - - - var dir = function( elem, dir, until ) { - var matched = [], - truncate = until !== undefined; - - while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { - if ( elem.nodeType === 1 ) { - if ( truncate && jQuery( elem ).is( until ) ) { - break; - } - matched.push( elem ); - } - } - return matched; - }; - - - var siblings = function( n, elem ) { - var matched = []; - - for ( ; n; n = n.nextSibling ) { - if ( n.nodeType === 1 && n !== elem ) { - matched.push( n ); - } - } - - return matched; - }; - - - var rneedsContext = jQuery.expr.match.needsContext; - - - - function nodeName( elem, name ) { - - return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); - - }; - var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); - - - - // Implement the identical functionality for filter and not - function winnow( elements, qualifier, not ) { - if ( isFunction( qualifier ) ) { - return jQuery.grep( elements, function( elem, i ) { - return !!qualifier.call( elem, i, elem ) !== not; - } ); - } - - // Single element - if ( qualifier.nodeType ) { - return jQuery.grep( elements, function( elem ) { - return ( elem === qualifier ) !== not; - } ); - } - - // Arraylike of elements (jQuery, arguments, Array) - if ( typeof qualifier !== "string" ) { - return jQuery.grep( elements, function( elem ) { - return ( indexOf.call( qualifier, elem ) > -1 ) !== not; - } ); - } - - // Filtered directly for both simple and complex selectors - return jQuery.filter( qualifier, elements, not ); - } - - jQuery.filter = function( expr, elems, not ) { - var elem = elems[ 0 ]; - - if ( not ) { - expr = ":not(" + expr + ")"; - } - - if ( elems.length === 1 && elem.nodeType === 1 ) { - return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; - } - - return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { - return elem.nodeType === 1; - } ) ); - }; - - jQuery.fn.extend( { - find: function( selector ) { - var i, ret, - len = this.length, - self = this; - - if ( typeof selector !== "string" ) { - return this.pushStack( jQuery( selector ).filter( function() { - for ( i = 0; i < len; i++ ) { - if ( jQuery.contains( self[ i ], this ) ) { - return true; - } - } - } ) ); - } - - ret = this.pushStack( [] ); - - for ( i = 0; i < len; i++ ) { - jQuery.find( selector, self[ i ], ret ); - } - - return len > 1 ? jQuery.uniqueSort( ret ) : ret; - }, - filter: function( selector ) { - return this.pushStack( winnow( this, selector || [], false ) ); - }, - not: function( selector ) { - return this.pushStack( winnow( this, selector || [], true ) ); - }, - is: function( selector ) { - return !!winnow( - this, - - // If this is a positional/relative selector, check membership in the returned set - // so $("p:first").is("p:last") won't return true for a doc with two "p". - typeof selector === "string" && rneedsContext.test( selector ) ? - jQuery( selector ) : - selector || [], - false - ).length; - } - } ); - - - // Initialize a jQuery object - - - // A central reference to the root jQuery(document) - var rootjQuery, - - // A simple way to check for HTML strings - // Prioritize #id over <tag> to avoid XSS via location.hash (#9521) - // Strict HTML recognition (#11290: must start with <) - // Shortcut simple #id case for speed - rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, - - init = jQuery.fn.init = function( selector, context, root ) { - var match, elem; - - // HANDLE: $(""), $(null), $(undefined), $(false) - if ( !selector ) { - return this; - } - - // Method init() accepts an alternate rootjQuery - // so migrate can support jQuery.sub (gh-2101) - root = root || rootjQuery; - - // Handle HTML strings - if ( typeof selector === "string" ) { - if ( selector[ 0 ] === "<" && - selector[ selector.length - 1 ] === ">" && - selector.length >= 3 ) { - - // Assume that strings that start and end with <> are HTML and skip the regex check - match = [ null, selector, null ]; - - } else { - match = rquickExpr.exec( selector ); - } - - // Match html or make sure no context is specified for #id - if ( match && ( match[ 1 ] || !context ) ) { - - // HANDLE: $(html) -> $(array) - if ( match[ 1 ] ) { - context = context instanceof jQuery ? context[ 0 ] : context; - - // Option to run scripts is true for back-compat - // Intentionally let the error be thrown if parseHTML is not present - jQuery.merge( this, jQuery.parseHTML( - match[ 1 ], - context && context.nodeType ? context.ownerDocument || context : document, - true - ) ); - - // HANDLE: $(html, props) - if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { - for ( match in context ) { - - // Properties of context are called as methods if possible - if ( isFunction( this[ match ] ) ) { - this[ match ]( context[ match ] ); - - // ...and otherwise set as attributes - } else { - this.attr( match, context[ match ] ); - } - } - } - - return this; - - // HANDLE: $(#id) - } else { - elem = document.getElementById( match[ 2 ] ); - - if ( elem ) { - - // Inject the element directly into the jQuery object - this[ 0 ] = elem; - this.length = 1; - } - return this; - } - - // HANDLE: $(expr, $(...)) - } else if ( !context || context.jquery ) { - return ( context || root ).find( selector ); - - // HANDLE: $(expr, context) - // (which is just equivalent to: $(context).find(expr) - } else { - return this.constructor( context ).find( selector ); - } - - // HANDLE: $(DOMElement) - } else if ( selector.nodeType ) { - this[ 0 ] = selector; - this.length = 1; - return this; - - // HANDLE: $(function) - // Shortcut for document ready - } else if ( isFunction( selector ) ) { - return root.ready !== undefined ? - root.ready( selector ) : - - // Execute immediately if ready is not present - selector( jQuery ); - } - - return jQuery.makeArray( selector, this ); - }; - - // Give the init function the jQuery prototype for later instantiation - init.prototype = jQuery.fn; - - // Initialize central reference - rootjQuery = jQuery( document ); - - - var rparentsprev = /^(?:parents|prev(?:Until|All))/, - - // Methods guaranteed to produce a unique set when starting from a unique set - guaranteedUnique = { - children: true, - contents: true, - next: true, - prev: true - }; - - jQuery.fn.extend( { - has: function( target ) { - var targets = jQuery( target, this ), - l = targets.length; - - return this.filter( function() { - var i = 0; - for ( ; i < l; i++ ) { - if ( jQuery.contains( this, targets[ i ] ) ) { - return true; - } - } - } ); - }, - - closest: function( selectors, context ) { - var cur, - i = 0, - l = this.length, - matched = [], - targets = typeof selectors !== "string" && jQuery( selectors ); - - // Positional selectors never match, since there's no _selection_ context - if ( !rneedsContext.test( selectors ) ) { - for ( ; i < l; i++ ) { - for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { - - // Always skip document fragments - if ( cur.nodeType < 11 && ( targets ? - targets.index( cur ) > -1 : - - // Don't pass non-elements to Sizzle - cur.nodeType === 1 && - jQuery.find.matchesSelector( cur, selectors ) ) ) { - - matched.push( cur ); - break; - } - } - } - } - - return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); - }, - - // Determine the position of an element within the set - index: function( elem ) { - - // No argument, return index in parent - if ( !elem ) { - return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; - } - - // Index in selector - if ( typeof elem === "string" ) { - return indexOf.call( jQuery( elem ), this[ 0 ] ); - } - - // Locate the position of the desired element - return indexOf.call( this, - - // If it receives a jQuery object, the first element is used - elem.jquery ? elem[ 0 ] : elem - ); - }, - - add: function( selector, context ) { - return this.pushStack( - jQuery.uniqueSort( - jQuery.merge( this.get(), jQuery( selector, context ) ) - ) - ); - }, - - addBack: function( selector ) { - return this.add( selector == null ? - this.prevObject : this.prevObject.filter( selector ) - ); - } - } ); - - function sibling( cur, dir ) { - while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} - return cur; - } - - jQuery.each( { - parent: function( elem ) { - var parent = elem.parentNode; - return parent && parent.nodeType !== 11 ? parent : null; - }, - parents: function( elem ) { - return dir( elem, "parentNode" ); - }, - parentsUntil: function( elem, _i, until ) { - return dir( elem, "parentNode", until ); - }, - next: function( elem ) { - return sibling( elem, "nextSibling" ); - }, - prev: function( elem ) { - return sibling( elem, "previousSibling" ); - }, - nextAll: function( elem ) { - return dir( elem, "nextSibling" ); - }, - prevAll: function( elem ) { - return dir( elem, "previousSibling" ); - }, - nextUntil: function( elem, _i, until ) { - return dir( elem, "nextSibling", until ); - }, - prevUntil: function( elem, _i, until ) { - return dir( elem, "previousSibling", until ); - }, - siblings: function( elem ) { - return siblings( ( elem.parentNode || {} ).firstChild, elem ); - }, - children: function( elem ) { - return siblings( elem.firstChild ); - }, - contents: function( elem ) { - if ( elem.contentDocument != null && - - // Support: IE 11+ - // <object> elements with no `data` attribute has an object - // `contentDocument` with a `null` prototype. - getProto( elem.contentDocument ) ) { - - return elem.contentDocument; - } - - // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only - // Treat the template element as a regular one in browsers that - // don't support it. - if ( nodeName( elem, "template" ) ) { - elem = elem.content || elem; - } - - return jQuery.merge( [], elem.childNodes ); - } - }, function( name, fn ) { - jQuery.fn[ name ] = function( until, selector ) { - var matched = jQuery.map( this, fn, until ); - - if ( name.slice( -5 ) !== "Until" ) { - selector = until; - } - - if ( selector && typeof selector === "string" ) { - matched = jQuery.filter( selector, matched ); - } - - if ( this.length > 1 ) { - - // Remove duplicates - if ( !guaranteedUnique[ name ] ) { - jQuery.uniqueSort( matched ); - } - - // Reverse order for parents* and prev-derivatives - if ( rparentsprev.test( name ) ) { - matched.reverse(); - } - } - - return this.pushStack( matched ); - }; - } ); - var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); - - - - // Convert String-formatted options into Object-formatted ones - function createOptions( options ) { - var object = {}; - jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { - object[ flag ] = true; - } ); - return object; - } - - /* - * Create a callback list using the following parameters: - * - * options: an optional list of space-separated options that will change how - * the callback list behaves or a more traditional option object - * - * By default a callback list will act like an event callback list and can be - * "fired" multiple times. - * - * Possible options: - * - * once: will ensure the callback list can only be fired once (like a Deferred) - * - * memory: will keep track of previous values and will call any callback added - * after the list has been fired right away with the latest "memorized" - * values (like a Deferred) - * - * unique: will ensure a callback can only be added once (no duplicate in the list) - * - * stopOnFalse: interrupt callings when a callback returns false - * - */ - jQuery.Callbacks = function( options ) { - - // Convert options from String-formatted to Object-formatted if needed - // (we check in cache first) - options = typeof options === "string" ? - createOptions( options ) : - jQuery.extend( {}, options ); - - var // Flag to know if list is currently firing - firing, - - // Last fire value for non-forgettable lists - memory, - - // Flag to know if list was already fired - fired, - - // Flag to prevent firing - locked, - - // Actual callback list - list = [], - - // Queue of execution data for repeatable lists - queue = [], - - // Index of currently firing callback (modified by add/remove as needed) - firingIndex = -1, - - // Fire callbacks - fire = function() { - - // Enforce single-firing - locked = locked || options.once; - - // Execute callbacks for all pending executions, - // respecting firingIndex overrides and runtime changes - fired = firing = true; - for ( ; queue.length; firingIndex = -1 ) { - memory = queue.shift(); - while ( ++firingIndex < list.length ) { - - // Run callback and check for early termination - if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && - options.stopOnFalse ) { - - // Jump to end and forget the data so .add doesn't re-fire - firingIndex = list.length; - memory = false; - } - } - } - - // Forget the data if we're done with it - if ( !options.memory ) { - memory = false; - } - - firing = false; - - // Clean up if we're done firing for good - if ( locked ) { - - // Keep an empty list if we have data for future add calls - if ( memory ) { - list = []; - - // Otherwise, this object is spent - } else { - list = ""; - } - } - }, - - // Actual Callbacks object - self = { - - // Add a callback or a collection of callbacks to the list - add: function() { - if ( list ) { - - // If we have memory from a past run, we should fire after adding - if ( memory && !firing ) { - firingIndex = list.length - 1; - queue.push( memory ); - } - - ( function add( args ) { - jQuery.each( args, function( _, arg ) { - if ( isFunction( arg ) ) { - if ( !options.unique || !self.has( arg ) ) { - list.push( arg ); - } - } else if ( arg && arg.length && toType( arg ) !== "string" ) { - - // Inspect recursively - add( arg ); - } - } ); - } )( arguments ); - - if ( memory && !firing ) { - fire(); - } - } - return this; - }, - - // Remove a callback from the list - remove: function() { - jQuery.each( arguments, function( _, arg ) { - var index; - while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { - list.splice( index, 1 ); - - // Handle firing indexes - if ( index <= firingIndex ) { - firingIndex--; - } - } - } ); - return this; - }, - - // Check if a given callback is in the list. - // If no argument is given, return whether or not list has callbacks attached. - has: function( fn ) { - return fn ? - jQuery.inArray( fn, list ) > -1 : - list.length > 0; - }, - - // Remove all callbacks from the list - empty: function() { - if ( list ) { - list = []; - } - return this; - }, - - // Disable .fire and .add - // Abort any current/pending executions - // Clear all callbacks and values - disable: function() { - locked = queue = []; - list = memory = ""; - return this; - }, - disabled: function() { - return !list; - }, - - // Disable .fire - // Also disable .add unless we have memory (since it would have no effect) - // Abort any pending executions - lock: function() { - locked = queue = []; - if ( !memory && !firing ) { - list = memory = ""; - } - return this; - }, - locked: function() { - return !!locked; - }, - - // Call all callbacks with the given context and arguments - fireWith: function( context, args ) { - if ( !locked ) { - args = args || []; - args = [ context, args.slice ? args.slice() : args ]; - queue.push( args ); - if ( !firing ) { - fire(); - } - } - return this; - }, - - // Call all the callbacks with the given arguments - fire: function() { - self.fireWith( this, arguments ); - return this; - }, - - // To know if the callbacks have already been called at least once - fired: function() { - return !!fired; - } - }; - - return self; - }; - - - function Identity( v ) { - return v; - } - function Thrower( ex ) { - throw ex; - } - - function adoptValue( value, resolve, reject, noValue ) { - var method; - - try { - - // Check for promise aspect first to privilege synchronous behavior - if ( value && isFunction( ( method = value.promise ) ) ) { - method.call( value ).done( resolve ).fail( reject ); - - // Other thenables - } else if ( value && isFunction( ( method = value.then ) ) ) { - method.call( value, resolve, reject ); - - // Other non-thenables - } else { - - // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: - // * false: [ value ].slice( 0 ) => resolve( value ) - // * true: [ value ].slice( 1 ) => resolve() - resolve.apply( undefined, [ value ].slice( noValue ) ); - } - - // For Promises/A+, convert exceptions into rejections - // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in - // Deferred#then to conditionally suppress rejection. - } catch ( value ) { - - // Support: Android 4.0 only - // Strict mode functions invoked without .call/.apply get global-object context - reject.apply( undefined, [ value ] ); - } - } - - jQuery.extend( { - - Deferred: function( func ) { - var tuples = [ - - // action, add listener, callbacks, - // ... .then handlers, argument index, [final state] - [ "notify", "progress", jQuery.Callbacks( "memory" ), - jQuery.Callbacks( "memory" ), 2 ], - [ "resolve", "done", jQuery.Callbacks( "once memory" ), - jQuery.Callbacks( "once memory" ), 0, "resolved" ], - [ "reject", "fail", jQuery.Callbacks( "once memory" ), - jQuery.Callbacks( "once memory" ), 1, "rejected" ] - ], - state = "pending", - promise = { - state: function() { - return state; - }, - always: function() { - deferred.done( arguments ).fail( arguments ); - return this; - }, - "catch": function( fn ) { - return promise.then( null, fn ); - }, - - // Keep pipe for back-compat - pipe: function( /* fnDone, fnFail, fnProgress */ ) { - var fns = arguments; - - return jQuery.Deferred( function( newDefer ) { - jQuery.each( tuples, function( _i, tuple ) { - - // Map tuples (progress, done, fail) to arguments (done, fail, progress) - var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; - - // deferred.progress(function() { bind to newDefer or newDefer.notify }) - // deferred.done(function() { bind to newDefer or newDefer.resolve }) - // deferred.fail(function() { bind to newDefer or newDefer.reject }) - deferred[ tuple[ 1 ] ]( function() { - var returned = fn && fn.apply( this, arguments ); - if ( returned && isFunction( returned.promise ) ) { - returned.promise() - .progress( newDefer.notify ) - .done( newDefer.resolve ) - .fail( newDefer.reject ); - } else { - newDefer[ tuple[ 0 ] + "With" ]( - this, - fn ? [ returned ] : arguments - ); - } - } ); - } ); - fns = null; - } ).promise(); - }, - then: function( onFulfilled, onRejected, onProgress ) { - var maxDepth = 0; - function resolve( depth, deferred, handler, special ) { - return function() { - var that = this, - args = arguments, - mightThrow = function() { - var returned, then; - - // Support: Promises/A+ section 2.3.3.3.3 - // https://promisesaplus.com/#point-59 - // Ignore double-resolution attempts - if ( depth < maxDepth ) { - return; - } - - returned = handler.apply( that, args ); - - // Support: Promises/A+ section 2.3.1 - // https://promisesaplus.com/#point-48 - if ( returned === deferred.promise() ) { - throw new TypeError( "Thenable self-resolution" ); - } - - // Support: Promises/A+ sections 2.3.3.1, 3.5 - // https://promisesaplus.com/#point-54 - // https://promisesaplus.com/#point-75 - // Retrieve `then` only once - then = returned && - - // Support: Promises/A+ section 2.3.4 - // https://promisesaplus.com/#point-64 - // Only check objects and functions for thenability - ( typeof returned === "object" || - typeof returned === "function" ) && - returned.then; - - // Handle a returned thenable - if ( isFunction( then ) ) { - - // Special processors (notify) just wait for resolution - if ( special ) { - then.call( - returned, - resolve( maxDepth, deferred, Identity, special ), - resolve( maxDepth, deferred, Thrower, special ) - ); - - // Normal processors (resolve) also hook into progress - } else { - - // ...and disregard older resolution values - maxDepth++; - - then.call( - returned, - resolve( maxDepth, deferred, Identity, special ), - resolve( maxDepth, deferred, Thrower, special ), - resolve( maxDepth, deferred, Identity, - deferred.notifyWith ) - ); - } - - // Handle all other returned values - } else { - - // Only substitute handlers pass on context - // and multiple values (non-spec behavior) - if ( handler !== Identity ) { - that = undefined; - args = [ returned ]; - } - - // Process the value(s) - // Default process is resolve - ( special || deferred.resolveWith )( that, args ); - } - }, - - // Only normal processors (resolve) catch and reject exceptions - process = special ? - mightThrow : - function() { - try { - mightThrow(); - } catch ( e ) { - - if ( jQuery.Deferred.exceptionHook ) { - jQuery.Deferred.exceptionHook( e, - process.stackTrace ); - } - - // Support: Promises/A+ section 2.3.3.3.4.1 - // https://promisesaplus.com/#point-61 - // Ignore post-resolution exceptions - if ( depth + 1 >= maxDepth ) { - - // Only substitute handlers pass on context - // and multiple values (non-spec behavior) - if ( handler !== Thrower ) { - that = undefined; - args = [ e ]; - } - - deferred.rejectWith( that, args ); - } - } - }; - - // Support: Promises/A+ section 2.3.3.3.1 - // https://promisesaplus.com/#point-57 - // Re-resolve promises immediately to dodge false rejection from - // subsequent errors - if ( depth ) { - process(); - } else { - - // Call an optional hook to record the stack, in case of exception - // since it's otherwise lost when execution goes async - if ( jQuery.Deferred.getStackHook ) { - process.stackTrace = jQuery.Deferred.getStackHook(); - } - window.setTimeout( process ); - } - }; - } - - return jQuery.Deferred( function( newDefer ) { - - // progress_handlers.add( ... ) - tuples[ 0 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onProgress ) ? - onProgress : - Identity, - newDefer.notifyWith - ) - ); - - // fulfilled_handlers.add( ... ) - tuples[ 1 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onFulfilled ) ? - onFulfilled : - Identity - ) - ); - - // rejected_handlers.add( ... ) - tuples[ 2 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onRejected ) ? - onRejected : - Thrower - ) - ); - } ).promise(); - }, - - // Get a promise for this deferred - // If obj is provided, the promise aspect is added to the object - promise: function( obj ) { - return obj != null ? jQuery.extend( obj, promise ) : promise; - } - }, - deferred = {}; - - // Add list-specific methods - jQuery.each( tuples, function( i, tuple ) { - var list = tuple[ 2 ], - stateString = tuple[ 5 ]; - - // promise.progress = list.add - // promise.done = list.add - // promise.fail = list.add - promise[ tuple[ 1 ] ] = list.add; - - // Handle state - if ( stateString ) { - list.add( - function() { - - // state = "resolved" (i.e., fulfilled) - // state = "rejected" - state = stateString; - }, - - // rejected_callbacks.disable - // fulfilled_callbacks.disable - tuples[ 3 - i ][ 2 ].disable, - - // rejected_handlers.disable - // fulfilled_handlers.disable - tuples[ 3 - i ][ 3 ].disable, - - // progress_callbacks.lock - tuples[ 0 ][ 2 ].lock, - - // progress_handlers.lock - tuples[ 0 ][ 3 ].lock - ); - } - - // progress_handlers.fire - // fulfilled_handlers.fire - // rejected_handlers.fire - list.add( tuple[ 3 ].fire ); - - // deferred.notify = function() { deferred.notifyWith(...) } - // deferred.resolve = function() { deferred.resolveWith(...) } - // deferred.reject = function() { deferred.rejectWith(...) } - deferred[ tuple[ 0 ] ] = function() { - deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); - return this; - }; - - // deferred.notifyWith = list.fireWith - // deferred.resolveWith = list.fireWith - // deferred.rejectWith = list.fireWith - deferred[ tuple[ 0 ] + "With" ] = list.fireWith; - } ); - - // Make the deferred a promise - promise.promise( deferred ); - - // Call given func if any - if ( func ) { - func.call( deferred, deferred ); - } - - // All done! - return deferred; - }, - - // Deferred helper - when: function( singleValue ) { - var - - // count of uncompleted subordinates - remaining = arguments.length, - - // count of unprocessed arguments - i = remaining, - - // subordinate fulfillment data - resolveContexts = Array( i ), - resolveValues = slice.call( arguments ), - - // the master Deferred - master = jQuery.Deferred(), - - // subordinate callback factory - updateFunc = function( i ) { - return function( value ) { - resolveContexts[ i ] = this; - resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; - if ( !( --remaining ) ) { - master.resolveWith( resolveContexts, resolveValues ); - } - }; - }; - - // Single- and empty arguments are adopted like Promise.resolve - if ( remaining <= 1 ) { - adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, - !remaining ); - - // Use .then() to unwrap secondary thenables (cf. gh-3000) - if ( master.state() === "pending" || - isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { - - return master.then(); - } - } - - // Multiple arguments are aggregated like Promise.all array elements - while ( i-- ) { - adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); - } - - return master.promise(); - } - } ); - - - // These usually indicate a programmer mistake during development, - // warn about them ASAP rather than swallowing them by default. - var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; - - jQuery.Deferred.exceptionHook = function( error, stack ) { - - // Support: IE 8 - 9 only - // Console exists when dev tools are open, which can happen at any time - if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { - window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); - } - }; - - - - - jQuery.readyException = function( error ) { - window.setTimeout( function() { - throw error; - } ); - }; - - - - - // The deferred used on DOM ready - var readyList = jQuery.Deferred(); - - jQuery.fn.ready = function( fn ) { - - readyList - .then( fn ) - - // Wrap jQuery.readyException in a function so that the lookup - // happens at the time of error handling instead of callback - // registration. - .catch( function( error ) { - jQuery.readyException( error ); - } ); - - return this; - }; - - jQuery.extend( { - - // Is the DOM ready to be used? Set to true once it occurs. - isReady: false, - - // A counter to track how many items to wait for before - // the ready event fires. See #6781 - readyWait: 1, - - // Handle when the DOM is ready - ready: function( wait ) { - - // Abort if there are pending holds or we're already ready - if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { - return; - } - - // Remember that the DOM is ready - jQuery.isReady = true; - - // If a normal DOM Ready event fired, decrement, and wait if need be - if ( wait !== true && --jQuery.readyWait > 0 ) { - return; - } - - // If there are functions bound, to execute - readyList.resolveWith( document, [ jQuery ] ); - } - } ); - - jQuery.ready.then = readyList.then; - - // The ready event handler and self cleanup method - function completed() { - document.removeEventListener( "DOMContentLoaded", completed ); - window.removeEventListener( "load", completed ); - jQuery.ready(); - } - - // Catch cases where $(document).ready() is called - // after the browser event has already occurred. - // Support: IE <=9 - 10 only - // Older IE sometimes signals "interactive" too soon - if ( document.readyState === "complete" || - ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { - - // Handle it asynchronously to allow scripts the opportunity to delay ready - window.setTimeout( jQuery.ready ); - - } else { - - // Use the handy event callback - document.addEventListener( "DOMContentLoaded", completed ); - - // A fallback to window.onload, that will always work - window.addEventListener( "load", completed ); - } - - - - - // Multifunctional method to get and set values of a collection - // The value/s can optionally be executed if it's a function - var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { - var i = 0, - len = elems.length, - bulk = key == null; - - // Sets many values - if ( toType( key ) === "object" ) { - chainable = true; - for ( i in key ) { - access( elems, fn, i, key[ i ], true, emptyGet, raw ); - } - - // Sets one value - } else if ( value !== undefined ) { - chainable = true; - - if ( !isFunction( value ) ) { - raw = true; - } - - if ( bulk ) { - - // Bulk operations run against the entire set - if ( raw ) { - fn.call( elems, value ); - fn = null; - - // ...except when executing function values - } else { - bulk = fn; - fn = function( elem, _key, value ) { - return bulk.call( jQuery( elem ), value ); - }; - } - } - - if ( fn ) { - for ( ; i < len; i++ ) { - fn( - elems[ i ], key, raw ? - value : - value.call( elems[ i ], i, fn( elems[ i ], key ) ) - ); - } - } - } - - if ( chainable ) { - return elems; - } - - // Gets - if ( bulk ) { - return fn.call( elems ); - } - - return len ? fn( elems[ 0 ], key ) : emptyGet; - }; - - - // Matches dashed string for camelizing - var rmsPrefix = /^-ms-/, - rdashAlpha = /-([a-z])/g; - - // Used by camelCase as callback to replace() - function fcamelCase( _all, letter ) { - return letter.toUpperCase(); - } - - // Convert dashed to camelCase; used by the css and data modules - // Support: IE <=9 - 11, Edge 12 - 15 - // Microsoft forgot to hump their vendor prefix (#9572) - function camelCase( string ) { - return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); - } - var acceptData = function( owner ) { - - // Accepts only: - // - Node - // - Node.ELEMENT_NODE - // - Node.DOCUMENT_NODE - // - Object - // - Any - return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); - }; - - - - - function Data() { - this.expando = jQuery.expando + Data.uid++; - } - - Data.uid = 1; - - Data.prototype = { - - cache: function( owner ) { - - // Check if the owner object already has a cache - var value = owner[ this.expando ]; - - // If not, create one - if ( !value ) { - value = {}; - - // We can accept data for non-element nodes in modern browsers, - // but we should not, see #8335. - // Always return an empty object. - if ( acceptData( owner ) ) { - - // If it is a node unlikely to be stringify-ed or looped over - // use plain assignment - if ( owner.nodeType ) { - owner[ this.expando ] = value; - - // Otherwise secure it in a non-enumerable property - // configurable must be true to allow the property to be - // deleted when data is removed - } else { - Object.defineProperty( owner, this.expando, { - value: value, - configurable: true - } ); - } - } - } - - return value; - }, - set: function( owner, data, value ) { - var prop, - cache = this.cache( owner ); - - // Handle: [ owner, key, value ] args - // Always use camelCase key (gh-2257) - if ( typeof data === "string" ) { - cache[ camelCase( data ) ] = value; - - // Handle: [ owner, { properties } ] args - } else { - - // Copy the properties one-by-one to the cache object - for ( prop in data ) { - cache[ camelCase( prop ) ] = data[ prop ]; - } - } - return cache; - }, - get: function( owner, key ) { - return key === undefined ? - this.cache( owner ) : - - // Always use camelCase key (gh-2257) - owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; - }, - access: function( owner, key, value ) { - - // In cases where either: - // - // 1. No key was specified - // 2. A string key was specified, but no value provided - // - // Take the "read" path and allow the get method to determine - // which value to return, respectively either: - // - // 1. The entire cache object - // 2. The data stored at the key - // - if ( key === undefined || - ( ( key && typeof key === "string" ) && value === undefined ) ) { - - return this.get( owner, key ); - } - - // When the key is not a string, or both a key and value - // are specified, set or extend (existing objects) with either: - // - // 1. An object of properties - // 2. A key and value - // - this.set( owner, key, value ); - - // Since the "set" path can have two possible entry points - // return the expected data based on which path was taken[*] - return value !== undefined ? value : key; - }, - remove: function( owner, key ) { - var i, - cache = owner[ this.expando ]; - - if ( cache === undefined ) { - return; - } - - if ( key !== undefined ) { - - // Support array or space separated string of keys - if ( Array.isArray( key ) ) { - - // If key is an array of keys... - // We always set camelCase keys, so remove that. - key = key.map( camelCase ); - } else { - key = camelCase( key ); - - // If a key with the spaces exists, use it. - // Otherwise, create an array by matching non-whitespace - key = key in cache ? - [ key ] : - ( key.match( rnothtmlwhite ) || [] ); - } - - i = key.length; - - while ( i-- ) { - delete cache[ key[ i ] ]; - } - } - - // Remove the expando if there's no more data - if ( key === undefined || jQuery.isEmptyObject( cache ) ) { - - // Support: Chrome <=35 - 45 - // Webkit & Blink performance suffers when deleting properties - // from DOM nodes, so set to undefined instead - // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) - if ( owner.nodeType ) { - owner[ this.expando ] = undefined; - } else { - delete owner[ this.expando ]; - } - } - }, - hasData: function( owner ) { - var cache = owner[ this.expando ]; - return cache !== undefined && !jQuery.isEmptyObject( cache ); - } - }; - var dataPriv = new Data(); - - var dataUser = new Data(); - - - - // Implementation Summary - // - // 1. Enforce API surface and semantic compatibility with 1.9.x branch - // 2. Improve the module's maintainability by reducing the storage - // paths to a single mechanism. - // 3. Use the same single mechanism to support "private" and "user" data. - // 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) - // 5. Avoid exposing implementation details on user objects (eg. expando properties) - // 6. Provide a clear path for implementation upgrade to WeakMap in 2014 - - var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, - rmultiDash = /[A-Z]/g; - - function getData( data ) { - if ( data === "true" ) { - return true; - } - - if ( data === "false" ) { - return false; - } - - if ( data === "null" ) { - return null; - } - - // Only convert to a number if it doesn't change the string - if ( data === +data + "" ) { - return +data; - } - - if ( rbrace.test( data ) ) { - return JSON.parse( data ); - } - - return data; - } - - function dataAttr( elem, key, data ) { - var name; - - // If nothing was found internally, try to fetch any - // data from the HTML5 data-* attribute - if ( data === undefined && elem.nodeType === 1 ) { - name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); - data = elem.getAttribute( name ); - - if ( typeof data === "string" ) { - try { - data = getData( data ); - } catch ( e ) {} - - // Make sure we set the data so it isn't changed later - dataUser.set( elem, key, data ); - } else { - data = undefined; - } - } - return data; - } - - jQuery.extend( { - hasData: function( elem ) { - return dataUser.hasData( elem ) || dataPriv.hasData( elem ); - }, - - data: function( elem, name, data ) { - return dataUser.access( elem, name, data ); - }, - - removeData: function( elem, name ) { - dataUser.remove( elem, name ); - }, - - // TODO: Now that all calls to _data and _removeData have been replaced - // with direct calls to dataPriv methods, these can be deprecated. - _data: function( elem, name, data ) { - return dataPriv.access( elem, name, data ); - }, - - _removeData: function( elem, name ) { - dataPriv.remove( elem, name ); - } - } ); - - jQuery.fn.extend( { - data: function( key, value ) { - var i, name, data, - elem = this[ 0 ], - attrs = elem && elem.attributes; - - // Gets all values - if ( key === undefined ) { - if ( this.length ) { - data = dataUser.get( elem ); - - if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { - i = attrs.length; - while ( i-- ) { - - // Support: IE 11 only - // The attrs elements can be null (#14894) - if ( attrs[ i ] ) { - name = attrs[ i ].name; - if ( name.indexOf( "data-" ) === 0 ) { - name = camelCase( name.slice( 5 ) ); - dataAttr( elem, name, data[ name ] ); - } - } - } - dataPriv.set( elem, "hasDataAttrs", true ); - } - } - - return data; - } - - // Sets multiple values - if ( typeof key === "object" ) { - return this.each( function() { - dataUser.set( this, key ); - } ); - } - - return access( this, function( value ) { - var data; - - // The calling jQuery object (element matches) is not empty - // (and therefore has an element appears at this[ 0 ]) and the - // `value` parameter was not undefined. An empty jQuery object - // will result in `undefined` for elem = this[ 0 ] which will - // throw an exception if an attempt to read a data cache is made. - if ( elem && value === undefined ) { - - // Attempt to get data from the cache - // The key will always be camelCased in Data - data = dataUser.get( elem, key ); - if ( data !== undefined ) { - return data; - } - - // Attempt to "discover" the data in - // HTML5 custom data-* attrs - data = dataAttr( elem, key ); - if ( data !== undefined ) { - return data; - } - - // We tried really hard, but the data doesn't exist. - return; - } - - // Set the data... - this.each( function() { - - // We always store the camelCased key - dataUser.set( this, key, value ); - } ); - }, null, value, arguments.length > 1, null, true ); - }, - - removeData: function( key ) { - return this.each( function() { - dataUser.remove( this, key ); - } ); - } - } ); - - - jQuery.extend( { - queue: function( elem, type, data ) { - var queue; - - if ( elem ) { - type = ( type || "fx" ) + "queue"; - queue = dataPriv.get( elem, type ); - - // Speed up dequeue by getting out quickly if this is just a lookup - if ( data ) { - if ( !queue || Array.isArray( data ) ) { - queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); - } else { - queue.push( data ); - } - } - return queue || []; - } - }, - - dequeue: function( elem, type ) { - type = type || "fx"; - - var queue = jQuery.queue( elem, type ), - startLength = queue.length, - fn = queue.shift(), - hooks = jQuery._queueHooks( elem, type ), - next = function() { - jQuery.dequeue( elem, type ); - }; - - // If the fx queue is dequeued, always remove the progress sentinel - if ( fn === "inprogress" ) { - fn = queue.shift(); - startLength--; - } - - if ( fn ) { - - // Add a progress sentinel to prevent the fx queue from being - // automatically dequeued - if ( type === "fx" ) { - queue.unshift( "inprogress" ); - } - - // Clear up the last queue stop function - delete hooks.stop; - fn.call( elem, next, hooks ); - } - - if ( !startLength && hooks ) { - hooks.empty.fire(); - } - }, - - // Not public - generate a queueHooks object, or return the current one - _queueHooks: function( elem, type ) { - var key = type + "queueHooks"; - return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { - empty: jQuery.Callbacks( "once memory" ).add( function() { - dataPriv.remove( elem, [ type + "queue", key ] ); - } ) - } ); - } - } ); - - jQuery.fn.extend( { - queue: function( type, data ) { - var setter = 2; - - if ( typeof type !== "string" ) { - data = type; - type = "fx"; - setter--; - } - - if ( arguments.length < setter ) { - return jQuery.queue( this[ 0 ], type ); - } - - return data === undefined ? - this : - this.each( function() { - var queue = jQuery.queue( this, type, data ); - - // Ensure a hooks for this queue - jQuery._queueHooks( this, type ); - - if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { - jQuery.dequeue( this, type ); - } - } ); - }, - dequeue: function( type ) { - return this.each( function() { - jQuery.dequeue( this, type ); - } ); - }, - clearQueue: function( type ) { - return this.queue( type || "fx", [] ); - }, - - // Get a promise resolved when queues of a certain type - // are emptied (fx is the type by default) - promise: function( type, obj ) { - var tmp, - count = 1, - defer = jQuery.Deferred(), - elements = this, - i = this.length, - resolve = function() { - if ( !( --count ) ) { - defer.resolveWith( elements, [ elements ] ); - } - }; - - if ( typeof type !== "string" ) { - obj = type; - type = undefined; - } - type = type || "fx"; - - while ( i-- ) { - tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); - if ( tmp && tmp.empty ) { - count++; - tmp.empty.add( resolve ); - } - } - resolve(); - return defer.promise( obj ); - } - } ); - var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; - - var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); - - - var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; - - var documentElement = document.documentElement; - - - - var isAttached = function( elem ) { - return jQuery.contains( elem.ownerDocument, elem ); - }, - composed = { composed: true }; - - // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only - // Check attachment across shadow DOM boundaries when possible (gh-3504) - // Support: iOS 10.0-10.2 only - // Early iOS 10 versions support `attachShadow` but not `getRootNode`, - // leading to errors. We need to check for `getRootNode`. - if ( documentElement.getRootNode ) { - isAttached = function( elem ) { - return jQuery.contains( elem.ownerDocument, elem ) || - elem.getRootNode( composed ) === elem.ownerDocument; - }; - } - var isHiddenWithinTree = function( elem, el ) { - - // isHiddenWithinTree might be called from jQuery#filter function; - // in that case, element will be second argument - elem = el || elem; - - // Inline style trumps all - return elem.style.display === "none" || - elem.style.display === "" && - - // Otherwise, check computed style - // Support: Firefox <=43 - 45 - // Disconnected elements can have computed display: none, so first confirm that elem is - // in the document. - isAttached( elem ) && - - jQuery.css( elem, "display" ) === "none"; - }; - - - - function adjustCSS( elem, prop, valueParts, tween ) { - var adjusted, scale, - maxIterations = 20, - currentValue = tween ? - function() { - return tween.cur(); - } : - function() { - return jQuery.css( elem, prop, "" ); - }, - initial = currentValue(), - unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), - - // Starting value computation is required for potential unit mismatches - initialInUnit = elem.nodeType && - ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && - rcssNum.exec( jQuery.css( elem, prop ) ); - - if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { - - // Support: Firefox <=54 - // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) - initial = initial / 2; - - // Trust units reported by jQuery.css - unit = unit || initialInUnit[ 3 ]; - - // Iteratively approximate from a nonzero starting point - initialInUnit = +initial || 1; - - while ( maxIterations-- ) { - - // Evaluate and update our best guess (doubling guesses that zero out). - // Finish if the scale equals or crosses 1 (making the old*new product non-positive). - jQuery.style( elem, prop, initialInUnit + unit ); - if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { - maxIterations = 0; - } - initialInUnit = initialInUnit / scale; - - } - - initialInUnit = initialInUnit * 2; - jQuery.style( elem, prop, initialInUnit + unit ); - - // Make sure we update the tween properties later on - valueParts = valueParts || []; - } - - if ( valueParts ) { - initialInUnit = +initialInUnit || +initial || 0; - - // Apply relative offset (+=/-=) if specified - adjusted = valueParts[ 1 ] ? - initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : - +valueParts[ 2 ]; - if ( tween ) { - tween.unit = unit; - tween.start = initialInUnit; - tween.end = adjusted; - } - } - return adjusted; - } - - - var defaultDisplayMap = {}; - - function getDefaultDisplay( elem ) { - var temp, - doc = elem.ownerDocument, - nodeName = elem.nodeName, - display = defaultDisplayMap[ nodeName ]; - - if ( display ) { - return display; - } - - temp = doc.body.appendChild( doc.createElement( nodeName ) ); - display = jQuery.css( temp, "display" ); - - temp.parentNode.removeChild( temp ); - - if ( display === "none" ) { - display = "block"; - } - defaultDisplayMap[ nodeName ] = display; - - return display; - } - - function showHide( elements, show ) { - var display, elem, - values = [], - index = 0, - length = elements.length; - - // Determine new display value for elements that need to change - for ( ; index < length; index++ ) { - elem = elements[ index ]; - if ( !elem.style ) { - continue; - } - - display = elem.style.display; - if ( show ) { - - // Since we force visibility upon cascade-hidden elements, an immediate (and slow) - // check is required in this first loop unless we have a nonempty display value (either - // inline or about-to-be-restored) - if ( display === "none" ) { - values[ index ] = dataPriv.get( elem, "display" ) || null; - if ( !values[ index ] ) { - elem.style.display = ""; - } - } - if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { - values[ index ] = getDefaultDisplay( elem ); - } - } else { - if ( display !== "none" ) { - values[ index ] = "none"; - - // Remember what we're overwriting - dataPriv.set( elem, "display", display ); - } - } - } - - // Set the display of the elements in a second loop to avoid constant reflow - for ( index = 0; index < length; index++ ) { - if ( values[ index ] != null ) { - elements[ index ].style.display = values[ index ]; - } - } - - return elements; - } - - jQuery.fn.extend( { - show: function() { - return showHide( this, true ); - }, - hide: function() { - return showHide( this ); - }, - toggle: function( state ) { - if ( typeof state === "boolean" ) { - return state ? this.show() : this.hide(); - } - - return this.each( function() { - if ( isHiddenWithinTree( this ) ) { - jQuery( this ).show(); - } else { - jQuery( this ).hide(); - } - } ); - } - } ); - var rcheckableType = ( /^(?:checkbox|radio)$/i ); - - var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); - - var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); - - - - ( function() { - var fragment = document.createDocumentFragment(), - div = fragment.appendChild( document.createElement( "div" ) ), - input = document.createElement( "input" ); - - // Support: Android 4.0 - 4.3 only - // Check state lost if the name is set (#11217) - // Support: Windows Web Apps (WWA) - // `name` and `type` must use .setAttribute for WWA (#14901) - input.setAttribute( "type", "radio" ); - input.setAttribute( "checked", "checked" ); - input.setAttribute( "name", "t" ); - - div.appendChild( input ); - - // Support: Android <=4.1 only - // Older WebKit doesn't clone checked state correctly in fragments - support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; - - // Support: IE <=11 only - // Make sure textarea (and checkbox) defaultValue is properly cloned - div.innerHTML = "<textarea>x</textarea>"; - support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; - - // Support: IE <=9 only - // IE <=9 replaces <option> tags with their contents when inserted outside of - // the select element. - div.innerHTML = "<option></option>"; - support.option = !!div.lastChild; - } )(); - - - // We have to close these tags to support XHTML (#13200) - var wrapMap = { - - // XHTML parsers do not magically insert elements in the - // same way that tag soup parsers do. So we cannot shorten - // this by omitting <tbody> or other required elements. - thead: [ 1, "<table>", "</table>" ], - col: [ 2, "<table><colgroup>", "</colgroup></table>" ], - tr: [ 2, "<table><tbody>", "</tbody></table>" ], - td: [ 3, "<table><tbody><tr>", "</tr></tbody></table>" ], - - _default: [ 0, "", "" ] - }; - - wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; - wrapMap.th = wrapMap.td; - - // Support: IE <=9 only - if ( !support.option ) { - wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ]; - } - - - function getAll( context, tag ) { - - // Support: IE <=9 - 11 only - // Use typeof to avoid zero-argument method invocation on host objects (#15151) - var ret; - - if ( typeof context.getElementsByTagName !== "undefined" ) { - ret = context.getElementsByTagName( tag || "*" ); - - } else if ( typeof context.querySelectorAll !== "undefined" ) { - ret = context.querySelectorAll( tag || "*" ); - - } else { - ret = []; - } - - if ( tag === undefined || tag && nodeName( context, tag ) ) { - return jQuery.merge( [ context ], ret ); - } - - return ret; - } - - - // Mark scripts as having already been evaluated - function setGlobalEval( elems, refElements ) { - var i = 0, - l = elems.length; - - for ( ; i < l; i++ ) { - dataPriv.set( - elems[ i ], - "globalEval", - !refElements || dataPriv.get( refElements[ i ], "globalEval" ) - ); - } - } - - - var rhtml = /<|&#?\w+;/; - - function buildFragment( elems, context, scripts, selection, ignored ) { - var elem, tmp, tag, wrap, attached, j, - fragment = context.createDocumentFragment(), - nodes = [], - i = 0, - l = elems.length; - - for ( ; i < l; i++ ) { - elem = elems[ i ]; - - if ( elem || elem === 0 ) { - - // Add nodes directly - if ( toType( elem ) === "object" ) { - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); - - // Convert non-html into a text node - } else if ( !rhtml.test( elem ) ) { - nodes.push( context.createTextNode( elem ) ); - - // Convert html into DOM nodes - } else { - tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); - - // Deserialize a standard representation - tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); - wrap = wrapMap[ tag ] || wrapMap._default; - tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; - - // Descend through wrappers to the right content - j = wrap[ 0 ]; - while ( j-- ) { - tmp = tmp.lastChild; - } - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( nodes, tmp.childNodes ); - - // Remember the top-level container - tmp = fragment.firstChild; - - // Ensure the created nodes are orphaned (#12392) - tmp.textContent = ""; - } - } - } - - // Remove wrapper from fragment - fragment.textContent = ""; - - i = 0; - while ( ( elem = nodes[ i++ ] ) ) { - - // Skip elements already in the context collection (trac-4087) - if ( selection && jQuery.inArray( elem, selection ) > -1 ) { - if ( ignored ) { - ignored.push( elem ); - } - continue; - } - - attached = isAttached( elem ); - - // Append to fragment - tmp = getAll( fragment.appendChild( elem ), "script" ); - - // Preserve script evaluation history - if ( attached ) { - setGlobalEval( tmp ); - } - - // Capture executables - if ( scripts ) { - j = 0; - while ( ( elem = tmp[ j++ ] ) ) { - if ( rscriptType.test( elem.type || "" ) ) { - scripts.push( elem ); - } - } - } - } - - return fragment; - } - - - var - rkeyEvent = /^key/, - rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, - rtypenamespace = /^([^.]*)(?:\.(.+)|)/; - - function returnTrue() { - return true; - } - - function returnFalse() { - return false; - } - - // Support: IE <=9 - 11+ - // focus() and blur() are asynchronous, except when they are no-op. - // So expect focus to be synchronous when the element is already active, - // and blur to be synchronous when the element is not already active. - // (focus and blur are always synchronous in other supported browsers, - // this just defines when we can count on it). - function expectSync( elem, type ) { - return ( elem === safeActiveElement() ) === ( type === "focus" ); - } - - // Support: IE <=9 only - // Accessing document.activeElement can throw unexpectedly - // https://bugs.jquery.com/ticket/13393 - function safeActiveElement() { - try { - return document.activeElement; - } catch ( err ) { } - } - - function on( elem, types, selector, data, fn, one ) { - var origFn, type; - - // Types can be a map of types/handlers - if ( typeof types === "object" ) { - - // ( types-Object, selector, data ) - if ( typeof selector !== "string" ) { - - // ( types-Object, data ) - data = data || selector; - selector = undefined; - } - for ( type in types ) { - on( elem, type, selector, data, types[ type ], one ); - } - return elem; - } - - if ( data == null && fn == null ) { - - // ( types, fn ) - fn = selector; - data = selector = undefined; - } else if ( fn == null ) { - if ( typeof selector === "string" ) { - - // ( types, selector, fn ) - fn = data; - data = undefined; - } else { - - // ( types, data, fn ) - fn = data; - data = selector; - selector = undefined; - } - } - if ( fn === false ) { - fn = returnFalse; - } else if ( !fn ) { - return elem; - } - - if ( one === 1 ) { - origFn = fn; - fn = function( event ) { - - // Can use an empty set, since event contains the info - jQuery().off( event ); - return origFn.apply( this, arguments ); - }; - - // Use same guid so caller can remove using origFn - fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); - } - return elem.each( function() { - jQuery.event.add( this, types, fn, data, selector ); - } ); - } - - /* - * Helper functions for managing events -- not part of the public interface. - * Props to Dean Edwards' addEvent library for many of the ideas. - */ - jQuery.event = { - - global: {}, - - add: function( elem, types, handler, data, selector ) { - - var handleObjIn, eventHandle, tmp, - events, t, handleObj, - special, handlers, type, namespaces, origType, - elemData = dataPriv.get( elem ); - - // Only attach events to objects that accept data - if ( !acceptData( elem ) ) { - return; - } - - // Caller can pass in an object of custom data in lieu of the handler - if ( handler.handler ) { - handleObjIn = handler; - handler = handleObjIn.handler; - selector = handleObjIn.selector; - } - - // Ensure that invalid selectors throw exceptions at attach time - // Evaluate against documentElement in case elem is a non-element node (e.g., document) - if ( selector ) { - jQuery.find.matchesSelector( documentElement, selector ); - } - - // Make sure that the handler has a unique ID, used to find/remove it later - if ( !handler.guid ) { - handler.guid = jQuery.guid++; - } - - // Init the element's event structure and main handler, if this is the first - if ( !( events = elemData.events ) ) { - events = elemData.events = Object.create( null ); - } - if ( !( eventHandle = elemData.handle ) ) { - eventHandle = elemData.handle = function( e ) { - - // Discard the second event of a jQuery.event.trigger() and - // when an event is called after a page has unloaded - return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? - jQuery.event.dispatch.apply( elem, arguments ) : undefined; - }; - } - - // Handle multiple events separated by a space - types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; - t = types.length; - while ( t-- ) { - tmp = rtypenamespace.exec( types[ t ] ) || []; - type = origType = tmp[ 1 ]; - namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); - - // There *must* be a type, no attaching namespace-only handlers - if ( !type ) { - continue; - } - - // If event changes its type, use the special event handlers for the changed type - special = jQuery.event.special[ type ] || {}; - - // If selector defined, determine special event api type, otherwise given type - type = ( selector ? special.delegateType : special.bindType ) || type; - - // Update special based on newly reset type - special = jQuery.event.special[ type ] || {}; - - // handleObj is passed to all event handlers - handleObj = jQuery.extend( { - type: type, - origType: origType, - data: data, - handler: handler, - guid: handler.guid, - selector: selector, - needsContext: selector && jQuery.expr.match.needsContext.test( selector ), - namespace: namespaces.join( "." ) - }, handleObjIn ); - - // Init the event handler queue if we're the first - if ( !( handlers = events[ type ] ) ) { - handlers = events[ type ] = []; - handlers.delegateCount = 0; - - // Only use addEventListener if the special events handler returns false - if ( !special.setup || - special.setup.call( elem, data, namespaces, eventHandle ) === false ) { - - if ( elem.addEventListener ) { - elem.addEventListener( type, eventHandle ); - } - } - } - - if ( special.add ) { - special.add.call( elem, handleObj ); - - if ( !handleObj.handler.guid ) { - handleObj.handler.guid = handler.guid; - } - } - - // Add to the element's handler list, delegates in front - if ( selector ) { - handlers.splice( handlers.delegateCount++, 0, handleObj ); - } else { - handlers.push( handleObj ); - } - - // Keep track of which events have ever been used, for event optimization - jQuery.event.global[ type ] = true; - } - - }, - - // Detach an event or set of events from an element - remove: function( elem, types, handler, selector, mappedTypes ) { - - var j, origCount, tmp, - events, t, handleObj, - special, handlers, type, namespaces, origType, - elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); - - if ( !elemData || !( events = elemData.events ) ) { - return; - } - - // Once for each type.namespace in types; type may be omitted - types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; - t = types.length; - while ( t-- ) { - tmp = rtypenamespace.exec( types[ t ] ) || []; - type = origType = tmp[ 1 ]; - namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); - - // Unbind all events (on this namespace, if provided) for the element - if ( !type ) { - for ( type in events ) { - jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); - } - continue; - } - - special = jQuery.event.special[ type ] || {}; - type = ( selector ? special.delegateType : special.bindType ) || type; - handlers = events[ type ] || []; - tmp = tmp[ 2 ] && - new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); - - // Remove matching events - origCount = j = handlers.length; - while ( j-- ) { - handleObj = handlers[ j ]; - - if ( ( mappedTypes || origType === handleObj.origType ) && - ( !handler || handler.guid === handleObj.guid ) && - ( !tmp || tmp.test( handleObj.namespace ) ) && - ( !selector || selector === handleObj.selector || - selector === "**" && handleObj.selector ) ) { - handlers.splice( j, 1 ); - - if ( handleObj.selector ) { - handlers.delegateCount--; - } - if ( special.remove ) { - special.remove.call( elem, handleObj ); - } - } - } - - // Remove generic event handler if we removed something and no more handlers exist - // (avoids potential for endless recursion during removal of special event handlers) - if ( origCount && !handlers.length ) { - if ( !special.teardown || - special.teardown.call( elem, namespaces, elemData.handle ) === false ) { - - jQuery.removeEvent( elem, type, elemData.handle ); - } - - delete events[ type ]; - } - } - - // Remove data and the expando if it's no longer used - if ( jQuery.isEmptyObject( events ) ) { - dataPriv.remove( elem, "handle events" ); - } - }, - - dispatch: function( nativeEvent ) { - - var i, j, ret, matched, handleObj, handlerQueue, - args = new Array( arguments.length ), - - // Make a writable jQuery.Event from the native event object - event = jQuery.event.fix( nativeEvent ), - - handlers = ( - dataPriv.get( this, "events" ) || Object.create( null ) - )[ event.type ] || [], - special = jQuery.event.special[ event.type ] || {}; - - // Use the fix-ed jQuery.Event rather than the (read-only) native event - args[ 0 ] = event; - - for ( i = 1; i < arguments.length; i++ ) { - args[ i ] = arguments[ i ]; - } - - event.delegateTarget = this; - - // Call the preDispatch hook for the mapped type, and let it bail if desired - if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { - return; - } - - // Determine handlers - handlerQueue = jQuery.event.handlers.call( this, event, handlers ); - - // Run delegates first; they may want to stop propagation beneath us - i = 0; - while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { - event.currentTarget = matched.elem; - - j = 0; - while ( ( handleObj = matched.handlers[ j++ ] ) && - !event.isImmediatePropagationStopped() ) { - - // If the event is namespaced, then each handler is only invoked if it is - // specially universal or its namespaces are a superset of the event's. - if ( !event.rnamespace || handleObj.namespace === false || - event.rnamespace.test( handleObj.namespace ) ) { - - event.handleObj = handleObj; - event.data = handleObj.data; - - ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || - handleObj.handler ).apply( matched.elem, args ); - - if ( ret !== undefined ) { - if ( ( event.result = ret ) === false ) { - event.preventDefault(); - event.stopPropagation(); - } - } - } - } - } - - // Call the postDispatch hook for the mapped type - if ( special.postDispatch ) { - special.postDispatch.call( this, event ); - } - - return event.result; - }, - - handlers: function( event, handlers ) { - var i, handleObj, sel, matchedHandlers, matchedSelectors, - handlerQueue = [], - delegateCount = handlers.delegateCount, - cur = event.target; - - // Find delegate handlers - if ( delegateCount && - - // Support: IE <=9 - // Black-hole SVG <use> instance trees (trac-13180) - cur.nodeType && - - // Support: Firefox <=42 - // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) - // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click - // Support: IE 11 only - // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) - !( event.type === "click" && event.button >= 1 ) ) { - - for ( ; cur !== this; cur = cur.parentNode || this ) { - - // Don't check non-elements (#13208) - // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) - if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { - matchedHandlers = []; - matchedSelectors = {}; - for ( i = 0; i < delegateCount; i++ ) { - handleObj = handlers[ i ]; - - // Don't conflict with Object.prototype properties (#13203) - sel = handleObj.selector + " "; - - if ( matchedSelectors[ sel ] === undefined ) { - matchedSelectors[ sel ] = handleObj.needsContext ? - jQuery( sel, this ).index( cur ) > -1 : - jQuery.find( sel, this, null, [ cur ] ).length; - } - if ( matchedSelectors[ sel ] ) { - matchedHandlers.push( handleObj ); - } - } - if ( matchedHandlers.length ) { - handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); - } - } - } - } - - // Add the remaining (directly-bound) handlers - cur = this; - if ( delegateCount < handlers.length ) { - handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); - } - - return handlerQueue; - }, - - addProp: function( name, hook ) { - Object.defineProperty( jQuery.Event.prototype, name, { - enumerable: true, - configurable: true, - - get: isFunction( hook ) ? - function() { - if ( this.originalEvent ) { - return hook( this.originalEvent ); - } - } : - function() { - if ( this.originalEvent ) { - return this.originalEvent[ name ]; - } - }, - - set: function( value ) { - Object.defineProperty( this, name, { - enumerable: true, - configurable: true, - writable: true, - value: value - } ); - } - } ); - }, - - fix: function( originalEvent ) { - return originalEvent[ jQuery.expando ] ? - originalEvent : - new jQuery.Event( originalEvent ); - }, - - special: { - load: { - - // Prevent triggered image.load events from bubbling to window.load - noBubble: true - }, - click: { - - // Utilize native event to ensure correct state for checkable inputs - setup: function( data ) { - - // For mutual compressibility with _default, replace `this` access with a local var. - // `|| data` is dead code meant only to preserve the variable through minification. - var el = this || data; - - // Claim the first handler - if ( rcheckableType.test( el.type ) && - el.click && nodeName( el, "input" ) ) { - - // dataPriv.set( el, "click", ... ) - leverageNative( el, "click", returnTrue ); - } - - // Return false to allow normal processing in the caller - return false; - }, - trigger: function( data ) { - - // For mutual compressibility with _default, replace `this` access with a local var. - // `|| data` is dead code meant only to preserve the variable through minification. - var el = this || data; - - // Force setup before triggering a click - if ( rcheckableType.test( el.type ) && - el.click && nodeName( el, "input" ) ) { - - leverageNative( el, "click" ); - } - - // Return non-false to allow normal event-path propagation - return true; - }, - - // For cross-browser consistency, suppress native .click() on links - // Also prevent it if we're currently inside a leveraged native-event stack - _default: function( event ) { - var target = event.target; - return rcheckableType.test( target.type ) && - target.click && nodeName( target, "input" ) && - dataPriv.get( target, "click" ) || - nodeName( target, "a" ); - } - }, - - beforeunload: { - postDispatch: function( event ) { - - // Support: Firefox 20+ - // Firefox doesn't alert if the returnValue field is not set. - if ( event.result !== undefined && event.originalEvent ) { - event.originalEvent.returnValue = event.result; - } - } - } - } - }; - - // Ensure the presence of an event listener that handles manually-triggered - // synthetic events by interrupting progress until reinvoked in response to - // *native* events that it fires directly, ensuring that state changes have - // already occurred before other listeners are invoked. - function leverageNative( el, type, expectSync ) { - - // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add - if ( !expectSync ) { - if ( dataPriv.get( el, type ) === undefined ) { - jQuery.event.add( el, type, returnTrue ); - } - return; - } - - // Register the controller as a special universal handler for all event namespaces - dataPriv.set( el, type, false ); - jQuery.event.add( el, type, { - namespace: false, - handler: function( event ) { - var notAsync, result, - saved = dataPriv.get( this, type ); - - if ( ( event.isTrigger & 1 ) && this[ type ] ) { - - // Interrupt processing of the outer synthetic .trigger()ed event - // Saved data should be false in such cases, but might be a leftover capture object - // from an async native handler (gh-4350) - if ( !saved.length ) { - - // Store arguments for use when handling the inner native event - // There will always be at least one argument (an event object), so this array - // will not be confused with a leftover capture object. - saved = slice.call( arguments ); - dataPriv.set( this, type, saved ); - - // Trigger the native event and capture its result - // Support: IE <=9 - 11+ - // focus() and blur() are asynchronous - notAsync = expectSync( this, type ); - this[ type ](); - result = dataPriv.get( this, type ); - if ( saved !== result || notAsync ) { - dataPriv.set( this, type, false ); - } else { - result = {}; - } - if ( saved !== result ) { - - // Cancel the outer synthetic event - event.stopImmediatePropagation(); - event.preventDefault(); - return result.value; - } - - // If this is an inner synthetic event for an event with a bubbling surrogate - // (focus or blur), assume that the surrogate already propagated from triggering the - // native event and prevent that from happening again here. - // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the - // bubbling surrogate propagates *after* the non-bubbling base), but that seems - // less bad than duplication. - } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { - event.stopPropagation(); - } - - // If this is a native event triggered above, everything is now in order - // Fire an inner synthetic event with the original arguments - } else if ( saved.length ) { - - // ...and capture the result - dataPriv.set( this, type, { - value: jQuery.event.trigger( - - // Support: IE <=9 - 11+ - // Extend with the prototype to reset the above stopImmediatePropagation() - jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), - saved.slice( 1 ), - this - ) - } ); - - // Abort handling of the native event - event.stopImmediatePropagation(); - } - } - } ); - } - - jQuery.removeEvent = function( elem, type, handle ) { - - // This "if" is needed for plain objects - if ( elem.removeEventListener ) { - elem.removeEventListener( type, handle ); - } - }; - - jQuery.Event = function( src, props ) { - - // Allow instantiation without the 'new' keyword - if ( !( this instanceof jQuery.Event ) ) { - return new jQuery.Event( src, props ); - } - - // Event object - if ( src && src.type ) { - this.originalEvent = src; - this.type = src.type; - - // Events bubbling up the document may have been marked as prevented - // by a handler lower down the tree; reflect the correct value. - this.isDefaultPrevented = src.defaultPrevented || - src.defaultPrevented === undefined && - - // Support: Android <=2.3 only - src.returnValue === false ? - returnTrue : - returnFalse; - - // Create target properties - // Support: Safari <=6 - 7 only - // Target should not be a text node (#504, #13143) - this.target = ( src.target && src.target.nodeType === 3 ) ? - src.target.parentNode : - src.target; - - this.currentTarget = src.currentTarget; - this.relatedTarget = src.relatedTarget; - - // Event type - } else { - this.type = src; - } - - // Put explicitly provided properties onto the event object - if ( props ) { - jQuery.extend( this, props ); - } - - // Create a timestamp if incoming event doesn't have one - this.timeStamp = src && src.timeStamp || Date.now(); - - // Mark it as fixed - this[ jQuery.expando ] = true; - }; - - // jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding - // https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html - jQuery.Event.prototype = { - constructor: jQuery.Event, - isDefaultPrevented: returnFalse, - isPropagationStopped: returnFalse, - isImmediatePropagationStopped: returnFalse, - isSimulated: false, - - preventDefault: function() { - var e = this.originalEvent; - - this.isDefaultPrevented = returnTrue; - - if ( e && !this.isSimulated ) { - e.preventDefault(); - } - }, - stopPropagation: function() { - var e = this.originalEvent; - - this.isPropagationStopped = returnTrue; - - if ( e && !this.isSimulated ) { - e.stopPropagation(); - } - }, - stopImmediatePropagation: function() { - var e = this.originalEvent; - - this.isImmediatePropagationStopped = returnTrue; - - if ( e && !this.isSimulated ) { - e.stopImmediatePropagation(); - } - - this.stopPropagation(); - } - }; - - // Includes all common event props including KeyEvent and MouseEvent specific props - jQuery.each( { - altKey: true, - bubbles: true, - cancelable: true, - changedTouches: true, - ctrlKey: true, - detail: true, - eventPhase: true, - metaKey: true, - pageX: true, - pageY: true, - shiftKey: true, - view: true, - "char": true, - code: true, - charCode: true, - key: true, - keyCode: true, - button: true, - buttons: true, - clientX: true, - clientY: true, - offsetX: true, - offsetY: true, - pointerId: true, - pointerType: true, - screenX: true, - screenY: true, - targetTouches: true, - toElement: true, - touches: true, - - which: function( event ) { - var button = event.button; - - // Add which for key events - if ( event.which == null && rkeyEvent.test( event.type ) ) { - return event.charCode != null ? event.charCode : event.keyCode; - } - - // Add which for click: 1 === left; 2 === middle; 3 === right - if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { - if ( button & 1 ) { - return 1; - } - - if ( button & 2 ) { - return 3; - } - - if ( button & 4 ) { - return 2; - } - - return 0; - } - - return event.which; - } - }, jQuery.event.addProp ); - - jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { - jQuery.event.special[ type ] = { - - // Utilize native event if possible so blur/focus sequence is correct - setup: function() { - - // Claim the first handler - // dataPriv.set( this, "focus", ... ) - // dataPriv.set( this, "blur", ... ) - leverageNative( this, type, expectSync ); - - // Return false to allow normal processing in the caller - return false; - }, - trigger: function() { - - // Force setup before trigger - leverageNative( this, type ); - - // Return non-false to allow normal event-path propagation - return true; - }, - - delegateType: delegateType - }; - } ); - - // Create mouseenter/leave events using mouseover/out and event-time checks - // so that event delegation works in jQuery. - // Do the same for pointerenter/pointerleave and pointerover/pointerout - // - // Support: Safari 7 only - // Safari sends mouseenter too often; see: - // https://bugs.chromium.org/p/chromium/issues/detail?id=470258 - // for the description of the bug (it existed in older Chrome versions as well). - jQuery.each( { - mouseenter: "mouseover", - mouseleave: "mouseout", - pointerenter: "pointerover", - pointerleave: "pointerout" - }, function( orig, fix ) { - jQuery.event.special[ orig ] = { - delegateType: fix, - bindType: fix, - - handle: function( event ) { - var ret, - target = this, - related = event.relatedTarget, - handleObj = event.handleObj; - - // For mouseenter/leave call the handler if related is outside the target. - // NB: No relatedTarget if the mouse left/entered the browser window - if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { - event.type = handleObj.origType; - ret = handleObj.handler.apply( this, arguments ); - event.type = fix; - } - return ret; - } - }; - } ); - - jQuery.fn.extend( { - - on: function( types, selector, data, fn ) { - return on( this, types, selector, data, fn ); - }, - one: function( types, selector, data, fn ) { - return on( this, types, selector, data, fn, 1 ); - }, - off: function( types, selector, fn ) { - var handleObj, type; - if ( types && types.preventDefault && types.handleObj ) { - - // ( event ) dispatched jQuery.Event - handleObj = types.handleObj; - jQuery( types.delegateTarget ).off( - handleObj.namespace ? - handleObj.origType + "." + handleObj.namespace : - handleObj.origType, - handleObj.selector, - handleObj.handler - ); - return this; - } - if ( typeof types === "object" ) { - - // ( types-object [, selector] ) - for ( type in types ) { - this.off( type, selector, types[ type ] ); - } - return this; - } - if ( selector === false || typeof selector === "function" ) { - - // ( types [, fn] ) - fn = selector; - selector = undefined; - } - if ( fn === false ) { - fn = returnFalse; - } - return this.each( function() { - jQuery.event.remove( this, types, fn, selector ); - } ); - } - } ); - - - var - - // Support: IE <=10 - 11, Edge 12 - 13 only - // In IE/Edge using regex groups here causes severe slowdowns. - // See https://connect.microsoft.com/IE/feedback/details/1736512/ - rnoInnerhtml = /<script|<style|<link/i, - - // checked="checked" or checked - rchecked = /checked\s*(?:[^=]|=\s*.checked.)/i, - rcleanScript = /^\s*<!(?:\[CDATA\[|--)|(?:\]\]|--)>\s*$/g; - - // Prefer a tbody over its parent table for containing new rows - function manipulationTarget( elem, content ) { - if ( nodeName( elem, "table" ) && - nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { - - return jQuery( elem ).children( "tbody" )[ 0 ] || elem; - } - - return elem; - } - - // Replace/restore the type attribute of script elements for safe DOM manipulation - function disableScript( elem ) { - elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; - return elem; - } - function restoreScript( elem ) { - if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { - elem.type = elem.type.slice( 5 ); - } else { - elem.removeAttribute( "type" ); - } - - return elem; - } - - function cloneCopyEvent( src, dest ) { - var i, l, type, pdataOld, udataOld, udataCur, events; - - if ( dest.nodeType !== 1 ) { - return; - } - - // 1. Copy private data: events, handlers, etc. - if ( dataPriv.hasData( src ) ) { - pdataOld = dataPriv.get( src ); - events = pdataOld.events; - - if ( events ) { - dataPriv.remove( dest, "handle events" ); - - for ( type in events ) { - for ( i = 0, l = events[ type ].length; i < l; i++ ) { - jQuery.event.add( dest, type, events[ type ][ i ] ); - } - } - } - } - - // 2. Copy user data - if ( dataUser.hasData( src ) ) { - udataOld = dataUser.access( src ); - udataCur = jQuery.extend( {}, udataOld ); - - dataUser.set( dest, udataCur ); - } - } - - // Fix IE bugs, see support tests - function fixInput( src, dest ) { - var nodeName = dest.nodeName.toLowerCase(); - - // Fails to persist the checked state of a cloned checkbox or radio button. - if ( nodeName === "input" && rcheckableType.test( src.type ) ) { - dest.checked = src.checked; - - // Fails to return the selected option to the default selected state when cloning options - } else if ( nodeName === "input" || nodeName === "textarea" ) { - dest.defaultValue = src.defaultValue; - } - } - - function domManip( collection, args, callback, ignored ) { - - // Flatten any nested arrays - args = flat( args ); - - var fragment, first, scripts, hasScripts, node, doc, - i = 0, - l = collection.length, - iNoClone = l - 1, - value = args[ 0 ], - valueIsFunction = isFunction( value ); - - // We can't cloneNode fragments that contain checked, in WebKit - if ( valueIsFunction || - ( l > 1 && typeof value === "string" && - !support.checkClone && rchecked.test( value ) ) ) { - return collection.each( function( index ) { - var self = collection.eq( index ); - if ( valueIsFunction ) { - args[ 0 ] = value.call( this, index, self.html() ); - } - domManip( self, args, callback, ignored ); - } ); - } - - if ( l ) { - fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); - first = fragment.firstChild; - - if ( fragment.childNodes.length === 1 ) { - fragment = first; - } - - // Require either new content or an interest in ignored elements to invoke the callback - if ( first || ignored ) { - scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); - hasScripts = scripts.length; - - // Use the original fragment for the last item - // instead of the first because it can end up - // being emptied incorrectly in certain situations (#8070). - for ( ; i < l; i++ ) { - node = fragment; - - if ( i !== iNoClone ) { - node = jQuery.clone( node, true, true ); - - // Keep references to cloned scripts for later restoration - if ( hasScripts ) { - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( scripts, getAll( node, "script" ) ); - } - } - - callback.call( collection[ i ], node, i ); - } - - if ( hasScripts ) { - doc = scripts[ scripts.length - 1 ].ownerDocument; - - // Reenable scripts - jQuery.map( scripts, restoreScript ); - - // Evaluate executable scripts on first document insertion - for ( i = 0; i < hasScripts; i++ ) { - node = scripts[ i ]; - if ( rscriptType.test( node.type || "" ) && - !dataPriv.access( node, "globalEval" ) && - jQuery.contains( doc, node ) ) { - - if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { - - // Optional AJAX dependency, but won't run scripts if not present - if ( jQuery._evalUrl && !node.noModule ) { - jQuery._evalUrl( node.src, { - nonce: node.nonce || node.getAttribute( "nonce" ) - }, doc ); - } - } else { - DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); - } - } - } - } - } - } - - return collection; - } - - function remove( elem, selector, keepData ) { - var node, - nodes = selector ? jQuery.filter( selector, elem ) : elem, - i = 0; - - for ( ; ( node = nodes[ i ] ) != null; i++ ) { - if ( !keepData && node.nodeType === 1 ) { - jQuery.cleanData( getAll( node ) ); - } - - if ( node.parentNode ) { - if ( keepData && isAttached( node ) ) { - setGlobalEval( getAll( node, "script" ) ); - } - node.parentNode.removeChild( node ); - } - } - - return elem; - } - - jQuery.extend( { - htmlPrefilter: function( html ) { - return html; - }, - - clone: function( elem, dataAndEvents, deepDataAndEvents ) { - var i, l, srcElements, destElements, - clone = elem.cloneNode( true ), - inPage = isAttached( elem ); - - // Fix IE cloning issues - if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && - !jQuery.isXMLDoc( elem ) ) { - - // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 - destElements = getAll( clone ); - srcElements = getAll( elem ); - - for ( i = 0, l = srcElements.length; i < l; i++ ) { - fixInput( srcElements[ i ], destElements[ i ] ); - } - } - - // Copy the events from the original to the clone - if ( dataAndEvents ) { - if ( deepDataAndEvents ) { - srcElements = srcElements || getAll( elem ); - destElements = destElements || getAll( clone ); - - for ( i = 0, l = srcElements.length; i < l; i++ ) { - cloneCopyEvent( srcElements[ i ], destElements[ i ] ); - } - } else { - cloneCopyEvent( elem, clone ); - } - } - - // Preserve script evaluation history - destElements = getAll( clone, "script" ); - if ( destElements.length > 0 ) { - setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); - } - - // Return the cloned set - return clone; - }, - - cleanData: function( elems ) { - var data, elem, type, - special = jQuery.event.special, - i = 0; - - for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { - if ( acceptData( elem ) ) { - if ( ( data = elem[ dataPriv.expando ] ) ) { - if ( data.events ) { - for ( type in data.events ) { - if ( special[ type ] ) { - jQuery.event.remove( elem, type ); - - // This is a shortcut to avoid jQuery.event.remove's overhead - } else { - jQuery.removeEvent( elem, type, data.handle ); - } - } - } - - // Support: Chrome <=35 - 45+ - // Assign undefined instead of using delete, see Data#remove - elem[ dataPriv.expando ] = undefined; - } - if ( elem[ dataUser.expando ] ) { - - // Support: Chrome <=35 - 45+ - // Assign undefined instead of using delete, see Data#remove - elem[ dataUser.expando ] = undefined; - } - } - } - } - } ); - - jQuery.fn.extend( { - detach: function( selector ) { - return remove( this, selector, true ); - }, - - remove: function( selector ) { - return remove( this, selector ); - }, - - text: function( value ) { - return access( this, function( value ) { - return value === undefined ? - jQuery.text( this ) : - this.empty().each( function() { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - this.textContent = value; - } - } ); - }, null, value, arguments.length ); - }, - - append: function() { - return domManip( this, arguments, function( elem ) { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - var target = manipulationTarget( this, elem ); - target.appendChild( elem ); - } - } ); - }, - - prepend: function() { - return domManip( this, arguments, function( elem ) { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - var target = manipulationTarget( this, elem ); - target.insertBefore( elem, target.firstChild ); - } - } ); - }, - - before: function() { - return domManip( this, arguments, function( elem ) { - if ( this.parentNode ) { - this.parentNode.insertBefore( elem, this ); - } - } ); - }, - - after: function() { - return domManip( this, arguments, function( elem ) { - if ( this.parentNode ) { - this.parentNode.insertBefore( elem, this.nextSibling ); - } - } ); - }, - - empty: function() { - var elem, - i = 0; - - for ( ; ( elem = this[ i ] ) != null; i++ ) { - if ( elem.nodeType === 1 ) { - - // Prevent memory leaks - jQuery.cleanData( getAll( elem, false ) ); - - // Remove any remaining nodes - elem.textContent = ""; - } - } - - return this; - }, - - clone: function( dataAndEvents, deepDataAndEvents ) { - dataAndEvents = dataAndEvents == null ? false : dataAndEvents; - deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; - - return this.map( function() { - return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); - } ); - }, - - html: function( value ) { - return access( this, function( value ) { - var elem = this[ 0 ] || {}, - i = 0, - l = this.length; - - if ( value === undefined && elem.nodeType === 1 ) { - return elem.innerHTML; - } - - // See if we can take a shortcut and just use innerHTML - if ( typeof value === "string" && !rnoInnerhtml.test( value ) && - !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { - - value = jQuery.htmlPrefilter( value ); - - try { - for ( ; i < l; i++ ) { - elem = this[ i ] || {}; - - // Remove element nodes and prevent memory leaks - if ( elem.nodeType === 1 ) { - jQuery.cleanData( getAll( elem, false ) ); - elem.innerHTML = value; - } - } - - elem = 0; - - // If using innerHTML throws an exception, use the fallback method - } catch ( e ) {} - } - - if ( elem ) { - this.empty().append( value ); - } - }, null, value, arguments.length ); - }, - - replaceWith: function() { - var ignored = []; - - // Make the changes, replacing each non-ignored context element with the new content - return domManip( this, arguments, function( elem ) { - var parent = this.parentNode; - - if ( jQuery.inArray( this, ignored ) < 0 ) { - jQuery.cleanData( getAll( this ) ); - if ( parent ) { - parent.replaceChild( elem, this ); - } - } - - // Force callback invocation - }, ignored ); - } - } ); - - jQuery.each( { - appendTo: "append", - prependTo: "prepend", - insertBefore: "before", - insertAfter: "after", - replaceAll: "replaceWith" - }, function( name, original ) { - jQuery.fn[ name ] = function( selector ) { - var elems, - ret = [], - insert = jQuery( selector ), - last = insert.length - 1, - i = 0; - - for ( ; i <= last; i++ ) { - elems = i === last ? this : this.clone( true ); - jQuery( insert[ i ] )[ original ]( elems ); - - // Support: Android <=4.0 only, PhantomJS 1 only - // .get() because push.apply(_, arraylike) throws on ancient WebKit - push.apply( ret, elems.get() ); - } - - return this.pushStack( ret ); - }; - } ); - var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); - - var getStyles = function( elem ) { - - // Support: IE <=11 only, Firefox <=30 (#15098, #14150) - // IE throws on elements created in popups - // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" - var view = elem.ownerDocument.defaultView; - - if ( !view || !view.opener ) { - view = window; - } - - return view.getComputedStyle( elem ); - }; - - var swap = function( elem, options, callback ) { - var ret, name, - old = {}; - - // Remember the old values, and insert the new ones - for ( name in options ) { - old[ name ] = elem.style[ name ]; - elem.style[ name ] = options[ name ]; - } - - ret = callback.call( elem ); - - // Revert the old values - for ( name in options ) { - elem.style[ name ] = old[ name ]; - } - - return ret; - }; - - - var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); - - - - ( function() { - - // Executing both pixelPosition & boxSizingReliable tests require only one layout - // so they're executed at the same time to save the second computation. - function computeStyleTests() { - - // This is a singleton, we need to execute it only once - if ( !div ) { - return; - } - - container.style.cssText = "position:absolute;left:-11111px;width:60px;" + - "margin-top:1px;padding:0;border:0"; - div.style.cssText = - "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + - "margin:auto;border:1px;padding:1px;" + - "width:60%;top:1%"; - documentElement.appendChild( container ).appendChild( div ); - - var divStyle = window.getComputedStyle( div ); - pixelPositionVal = divStyle.top !== "1%"; - - // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 - reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; - - // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 - // Some styles come back with percentage values, even though they shouldn't - div.style.right = "60%"; - pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; - - // Support: IE 9 - 11 only - // Detect misreporting of content dimensions for box-sizing:border-box elements - boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; - - // Support: IE 9 only - // Detect overflow:scroll screwiness (gh-3699) - // Support: Chrome <=64 - // Don't get tricked when zoom affects offsetWidth (gh-4029) - div.style.position = "absolute"; - scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; - - documentElement.removeChild( container ); - - // Nullify the div so it wouldn't be stored in the memory and - // it will also be a sign that checks already performed - div = null; - } - - function roundPixelMeasures( measure ) { - return Math.round( parseFloat( measure ) ); - } - - var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, - reliableTrDimensionsVal, reliableMarginLeftVal, - container = document.createElement( "div" ), - div = document.createElement( "div" ); - - // Finish early in limited (non-browser) environments - if ( !div.style ) { - return; - } - - // Support: IE <=9 - 11 only - // Style of cloned element affects source element cloned (#8908) - div.style.backgroundClip = "content-box"; - div.cloneNode( true ).style.backgroundClip = ""; - support.clearCloneStyle = div.style.backgroundClip === "content-box"; - - jQuery.extend( support, { - boxSizingReliable: function() { - computeStyleTests(); - return boxSizingReliableVal; - }, - pixelBoxStyles: function() { - computeStyleTests(); - return pixelBoxStylesVal; - }, - pixelPosition: function() { - computeStyleTests(); - return pixelPositionVal; - }, - reliableMarginLeft: function() { - computeStyleTests(); - return reliableMarginLeftVal; - }, - scrollboxSize: function() { - computeStyleTests(); - return scrollboxSizeVal; - }, - - // Support: IE 9 - 11+, Edge 15 - 18+ - // IE/Edge misreport `getComputedStyle` of table rows with width/height - // set in CSS while `offset*` properties report correct values. - // Behavior in IE 9 is more subtle than in newer versions & it passes - // some versions of this test; make sure not to make it pass there! - reliableTrDimensions: function() { - var table, tr, trChild, trStyle; - if ( reliableTrDimensionsVal == null ) { - table = document.createElement( "table" ); - tr = document.createElement( "tr" ); - trChild = document.createElement( "div" ); - - table.style.cssText = "position:absolute;left:-11111px"; - tr.style.height = "1px"; - trChild.style.height = "9px"; - - documentElement - .appendChild( table ) - .appendChild( tr ) - .appendChild( trChild ); - - trStyle = window.getComputedStyle( tr ); - reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; - - documentElement.removeChild( table ); - } - return reliableTrDimensionsVal; - } - } ); - } )(); - - - function curCSS( elem, name, computed ) { - var width, minWidth, maxWidth, ret, - - // Support: Firefox 51+ - // Retrieving style before computed somehow - // fixes an issue with getting wrong values - // on detached elements - style = elem.style; - - computed = computed || getStyles( elem ); - - // getPropertyValue is needed for: - // .css('filter') (IE 9 only, #12537) - // .css('--customProperty) (#3144) - if ( computed ) { - ret = computed.getPropertyValue( name ) || computed[ name ]; - - if ( ret === "" && !isAttached( elem ) ) { - ret = jQuery.style( elem, name ); - } - - // A tribute to the "awesome hack by Dean Edwards" - // Android Browser returns percentage for some values, - // but width seems to be reliably pixels. - // This is against the CSSOM draft spec: - // https://drafts.csswg.org/cssom/#resolved-values - if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { - - // Remember the original values - width = style.width; - minWidth = style.minWidth; - maxWidth = style.maxWidth; - - // Put in the new values to get a computed value out - style.minWidth = style.maxWidth = style.width = ret; - ret = computed.width; - - // Revert the changed values - style.width = width; - style.minWidth = minWidth; - style.maxWidth = maxWidth; - } - } - - return ret !== undefined ? - - // Support: IE <=9 - 11 only - // IE returns zIndex value as an integer. - ret + "" : - ret; - } - - - function addGetHookIf( conditionFn, hookFn ) { - - // Define the hook, we'll check on the first run if it's really needed. - return { - get: function() { - if ( conditionFn() ) { - - // Hook not needed (or it's not possible to use it due - // to missing dependency), remove it. - delete this.get; - return; - } - - // Hook needed; redefine it so that the support test is not executed again. - return ( this.get = hookFn ).apply( this, arguments ); - } - }; - } - - - var cssPrefixes = [ "Webkit", "Moz", "ms" ], - emptyStyle = document.createElement( "div" ).style, - vendorProps = {}; - - // Return a vendor-prefixed property or undefined - function vendorPropName( name ) { - - // Check for vendor prefixed names - var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), - i = cssPrefixes.length; - - while ( i-- ) { - name = cssPrefixes[ i ] + capName; - if ( name in emptyStyle ) { - return name; - } - } - } - - // Return a potentially-mapped jQuery.cssProps or vendor prefixed property - function finalPropName( name ) { - var final = jQuery.cssProps[ name ] || vendorProps[ name ]; - - if ( final ) { - return final; - } - if ( name in emptyStyle ) { - return name; - } - return vendorProps[ name ] = vendorPropName( name ) || name; - } - - - var - - // Swappable if display is none or starts with table - // except "table", "table-cell", or "table-caption" - // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display - rdisplayswap = /^(none|table(?!-c[ea]).+)/, - rcustomProp = /^--/, - cssShow = { position: "absolute", visibility: "hidden", display: "block" }, - cssNormalTransform = { - letterSpacing: "0", - fontWeight: "400" - }; - - function setPositiveNumber( _elem, value, subtract ) { - - // Any relative (+/-) values have already been - // normalized at this point - var matches = rcssNum.exec( value ); - return matches ? - - // Guard against undefined "subtract", e.g., when used as in cssHooks - Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : - value; - } - - function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { - var i = dimension === "width" ? 1 : 0, - extra = 0, - delta = 0; - - // Adjustment may not be necessary - if ( box === ( isBorderBox ? "border" : "content" ) ) { - return 0; - } - - for ( ; i < 4; i += 2 ) { - - // Both box models exclude margin - if ( box === "margin" ) { - delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); - } - - // If we get here with a content-box, we're seeking "padding" or "border" or "margin" - if ( !isBorderBox ) { - - // Add padding - delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); - - // For "border" or "margin", add border - if ( box !== "padding" ) { - delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - - // But still keep track of it otherwise - } else { - extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - } - - // If we get here with a border-box (content + padding + border), we're seeking "content" or - // "padding" or "margin" - } else { - - // For "content", subtract padding - if ( box === "content" ) { - delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); - } - - // For "content" or "padding", subtract border - if ( box !== "margin" ) { - delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - } - } - } - - // Account for positive content-box scroll gutter when requested by providing computedVal - if ( !isBorderBox && computedVal >= 0 ) { - - // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border - // Assuming integer scroll gutter, subtract the rest and round down - delta += Math.max( 0, Math.ceil( - elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - - computedVal - - delta - - extra - - 0.5 - - // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter - // Use an explicit zero to avoid NaN (gh-3964) - ) ) || 0; - } - - return delta; - } - - function getWidthOrHeight( elem, dimension, extra ) { - - // Start with computed style - var styles = getStyles( elem ), - - // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). - // Fake content-box until we know it's needed to know the true value. - boxSizingNeeded = !support.boxSizingReliable() || extra, - isBorderBox = boxSizingNeeded && - jQuery.css( elem, "boxSizing", false, styles ) === "border-box", - valueIsBorderBox = isBorderBox, - - val = curCSS( elem, dimension, styles ), - offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); - - // Support: Firefox <=54 - // Return a confounding non-pixel value or feign ignorance, as appropriate. - if ( rnumnonpx.test( val ) ) { - if ( !extra ) { - return val; - } - val = "auto"; - } - - - // Support: IE 9 - 11 only - // Use offsetWidth/offsetHeight for when box sizing is unreliable. - // In those cases, the computed value can be trusted to be border-box. - if ( ( !support.boxSizingReliable() && isBorderBox || - - // Support: IE 10 - 11+, Edge 15 - 18+ - // IE/Edge misreport `getComputedStyle` of table rows with width/height - // set in CSS while `offset*` properties report correct values. - // Interestingly, in some cases IE 9 doesn't suffer from this issue. - !support.reliableTrDimensions() && nodeName( elem, "tr" ) || - - // Fall back to offsetWidth/offsetHeight when value is "auto" - // This happens for inline elements with no explicit setting (gh-3571) - val === "auto" || - - // Support: Android <=4.1 - 4.3 only - // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) - !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && - - // Make sure the element is visible & connected - elem.getClientRects().length ) { - - isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; - - // Where available, offsetWidth/offsetHeight approximate border box dimensions. - // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the - // retrieved value as a content box dimension. - valueIsBorderBox = offsetProp in elem; - if ( valueIsBorderBox ) { - val = elem[ offsetProp ]; - } - } - - // Normalize "" and auto - val = parseFloat( val ) || 0; - - // Adjust for the element's box model - return ( val + - boxModelAdjustment( - elem, - dimension, - extra || ( isBorderBox ? "border" : "content" ), - valueIsBorderBox, - styles, - - // Provide the current computed size to request scroll gutter calculation (gh-3589) - val - ) - ) + "px"; - } - - jQuery.extend( { - - // Add in style property hooks for overriding the default - // behavior of getting and setting a style property - cssHooks: { - opacity: { - get: function( elem, computed ) { - if ( computed ) { - - // We should always get a number back from opacity - var ret = curCSS( elem, "opacity" ); - return ret === "" ? "1" : ret; - } - } - } - }, - - // Don't automatically add "px" to these possibly-unitless properties - cssNumber: { - "animationIterationCount": true, - "columnCount": true, - "fillOpacity": true, - "flexGrow": true, - "flexShrink": true, - "fontWeight": true, - "gridArea": true, - "gridColumn": true, - "gridColumnEnd": true, - "gridColumnStart": true, - "gridRow": true, - "gridRowEnd": true, - "gridRowStart": true, - "lineHeight": true, - "opacity": true, - "order": true, - "orphans": true, - "widows": true, - "zIndex": true, - "zoom": true - }, - - // Add in properties whose names you wish to fix before - // setting or getting the value - cssProps: {}, - - // Get and set the style property on a DOM Node - style: function( elem, name, value, extra ) { - - // Don't set styles on text and comment nodes - if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { - return; - } - - // Make sure that we're working with the right name - var ret, type, hooks, - origName = camelCase( name ), - isCustomProp = rcustomProp.test( name ), - style = elem.style; - - // Make sure that we're working with the right name. We don't - // want to query the value if it is a CSS custom property - // since they are user-defined. - if ( !isCustomProp ) { - name = finalPropName( origName ); - } - - // Gets hook for the prefixed version, then unprefixed version - hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; - - // Check if we're setting a value - if ( value !== undefined ) { - type = typeof value; - - // Convert "+=" or "-=" to relative numbers (#7345) - if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { - value = adjustCSS( elem, name, ret ); - - // Fixes bug #9237 - type = "number"; - } - - // Make sure that null and NaN values aren't set (#7116) - if ( value == null || value !== value ) { - return; - } - - // If a number was passed in, add the unit (except for certain CSS properties) - // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append - // "px" to a few hardcoded values. - if ( type === "number" && !isCustomProp ) { - value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); - } - - // background-* props affect original clone's values - if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { - style[ name ] = "inherit"; - } - - // If a hook was provided, use that value, otherwise just set the specified value - if ( !hooks || !( "set" in hooks ) || - ( value = hooks.set( elem, value, extra ) ) !== undefined ) { - - if ( isCustomProp ) { - style.setProperty( name, value ); - } else { - style[ name ] = value; - } - } - - } else { - - // If a hook was provided get the non-computed value from there - if ( hooks && "get" in hooks && - ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { - - return ret; - } - - // Otherwise just get the value from the style object - return style[ name ]; - } - }, - - css: function( elem, name, extra, styles ) { - var val, num, hooks, - origName = camelCase( name ), - isCustomProp = rcustomProp.test( name ); - - // Make sure that we're working with the right name. We don't - // want to modify the value if it is a CSS custom property - // since they are user-defined. - if ( !isCustomProp ) { - name = finalPropName( origName ); - } - - // Try prefixed name followed by the unprefixed name - hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; - - // If a hook was provided get the computed value from there - if ( hooks && "get" in hooks ) { - val = hooks.get( elem, true, extra ); - } - - // Otherwise, if a way to get the computed value exists, use that - if ( val === undefined ) { - val = curCSS( elem, name, styles ); - } - - // Convert "normal" to computed value - if ( val === "normal" && name in cssNormalTransform ) { - val = cssNormalTransform[ name ]; - } - - // Make numeric if forced or a qualifier was provided and val looks numeric - if ( extra === "" || extra ) { - num = parseFloat( val ); - return extra === true || isFinite( num ) ? num || 0 : val; - } - - return val; - } - } ); - - jQuery.each( [ "height", "width" ], function( _i, dimension ) { - jQuery.cssHooks[ dimension ] = { - get: function( elem, computed, extra ) { - if ( computed ) { - - // Certain elements can have dimension info if we invisibly show them - // but it must have a current display style that would benefit - return rdisplayswap.test( jQuery.css( elem, "display" ) ) && - - // Support: Safari 8+ - // Table columns in Safari have non-zero offsetWidth & zero - // getBoundingClientRect().width unless display is changed. - // Support: IE <=11 only - // Running getBoundingClientRect on a disconnected node - // in IE throws an error. - ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? - swap( elem, cssShow, function() { - return getWidthOrHeight( elem, dimension, extra ); - } ) : - getWidthOrHeight( elem, dimension, extra ); - } - }, - - set: function( elem, value, extra ) { - var matches, - styles = getStyles( elem ), - - // Only read styles.position if the test has a chance to fail - // to avoid forcing a reflow. - scrollboxSizeBuggy = !support.scrollboxSize() && - styles.position === "absolute", - - // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) - boxSizingNeeded = scrollboxSizeBuggy || extra, - isBorderBox = boxSizingNeeded && - jQuery.css( elem, "boxSizing", false, styles ) === "border-box", - subtract = extra ? - boxModelAdjustment( - elem, - dimension, - extra, - isBorderBox, - styles - ) : - 0; - - // Account for unreliable border-box dimensions by comparing offset* to computed and - // faking a content-box to get border and padding (gh-3699) - if ( isBorderBox && scrollboxSizeBuggy ) { - subtract -= Math.ceil( - elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - - parseFloat( styles[ dimension ] ) - - boxModelAdjustment( elem, dimension, "border", false, styles ) - - 0.5 - ); - } - - // Convert to pixels if value adjustment is needed - if ( subtract && ( matches = rcssNum.exec( value ) ) && - ( matches[ 3 ] || "px" ) !== "px" ) { - - elem.style[ dimension ] = value; - value = jQuery.css( elem, dimension ); - } - - return setPositiveNumber( elem, value, subtract ); - } - }; - } ); - - jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, - function( elem, computed ) { - if ( computed ) { - return ( parseFloat( curCSS( elem, "marginLeft" ) ) || - elem.getBoundingClientRect().left - - swap( elem, { marginLeft: 0 }, function() { - return elem.getBoundingClientRect().left; - } ) - ) + "px"; - } - } - ); - - // These hooks are used by animate to expand properties - jQuery.each( { - margin: "", - padding: "", - border: "Width" - }, function( prefix, suffix ) { - jQuery.cssHooks[ prefix + suffix ] = { - expand: function( value ) { - var i = 0, - expanded = {}, - - // Assumes a single number if not a string - parts = typeof value === "string" ? value.split( " " ) : [ value ]; - - for ( ; i < 4; i++ ) { - expanded[ prefix + cssExpand[ i ] + suffix ] = - parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; - } - - return expanded; - } - }; - - if ( prefix !== "margin" ) { - jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; - } - } ); - - jQuery.fn.extend( { - css: function( name, value ) { - return access( this, function( elem, name, value ) { - var styles, len, - map = {}, - i = 0; - - if ( Array.isArray( name ) ) { - styles = getStyles( elem ); - len = name.length; - - for ( ; i < len; i++ ) { - map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); - } - - return map; - } - - return value !== undefined ? - jQuery.style( elem, name, value ) : - jQuery.css( elem, name ); - }, name, value, arguments.length > 1 ); - } - } ); - - - function Tween( elem, options, prop, end, easing ) { - return new Tween.prototype.init( elem, options, prop, end, easing ); - } - jQuery.Tween = Tween; - - Tween.prototype = { - constructor: Tween, - init: function( elem, options, prop, end, easing, unit ) { - this.elem = elem; - this.prop = prop; - this.easing = easing || jQuery.easing._default; - this.options = options; - this.start = this.now = this.cur(); - this.end = end; - this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); - }, - cur: function() { - var hooks = Tween.propHooks[ this.prop ]; - - return hooks && hooks.get ? - hooks.get( this ) : - Tween.propHooks._default.get( this ); - }, - run: function( percent ) { - var eased, - hooks = Tween.propHooks[ this.prop ]; - - if ( this.options.duration ) { - this.pos = eased = jQuery.easing[ this.easing ]( - percent, this.options.duration * percent, 0, 1, this.options.duration - ); - } else { - this.pos = eased = percent; - } - this.now = ( this.end - this.start ) * eased + this.start; - - if ( this.options.step ) { - this.options.step.call( this.elem, this.now, this ); - } - - if ( hooks && hooks.set ) { - hooks.set( this ); - } else { - Tween.propHooks._default.set( this ); - } - return this; - } - }; - - Tween.prototype.init.prototype = Tween.prototype; - - Tween.propHooks = { - _default: { - get: function( tween ) { - var result; - - // Use a property on the element directly when it is not a DOM element, - // or when there is no matching style property that exists. - if ( tween.elem.nodeType !== 1 || - tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { - return tween.elem[ tween.prop ]; - } - - // Passing an empty string as a 3rd parameter to .css will automatically - // attempt a parseFloat and fallback to a string if the parse fails. - // Simple values such as "10px" are parsed to Float; - // complex values such as "rotate(1rad)" are returned as-is. - result = jQuery.css( tween.elem, tween.prop, "" ); - - // Empty strings, null, undefined and "auto" are converted to 0. - return !result || result === "auto" ? 0 : result; - }, - set: function( tween ) { - - // Use step hook for back compat. - // Use cssHook if its there. - // Use .style if available and use plain properties where available. - if ( jQuery.fx.step[ tween.prop ] ) { - jQuery.fx.step[ tween.prop ]( tween ); - } else if ( tween.elem.nodeType === 1 && ( - jQuery.cssHooks[ tween.prop ] || - tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { - jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); - } else { - tween.elem[ tween.prop ] = tween.now; - } - } - } - }; - - // Support: IE <=9 only - // Panic based approach to setting things on disconnected nodes - Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { - set: function( tween ) { - if ( tween.elem.nodeType && tween.elem.parentNode ) { - tween.elem[ tween.prop ] = tween.now; - } - } - }; - - jQuery.easing = { - linear: function( p ) { - return p; - }, - swing: function( p ) { - return 0.5 - Math.cos( p * Math.PI ) / 2; - }, - _default: "swing" - }; - - jQuery.fx = Tween.prototype.init; - - // Back compat <1.8 extension point - jQuery.fx.step = {}; - - - - - var - fxNow, inProgress, - rfxtypes = /^(?:toggle|show|hide)$/, - rrun = /queueHooks$/; - - function schedule() { - if ( inProgress ) { - if ( document.hidden === false && window.requestAnimationFrame ) { - window.requestAnimationFrame( schedule ); - } else { - window.setTimeout( schedule, jQuery.fx.interval ); - } - - jQuery.fx.tick(); - } - } - - // Animations created synchronously will run synchronously - function createFxNow() { - window.setTimeout( function() { - fxNow = undefined; - } ); - return ( fxNow = Date.now() ); - } - - // Generate parameters to create a standard animation - function genFx( type, includeWidth ) { - var which, - i = 0, - attrs = { height: type }; - - // If we include width, step value is 1 to do all cssExpand values, - // otherwise step value is 2 to skip over Left and Right - includeWidth = includeWidth ? 1 : 0; - for ( ; i < 4; i += 2 - includeWidth ) { - which = cssExpand[ i ]; - attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; - } - - if ( includeWidth ) { - attrs.opacity = attrs.width = type; - } - - return attrs; - } - - function createTween( value, prop, animation ) { - var tween, - collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), - index = 0, - length = collection.length; - for ( ; index < length; index++ ) { - if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { - - // We're done with this property - return tween; - } - } - } - - function defaultPrefilter( elem, props, opts ) { - var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, - isBox = "width" in props || "height" in props, - anim = this, - orig = {}, - style = elem.style, - hidden = elem.nodeType && isHiddenWithinTree( elem ), - dataShow = dataPriv.get( elem, "fxshow" ); - - // Queue-skipping animations hijack the fx hooks - if ( !opts.queue ) { - hooks = jQuery._queueHooks( elem, "fx" ); - if ( hooks.unqueued == null ) { - hooks.unqueued = 0; - oldfire = hooks.empty.fire; - hooks.empty.fire = function() { - if ( !hooks.unqueued ) { - oldfire(); - } - }; - } - hooks.unqueued++; - - anim.always( function() { - - // Ensure the complete handler is called before this completes - anim.always( function() { - hooks.unqueued--; - if ( !jQuery.queue( elem, "fx" ).length ) { - hooks.empty.fire(); - } - } ); - } ); - } - - // Detect show/hide animations - for ( prop in props ) { - value = props[ prop ]; - if ( rfxtypes.test( value ) ) { - delete props[ prop ]; - toggle = toggle || value === "toggle"; - if ( value === ( hidden ? "hide" : "show" ) ) { - - // Pretend to be hidden if this is a "show" and - // there is still data from a stopped show/hide - if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { - hidden = true; - - // Ignore all other no-op show/hide data - } else { - continue; - } - } - orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); - } - } - - // Bail out if this is a no-op like .hide().hide() - propTween = !jQuery.isEmptyObject( props ); - if ( !propTween && jQuery.isEmptyObject( orig ) ) { - return; - } - - // Restrict "overflow" and "display" styles during box animations - if ( isBox && elem.nodeType === 1 ) { - - // Support: IE <=9 - 11, Edge 12 - 15 - // Record all 3 overflow attributes because IE does not infer the shorthand - // from identically-valued overflowX and overflowY and Edge just mirrors - // the overflowX value there. - opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; - - // Identify a display type, preferring old show/hide data over the CSS cascade - restoreDisplay = dataShow && dataShow.display; - if ( restoreDisplay == null ) { - restoreDisplay = dataPriv.get( elem, "display" ); - } - display = jQuery.css( elem, "display" ); - if ( display === "none" ) { - if ( restoreDisplay ) { - display = restoreDisplay; - } else { - - // Get nonempty value(s) by temporarily forcing visibility - showHide( [ elem ], true ); - restoreDisplay = elem.style.display || restoreDisplay; - display = jQuery.css( elem, "display" ); - showHide( [ elem ] ); - } - } - - // Animate inline elements as inline-block - if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { - if ( jQuery.css( elem, "float" ) === "none" ) { - - // Restore the original display value at the end of pure show/hide animations - if ( !propTween ) { - anim.done( function() { - style.display = restoreDisplay; - } ); - if ( restoreDisplay == null ) { - display = style.display; - restoreDisplay = display === "none" ? "" : display; - } - } - style.display = "inline-block"; - } - } - } - - if ( opts.overflow ) { - style.overflow = "hidden"; - anim.always( function() { - style.overflow = opts.overflow[ 0 ]; - style.overflowX = opts.overflow[ 1 ]; - style.overflowY = opts.overflow[ 2 ]; - } ); - } - - // Implement show/hide animations - propTween = false; - for ( prop in orig ) { - - // General show/hide setup for this element animation - if ( !propTween ) { - if ( dataShow ) { - if ( "hidden" in dataShow ) { - hidden = dataShow.hidden; - } - } else { - dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); - } - - // Store hidden/visible for toggle so `.stop().toggle()` "reverses" - if ( toggle ) { - dataShow.hidden = !hidden; - } - - // Show elements before animating them - if ( hidden ) { - showHide( [ elem ], true ); - } - - /* eslint-disable no-loop-func */ - - anim.done( function() { - - /* eslint-enable no-loop-func */ - - // The final step of a "hide" animation is actually hiding the element - if ( !hidden ) { - showHide( [ elem ] ); - } - dataPriv.remove( elem, "fxshow" ); - for ( prop in orig ) { - jQuery.style( elem, prop, orig[ prop ] ); - } - } ); - } - - // Per-property setup - propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); - if ( !( prop in dataShow ) ) { - dataShow[ prop ] = propTween.start; - if ( hidden ) { - propTween.end = propTween.start; - propTween.start = 0; - } - } - } - } - - function propFilter( props, specialEasing ) { - var index, name, easing, value, hooks; - - // camelCase, specialEasing and expand cssHook pass - for ( index in props ) { - name = camelCase( index ); - easing = specialEasing[ name ]; - value = props[ index ]; - if ( Array.isArray( value ) ) { - easing = value[ 1 ]; - value = props[ index ] = value[ 0 ]; - } - - if ( index !== name ) { - props[ name ] = value; - delete props[ index ]; - } - - hooks = jQuery.cssHooks[ name ]; - if ( hooks && "expand" in hooks ) { - value = hooks.expand( value ); - delete props[ name ]; - - // Not quite $.extend, this won't overwrite existing keys. - // Reusing 'index' because we have the correct "name" - for ( index in value ) { - if ( !( index in props ) ) { - props[ index ] = value[ index ]; - specialEasing[ index ] = easing; - } - } - } else { - specialEasing[ name ] = easing; - } - } - } - - function Animation( elem, properties, options ) { - var result, - stopped, - index = 0, - length = Animation.prefilters.length, - deferred = jQuery.Deferred().always( function() { - - // Don't match elem in the :animated selector - delete tick.elem; - } ), - tick = function() { - if ( stopped ) { - return false; - } - var currentTime = fxNow || createFxNow(), - remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), - - // Support: Android 2.3 only - // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) - temp = remaining / animation.duration || 0, - percent = 1 - temp, - index = 0, - length = animation.tweens.length; - - for ( ; index < length; index++ ) { - animation.tweens[ index ].run( percent ); - } - - deferred.notifyWith( elem, [ animation, percent, remaining ] ); - - // If there's more to do, yield - if ( percent < 1 && length ) { - return remaining; - } - - // If this was an empty animation, synthesize a final progress notification - if ( !length ) { - deferred.notifyWith( elem, [ animation, 1, 0 ] ); - } - - // Resolve the animation and report its conclusion - deferred.resolveWith( elem, [ animation ] ); - return false; - }, - animation = deferred.promise( { - elem: elem, - props: jQuery.extend( {}, properties ), - opts: jQuery.extend( true, { - specialEasing: {}, - easing: jQuery.easing._default - }, options ), - originalProperties: properties, - originalOptions: options, - startTime: fxNow || createFxNow(), - duration: options.duration, - tweens: [], - createTween: function( prop, end ) { - var tween = jQuery.Tween( elem, animation.opts, prop, end, - animation.opts.specialEasing[ prop ] || animation.opts.easing ); - animation.tweens.push( tween ); - return tween; - }, - stop: function( gotoEnd ) { - var index = 0, - - // If we are going to the end, we want to run all the tweens - // otherwise we skip this part - length = gotoEnd ? animation.tweens.length : 0; - if ( stopped ) { - return this; - } - stopped = true; - for ( ; index < length; index++ ) { - animation.tweens[ index ].run( 1 ); - } - - // Resolve when we played the last frame; otherwise, reject - if ( gotoEnd ) { - deferred.notifyWith( elem, [ animation, 1, 0 ] ); - deferred.resolveWith( elem, [ animation, gotoEnd ] ); - } else { - deferred.rejectWith( elem, [ animation, gotoEnd ] ); - } - return this; - } - } ), - props = animation.props; - - propFilter( props, animation.opts.specialEasing ); - - for ( ; index < length; index++ ) { - result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); - if ( result ) { - if ( isFunction( result.stop ) ) { - jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = - result.stop.bind( result ); - } - return result; - } - } - - jQuery.map( props, createTween, animation ); - - if ( isFunction( animation.opts.start ) ) { - animation.opts.start.call( elem, animation ); - } - - // Attach callbacks from options - animation - .progress( animation.opts.progress ) - .done( animation.opts.done, animation.opts.complete ) - .fail( animation.opts.fail ) - .always( animation.opts.always ); - - jQuery.fx.timer( - jQuery.extend( tick, { - elem: elem, - anim: animation, - queue: animation.opts.queue - } ) - ); - - return animation; - } - - jQuery.Animation = jQuery.extend( Animation, { - - tweeners: { - "*": [ function( prop, value ) { - var tween = this.createTween( prop, value ); - adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); - return tween; - } ] - }, - - tweener: function( props, callback ) { - if ( isFunction( props ) ) { - callback = props; - props = [ "*" ]; - } else { - props = props.match( rnothtmlwhite ); - } - - var prop, - index = 0, - length = props.length; - - for ( ; index < length; index++ ) { - prop = props[ index ]; - Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; - Animation.tweeners[ prop ].unshift( callback ); - } - }, - - prefilters: [ defaultPrefilter ], - - prefilter: function( callback, prepend ) { - if ( prepend ) { - Animation.prefilters.unshift( callback ); - } else { - Animation.prefilters.push( callback ); - } - } - } ); - - jQuery.speed = function( speed, easing, fn ) { - var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { - complete: fn || !fn && easing || - isFunction( speed ) && speed, - duration: speed, - easing: fn && easing || easing && !isFunction( easing ) && easing - }; - - // Go to the end state if fx are off - if ( jQuery.fx.off ) { - opt.duration = 0; - - } else { - if ( typeof opt.duration !== "number" ) { - if ( opt.duration in jQuery.fx.speeds ) { - opt.duration = jQuery.fx.speeds[ opt.duration ]; - - } else { - opt.duration = jQuery.fx.speeds._default; - } - } - } - - // Normalize opt.queue - true/undefined/null -> "fx" - if ( opt.queue == null || opt.queue === true ) { - opt.queue = "fx"; - } - - // Queueing - opt.old = opt.complete; - - opt.complete = function() { - if ( isFunction( opt.old ) ) { - opt.old.call( this ); - } - - if ( opt.queue ) { - jQuery.dequeue( this, opt.queue ); - } - }; - - return opt; - }; - - jQuery.fn.extend( { - fadeTo: function( speed, to, easing, callback ) { - - // Show any hidden elements after setting opacity to 0 - return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() - - // Animate to the value specified - .end().animate( { opacity: to }, speed, easing, callback ); - }, - animate: function( prop, speed, easing, callback ) { - var empty = jQuery.isEmptyObject( prop ), - optall = jQuery.speed( speed, easing, callback ), - doAnimation = function() { - - // Operate on a copy of prop so per-property easing won't be lost - var anim = Animation( this, jQuery.extend( {}, prop ), optall ); - - // Empty animations, or finishing resolves immediately - if ( empty || dataPriv.get( this, "finish" ) ) { - anim.stop( true ); - } - }; - doAnimation.finish = doAnimation; - - return empty || optall.queue === false ? - this.each( doAnimation ) : - this.queue( optall.queue, doAnimation ); - }, - stop: function( type, clearQueue, gotoEnd ) { - var stopQueue = function( hooks ) { - var stop = hooks.stop; - delete hooks.stop; - stop( gotoEnd ); - }; - - if ( typeof type !== "string" ) { - gotoEnd = clearQueue; - clearQueue = type; - type = undefined; - } - if ( clearQueue ) { - this.queue( type || "fx", [] ); - } - - return this.each( function() { - var dequeue = true, - index = type != null && type + "queueHooks", - timers = jQuery.timers, - data = dataPriv.get( this ); - - if ( index ) { - if ( data[ index ] && data[ index ].stop ) { - stopQueue( data[ index ] ); - } - } else { - for ( index in data ) { - if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { - stopQueue( data[ index ] ); - } - } - } - - for ( index = timers.length; index--; ) { - if ( timers[ index ].elem === this && - ( type == null || timers[ index ].queue === type ) ) { - - timers[ index ].anim.stop( gotoEnd ); - dequeue = false; - timers.splice( index, 1 ); - } - } - - // Start the next in the queue if the last step wasn't forced. - // Timers currently will call their complete callbacks, which - // will dequeue but only if they were gotoEnd. - if ( dequeue || !gotoEnd ) { - jQuery.dequeue( this, type ); - } - } ); - }, - finish: function( type ) { - if ( type !== false ) { - type = type || "fx"; - } - return this.each( function() { - var index, - data = dataPriv.get( this ), - queue = data[ type + "queue" ], - hooks = data[ type + "queueHooks" ], - timers = jQuery.timers, - length = queue ? queue.length : 0; - - // Enable finishing flag on private data - data.finish = true; - - // Empty the queue first - jQuery.queue( this, type, [] ); - - if ( hooks && hooks.stop ) { - hooks.stop.call( this, true ); - } - - // Look for any active animations, and finish them - for ( index = timers.length; index--; ) { - if ( timers[ index ].elem === this && timers[ index ].queue === type ) { - timers[ index ].anim.stop( true ); - timers.splice( index, 1 ); - } - } - - // Look for any animations in the old queue and finish them - for ( index = 0; index < length; index++ ) { - if ( queue[ index ] && queue[ index ].finish ) { - queue[ index ].finish.call( this ); - } - } - - // Turn off finishing flag - delete data.finish; - } ); - } - } ); - - jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { - var cssFn = jQuery.fn[ name ]; - jQuery.fn[ name ] = function( speed, easing, callback ) { - return speed == null || typeof speed === "boolean" ? - cssFn.apply( this, arguments ) : - this.animate( genFx( name, true ), speed, easing, callback ); - }; - } ); - - // Generate shortcuts for custom animations - jQuery.each( { - slideDown: genFx( "show" ), - slideUp: genFx( "hide" ), - slideToggle: genFx( "toggle" ), - fadeIn: { opacity: "show" }, - fadeOut: { opacity: "hide" }, - fadeToggle: { opacity: "toggle" } - }, function( name, props ) { - jQuery.fn[ name ] = function( speed, easing, callback ) { - return this.animate( props, speed, easing, callback ); - }; - } ); - - jQuery.timers = []; - jQuery.fx.tick = function() { - var timer, - i = 0, - timers = jQuery.timers; - - fxNow = Date.now(); - - for ( ; i < timers.length; i++ ) { - timer = timers[ i ]; - - // Run the timer and safely remove it when done (allowing for external removal) - if ( !timer() && timers[ i ] === timer ) { - timers.splice( i--, 1 ); - } - } - - if ( !timers.length ) { - jQuery.fx.stop(); - } - fxNow = undefined; - }; - - jQuery.fx.timer = function( timer ) { - jQuery.timers.push( timer ); - jQuery.fx.start(); - }; - - jQuery.fx.interval = 13; - jQuery.fx.start = function() { - if ( inProgress ) { - return; - } - - inProgress = true; - schedule(); - }; - - jQuery.fx.stop = function() { - inProgress = null; - }; - - jQuery.fx.speeds = { - slow: 600, - fast: 200, - - // Default speed - _default: 400 - }; - - - // Based off of the plugin by Clint Helfers, with permission. - // https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ - jQuery.fn.delay = function( time, type ) { - time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; - type = type || "fx"; - - return this.queue( type, function( next, hooks ) { - var timeout = window.setTimeout( next, time ); - hooks.stop = function() { - window.clearTimeout( timeout ); - }; - } ); - }; - - - ( function() { - var input = document.createElement( "input" ), - select = document.createElement( "select" ), - opt = select.appendChild( document.createElement( "option" ) ); - - input.type = "checkbox"; - - // Support: Android <=4.3 only - // Default value for a checkbox should be "on" - support.checkOn = input.value !== ""; - - // Support: IE <=11 only - // Must access selectedIndex to make default options select - support.optSelected = opt.selected; - - // Support: IE <=11 only - // An input loses its value after becoming a radio - input = document.createElement( "input" ); - input.value = "t"; - input.type = "radio"; - support.radioValue = input.value === "t"; - } )(); - - - var boolHook, - attrHandle = jQuery.expr.attrHandle; - - jQuery.fn.extend( { - attr: function( name, value ) { - return access( this, jQuery.attr, name, value, arguments.length > 1 ); - }, - - removeAttr: function( name ) { - return this.each( function() { - jQuery.removeAttr( this, name ); - } ); - } - } ); - - jQuery.extend( { - attr: function( elem, name, value ) { - var ret, hooks, - nType = elem.nodeType; - - // Don't get/set attributes on text, comment and attribute nodes - if ( nType === 3 || nType === 8 || nType === 2 ) { - return; - } - - // Fallback to prop when attributes are not supported - if ( typeof elem.getAttribute === "undefined" ) { - return jQuery.prop( elem, name, value ); - } - - // Attribute hooks are determined by the lowercase version - // Grab necessary hook if one is defined - if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { - hooks = jQuery.attrHooks[ name.toLowerCase() ] || - ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); - } - - if ( value !== undefined ) { - if ( value === null ) { - jQuery.removeAttr( elem, name ); - return; - } - - if ( hooks && "set" in hooks && - ( ret = hooks.set( elem, value, name ) ) !== undefined ) { - return ret; - } - - elem.setAttribute( name, value + "" ); - return value; - } - - if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { - return ret; - } - - ret = jQuery.find.attr( elem, name ); - - // Non-existent attributes return null, we normalize to undefined - return ret == null ? undefined : ret; - }, - - attrHooks: { - type: { - set: function( elem, value ) { - if ( !support.radioValue && value === "radio" && - nodeName( elem, "input" ) ) { - var val = elem.value; - elem.setAttribute( "type", value ); - if ( val ) { - elem.value = val; - } - return value; - } - } - } - }, - - removeAttr: function( elem, value ) { - var name, - i = 0, - - // Attribute names can contain non-HTML whitespace characters - // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 - attrNames = value && value.match( rnothtmlwhite ); - - if ( attrNames && elem.nodeType === 1 ) { - while ( ( name = attrNames[ i++ ] ) ) { - elem.removeAttribute( name ); - } - } - } - } ); - - // Hooks for boolean attributes - boolHook = { - set: function( elem, value, name ) { - if ( value === false ) { - - // Remove boolean attributes when set to false - jQuery.removeAttr( elem, name ); - } else { - elem.setAttribute( name, name ); - } - return name; - } - }; - - jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { - var getter = attrHandle[ name ] || jQuery.find.attr; - - attrHandle[ name ] = function( elem, name, isXML ) { - var ret, handle, - lowercaseName = name.toLowerCase(); - - if ( !isXML ) { - - // Avoid an infinite loop by temporarily removing this function from the getter - handle = attrHandle[ lowercaseName ]; - attrHandle[ lowercaseName ] = ret; - ret = getter( elem, name, isXML ) != null ? - lowercaseName : - null; - attrHandle[ lowercaseName ] = handle; - } - return ret; - }; - } ); - - - - - var rfocusable = /^(?:input|select|textarea|button)$/i, - rclickable = /^(?:a|area)$/i; - - jQuery.fn.extend( { - prop: function( name, value ) { - return access( this, jQuery.prop, name, value, arguments.length > 1 ); - }, - - removeProp: function( name ) { - return this.each( function() { - delete this[ jQuery.propFix[ name ] || name ]; - } ); - } - } ); - - jQuery.extend( { - prop: function( elem, name, value ) { - var ret, hooks, - nType = elem.nodeType; - - // Don't get/set properties on text, comment and attribute nodes - if ( nType === 3 || nType === 8 || nType === 2 ) { - return; - } - - if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { - - // Fix name and attach hooks - name = jQuery.propFix[ name ] || name; - hooks = jQuery.propHooks[ name ]; - } - - if ( value !== undefined ) { - if ( hooks && "set" in hooks && - ( ret = hooks.set( elem, value, name ) ) !== undefined ) { - return ret; - } - - return ( elem[ name ] = value ); - } - - if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { - return ret; - } - - return elem[ name ]; - }, - - propHooks: { - tabIndex: { - get: function( elem ) { - - // Support: IE <=9 - 11 only - // elem.tabIndex doesn't always return the - // correct value when it hasn't been explicitly set - // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ - // Use proper attribute retrieval(#12072) - var tabindex = jQuery.find.attr( elem, "tabindex" ); - - if ( tabindex ) { - return parseInt( tabindex, 10 ); - } - - if ( - rfocusable.test( elem.nodeName ) || - rclickable.test( elem.nodeName ) && - elem.href - ) { - return 0; - } - - return -1; - } - } - }, - - propFix: { - "for": "htmlFor", - "class": "className" - } - } ); - - // Support: IE <=11 only - // Accessing the selectedIndex property - // forces the browser to respect setting selected - // on the option - // The getter ensures a default option is selected - // when in an optgroup - // eslint rule "no-unused-expressions" is disabled for this code - // since it considers such accessions noop - if ( !support.optSelected ) { - jQuery.propHooks.selected = { - get: function( elem ) { - - /* eslint no-unused-expressions: "off" */ - - var parent = elem.parentNode; - if ( parent && parent.parentNode ) { - parent.parentNode.selectedIndex; - } - return null; - }, - set: function( elem ) { - - /* eslint no-unused-expressions: "off" */ - - var parent = elem.parentNode; - if ( parent ) { - parent.selectedIndex; - - if ( parent.parentNode ) { - parent.parentNode.selectedIndex; - } - } - } - }; - } - - jQuery.each( [ - "tabIndex", - "readOnly", - "maxLength", - "cellSpacing", - "cellPadding", - "rowSpan", - "colSpan", - "useMap", - "frameBorder", - "contentEditable" - ], function() { - jQuery.propFix[ this.toLowerCase() ] = this; - } ); - - - - - // Strip and collapse whitespace according to HTML spec - // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace - function stripAndCollapse( value ) { - var tokens = value.match( rnothtmlwhite ) || []; - return tokens.join( " " ); - } - - - function getClass( elem ) { - return elem.getAttribute && elem.getAttribute( "class" ) || ""; - } - - function classesToArray( value ) { - if ( Array.isArray( value ) ) { - return value; - } - if ( typeof value === "string" ) { - return value.match( rnothtmlwhite ) || []; - } - return []; - } - - jQuery.fn.extend( { - addClass: function( value ) { - var classes, elem, cur, curValue, clazz, j, finalValue, - i = 0; - - if ( isFunction( value ) ) { - return this.each( function( j ) { - jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); - } ); - } - - classes = classesToArray( value ); - - if ( classes.length ) { - while ( ( elem = this[ i++ ] ) ) { - curValue = getClass( elem ); - cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); - - if ( cur ) { - j = 0; - while ( ( clazz = classes[ j++ ] ) ) { - if ( cur.indexOf( " " + clazz + " " ) < 0 ) { - cur += clazz + " "; - } - } - - // Only assign if different to avoid unneeded rendering. - finalValue = stripAndCollapse( cur ); - if ( curValue !== finalValue ) { - elem.setAttribute( "class", finalValue ); - } - } - } - } - - return this; - }, - - removeClass: function( value ) { - var classes, elem, cur, curValue, clazz, j, finalValue, - i = 0; - - if ( isFunction( value ) ) { - return this.each( function( j ) { - jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); - } ); - } - - if ( !arguments.length ) { - return this.attr( "class", "" ); - } - - classes = classesToArray( value ); - - if ( classes.length ) { - while ( ( elem = this[ i++ ] ) ) { - curValue = getClass( elem ); - - // This expression is here for better compressibility (see addClass) - cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); - - if ( cur ) { - j = 0; - while ( ( clazz = classes[ j++ ] ) ) { - - // Remove *all* instances - while ( cur.indexOf( " " + clazz + " " ) > -1 ) { - cur = cur.replace( " " + clazz + " ", " " ); - } - } - - // Only assign if different to avoid unneeded rendering. - finalValue = stripAndCollapse( cur ); - if ( curValue !== finalValue ) { - elem.setAttribute( "class", finalValue ); - } - } - } - } - - return this; - }, - - toggleClass: function( value, stateVal ) { - var type = typeof value, - isValidValue = type === "string" || Array.isArray( value ); - - if ( typeof stateVal === "boolean" && isValidValue ) { - return stateVal ? this.addClass( value ) : this.removeClass( value ); - } - - if ( isFunction( value ) ) { - return this.each( function( i ) { - jQuery( this ).toggleClass( - value.call( this, i, getClass( this ), stateVal ), - stateVal - ); - } ); - } - - return this.each( function() { - var className, i, self, classNames; - - if ( isValidValue ) { - - // Toggle individual class names - i = 0; - self = jQuery( this ); - classNames = classesToArray( value ); - - while ( ( className = classNames[ i++ ] ) ) { - - // Check each className given, space separated list - if ( self.hasClass( className ) ) { - self.removeClass( className ); - } else { - self.addClass( className ); - } - } - - // Toggle whole class name - } else if ( value === undefined || type === "boolean" ) { - className = getClass( this ); - if ( className ) { - - // Store className if set - dataPriv.set( this, "__className__", className ); - } - - // If the element has a class name or if we're passed `false`, - // then remove the whole classname (if there was one, the above saved it). - // Otherwise bring back whatever was previously saved (if anything), - // falling back to the empty string if nothing was stored. - if ( this.setAttribute ) { - this.setAttribute( "class", - className || value === false ? - "" : - dataPriv.get( this, "__className__" ) || "" - ); - } - } - } ); - }, - - hasClass: function( selector ) { - var className, elem, - i = 0; - - className = " " + selector + " "; - while ( ( elem = this[ i++ ] ) ) { - if ( elem.nodeType === 1 && - ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { - return true; - } - } - - return false; - } - } ); - - - - - var rreturn = /\r/g; - - jQuery.fn.extend( { - val: function( value ) { - var hooks, ret, valueIsFunction, - elem = this[ 0 ]; - - if ( !arguments.length ) { - if ( elem ) { - hooks = jQuery.valHooks[ elem.type ] || - jQuery.valHooks[ elem.nodeName.toLowerCase() ]; - - if ( hooks && - "get" in hooks && - ( ret = hooks.get( elem, "value" ) ) !== undefined - ) { - return ret; - } - - ret = elem.value; - - // Handle most common string cases - if ( typeof ret === "string" ) { - return ret.replace( rreturn, "" ); - } - - // Handle cases where value is null/undef or number - return ret == null ? "" : ret; - } - - return; - } - - valueIsFunction = isFunction( value ); - - return this.each( function( i ) { - var val; - - if ( this.nodeType !== 1 ) { - return; - } - - if ( valueIsFunction ) { - val = value.call( this, i, jQuery( this ).val() ); - } else { - val = value; - } - - // Treat null/undefined as ""; convert numbers to string - if ( val == null ) { - val = ""; - - } else if ( typeof val === "number" ) { - val += ""; - - } else if ( Array.isArray( val ) ) { - val = jQuery.map( val, function( value ) { - return value == null ? "" : value + ""; - } ); - } - - hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; - - // If set returns undefined, fall back to normal setting - if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { - this.value = val; - } - } ); - } - } ); - - jQuery.extend( { - valHooks: { - option: { - get: function( elem ) { - - var val = jQuery.find.attr( elem, "value" ); - return val != null ? - val : - - // Support: IE <=10 - 11 only - // option.text throws exceptions (#14686, #14858) - // Strip and collapse whitespace - // https://html.spec.whatwg.org/#strip-and-collapse-whitespace - stripAndCollapse( jQuery.text( elem ) ); - } - }, - select: { - get: function( elem ) { - var value, option, i, - options = elem.options, - index = elem.selectedIndex, - one = elem.type === "select-one", - values = one ? null : [], - max = one ? index + 1 : options.length; - - if ( index < 0 ) { - i = max; - - } else { - i = one ? index : 0; - } - - // Loop through all the selected options - for ( ; i < max; i++ ) { - option = options[ i ]; - - // Support: IE <=9 only - // IE8-9 doesn't update selected after form reset (#2551) - if ( ( option.selected || i === index ) && - - // Don't return options that are disabled or in a disabled optgroup - !option.disabled && - ( !option.parentNode.disabled || - !nodeName( option.parentNode, "optgroup" ) ) ) { - - // Get the specific value for the option - value = jQuery( option ).val(); - - // We don't need an array for one selects - if ( one ) { - return value; - } - - // Multi-Selects return an array - values.push( value ); - } - } - - return values; - }, - - set: function( elem, value ) { - var optionSet, option, - options = elem.options, - values = jQuery.makeArray( value ), - i = options.length; - - while ( i-- ) { - option = options[ i ]; - - /* eslint-disable no-cond-assign */ - - if ( option.selected = - jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 - ) { - optionSet = true; - } - - /* eslint-enable no-cond-assign */ - } - - // Force browsers to behave consistently when non-matching value is set - if ( !optionSet ) { - elem.selectedIndex = -1; - } - return values; - } - } - } - } ); - - // Radios and checkboxes getter/setter - jQuery.each( [ "radio", "checkbox" ], function() { - jQuery.valHooks[ this ] = { - set: function( elem, value ) { - if ( Array.isArray( value ) ) { - return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); - } - } - }; - if ( !support.checkOn ) { - jQuery.valHooks[ this ].get = function( elem ) { - return elem.getAttribute( "value" ) === null ? "on" : elem.value; - }; - } - } ); - - - - - // Return jQuery for attributes-only inclusion - - - support.focusin = "onfocusin" in window; - - - var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, - stopPropagationCallback = function( e ) { - e.stopPropagation(); - }; - - jQuery.extend( jQuery.event, { - - trigger: function( event, data, elem, onlyHandlers ) { - - var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, - eventPath = [ elem || document ], - type = hasOwn.call( event, "type" ) ? event.type : event, - namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; - - cur = lastElement = tmp = elem = elem || document; - - // Don't do events on text and comment nodes - if ( elem.nodeType === 3 || elem.nodeType === 8 ) { - return; - } - - // focus/blur morphs to focusin/out; ensure we're not firing them right now - if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { - return; - } - - if ( type.indexOf( "." ) > -1 ) { - - // Namespaced trigger; create a regexp to match event type in handle() - namespaces = type.split( "." ); - type = namespaces.shift(); - namespaces.sort(); - } - ontype = type.indexOf( ":" ) < 0 && "on" + type; - - // Caller can pass in a jQuery.Event object, Object, or just an event type string - event = event[ jQuery.expando ] ? - event : - new jQuery.Event( type, typeof event === "object" && event ); - - // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) - event.isTrigger = onlyHandlers ? 2 : 3; - event.namespace = namespaces.join( "." ); - event.rnamespace = event.namespace ? - new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : - null; - - // Clean up the event in case it is being reused - event.result = undefined; - if ( !event.target ) { - event.target = elem; - } - - // Clone any incoming data and prepend the event, creating the handler arg list - data = data == null ? - [ event ] : - jQuery.makeArray( data, [ event ] ); - - // Allow special events to draw outside the lines - special = jQuery.event.special[ type ] || {}; - if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { - return; - } - - // Determine event propagation path in advance, per W3C events spec (#9951) - // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) - if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { - - bubbleType = special.delegateType || type; - if ( !rfocusMorph.test( bubbleType + type ) ) { - cur = cur.parentNode; - } - for ( ; cur; cur = cur.parentNode ) { - eventPath.push( cur ); - tmp = cur; - } - - // Only add window if we got to document (e.g., not plain obj or detached DOM) - if ( tmp === ( elem.ownerDocument || document ) ) { - eventPath.push( tmp.defaultView || tmp.parentWindow || window ); - } - } - - // Fire handlers on the event path - i = 0; - while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { - lastElement = cur; - event.type = i > 1 ? - bubbleType : - special.bindType || type; - - // jQuery handler - handle = ( - dataPriv.get( cur, "events" ) || Object.create( null ) - )[ event.type ] && - dataPriv.get( cur, "handle" ); - if ( handle ) { - handle.apply( cur, data ); - } - - // Native handler - handle = ontype && cur[ ontype ]; - if ( handle && handle.apply && acceptData( cur ) ) { - event.result = handle.apply( cur, data ); - if ( event.result === false ) { - event.preventDefault(); - } - } - } - event.type = type; - - // If nobody prevented the default action, do it now - if ( !onlyHandlers && !event.isDefaultPrevented() ) { - - if ( ( !special._default || - special._default.apply( eventPath.pop(), data ) === false ) && - acceptData( elem ) ) { - - // Call a native DOM method on the target with the same name as the event. - // Don't do default actions on window, that's where global variables be (#6170) - if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { - - // Don't re-trigger an onFOO event when we call its FOO() method - tmp = elem[ ontype ]; - - if ( tmp ) { - elem[ ontype ] = null; - } - - // Prevent re-triggering of the same event, since we already bubbled it above - jQuery.event.triggered = type; - - if ( event.isPropagationStopped() ) { - lastElement.addEventListener( type, stopPropagationCallback ); - } - - elem[ type ](); - - if ( event.isPropagationStopped() ) { - lastElement.removeEventListener( type, stopPropagationCallback ); - } - - jQuery.event.triggered = undefined; - - if ( tmp ) { - elem[ ontype ] = tmp; - } - } - } - } - - return event.result; - }, - - // Piggyback on a donor event to simulate a different one - // Used only for `focus(in | out)` events - simulate: function( type, elem, event ) { - var e = jQuery.extend( - new jQuery.Event(), - event, - { - type: type, - isSimulated: true - } - ); - - jQuery.event.trigger( e, null, elem ); - } - - } ); - - jQuery.fn.extend( { - - trigger: function( type, data ) { - return this.each( function() { - jQuery.event.trigger( type, data, this ); - } ); - }, - triggerHandler: function( type, data ) { - var elem = this[ 0 ]; - if ( elem ) { - return jQuery.event.trigger( type, data, elem, true ); - } - } - } ); - - - // Support: Firefox <=44 - // Firefox doesn't have focus(in | out) events - // Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 - // - // Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 - // focus(in | out) events fire after focus & blur events, - // which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order - // Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 - if ( !support.focusin ) { - jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { - - // Attach a single capturing handler on the document while someone wants focusin/focusout - var handler = function( event ) { - jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); - }; - - jQuery.event.special[ fix ] = { - setup: function() { - - // Handle: regular nodes (via `this.ownerDocument`), window - // (via `this.document`) & document (via `this`). - var doc = this.ownerDocument || this.document || this, - attaches = dataPriv.access( doc, fix ); - - if ( !attaches ) { - doc.addEventListener( orig, handler, true ); - } - dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); - }, - teardown: function() { - var doc = this.ownerDocument || this.document || this, - attaches = dataPriv.access( doc, fix ) - 1; - - if ( !attaches ) { - doc.removeEventListener( orig, handler, true ); - dataPriv.remove( doc, fix ); - - } else { - dataPriv.access( doc, fix, attaches ); - } - } - }; - } ); - } - var location = window.location; - - var nonce = { guid: Date.now() }; - - var rquery = ( /\?/ ); - - - - // Cross-browser xml parsing - jQuery.parseXML = function( data ) { - var xml; - if ( !data || typeof data !== "string" ) { - return null; - } - - // Support: IE 9 - 11 only - // IE throws on parseFromString with invalid input. - try { - xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); - } catch ( e ) { - xml = undefined; - } - - if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { - jQuery.error( "Invalid XML: " + data ); - } - return xml; - }; - - - var - rbracket = /\[\]$/, - rCRLF = /\r?\n/g, - rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, - rsubmittable = /^(?:input|select|textarea|keygen)/i; - - function buildParams( prefix, obj, traditional, add ) { - var name; - - if ( Array.isArray( obj ) ) { - - // Serialize array item. - jQuery.each( obj, function( i, v ) { - if ( traditional || rbracket.test( prefix ) ) { - - // Treat each array item as a scalar. - add( prefix, v ); - - } else { - - // Item is non-scalar (array or object), encode its numeric index. - buildParams( - prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", - v, - traditional, - add - ); - } - } ); - - } else if ( !traditional && toType( obj ) === "object" ) { - - // Serialize object item. - for ( name in obj ) { - buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); - } - - } else { - - // Serialize scalar item. - add( prefix, obj ); - } - } - - // Serialize an array of form elements or a set of - // key/values into a query string - jQuery.param = function( a, traditional ) { - var prefix, - s = [], - add = function( key, valueOrFunction ) { - - // If value is a function, invoke it and use its return value - var value = isFunction( valueOrFunction ) ? - valueOrFunction() : - valueOrFunction; - - s[ s.length ] = encodeURIComponent( key ) + "=" + - encodeURIComponent( value == null ? "" : value ); - }; - - if ( a == null ) { - return ""; - } - - // If an array was passed in, assume that it is an array of form elements. - if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { - - // Serialize the form elements - jQuery.each( a, function() { - add( this.name, this.value ); - } ); - - } else { - - // If traditional, encode the "old" way (the way 1.3.2 or older - // did it), otherwise encode params recursively. - for ( prefix in a ) { - buildParams( prefix, a[ prefix ], traditional, add ); - } - } - - // Return the resulting serialization - return s.join( "&" ); - }; - - jQuery.fn.extend( { - serialize: function() { - return jQuery.param( this.serializeArray() ); - }, - serializeArray: function() { - return this.map( function() { - - // Can add propHook for "elements" to filter or add form elements - var elements = jQuery.prop( this, "elements" ); - return elements ? jQuery.makeArray( elements ) : this; - } ) - .filter( function() { - var type = this.type; - - // Use .is( ":disabled" ) so that fieldset[disabled] works - return this.name && !jQuery( this ).is( ":disabled" ) && - rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && - ( this.checked || !rcheckableType.test( type ) ); - } ) - .map( function( _i, elem ) { - var val = jQuery( this ).val(); - - if ( val == null ) { - return null; - } - - if ( Array.isArray( val ) ) { - return jQuery.map( val, function( val ) { - return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; - } ); - } - - return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; - } ).get(); - } - } ); - - - var - r20 = /%20/g, - rhash = /#.*$/, - rantiCache = /([?&])_=[^&]*/, - rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, - - // #7653, #8125, #8152: local protocol detection - rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, - rnoContent = /^(?:GET|HEAD)$/, - rprotocol = /^\/\//, - - /* Prefilters - * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) - * 2) These are called: - * - BEFORE asking for a transport - * - AFTER param serialization (s.data is a string if s.processData is true) - * 3) key is the dataType - * 4) the catchall symbol "*" can be used - * 5) execution will start with transport dataType and THEN continue down to "*" if needed - */ - prefilters = {}, - - /* Transports bindings - * 1) key is the dataType - * 2) the catchall symbol "*" can be used - * 3) selection will start with transport dataType and THEN go to "*" if needed - */ - transports = {}, - - // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression - allTypes = "*/".concat( "*" ), - - // Anchor tag for parsing the document origin - originAnchor = document.createElement( "a" ); - originAnchor.href = location.href; - - // Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport - function addToPrefiltersOrTransports( structure ) { - - // dataTypeExpression is optional and defaults to "*" - return function( dataTypeExpression, func ) { - - if ( typeof dataTypeExpression !== "string" ) { - func = dataTypeExpression; - dataTypeExpression = "*"; - } - - var dataType, - i = 0, - dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; - - if ( isFunction( func ) ) { - - // For each dataType in the dataTypeExpression - while ( ( dataType = dataTypes[ i++ ] ) ) { - - // Prepend if requested - if ( dataType[ 0 ] === "+" ) { - dataType = dataType.slice( 1 ) || "*"; - ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); - - // Otherwise append - } else { - ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); - } - } - } - }; - } - - // Base inspection function for prefilters and transports - function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { - - var inspected = {}, - seekingTransport = ( structure === transports ); - - function inspect( dataType ) { - var selected; - inspected[ dataType ] = true; - jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { - var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); - if ( typeof dataTypeOrTransport === "string" && - !seekingTransport && !inspected[ dataTypeOrTransport ] ) { - - options.dataTypes.unshift( dataTypeOrTransport ); - inspect( dataTypeOrTransport ); - return false; - } else if ( seekingTransport ) { - return !( selected = dataTypeOrTransport ); - } - } ); - return selected; - } - - return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); - } - - // A special extend for ajax options - // that takes "flat" options (not to be deep extended) - // Fixes #9887 - function ajaxExtend( target, src ) { - var key, deep, - flatOptions = jQuery.ajaxSettings.flatOptions || {}; - - for ( key in src ) { - if ( src[ key ] !== undefined ) { - ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; - } - } - if ( deep ) { - jQuery.extend( true, target, deep ); - } - - return target; - } - - /* Handles responses to an ajax request: - * - finds the right dataType (mediates between content-type and expected dataType) - * - returns the corresponding response - */ - function ajaxHandleResponses( s, jqXHR, responses ) { - - var ct, type, finalDataType, firstDataType, - contents = s.contents, - dataTypes = s.dataTypes; - - // Remove auto dataType and get content-type in the process - while ( dataTypes[ 0 ] === "*" ) { - dataTypes.shift(); - if ( ct === undefined ) { - ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); - } - } - - // Check if we're dealing with a known content-type - if ( ct ) { - for ( type in contents ) { - if ( contents[ type ] && contents[ type ].test( ct ) ) { - dataTypes.unshift( type ); - break; - } - } - } - - // Check to see if we have a response for the expected dataType - if ( dataTypes[ 0 ] in responses ) { - finalDataType = dataTypes[ 0 ]; - } else { - - // Try convertible dataTypes - for ( type in responses ) { - if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { - finalDataType = type; - break; - } - if ( !firstDataType ) { - firstDataType = type; - } - } - - // Or just use first one - finalDataType = finalDataType || firstDataType; - } - - // If we found a dataType - // We add the dataType to the list if needed - // and return the corresponding response - if ( finalDataType ) { - if ( finalDataType !== dataTypes[ 0 ] ) { - dataTypes.unshift( finalDataType ); - } - return responses[ finalDataType ]; - } - } - - /* Chain conversions given the request and the original response - * Also sets the responseXXX fields on the jqXHR instance - */ - function ajaxConvert( s, response, jqXHR, isSuccess ) { - var conv2, current, conv, tmp, prev, - converters = {}, - - // Work with a copy of dataTypes in case we need to modify it for conversion - dataTypes = s.dataTypes.slice(); - - // Create converters map with lowercased keys - if ( dataTypes[ 1 ] ) { - for ( conv in s.converters ) { - converters[ conv.toLowerCase() ] = s.converters[ conv ]; - } - } - - current = dataTypes.shift(); - - // Convert to each sequential dataType - while ( current ) { - - if ( s.responseFields[ current ] ) { - jqXHR[ s.responseFields[ current ] ] = response; - } - - // Apply the dataFilter if provided - if ( !prev && isSuccess && s.dataFilter ) { - response = s.dataFilter( response, s.dataType ); - } - - prev = current; - current = dataTypes.shift(); - - if ( current ) { - - // There's only work to do if current dataType is non-auto - if ( current === "*" ) { - - current = prev; - - // Convert response if prev dataType is non-auto and differs from current - } else if ( prev !== "*" && prev !== current ) { - - // Seek a direct converter - conv = converters[ prev + " " + current ] || converters[ "* " + current ]; - - // If none found, seek a pair - if ( !conv ) { - for ( conv2 in converters ) { - - // If conv2 outputs current - tmp = conv2.split( " " ); - if ( tmp[ 1 ] === current ) { - - // If prev can be converted to accepted input - conv = converters[ prev + " " + tmp[ 0 ] ] || - converters[ "* " + tmp[ 0 ] ]; - if ( conv ) { - - // Condense equivalence converters - if ( conv === true ) { - conv = converters[ conv2 ]; - - // Otherwise, insert the intermediate dataType - } else if ( converters[ conv2 ] !== true ) { - current = tmp[ 0 ]; - dataTypes.unshift( tmp[ 1 ] ); - } - break; - } - } - } - } - - // Apply converter (if not an equivalence) - if ( conv !== true ) { - - // Unless errors are allowed to bubble, catch and return them - if ( conv && s.throws ) { - response = conv( response ); - } else { - try { - response = conv( response ); - } catch ( e ) { - return { - state: "parsererror", - error: conv ? e : "No conversion from " + prev + " to " + current - }; - } - } - } - } - } - } - - return { state: "success", data: response }; - } - - jQuery.extend( { - - // Counter for holding the number of active queries - active: 0, - - // Last-Modified header cache for next request - lastModified: {}, - etag: {}, - - ajaxSettings: { - url: location.href, - type: "GET", - isLocal: rlocalProtocol.test( location.protocol ), - global: true, - processData: true, - async: true, - contentType: "application/x-www-form-urlencoded; charset=UTF-8", - - /* - timeout: 0, - data: null, - dataType: null, - username: null, - password: null, - cache: null, - throws: false, - traditional: false, - headers: {}, - */ - - accepts: { - "*": allTypes, - text: "text/plain", - html: "text/html", - xml: "application/xml, text/xml", - json: "application/json, text/javascript" - }, - - contents: { - xml: /\bxml\b/, - html: /\bhtml/, - json: /\bjson\b/ - }, - - responseFields: { - xml: "responseXML", - text: "responseText", - json: "responseJSON" - }, - - // Data converters - // Keys separate source (or catchall "*") and destination types with a single space - converters: { - - // Convert anything to text - "* text": String, - - // Text to html (true = no transformation) - "text html": true, - - // Evaluate text as a json expression - "text json": JSON.parse, - - // Parse text as xml - "text xml": jQuery.parseXML - }, - - // For options that shouldn't be deep extended: - // you can add your own custom options here if - // and when you create one that shouldn't be - // deep extended (see ajaxExtend) - flatOptions: { - url: true, - context: true - } - }, - - // Creates a full fledged settings object into target - // with both ajaxSettings and settings fields. - // If target is omitted, writes into ajaxSettings. - ajaxSetup: function( target, settings ) { - return settings ? - - // Building a settings object - ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : - - // Extending ajaxSettings - ajaxExtend( jQuery.ajaxSettings, target ); - }, - - ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), - ajaxTransport: addToPrefiltersOrTransports( transports ), - - // Main method - ajax: function( url, options ) { - - // If url is an object, simulate pre-1.5 signature - if ( typeof url === "object" ) { - options = url; - url = undefined; - } - - // Force options to be an object - options = options || {}; - - var transport, - - // URL without anti-cache param - cacheURL, - - // Response headers - responseHeadersString, - responseHeaders, - - // timeout handle - timeoutTimer, - - // Url cleanup var - urlAnchor, - - // Request state (becomes false upon send and true upon completion) - completed, - - // To know if global events are to be dispatched - fireGlobals, - - // Loop variable - i, - - // uncached part of the url - uncached, - - // Create the final options object - s = jQuery.ajaxSetup( {}, options ), - - // Callbacks context - callbackContext = s.context || s, - - // Context for global events is callbackContext if it is a DOM node or jQuery collection - globalEventContext = s.context && - ( callbackContext.nodeType || callbackContext.jquery ) ? - jQuery( callbackContext ) : - jQuery.event, - - // Deferreds - deferred = jQuery.Deferred(), - completeDeferred = jQuery.Callbacks( "once memory" ), - - // Status-dependent callbacks - statusCode = s.statusCode || {}, - - // Headers (they are sent all at once) - requestHeaders = {}, - requestHeadersNames = {}, - - // Default abort message - strAbort = "canceled", - - // Fake xhr - jqXHR = { - readyState: 0, - - // Builds headers hashtable if needed - getResponseHeader: function( key ) { - var match; - if ( completed ) { - if ( !responseHeaders ) { - responseHeaders = {}; - while ( ( match = rheaders.exec( responseHeadersString ) ) ) { - responseHeaders[ match[ 1 ].toLowerCase() + " " ] = - ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) - .concat( match[ 2 ] ); - } - } - match = responseHeaders[ key.toLowerCase() + " " ]; - } - return match == null ? null : match.join( ", " ); - }, - - // Raw string - getAllResponseHeaders: function() { - return completed ? responseHeadersString : null; - }, - - // Caches the header - setRequestHeader: function( name, value ) { - if ( completed == null ) { - name = requestHeadersNames[ name.toLowerCase() ] = - requestHeadersNames[ name.toLowerCase() ] || name; - requestHeaders[ name ] = value; - } - return this; - }, - - // Overrides response content-type header - overrideMimeType: function( type ) { - if ( completed == null ) { - s.mimeType = type; - } - return this; - }, - - // Status-dependent callbacks - statusCode: function( map ) { - var code; - if ( map ) { - if ( completed ) { - - // Execute the appropriate callbacks - jqXHR.always( map[ jqXHR.status ] ); - } else { - - // Lazy-add the new callbacks in a way that preserves old ones - for ( code in map ) { - statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; - } - } - } - return this; - }, - - // Cancel the request - abort: function( statusText ) { - var finalText = statusText || strAbort; - if ( transport ) { - transport.abort( finalText ); - } - done( 0, finalText ); - return this; - } - }; - - // Attach deferreds - deferred.promise( jqXHR ); - - // Add protocol if not provided (prefilters might expect it) - // Handle falsy url in the settings object (#10093: consistency with old signature) - // We also use the url parameter if available - s.url = ( ( url || s.url || location.href ) + "" ) - .replace( rprotocol, location.protocol + "//" ); - - // Alias method option to type as per ticket #12004 - s.type = options.method || options.type || s.method || s.type; - - // Extract dataTypes list - s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; - - // A cross-domain request is in order when the origin doesn't match the current origin. - if ( s.crossDomain == null ) { - urlAnchor = document.createElement( "a" ); - - // Support: IE <=8 - 11, Edge 12 - 15 - // IE throws exception on accessing the href property if url is malformed, - // e.g. http://example.com:80x/ - try { - urlAnchor.href = s.url; - - // Support: IE <=8 - 11 only - // Anchor's host property isn't correctly set when s.url is relative - urlAnchor.href = urlAnchor.href; - s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== - urlAnchor.protocol + "//" + urlAnchor.host; - } catch ( e ) { - - // If there is an error parsing the URL, assume it is crossDomain, - // it can be rejected by the transport if it is invalid - s.crossDomain = true; - } - } - - // Convert data if not already a string - if ( s.data && s.processData && typeof s.data !== "string" ) { - s.data = jQuery.param( s.data, s.traditional ); - } - - // Apply prefilters - inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); - - // If request was aborted inside a prefilter, stop there - if ( completed ) { - return jqXHR; - } - - // We can fire global events as of now if asked to - // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) - fireGlobals = jQuery.event && s.global; - - // Watch for a new set of requests - if ( fireGlobals && jQuery.active++ === 0 ) { - jQuery.event.trigger( "ajaxStart" ); - } - - // Uppercase the type - s.type = s.type.toUpperCase(); - - // Determine if request has content - s.hasContent = !rnoContent.test( s.type ); - - // Save the URL in case we're toying with the If-Modified-Since - // and/or If-None-Match header later on - // Remove hash to simplify url manipulation - cacheURL = s.url.replace( rhash, "" ); - - // More options handling for requests with no content - if ( !s.hasContent ) { - - // Remember the hash so we can put it back - uncached = s.url.slice( cacheURL.length ); - - // If data is available and should be processed, append data to url - if ( s.data && ( s.processData || typeof s.data === "string" ) ) { - cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; - - // #9682: remove data so that it's not used in an eventual retry - delete s.data; - } - - // Add or update anti-cache param if needed - if ( s.cache === false ) { - cacheURL = cacheURL.replace( rantiCache, "$1" ); - uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + - uncached; - } - - // Put hash and anti-cache on the URL that will be requested (gh-1732) - s.url = cacheURL + uncached; - - // Change '%20' to '+' if this is encoded form body content (gh-2658) - } else if ( s.data && s.processData && - ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { - s.data = s.data.replace( r20, "+" ); - } - - // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. - if ( s.ifModified ) { - if ( jQuery.lastModified[ cacheURL ] ) { - jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); - } - if ( jQuery.etag[ cacheURL ] ) { - jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); - } - } - - // Set the correct header, if data is being sent - if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { - jqXHR.setRequestHeader( "Content-Type", s.contentType ); - } - - // Set the Accepts header for the server, depending on the dataType - jqXHR.setRequestHeader( - "Accept", - s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? - s.accepts[ s.dataTypes[ 0 ] ] + - ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : - s.accepts[ "*" ] - ); - - // Check for headers option - for ( i in s.headers ) { - jqXHR.setRequestHeader( i, s.headers[ i ] ); - } - - // Allow custom headers/mimetypes and early abort - if ( s.beforeSend && - ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { - - // Abort if not done already and return - return jqXHR.abort(); - } - - // Aborting is no longer a cancellation - strAbort = "abort"; - - // Install callbacks on deferreds - completeDeferred.add( s.complete ); - jqXHR.done( s.success ); - jqXHR.fail( s.error ); - - // Get transport - transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); - - // If no transport, we auto-abort - if ( !transport ) { - done( -1, "No Transport" ); - } else { - jqXHR.readyState = 1; - - // Send global event - if ( fireGlobals ) { - globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); - } - - // If request was aborted inside ajaxSend, stop there - if ( completed ) { - return jqXHR; - } - - // Timeout - if ( s.async && s.timeout > 0 ) { - timeoutTimer = window.setTimeout( function() { - jqXHR.abort( "timeout" ); - }, s.timeout ); - } - - try { - completed = false; - transport.send( requestHeaders, done ); - } catch ( e ) { - - // Rethrow post-completion exceptions - if ( completed ) { - throw e; - } - - // Propagate others as results - done( -1, e ); - } - } - - // Callback for when everything is done - function done( status, nativeStatusText, responses, headers ) { - var isSuccess, success, error, response, modified, - statusText = nativeStatusText; - - // Ignore repeat invocations - if ( completed ) { - return; - } - - completed = true; - - // Clear timeout if it exists - if ( timeoutTimer ) { - window.clearTimeout( timeoutTimer ); - } - - // Dereference transport for early garbage collection - // (no matter how long the jqXHR object will be used) - transport = undefined; - - // Cache response headers - responseHeadersString = headers || ""; - - // Set readyState - jqXHR.readyState = status > 0 ? 4 : 0; - - // Determine if successful - isSuccess = status >= 200 && status < 300 || status === 304; - - // Get response data - if ( responses ) { - response = ajaxHandleResponses( s, jqXHR, responses ); - } - - // Use a noop converter for missing script - if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { - s.converters[ "text script" ] = function() {}; - } - - // Convert no matter what (that way responseXXX fields are always set) - response = ajaxConvert( s, response, jqXHR, isSuccess ); - - // If successful, handle type chaining - if ( isSuccess ) { - - // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. - if ( s.ifModified ) { - modified = jqXHR.getResponseHeader( "Last-Modified" ); - if ( modified ) { - jQuery.lastModified[ cacheURL ] = modified; - } - modified = jqXHR.getResponseHeader( "etag" ); - if ( modified ) { - jQuery.etag[ cacheURL ] = modified; - } - } - - // if no content - if ( status === 204 || s.type === "HEAD" ) { - statusText = "nocontent"; - - // if not modified - } else if ( status === 304 ) { - statusText = "notmodified"; - - // If we have data, let's convert it - } else { - statusText = response.state; - success = response.data; - error = response.error; - isSuccess = !error; - } - } else { - - // Extract error from statusText and normalize for non-aborts - error = statusText; - if ( status || !statusText ) { - statusText = "error"; - if ( status < 0 ) { - status = 0; - } - } - } - - // Set data for the fake xhr object - jqXHR.status = status; - jqXHR.statusText = ( nativeStatusText || statusText ) + ""; - - // Success/Error - if ( isSuccess ) { - deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); - } else { - deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); - } - - // Status-dependent callbacks - jqXHR.statusCode( statusCode ); - statusCode = undefined; - - if ( fireGlobals ) { - globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", - [ jqXHR, s, isSuccess ? success : error ] ); - } - - // Complete - completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); - - if ( fireGlobals ) { - globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); - - // Handle the global AJAX counter - if ( !( --jQuery.active ) ) { - jQuery.event.trigger( "ajaxStop" ); - } - } - } - - return jqXHR; - }, - - getJSON: function( url, data, callback ) { - return jQuery.get( url, data, callback, "json" ); - }, - - getScript: function( url, callback ) { - return jQuery.get( url, undefined, callback, "script" ); - } - } ); - - jQuery.each( [ "get", "post" ], function( _i, method ) { - jQuery[ method ] = function( url, data, callback, type ) { - - // Shift arguments if data argument was omitted - if ( isFunction( data ) ) { - type = type || callback; - callback = data; - data = undefined; - } - - // The url can be an options object (which then must have .url) - return jQuery.ajax( jQuery.extend( { - url: url, - type: method, - dataType: type, - data: data, - success: callback - }, jQuery.isPlainObject( url ) && url ) ); - }; - } ); - - jQuery.ajaxPrefilter( function( s ) { - var i; - for ( i in s.headers ) { - if ( i.toLowerCase() === "content-type" ) { - s.contentType = s.headers[ i ] || ""; - } - } - } ); - - - jQuery._evalUrl = function( url, options, doc ) { - return jQuery.ajax( { - url: url, - - // Make this explicit, since user can override this through ajaxSetup (#11264) - type: "GET", - dataType: "script", - cache: true, - async: false, - global: false, - - // Only evaluate the response if it is successful (gh-4126) - // dataFilter is not invoked for failure responses, so using it instead - // of the default converter is kludgy but it works. - converters: { - "text script": function() {} - }, - dataFilter: function( response ) { - jQuery.globalEval( response, options, doc ); - } - } ); - }; - - - jQuery.fn.extend( { - wrapAll: function( html ) { - var wrap; - - if ( this[ 0 ] ) { - if ( isFunction( html ) ) { - html = html.call( this[ 0 ] ); - } - - // The elements to wrap the target around - wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); - - if ( this[ 0 ].parentNode ) { - wrap.insertBefore( this[ 0 ] ); - } - - wrap.map( function() { - var elem = this; - - while ( elem.firstElementChild ) { - elem = elem.firstElementChild; - } - - return elem; - } ).append( this ); - } - - return this; - }, - - wrapInner: function( html ) { - if ( isFunction( html ) ) { - return this.each( function( i ) { - jQuery( this ).wrapInner( html.call( this, i ) ); - } ); - } - - return this.each( function() { - var self = jQuery( this ), - contents = self.contents(); - - if ( contents.length ) { - contents.wrapAll( html ); - - } else { - self.append( html ); - } - } ); - }, - - wrap: function( html ) { - var htmlIsFunction = isFunction( html ); - - return this.each( function( i ) { - jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); - } ); - }, - - unwrap: function( selector ) { - this.parent( selector ).not( "body" ).each( function() { - jQuery( this ).replaceWith( this.childNodes ); - } ); - return this; - } - } ); - - - jQuery.expr.pseudos.hidden = function( elem ) { - return !jQuery.expr.pseudos.visible( elem ); - }; - jQuery.expr.pseudos.visible = function( elem ) { - return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); - }; - - - - - jQuery.ajaxSettings.xhr = function() { - try { - return new window.XMLHttpRequest(); - } catch ( e ) {} - }; - - var xhrSuccessStatus = { - - // File protocol always yields status code 0, assume 200 - 0: 200, - - // Support: IE <=9 only - // #1450: sometimes IE returns 1223 when it should be 204 - 1223: 204 - }, - xhrSupported = jQuery.ajaxSettings.xhr(); - - support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); - support.ajax = xhrSupported = !!xhrSupported; - - jQuery.ajaxTransport( function( options ) { - var callback, errorCallback; - - // Cross domain only allowed if supported through XMLHttpRequest - if ( support.cors || xhrSupported && !options.crossDomain ) { - return { - send: function( headers, complete ) { - var i, - xhr = options.xhr(); - - xhr.open( - options.type, - options.url, - options.async, - options.username, - options.password - ); - - // Apply custom fields if provided - if ( options.xhrFields ) { - for ( i in options.xhrFields ) { - xhr[ i ] = options.xhrFields[ i ]; - } - } - - // Override mime type if needed - if ( options.mimeType && xhr.overrideMimeType ) { - xhr.overrideMimeType( options.mimeType ); - } - - // X-Requested-With header - // For cross-domain requests, seeing as conditions for a preflight are - // akin to a jigsaw puzzle, we simply never set it to be sure. - // (it can always be set on a per-request basis or even using ajaxSetup) - // For same-domain requests, won't change header if already provided. - if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { - headers[ "X-Requested-With" ] = "XMLHttpRequest"; - } - - // Set headers - for ( i in headers ) { - xhr.setRequestHeader( i, headers[ i ] ); - } - - // Callback - callback = function( type ) { - return function() { - if ( callback ) { - callback = errorCallback = xhr.onload = - xhr.onerror = xhr.onabort = xhr.ontimeout = - xhr.onreadystatechange = null; - - if ( type === "abort" ) { - xhr.abort(); - } else if ( type === "error" ) { - - // Support: IE <=9 only - // On a manual native abort, IE9 throws - // errors on any property access that is not readyState - if ( typeof xhr.status !== "number" ) { - complete( 0, "error" ); - } else { - complete( - - // File: protocol always yields status 0; see #8605, #14207 - xhr.status, - xhr.statusText - ); - } - } else { - complete( - xhrSuccessStatus[ xhr.status ] || xhr.status, - xhr.statusText, - - // Support: IE <=9 only - // IE9 has no XHR2 but throws on binary (trac-11426) - // For XHR2 non-text, let the caller handle it (gh-2498) - ( xhr.responseType || "text" ) !== "text" || - typeof xhr.responseText !== "string" ? - { binary: xhr.response } : - { text: xhr.responseText }, - xhr.getAllResponseHeaders() - ); - } - } - }; - }; - - // Listen to events - xhr.onload = callback(); - errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); - - // Support: IE 9 only - // Use onreadystatechange to replace onabort - // to handle uncaught aborts - if ( xhr.onabort !== undefined ) { - xhr.onabort = errorCallback; - } else { - xhr.onreadystatechange = function() { - - // Check readyState before timeout as it changes - if ( xhr.readyState === 4 ) { - - // Allow onerror to be called first, - // but that will not handle a native abort - // Also, save errorCallback to a variable - // as xhr.onerror cannot be accessed - window.setTimeout( function() { - if ( callback ) { - errorCallback(); - } - } ); - } - }; - } - - // Create the abort callback - callback = callback( "abort" ); - - try { - - // Do send the request (this may raise an exception) - xhr.send( options.hasContent && options.data || null ); - } catch ( e ) { - - // #14683: Only rethrow if this hasn't been notified as an error yet - if ( callback ) { - throw e; - } - } - }, - - abort: function() { - if ( callback ) { - callback(); - } - } - }; - } - } ); - - - - - // Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) - jQuery.ajaxPrefilter( function( s ) { - if ( s.crossDomain ) { - s.contents.script = false; - } - } ); - - // Install script dataType - jQuery.ajaxSetup( { - accepts: { - script: "text/javascript, application/javascript, " + - "application/ecmascript, application/x-ecmascript" - }, - contents: { - script: /\b(?:java|ecma)script\b/ - }, - converters: { - "text script": function( text ) { - jQuery.globalEval( text ); - return text; - } - } - } ); - - // Handle cache's special case and crossDomain - jQuery.ajaxPrefilter( "script", function( s ) { - if ( s.cache === undefined ) { - s.cache = false; - } - if ( s.crossDomain ) { - s.type = "GET"; - } - } ); - - // Bind script tag hack transport - jQuery.ajaxTransport( "script", function( s ) { - - // This transport only deals with cross domain or forced-by-attrs requests - if ( s.crossDomain || s.scriptAttrs ) { - var script, callback; - return { - send: function( _, complete ) { - script = jQuery( "<script>" ) - .attr( s.scriptAttrs || {} ) - .prop( { charset: s.scriptCharset, src: s.url } ) - .on( "load error", callback = function( evt ) { - script.remove(); - callback = null; - if ( evt ) { - complete( evt.type === "error" ? 404 : 200, evt.type ); - } - } ); - - // Use native DOM manipulation to avoid our domManip AJAX trickery - document.head.appendChild( script[ 0 ] ); - }, - abort: function() { - if ( callback ) { - callback(); - } - } - }; - } - } ); - - - - - var oldCallbacks = [], - rjsonp = /(=)\?(?=&|$)|\?\?/; - - // Default jsonp settings - jQuery.ajaxSetup( { - jsonp: "callback", - jsonpCallback: function() { - var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) ); - this[ callback ] = true; - return callback; - } - } ); - - // Detect, normalize options and install callbacks for jsonp requests - jQuery.ajaxPrefilter( "json jsonp", function( s, originalSettings, jqXHR ) { - - var callbackName, overwritten, responseContainer, - jsonProp = s.jsonp !== false && ( rjsonp.test( s.url ) ? - "url" : - typeof s.data === "string" && - ( s.contentType || "" ) - .indexOf( "application/x-www-form-urlencoded" ) === 0 && - rjsonp.test( s.data ) && "data" - ); - - // Handle iff the expected data type is "jsonp" or we have a parameter to set - if ( jsonProp || s.dataTypes[ 0 ] === "jsonp" ) { - - // Get callback name, remembering preexisting value associated with it - callbackName = s.jsonpCallback = isFunction( s.jsonpCallback ) ? - s.jsonpCallback() : - s.jsonpCallback; - - // Insert callback into url or form data - if ( jsonProp ) { - s[ jsonProp ] = s[ jsonProp ].replace( rjsonp, "$1" + callbackName ); - } else if ( s.jsonp !== false ) { - s.url += ( rquery.test( s.url ) ? "&" : "?" ) + s.jsonp + "=" + callbackName; - } - - // Use data converter to retrieve json after script execution - s.converters[ "script json" ] = function() { - if ( !responseContainer ) { - jQuery.error( callbackName + " was not called" ); - } - return responseContainer[ 0 ]; - }; - - // Force json dataType - s.dataTypes[ 0 ] = "json"; - - // Install callback - overwritten = window[ callbackName ]; - window[ callbackName ] = function() { - responseContainer = arguments; - }; - - // Clean-up function (fires after converters) - jqXHR.always( function() { - - // If previous value didn't exist - remove it - if ( overwritten === undefined ) { - jQuery( window ).removeProp( callbackName ); - - // Otherwise restore preexisting value - } else { - window[ callbackName ] = overwritten; - } - - // Save back as free - if ( s[ callbackName ] ) { - - // Make sure that re-using the options doesn't screw things around - s.jsonpCallback = originalSettings.jsonpCallback; - - // Save the callback name for future use - oldCallbacks.push( callbackName ); - } - - // Call if it was a function and we have a response - if ( responseContainer && isFunction( overwritten ) ) { - overwritten( responseContainer[ 0 ] ); - } - - responseContainer = overwritten = undefined; - } ); - - // Delegate to script - return "script"; - } - } ); - - - - - // Support: Safari 8 only - // In Safari 8 documents created via document.implementation.createHTMLDocument - // collapse sibling forms: the second one becomes a child of the first one. - // Because of that, this security measure has to be disabled in Safari 8. - // https://bugs.webkit.org/show_bug.cgi?id=137337 - support.createHTMLDocument = ( function() { - var body = document.implementation.createHTMLDocument( "" ).body; - body.innerHTML = "<form></form><form></form>"; - return body.childNodes.length === 2; - } )(); - - - // Argument "data" should be string of html - // context (optional): If specified, the fragment will be created in this context, - // defaults to document - // keepScripts (optional): If true, will include scripts passed in the html string - jQuery.parseHTML = function( data, context, keepScripts ) { - if ( typeof data !== "string" ) { - return []; - } - if ( typeof context === "boolean" ) { - keepScripts = context; - context = false; - } - - var base, parsed, scripts; - - if ( !context ) { - - // Stop scripts or inline event handlers from being executed immediately - // by using document.implementation - if ( support.createHTMLDocument ) { - context = document.implementation.createHTMLDocument( "" ); - - // Set the base href for the created document - // so any parsed elements with URLs - // are based on the document's URL (gh-2965) - base = context.createElement( "base" ); - base.href = document.location.href; - context.head.appendChild( base ); - } else { - context = document; - } - } - - parsed = rsingleTag.exec( data ); - scripts = !keepScripts && []; - - // Single tag - if ( parsed ) { - return [ context.createElement( parsed[ 1 ] ) ]; - } - - parsed = buildFragment( [ data ], context, scripts ); - - if ( scripts && scripts.length ) { - jQuery( scripts ).remove(); - } - - return jQuery.merge( [], parsed.childNodes ); - }; - - - /** - * Load a url into a page - */ - jQuery.fn.load = function( url, params, callback ) { - var selector, type, response, - self = this, - off = url.indexOf( " " ); - - if ( off > -1 ) { - selector = stripAndCollapse( url.slice( off ) ); - url = url.slice( 0, off ); - } - - // If it's a function - if ( isFunction( params ) ) { - - // We assume that it's the callback - callback = params; - params = undefined; - - // Otherwise, build a param string - } else if ( params && typeof params === "object" ) { - type = "POST"; - } - - // If we have elements to modify, make the request - if ( self.length > 0 ) { - jQuery.ajax( { - url: url, - - // If "type" variable is undefined, then "GET" method will be used. - // Make value of this field explicit since - // user can override it through ajaxSetup method - type: type || "GET", - dataType: "html", - data: params - } ).done( function( responseText ) { - - // Save response for use in complete callback - response = arguments; - - self.html( selector ? - - // If a selector was specified, locate the right elements in a dummy div - // Exclude scripts to avoid IE 'Permission Denied' errors - jQuery( "<div>" ).append( jQuery.parseHTML( responseText ) ).find( selector ) : - - // Otherwise use the full result - responseText ); - - // If the request succeeds, this function gets "data", "status", "jqXHR" - // but they are ignored because response was set above. - // If it fails, this function gets "jqXHR", "status", "error" - } ).always( callback && function( jqXHR, status ) { - self.each( function() { - callback.apply( this, response || [ jqXHR.responseText, status, jqXHR ] ); - } ); - } ); - } - - return this; - }; - - - - - jQuery.expr.pseudos.animated = function( elem ) { - return jQuery.grep( jQuery.timers, function( fn ) { - return elem === fn.elem; - } ).length; - }; - - - - - jQuery.offset = { - setOffset: function( elem, options, i ) { - var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition, - position = jQuery.css( elem, "position" ), - curElem = jQuery( elem ), - props = {}; - - // Set position first, in-case top/left are set even on static elem - if ( position === "static" ) { - elem.style.position = "relative"; - } - - curOffset = curElem.offset(); - curCSSTop = jQuery.css( elem, "top" ); - curCSSLeft = jQuery.css( elem, "left" ); - calculatePosition = ( position === "absolute" || position === "fixed" ) && - ( curCSSTop + curCSSLeft ).indexOf( "auto" ) > -1; - - // Need to be able to calculate position if either - // top or left is auto and position is either absolute or fixed - if ( calculatePosition ) { - curPosition = curElem.position(); - curTop = curPosition.top; - curLeft = curPosition.left; - - } else { - curTop = parseFloat( curCSSTop ) || 0; - curLeft = parseFloat( curCSSLeft ) || 0; - } - - if ( isFunction( options ) ) { - - // Use jQuery.extend here to allow modification of coordinates argument (gh-1848) - options = options.call( elem, i, jQuery.extend( {}, curOffset ) ); - } - - if ( options.top != null ) { - props.top = ( options.top - curOffset.top ) + curTop; - } - if ( options.left != null ) { - props.left = ( options.left - curOffset.left ) + curLeft; - } - - if ( "using" in options ) { - options.using.call( elem, props ); - - } else { - if ( typeof props.top === "number" ) { - props.top += "px"; - } - if ( typeof props.left === "number" ) { - props.left += "px"; - } - curElem.css( props ); - } - } - }; - - jQuery.fn.extend( { - - // offset() relates an element's border box to the document origin - offset: function( options ) { - - // Preserve chaining for setter - if ( arguments.length ) { - return options === undefined ? - this : - this.each( function( i ) { - jQuery.offset.setOffset( this, options, i ); - } ); - } - - var rect, win, - elem = this[ 0 ]; - - if ( !elem ) { - return; - } - - // Return zeros for disconnected and hidden (display: none) elements (gh-2310) - // Support: IE <=11 only - // Running getBoundingClientRect on a - // disconnected node in IE throws an error - if ( !elem.getClientRects().length ) { - return { top: 0, left: 0 }; - } - - // Get document-relative position by adding viewport scroll to viewport-relative gBCR - rect = elem.getBoundingClientRect(); - win = elem.ownerDocument.defaultView; - return { - top: rect.top + win.pageYOffset, - left: rect.left + win.pageXOffset - }; - }, - - // position() relates an element's margin box to its offset parent's padding box - // This corresponds to the behavior of CSS absolute positioning - position: function() { - if ( !this[ 0 ] ) { - return; - } - - var offsetParent, offset, doc, - elem = this[ 0 ], - parentOffset = { top: 0, left: 0 }; - - // position:fixed elements are offset from the viewport, which itself always has zero offset - if ( jQuery.css( elem, "position" ) === "fixed" ) { - - // Assume position:fixed implies availability of getBoundingClientRect - offset = elem.getBoundingClientRect(); - - } else { - offset = this.offset(); - - // Account for the *real* offset parent, which can be the document or its root element - // when a statically positioned element is identified - doc = elem.ownerDocument; - offsetParent = elem.offsetParent || doc.documentElement; - while ( offsetParent && - ( offsetParent === doc.body || offsetParent === doc.documentElement ) && - jQuery.css( offsetParent, "position" ) === "static" ) { - - offsetParent = offsetParent.parentNode; - } - if ( offsetParent && offsetParent !== elem && offsetParent.nodeType === 1 ) { - - // Incorporate borders into its offset, since they are outside its content origin - parentOffset = jQuery( offsetParent ).offset(); - parentOffset.top += jQuery.css( offsetParent, "borderTopWidth", true ); - parentOffset.left += jQuery.css( offsetParent, "borderLeftWidth", true ); - } - } - - // Subtract parent offsets and element margins - return { - top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ), - left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true ) - }; - }, - - // This method will return documentElement in the following cases: - // 1) For the element inside the iframe without offsetParent, this method will return - // documentElement of the parent window - // 2) For the hidden or detached element - // 3) For body or html element, i.e. in case of the html node - it will return itself - // - // but those exceptions were never presented as a real life use-cases - // and might be considered as more preferable results. - // - // This logic, however, is not guaranteed and can change at any point in the future - offsetParent: function() { - return this.map( function() { - var offsetParent = this.offsetParent; - - while ( offsetParent && jQuery.css( offsetParent, "position" ) === "static" ) { - offsetParent = offsetParent.offsetParent; - } - - return offsetParent || documentElement; - } ); - } - } ); - - // Create scrollLeft and scrollTop methods - jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) { - var top = "pageYOffset" === prop; - - jQuery.fn[ method ] = function( val ) { - return access( this, function( elem, method, val ) { - - // Coalesce documents and windows - var win; - if ( isWindow( elem ) ) { - win = elem; - } else if ( elem.nodeType === 9 ) { - win = elem.defaultView; - } - - if ( val === undefined ) { - return win ? 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• html/_static/language_data.js
  • @@ -5,12 +5,12 @@
    * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. * - * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ - var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"]; + var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; /* Non-minified version is copied as a separate JS file, is available */
  • @@ -197,101 +197,3 @@ var Stemmer = function() {
    } } - - - - var splitChars = (function() { - var result = {}; - var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648, - 1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702, - 2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971, - 2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345, - 3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761, - 3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823, - 4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125, - 8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695, - 11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587, - 43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141]; - var i, j, start, end; - for (i = 0; i < singles.length; i++) { - result[singles[i]] = true; - } - var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709], - [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161], - [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568], - [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807], - [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047], - [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383], - [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450], - [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547], - [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673], - [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820], - [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946], - [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023], - [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173], - [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332], - [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481], - [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718], - [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791], - [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095], - [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205], - [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687], - [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968], - [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869], - [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102], - [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271], - [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592], - [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822], - [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167], - [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959], - [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143], - [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318], - [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483], - [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101], - [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567], - [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292], - [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444], - [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783], - [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311], - [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511], - [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774], - [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071], - [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263], - [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519], - [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647], - [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967], - [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295], - [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274], - [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007], - [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381], - [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]]; - for (i = 0; i < ranges.length; i++) { - start = ranges[i][0]; - end = ranges[i][1]; - for (j = start; j <= end; j++) { - result[j] = true; - } - } - return result; - })(); - - function splitQuery(query) { - var result = []; - var start = -1; - for (var i = 0; i < query.length; i++) { - if (splitChars[query.charCodeAt(i)]) { - if (start !== -1) { - result.push(query.slice(start, i)); - start = -1; - } - } else if (start === -1) { - start = i; - } - } - if (start !== -1) { - result.push(query.slice(start)); - } - return result; - } - -
• html/_static/searchtools.js
  • @@ -4,22 +4,24 @@
    * * Sphinx JavaScript utilities for the full-text search. * - * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. * :license: BSD, see LICENSE for details. * */ + "use strict"; - if (!Scorer) { - /** - * Simple result scoring code. - */ + /** + * Simple result scoring code. + */ + if (typeof Scorer === "undefined") { var Scorer = { // Implement the following function to further tweak the score for each result - // The function takes a result array [filename, title, anchor, descr, score] + // The function takes a result array [docname, title, anchor, descr, score, filename] // and returns the new score. /* - score: function(result) { - return result[4]; + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score }, */
  • @@ -28,9 +30,11 @@ if (!Scorer) {
    // or matches in the last dotted part of the object name objPartialMatch: 6, // Additive scores depending on the priority of the object - objPrio: {0: 15, // used to be importantResults - 1: 5, // used to be objectResults - 2: -5}, // used to be unimportantResults + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, // Used when the priority is not in the mapping. objPrioDefault: 0,
  • @@ -39,456 +43,495 @@ if (!Scorer) {
    partialTitle: 7, // query found in terms term: 5, - partialTerm: 2 + partialTerm: 2, }; } - if (!splitQuery) { - function splitQuery(query) { - return query.split(/\s+/); + const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); + }; + + /** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + + const _displayItem = (item, searchTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = docUrlRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = docUrlRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms) + ); + }); + Search.output.appendChild(listItem); + }; + const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + `Search finished, found ${resultCount} page(s) matching the search query.` + ); + }; + const _displayNextItem = ( + results, + resultCount, + searchTerms + ) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); + }; + + /** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ + if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings } /** * Search Module */ - var Search = { - - _index : null, - _queued_query : null, - _pulse_status : -1, - - htmlToText : function(htmlString) { - var virtualDocument = document.implementation.createHTMLDocument('virtual'); - var htmlElement = $(htmlString, virtualDocument); - htmlElement.find('.headerlink').remove(); - docContent = htmlElement.find('[role=main]')[0]; - if(docContent === undefined) { - console.warn("Content block not found. Sphinx search tries to obtain it " + - "via '[role=main]'. Could you check your theme or template."); - return ""; - } - return docContent.textContent || docContent.innerText; + const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() }); + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent !== undefined) return docContent.textContent; + console.warn( + "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template." + ); + return ""; }, - init : function() { - var params = $.getQueryParameters(); - if (params.q) { - var query = params.q[0]; - $('input[name="q"]')[0].value = query; - this.performSearch(query); - } + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); }, - loadIndex : function(url) { - $.ajax({type: "GET", url: url, data: null, - dataType: "script", cache: true, - complete: function(jqxhr, textstatus) { - if (textstatus != "success") { - document.getElementById("searchindexloader").src = url; - } - }}); - }, + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), - setIndex : function(index) { - var q; - this._index = index; - if ((q = this._queued_query) !== null) { - this._queued_query = null; - Search.query(q); + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); } }, - hasIndex : function() { - return this._index !== null; - }, + hasIndex: () => Search._index !== null, - deferQuery : function(query) { - this._queued_query = query; - }, + deferQuery: (query) => (Search._queued_query = query), - stopPulse : function() { - this._pulse_status = 0; - }, + stopPulse: () => (Search._pulse_status = -1), - startPulse : function() { - if (this._pulse_status >= 0) - return; - function pulse() { - var i; + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { Search._pulse_status = (Search._pulse_status + 1) % 4; - var dotString = ''; - for (i = 0; i < Search._pulse_status; i++) - dotString += '.'; - Search.dots.text(dotString); - if (Search._pulse_status > -1) - window.setTimeout(pulse, 500); - } + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; pulse(); }, /** * perform a search for something (or wait until index is loaded) */ - performSearch : function(query) { + performSearch: (query) => { // create the required interface elements - this.out = $('#search-results'); - this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out); - this.dots = $('<span></span>').appendTo(this.title); - this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out); - this.output = $('<ul class="search"/>').appendTo(this.out); - - $('#search-progress').text(_('Preparing search...')); - this.startPulse(); + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); // index already loaded, the browser was quick! - if (this.hasIndex()) - this.query(query); - else - this.deferQuery(query); + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); }, /** * execute search (requires search index to be loaded) */ - query : function(query) { - var i; - - // stem the searchterms and add them to the correct list - var stemmer = new Stemmer(); - var searchterms = []; - var excluded = []; - var hlterms = []; - var tmp = splitQuery(query); - var objectterms = []; - for (i = 0; i < tmp.length; i++) { - if (tmp[i] !== "") { - objectterms.push(tmp[i].toLowerCase()); - } + query: (query) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; - if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i] === "") { - // skip this "word" - continue; - } // stem the word - var word = stemmer.stemWord(tmp[i].toLowerCase()); - // prevent stemmer from cutting word smaller than two chars - if(word.length < 3 && tmp[i].length >= 3) { - word = tmp[i]; - } - var toAppend; + let word = stemmer.stemWord(queryTermLower); // select the correct list - if (word[0] == '-') { - toAppend = excluded; - word = word.substr(1); - } + if (word[0] === "-") excludedTerms.add(word.substr(1)); else { - toAppend = searchterms; - hlterms.push(tmp[i].toLowerCase()); + searchTerms.add(word); + highlightTerms.add(queryTermLower); } - // only add if not already in the list - if (!$u.contains(toAppend, word)) - toAppend.push(word); - } - var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" ")); + }); - // console.debug('SEARCH: searching for:'); - // console.info('required: ', searchterms); - // console.info('excluded: ', excluded); + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } - // prepare search - var terms = this._index.terms; - var titleterms = this._index.titleterms; + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + // array of [docname, title, anchor, descr, score, filename] + let results = []; + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + results.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } - // array of [filename, title, anchor, descr, score] - var results = []; - $('#search-progress').empty(); + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id] of foundEntries) { + let score = Math.round(100 * queryLower.length / entry.length) + results.push([ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } // lookup as object - for (i = 0; i < objectterms.length; i++) { - var others = [].concat(objectterms.slice(0, i), - objectterms.slice(i+1, objectterms.length)); - results = results.concat(this.performObjectSearch(objectterms[i], others)); - } + objectTerms.forEach((term) => + results.push(...Search.performObjectSearch(term, objectTerms)) + ); // lookup as search terms in fulltext - results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms)); + results.push(...Search.performTermsSearch(searchTerms, excludedTerms)); // let the scorer override scores with a custom scoring function - if (Scorer.score) { - for (i = 0; i < results.length; i++) - results[i][4] = Scorer.score(results[i]); - } + if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item))); // now sort the results by score (in opposite order of appearance, since the // display function below uses pop() to retrieve items) and then // alphabetically - results.sort(function(a, b) { - var left = a[4]; - var right = b[4]; - if (left > right) { - return 1; - } else if (left < right) { - return -1; - } else { + results.sort((a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { // same score: sort alphabetically - left = a[1].toLowerCase(); - right = b[1].toLowerCase(); - return (left > right) ? -1 : ((left < right) ? 1 : 0); + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional } + return leftScore > rightScore ? 1 : -1; }); + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + results = results.reverse(); + // for debugging //Search.lastresults = results.slice(); // a copy - //console.info('search results:', Search.lastresults); + // console.info("search results:", Search.lastresults); // print the results - var resultCount = results.length; - function displayNextItem() { - // results left, load the summary and display it - if (results.length) { - var item = results.pop(); - var listItem = $('<li></li>'); - var requestUrl = ""; - var linkUrl = ""; - if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') { - // dirhtml builder - var dirname = item[0] + '/'; - if (dirname.match(/\/index\/$/)) { - dirname = dirname.substring(0, dirname.length-6); - } else if (dirname == 'index/') { - dirname = ''; - } - requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname; - linkUrl = requestUrl; - - } else { - // normal html builders - requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX; - linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX; - } - listItem.append($('<a/>').attr('href', - linkUrl + - highlightstring + item[2]).html(item[1])); - if (item[3]) { - listItem.append($('<span> (' + item[3] + ')</span>')); - Search.output.append(listItem); - setTimeout(function() { - displayNextItem(); - }, 5); - } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) { - $.ajax({url: requestUrl, - dataType: "text", - complete: function(jqxhr, textstatus) { - var data = jqxhr.responseText; - if (data !== '' && data !== undefined) { - var summary = Search.makeSearchSummary(data, searchterms, hlterms); - if (summary) { - listItem.append(summary); - } - } - Search.output.append(listItem); - setTimeout(function() { - displayNextItem(); - }, 5); - }}); - } else { - // no source available, just display title - Search.output.append(listItem); - setTimeout(function() { - displayNextItem(); - }, 5); - } - } - // search finished, update title and status message - else { - Search.stopPulse(); - Search.title.text(_('Search Results')); - if (!resultCount) - Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.')); - else - Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount)); - Search.status.fadeIn(500); - } - } - displayNextItem(); + _displayNextItem(results, results.length, searchTerms); }, /** * search for object names */ - performObjectSearch : function(object, otherterms) { - var filenames = this._index.filenames; - var docnames = this._index.docnames; - var objects = this._index.objects; - var objnames = this._index.objnames; - var titles = this._index.titles; - - var i; - var results = []; - - for (var prefix in objects) { - for (var iMatch = 0; iMatch != objects[prefix].length; ++iMatch) { - var match = objects[prefix][iMatch]; - var name = match[4]; - var fullname = (prefix ? prefix + '.' : '') + name; - var fullnameLower = fullname.toLowerCase() - if (fullnameLower.indexOf(object) > -1) { - var score = 0; - var parts = fullnameLower.split('.'); - // check for different match types: exact matches of full name or - // "last name" (i.e. last dotted part) - if (fullnameLower == object || parts[parts.length - 1] == object) { - score += Scorer.objNameMatch; - // matches in last name - } else if (parts[parts.length - 1].indexOf(object) > -1) { - score += Scorer.objPartialMatch; - } - var objname = objnames[match[1]][2]; - var title = titles[match[0]]; - // If more than one term searched for, we require other words to be - // found in the name/title/description - if (otherterms.length > 0) { - var haystack = (prefix + ' ' + name + ' ' + - objname + ' ' + title).toLowerCase(); - var allfound = true; - for (i = 0; i < otherterms.length; i++) { - if (haystack.indexOf(otherterms[i]) == -1) { - allfound = false; - break; - } - } - if (!allfound) { - continue; - } - } - var descr = objname + _(', in ') + title; - - var anchor = match[3]; - if (anchor === '') - anchor = fullname; - else if (anchor == '-') - anchor = objnames[match[1]][1] + '-' + fullname; - // add custom score for some objects according to scorer - if (Scorer.objPrio.hasOwnProperty(match[2])) { - score += Scorer.objPrio[match[2]]; - } else { - score += Scorer.objPrioDefault; - } - results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]); - } + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; } - } + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); return results; }, - /** - * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions - */ - escapeRegExp : function(string) { - return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string - }, - /** * search for full-text terms in the index */ - performTermsSearch : function(searchterms, excluded, terms, titleterms) { - var docnames = this._index.docnames; - var filenames = this._index.filenames; - var titles = this._index.titles; + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; - var i, j, file; - var fileMap = {}; - var scoreMap = {}; - var results = []; + const scoreMap = new Map(); + const fileMap = new Map(); // perform the search on the required terms - for (i = 0; i < searchterms.length; i++) { - var word = searchterms[i]; - var files = []; - var _o = [ - {files: terms[word], score: Scorer.term}, - {files: titleterms[word], score: Scorer.title} + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, ]; // add support for partial matches if (word.length > 2) { - var word_regex = this.escapeRegExp(word); - for (var w in terms) { - if (w.match(word_regex) && !terms[word]) { - _o.push({files: terms[w], score: Scorer.partialTerm}) - } - } - for (var w in titleterms) { - if (w.match(word_regex) && !titleterms[word]) { - _o.push({files: titleterms[w], score: Scorer.partialTitle}) - } - } + const escapedWord = _escapeRegExp(word); + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord) && !terms[word]) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord) && !titleTerms[word]) + arr.push({ files: titleTerms[word], score: Scorer.partialTitle }); + }); } // no match but word was a required one - if ($u.every(_o, function(o){return o.files === undefined;})) { - break; - } + if (arr.every((record) => record.files === undefined)) return; + // found search word in contents - $u.each(_o, function(o) { - var _files = o.files; - if (_files === undefined) - return - - if (_files.length === undefined) - _files = [_files]; - files = files.concat(_files); - - // set score for the word in each file to Scorer.term - for (j = 0; j < _files.length; j++) { - file = _files[j]; - if (!(file in scoreMap)) - scoreMap[file] = {}; - scoreMap[file][word] = o.score; - } + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); }); // create the mapping - for (j = 0; j < files.length; j++) { - file = files[j]; - if (file in fileMap && fileMap[file].indexOf(word) === -1) - fileMap[file].push(word); - else - fileMap[file] = [word]; - } - } + files.forEach((file) => { + if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1) + fileMap.get(file).push(word); + else fileMap.set(file, [word]); + }); + }); // now check if the files don't contain excluded terms - for (file in fileMap) { - var valid = true; - + const results = []; + for (const [file, wordList] of fileMap) { // check if all requirements are matched - var filteredTermCount = // as search terms with length < 3 are discarded: ignore - searchterms.filter(function(term){return term.length > 2}).length + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; if ( - fileMap[file].length != searchterms.length && - fileMap[file].length != filteredTermCount - ) continue; + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; // ensure that none of the excluded terms is in the search result - for (i = 0; i < excluded.length; i++) { - if (terms[excluded[i]] == file || - titleterms[excluded[i]] == file || - $u.contains(terms[excluded[i]] || [], file) || - $u.contains(titleterms[excluded[i]] || [], file)) { - valid = false; - break; - } - } + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; - // if we have still a valid result we can add it to the result list - if (valid) { - // select one (max) score for the file. - // for better ranking, we should calculate ranking by using words statistics like basic tf-idf... - var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]})); - results.push([docnames[file], titles[file], '', null, score, filenames[file]]); - } + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); } return results; },
  • @@ -496,34 +539,28 @@ var Search = {
    /** * helper function to return a node containing the * search summary for a given text. keywords is a list - * of stemmed words, hlwords is the list of normal, unstemmed - * words. the first one is used to find the occurrence, the - * latter for highlighting it. + * of stemmed words. */ - makeSearchSummary : function(htmlText, keywords, hlwords) { - var text = Search.htmlToText(htmlText); - if (text == "") { - return null; - } - var textLower = text.toLowerCase(); - var start = 0; - $.each(keywords, function() { - var i = textLower.indexOf(this.toLowerCase()); - if (i > -1) - start = i; - }); - start = Math.max(start - 120, 0); - var excerpt = ((start > 0) ? '...' : '') + - $.trim(text.substr(start, 240)) + - ((start + 240 - text.length) ? '...' : ''); - var rv = $('<p class="context"></p>').text(excerpt); - $.each(hlwords, function() { - rv = rv.highlightText(this, 'highlighted'); - }); - return rv; - } + makeSearchSummary: (htmlText, keywords) => { + const text = Search.htmlToText(htmlText); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, }; - $(document).ready(function() { - Search.init(); - }); + _ready(Search.init);
• html/_static/sphinx_highlight.js (new)
  • @@ -0,0 +1,144 @@
    + /* Highlighting utilities for Sphinx HTML documentation. */ + "use strict"; + + const SPHINX_HIGHLIGHT_ENABLED = true + + /** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ + const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + parent.insertBefore( + span, + parent.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } + }; + const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); + }; + + /** + * Small JavaScript module for the documentation. + */ + const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '<p class="highlight-link">' + + '<a href="javascript:SphinxHighlight.hideSearchWords()">' + + _("Hide Search Matches") + + "</a></p>" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, + }; + + _ready(SphinxHighlight.highlightSearchWords); + _ready(SphinxHighlight.initEscapeListener);
• html/_static/underscore-1.13.1.js (deleted)
  • @@ -1,2042 +0,0 @@
    - (function (global, factory) { - typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() : - typeof define === 'function' && define.amd ? define('underscore', factory) : - (global = typeof globalThis !== 'undefined' ? globalThis : global || self, (function () { - var current = global._; - var exports = global._ = factory(); - exports.noConflict = function () { global._ = current; return exports; }; - }())); - }(this, (function () { - // Underscore.js 1.13.1 - // https://underscorejs.org - // (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors - // Underscore may be freely distributed under the MIT license. - - // Current version. - var VERSION = '1.13.1'; - - // Establish the root object, `window` (`self`) in the browser, `global` - // on the server, or `this` in some virtual machines. We use `self` - // instead of `window` for `WebWorker` support. - var root = typeof self == 'object' && self.self === self && self || - typeof global == 'object' && global.global === global && global || - Function('return this')() || - {}; - - // Save bytes in the minified (but not gzipped) version: - var ArrayProto = Array.prototype, ObjProto = Object.prototype; - var SymbolProto = typeof Symbol !== 'undefined' ? Symbol.prototype : null; - - // Create quick reference variables for speed access to core prototypes. - var push = ArrayProto.push, - slice = ArrayProto.slice, - toString = ObjProto.toString, - hasOwnProperty = ObjProto.hasOwnProperty; - - // Modern feature detection. - var supportsArrayBuffer = typeof ArrayBuffer !== 'undefined', - supportsDataView = typeof DataView !== 'undefined'; - - // All **ECMAScript 5+** native function implementations that we hope to use - // are declared here. - var nativeIsArray = Array.isArray, - nativeKeys = Object.keys, - nativeCreate = Object.create, - nativeIsView = supportsArrayBuffer && ArrayBuffer.isView; - - // Create references to these builtin functions because we override them. - var _isNaN = isNaN, - _isFinite = isFinite; - - // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed. - var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString'); - var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString', - 'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString']; - - // The largest integer that can be represented exactly. - var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1; - - // Some functions take a variable number of arguments, or a few expected - // arguments at the beginning and then a variable number of values to operate - // on. This helper accumulates all remaining arguments past the function’s - // argument length (or an explicit `startIndex`), into an array that becomes - // the last argument. Similar to ES6’s "rest parameter". - function restArguments(func, startIndex) { - startIndex = startIndex == null ? func.length - 1 : +startIndex; - return function() { - var length = Math.max(arguments.length - startIndex, 0), - rest = Array(length), - index = 0; - for (; index < length; index++) { - rest[index] = arguments[index + startIndex]; - } - switch (startIndex) { - case 0: return func.call(this, rest); - case 1: return func.call(this, arguments[0], rest); - case 2: return func.call(this, arguments[0], arguments[1], rest); - } - var args = Array(startIndex + 1); - for (index = 0; index < startIndex; index++) { - args[index] = arguments[index]; - } - args[startIndex] = rest; - return func.apply(this, args); - }; - } - - // Is a given variable an object? - function isObject(obj) { - var type = typeof obj; - return type === 'function' || type === 'object' && !!obj; - } - - // Is a given value equal to null? - function isNull(obj) { - return obj === null; - } - - // Is a given variable undefined? - function isUndefined(obj) { - return obj === void 0; - } - - // Is a given value a boolean? - function isBoolean(obj) { - return obj === true || obj === false || toString.call(obj) === '[object Boolean]'; - } - - // Is a given value a DOM element? - function isElement(obj) { - return !!(obj && obj.nodeType === 1); - } - - // Internal function for creating a `toString`-based type tester. - function tagTester(name) { - var tag = '[object ' + name + ']'; - return function(obj) { - return toString.call(obj) === tag; - }; - } - - var isString = tagTester('String'); - - var isNumber = tagTester('Number'); - - var isDate = tagTester('Date'); - - var isRegExp = tagTester('RegExp'); - - var isError = tagTester('Error'); - - var isSymbol = tagTester('Symbol'); - - var isArrayBuffer = tagTester('ArrayBuffer'); - - var isFunction = tagTester('Function'); - - // Optimize `isFunction` if appropriate. Work around some `typeof` bugs in old - // v8, IE 11 (#1621), Safari 8 (#1929), and PhantomJS (#2236). - var nodelist = root.document && root.document.childNodes; - if (typeof /./ != 'function' && typeof Int8Array != 'object' && typeof nodelist != 'function') { - isFunction = function(obj) { - return typeof obj == 'function' || false; - }; - } - - var isFunction$1 = isFunction; - - var hasObjectTag = tagTester('Object'); - - // In IE 10 - Edge 13, `DataView` has string tag `'[object Object]'`. - // In IE 11, the most common among them, this problem also applies to - // `Map`, `WeakMap` and `Set`. - var hasStringTagBug = ( - supportsDataView && hasObjectTag(new DataView(new ArrayBuffer(8))) - ), - isIE11 = (typeof Map !== 'undefined' && hasObjectTag(new Map)); - - var isDataView = tagTester('DataView'); - - // In IE 10 - Edge 13, we need a different heuristic - // to determine whether an object is a `DataView`. - function ie10IsDataView(obj) { - return obj != null && isFunction$1(obj.getInt8) && isArrayBuffer(obj.buffer); - } - - var isDataView$1 = (hasStringTagBug ? ie10IsDataView : isDataView); - - // Is a given value an array? - // Delegates to ECMA5's native `Array.isArray`. - var isArray = nativeIsArray || tagTester('Array'); - - // Internal function to check whether `key` is an own property name of `obj`. - function has$1(obj, key) { - return obj != null && hasOwnProperty.call(obj, key); - } - - var isArguments = tagTester('Arguments'); - - // Define a fallback version of the method in browsers (ahem, IE < 9), where - // there isn't any inspectable "Arguments" type. - (function() { - if (!isArguments(arguments)) { - isArguments = function(obj) { - return has$1(obj, 'callee'); - }; - } - }()); - - var isArguments$1 = isArguments; - - // Is a given object a finite number? - function isFinite$1(obj) { - return !isSymbol(obj) && _isFinite(obj) && !isNaN(parseFloat(obj)); - } - - // Is the given value `NaN`? - function isNaN$1(obj) { - return isNumber(obj) && _isNaN(obj); - } - - // Predicate-generating function. Often useful outside of Underscore. - function constant(value) { - return function() { - return value; - }; - } - - // Common internal logic for `isArrayLike` and `isBufferLike`. - function createSizePropertyCheck(getSizeProperty) { - return function(collection) { - var sizeProperty = getSizeProperty(collection); - return typeof sizeProperty == 'number' && sizeProperty >= 0 && sizeProperty <= MAX_ARRAY_INDEX; - } - } - - // Internal helper to generate a function to obtain property `key` from `obj`. - function shallowProperty(key) { - return function(obj) { - return obj == null ? void 0 : obj[key]; - }; - } - - // Internal helper to obtain the `byteLength` property of an object. - var getByteLength = shallowProperty('byteLength'); - - // Internal helper to determine whether we should spend extensive checks against - // `ArrayBuffer` et al. - var isBufferLike = createSizePropertyCheck(getByteLength); - - // Is a given value a typed array? - var typedArrayPattern = /\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/; - function isTypedArray(obj) { - // `ArrayBuffer.isView` is the most future-proof, so use it when available. - // Otherwise, fall back on the above regular expression. - return nativeIsView ? (nativeIsView(obj) && !isDataView$1(obj)) : - isBufferLike(obj) && typedArrayPattern.test(toString.call(obj)); - } - - var isTypedArray$1 = supportsArrayBuffer ? isTypedArray : constant(false); - - // Internal helper to obtain the `length` property of an object. - var getLength = shallowProperty('length'); - - // Internal helper to create a simple lookup structure. - // `collectNonEnumProps` used to depend on `_.contains`, but this led to - // circular imports. `emulatedSet` is a one-off solution that only works for - // arrays of strings. - function emulatedSet(keys) { - var hash = {}; - for (var l = keys.length, i = 0; i < l; ++i) hash[keys[i]] = true; - return { - contains: function(key) { return hash[key]; }, - push: function(key) { - hash[key] = true; - return keys.push(key); - } - }; - } - - // Internal helper. Checks `keys` for the presence of keys in IE < 9 that won't - // be iterated by `for key in ...` and thus missed. Extends `keys` in place if - // needed. - function collectNonEnumProps(obj, keys) { - keys = emulatedSet(keys); - var nonEnumIdx = nonEnumerableProps.length; - var constructor = obj.constructor; - var proto = isFunction$1(constructor) && constructor.prototype || ObjProto; - - // Constructor is a special case. - var prop = 'constructor'; - if (has$1(obj, prop) && !keys.contains(prop)) keys.push(prop); - - while (nonEnumIdx--) { - prop = nonEnumerableProps[nonEnumIdx]; - if (prop in obj && obj[prop] !== proto[prop] && !keys.contains(prop)) { - keys.push(prop); - } - } - } - - // Retrieve the names of an object's own properties. - // Delegates to **ECMAScript 5**'s native `Object.keys`. - function keys(obj) { - if (!isObject(obj)) return []; - if (nativeKeys) return nativeKeys(obj); - var keys = []; - for (var key in obj) if (has$1(obj, key)) keys.push(key); - // Ahem, IE < 9. - if (hasEnumBug) collectNonEnumProps(obj, keys); - return keys; - } - - // Is a given array, string, or object empty? - // An "empty" object has no enumerable own-properties. - function isEmpty(obj) { - if (obj == null) return true; - // Skip the more expensive `toString`-based type checks if `obj` has no - // `.length`. - var length = getLength(obj); - if (typeof length == 'number' && ( - isArray(obj) || isString(obj) || isArguments$1(obj) - )) return length === 0; - return getLength(keys(obj)) === 0; - } - - // Returns whether an object has a given set of `key:value` pairs. - function isMatch(object, attrs) { - var _keys = keys(attrs), length = _keys.length; - if (object == null) return !length; - var obj = Object(object); - for (var i = 0; i < length; i++) { - var key = _keys[i]; - if (attrs[key] !== obj[key] || !(key in obj)) return false; - } - return true; - } - - // If Underscore is called as a function, it returns a wrapped object that can - // be used OO-style. This wrapper holds altered versions of all functions added - // through `_.mixin`. Wrapped objects may be chained. - function _$1(obj) { - if (obj instanceof _$1) return obj; - if (!(this instanceof _$1)) return new _$1(obj); - this._wrapped = obj; - } - - _$1.VERSION = VERSION; - - // Extracts the result from a wrapped and chained object. - _$1.prototype.value = function() { - return this._wrapped; - }; - - // Provide unwrapping proxies for some methods used in engine operations - // such as arithmetic and JSON stringification. - _$1.prototype.valueOf = _$1.prototype.toJSON = _$1.prototype.value; - - _$1.prototype.toString = function() { - return String(this._wrapped); - }; - - // Internal function to wrap or shallow-copy an ArrayBuffer, - // typed array or DataView to a new view, reusing the buffer. - function toBufferView(bufferSource) { - return new Uint8Array( - bufferSource.buffer || bufferSource, - bufferSource.byteOffset || 0, - getByteLength(bufferSource) - ); - } - - // We use this string twice, so give it a name for minification. - var tagDataView = '[object DataView]'; - - // Internal recursive comparison function for `_.isEqual`. - function eq(a, b, aStack, bStack) { - // Identical objects are equal. `0 === -0`, but they aren't identical. - // See the [Harmony `egal` proposal](https://wiki.ecmascript.org/doku.php?id=harmony:egal). - if (a === b) return a !== 0 || 1 / a === 1 / b; - // `null` or `undefined` only equal to itself (strict comparison). - if (a == null || b == null) return false; - // `NaN`s are equivalent, but non-reflexive. - if (a !== a) return b !== b; - // Exhaust primitive checks - var type = typeof a; - if (type !== 'function' && type !== 'object' && typeof b != 'object') return false; - return deepEq(a, b, aStack, bStack); - } - - // Internal recursive comparison function for `_.isEqual`. - function deepEq(a, b, aStack, bStack) { - // Unwrap any wrapped objects. - if (a instanceof _$1) a = a._wrapped; - if (b instanceof _$1) b = b._wrapped; - // Compare `[[Class]]` names. - var className = toString.call(a); - if (className !== toString.call(b)) return false; - // Work around a bug in IE 10 - Edge 13. - if (hasStringTagBug && className == '[object Object]' && isDataView$1(a)) { - if (!isDataView$1(b)) return false; - className = tagDataView; - } - switch (className) { - // These types are compared by value. - case '[object RegExp]': - // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i') - case '[object String]': - // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is - // equivalent to `new String("5")`. - return '' + a === '' + b; - case '[object Number]': - // `NaN`s are equivalent, but non-reflexive. - // Object(NaN) is equivalent to NaN. - if (+a !== +a) return +b !== +b; - // An `egal` comparison is performed for other numeric values. - return +a === 0 ? 1 / +a === 1 / b : +a === +b; - case '[object Date]': - case '[object Boolean]': - // Coerce dates and booleans to numeric primitive values. Dates are compared by their - // millisecond representations. Note that invalid dates with millisecond representations - // of `NaN` are not equivalent. - return +a === +b; - case '[object Symbol]': - return SymbolProto.valueOf.call(a) === SymbolProto.valueOf.call(b); - case '[object ArrayBuffer]': - case tagDataView: - // Coerce to typed array so we can fall through. - return deepEq(toBufferView(a), toBufferView(b), aStack, bStack); - } - - var areArrays = className === '[object Array]'; - if (!areArrays && isTypedArray$1(a)) { - var byteLength = getByteLength(a); - if (byteLength !== getByteLength(b)) return false; - if (a.buffer === b.buffer && a.byteOffset === b.byteOffset) return true; - areArrays = true; - } - if (!areArrays) { - if (typeof a != 'object' || typeof b != 'object') return false; - - // Objects with different constructors are not equivalent, but `Object`s or `Array`s - // from different frames are. - var aCtor = a.constructor, bCtor = b.constructor; - if (aCtor !== bCtor && !(isFunction$1(aCtor) && aCtor instanceof aCtor && - isFunction$1(bCtor) && bCtor instanceof bCtor) - && ('constructor' in a && 'constructor' in b)) { - return false; - } - } - // Assume equality for cyclic structures. The algorithm for detecting cyclic - // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`. - - // Initializing stack of traversed objects. - // It's done here since we only need them for objects and arrays comparison. - aStack = aStack || []; - bStack = bStack || []; - var length = aStack.length; - while (length--) { - // Linear search. Performance is inversely proportional to the number of - // unique nested structures. - if (aStack[length] === a) return bStack[length] === b; - } - - // Add the first object to the stack of traversed objects. - aStack.push(a); - bStack.push(b); - - // Recursively compare objects and arrays. - if (areArrays) { - // Compare array lengths to determine if a deep comparison is necessary. - length = a.length; - if (length !== b.length) return false; - // Deep compare the contents, ignoring non-numeric properties. - while (length--) { - if (!eq(a[length], b[length], aStack, bStack)) return false; - } - } else { - // Deep compare objects. - var _keys = keys(a), key; - length = _keys.length; - // Ensure that both objects contain the same number of properties before comparing deep equality. - if (keys(b).length !== length) return false; - while (length--) { - // Deep compare each member - key = _keys[length]; - if (!(has$1(b, key) && eq(a[key], b[key], aStack, bStack))) return false; - } - } - // Remove the first object from the stack of traversed objects. - aStack.pop(); - bStack.pop(); - return true; - } - - // Perform a deep comparison to check if two objects are equal. - function isEqual(a, b) { - return eq(a, b); - } - - // Retrieve all the enumerable property names of an object. - function allKeys(obj) { - if (!isObject(obj)) return []; - var keys = []; - for (var key in obj) keys.push(key); - // Ahem, IE < 9. - if (hasEnumBug) collectNonEnumProps(obj, keys); - return keys; - } - - // Since the regular `Object.prototype.toString` type tests don't work for - // some types in IE 11, we use a fingerprinting heuristic instead, based - // on the methods. It's not great, but it's the best we got. - // The fingerprint method lists are defined below. - function ie11fingerprint(methods) { - var length = getLength(methods); - return function(obj) { - if (obj == null) return false; - // `Map`, `WeakMap` and `Set` have no enumerable keys. - var keys = allKeys(obj); - if (getLength(keys)) return false; - for (var i = 0; i < length; i++) { - if (!isFunction$1(obj[methods[i]])) return false; - } - // If we are testing against `WeakMap`, we need to ensure that - // `obj` doesn't have a `forEach` method in order to distinguish - // it from a regular `Map`. - return methods !== weakMapMethods || !isFunction$1(obj[forEachName]); - }; - } - - // In the interest of compact minification, we write - // each string in the fingerprints only once. - var forEachName = 'forEach', - hasName = 'has', - commonInit = ['clear', 'delete'], - mapTail = ['get', hasName, 'set']; - - // `Map`, `WeakMap` and `Set` each have slightly different - // combinations of the above sublists. - var mapMethods = commonInit.concat(forEachName, mapTail), - weakMapMethods = commonInit.concat(mapTail), - setMethods = ['add'].concat(commonInit, forEachName, hasName); - - var isMap = isIE11 ? ie11fingerprint(mapMethods) : tagTester('Map'); - - var isWeakMap = isIE11 ? ie11fingerprint(weakMapMethods) : tagTester('WeakMap'); - - var isSet = isIE11 ? ie11fingerprint(setMethods) : tagTester('Set'); - - var isWeakSet = tagTester('WeakSet'); - - // Retrieve the values of an object's properties. - function values(obj) { - var _keys = keys(obj); - var length = _keys.length; - var values = Array(length); - for (var i = 0; i < length; i++) { - values[i] = obj[_keys[i]]; - } - return values; - } - - // Convert an object into a list of `[key, value]` pairs. - // The opposite of `_.object` with one argument. - function pairs(obj) { - var _keys = keys(obj); - var length = _keys.length; - var pairs = Array(length); - for (var i = 0; i < length; i++) { - pairs[i] = [_keys[i], obj[_keys[i]]]; - } - return pairs; - } - - // Invert the keys and values of an object. The values must be serializable. - function invert(obj) { - var result = {}; - var _keys = keys(obj); - for (var i = 0, length = _keys.length; i < length; i++) { - result[obj[_keys[i]]] = _keys[i]; - } - return result; - } - - // Return a sorted list of the function names available on the object. - function functions(obj) { - var names = []; - for (var key in obj) { - if (isFunction$1(obj[key])) names.push(key); - } - return names.sort(); - } - - // An internal function for creating assigner functions. - function createAssigner(keysFunc, defaults) { - return function(obj) { - var length = arguments.length; - if (defaults) obj = Object(obj); - if (length < 2 || obj == null) return obj; - for (var index = 1; index < length; index++) { - var source = arguments[index], - keys = keysFunc(source), - l = keys.length; - for (var i = 0; i < l; i++) { - var key = keys[i]; - if (!defaults || obj[key] === void 0) obj[key] = source[key]; - } - } - return obj; - }; - } - - // Extend a given object with all the properties in passed-in object(s). - var extend = createAssigner(allKeys); - - // Assigns a given object with all the own properties in the passed-in - // object(s). - // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign) - var extendOwn = createAssigner(keys); - - // Fill in a given object with default properties. - var defaults = createAssigner(allKeys, true); - - // Create a naked function reference for surrogate-prototype-swapping. - function ctor() { - return function(){}; - } - - // An internal function for creating a new object that inherits from another. - function baseCreate(prototype) { - if (!isObject(prototype)) return {}; - if (nativeCreate) return nativeCreate(prototype); - var Ctor = ctor(); - Ctor.prototype = prototype; - var result = new Ctor; - Ctor.prototype = null; - return result; - } - - // Creates an object that inherits from the given prototype object. - // If additional properties are provided then they will be added to the - // created object. - function create(prototype, props) { - var result = baseCreate(prototype); - if (props) extendOwn(result, props); - return result; - } - - // Create a (shallow-cloned) duplicate of an object. - function clone(obj) { - if (!isObject(obj)) return obj; - return isArray(obj) ? obj.slice() : extend({}, obj); - } - - // Invokes `interceptor` with the `obj` and then returns `obj`. - // The primary purpose of this method is to "tap into" a method chain, in - // order to perform operations on intermediate results within the chain. - function tap(obj, interceptor) { - interceptor(obj); - return obj; - } - - // Normalize a (deep) property `path` to array. - // Like `_.iteratee`, this function can be customized. - function toPath$1(path) { - return isArray(path) ? path : [path]; - } - _$1.toPath = toPath$1; - - // Internal wrapper for `_.toPath` to enable minification. - // Similar to `cb` for `_.iteratee`. - function toPath(path) { - return _$1.toPath(path); - } - - // Internal function to obtain a nested property in `obj` along `path`. - function deepGet(obj, path) { - var length = path.length; - for (var i = 0; i < length; i++) { - if (obj == null) return void 0; - obj = obj[path[i]]; - } - return length ? obj : void 0; - } - - // Get the value of the (deep) property on `path` from `object`. - // If any property in `path` does not exist or if the value is - // `undefined`, return `defaultValue` instead. - // The `path` is normalized through `_.toPath`. - function get(object, path, defaultValue) { - var value = deepGet(object, toPath(path)); - return isUndefined(value) ? defaultValue : value; - } - - // Shortcut function for checking if an object has a given property directly on - // itself (in other words, not on a prototype). Unlike the internal `has` - // function, this public version can also traverse nested properties. - function has(obj, path) { - path = toPath(path); - var length = path.length; - for (var i = 0; i < length; i++) { - var key = path[i]; - if (!has$1(obj, key)) return false; - obj = obj[key]; - } - return !!length; - } - - // Keep the identity function around for default iteratees. - function identity(value) { - return value; - } - - // Returns a predicate for checking whether an object has a given set of - // `key:value` pairs. - function matcher(attrs) { - attrs = extendOwn({}, attrs); - return function(obj) { - return isMatch(obj, attrs); - }; - } - - // Creates a function that, when passed an object, will traverse that object’s - // properties down the given `path`, specified as an array of keys or indices. - function property(path) { - path = toPath(path); - return function(obj) { - return deepGet(obj, path); - }; - } - - // Internal function that returns an efficient (for current engines) version - // of the passed-in callback, to be repeatedly applied in other Underscore - // functions. - function optimizeCb(func, context, argCount) { - if (context === void 0) return func; - switch (argCount == null ? 3 : argCount) { - case 1: return function(value) { - return func.call(context, value); - }; - // The 2-argument case is omitted because we’re not using it. - case 3: return function(value, index, collection) { - return func.call(context, value, index, collection); - }; - case 4: return function(accumulator, value, index, collection) { - return func.call(context, accumulator, value, index, collection); - }; - } - return function() { - return func.apply(context, arguments); - }; - } - - // An internal function to generate callbacks that can be applied to each - // element in a collection, returning the desired result — either `_.identity`, - // an arbitrary callback, a property matcher, or a property accessor. - function baseIteratee(value, context, argCount) { - if (value == null) return identity; - if (isFunction$1(value)) return optimizeCb(value, context, argCount); - if (isObject(value) && !isArray(value)) return matcher(value); - return property(value); - } - - // External wrapper for our callback generator. Users may customize - // `_.iteratee` if they want additional predicate/iteratee shorthand styles. - // This abstraction hides the internal-only `argCount` argument. - function iteratee(value, context) { - return baseIteratee(value, context, Infinity); - } - _$1.iteratee = iteratee; - - // The function we call internally to generate a callback. It invokes - // `_.iteratee` if overridden, otherwise `baseIteratee`. - function cb(value, context, argCount) { - if (_$1.iteratee !== iteratee) return _$1.iteratee(value, context); - return baseIteratee(value, context, argCount); - } - - // Returns the results of applying the `iteratee` to each element of `obj`. - // In contrast to `_.map` it returns an object. - function mapObject(obj, iteratee, context) { - iteratee = cb(iteratee, context); - var _keys = keys(obj), - length = _keys.length, - results = {}; - for (var index = 0; index < length; index++) { - var currentKey = _keys[index]; - results[currentKey] = iteratee(obj[currentKey], currentKey, obj); - } - return results; - } - - // Predicate-generating function. Often useful outside of Underscore. - function noop(){} - - // Generates a function for a given object that returns a given property. - function propertyOf(obj) { - if (obj == null) return noop; - return function(path) { - return get(obj, path); - }; - } - - // Run a function **n** times. - function times(n, iteratee, context) { - var accum = Array(Math.max(0, n)); - iteratee = optimizeCb(iteratee, context, 1); - for (var i = 0; i < n; i++) accum[i] = iteratee(i); - return accum; - } - - // Return a random integer between `min` and `max` (inclusive). - function random(min, max) { - if (max == null) { - max = min; - min = 0; - } - return min + Math.floor(Math.random() * (max - min + 1)); - } - - // A (possibly faster) way to get the current timestamp as an integer. - var now = Date.now || function() { - return new Date().getTime(); - }; - - // Internal helper to generate functions for escaping and unescaping strings - // to/from HTML interpolation. - function createEscaper(map) { - var escaper = function(match) { - return map[match]; - }; - // Regexes for identifying a key that needs to be escaped. - var source = '(?:' + keys(map).join('|') + ')'; - var testRegexp = RegExp(source); - var replaceRegexp = RegExp(source, 'g'); - return function(string) { - string = string == null ? '' : '' + string; - return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string; - }; - } - - // Internal list of HTML entities for escaping. - var escapeMap = { - '&': '&amp;', - '<': '&lt;', - '>': '&gt;', - '"': '&quot;', - "'": '&#x27;', - '`': '&#x60;' - }; - - // Function for escaping strings to HTML interpolation. - var _escape = createEscaper(escapeMap); - - // Internal list of HTML entities for unescaping. - var unescapeMap = invert(escapeMap); - - // Function for unescaping strings from HTML interpolation. - var _unescape = createEscaper(unescapeMap); - - // By default, Underscore uses ERB-style template delimiters. Change the - // following template settings to use alternative delimiters. - var templateSettings = _$1.templateSettings = { - evaluate: /<%([\s\S]+?)%>/g, - interpolate: /<%=([\s\S]+?)%>/g, - escape: /<%-([\s\S]+?)%>/g - }; - - // When customizing `_.templateSettings`, if you don't want to define an - // interpolation, evaluation or escaping regex, we need one that is - // guaranteed not to match. - var noMatch = /(.)^/; - - // Certain characters need to be escaped so that they can be put into a - // string literal. - var escapes = { - "'": "'", - '\\': '\\', - '\r': 'r', - '\n': 'n', - '\u2028': 'u2028', - '\u2029': 'u2029' - }; - - var escapeRegExp = /\\|'|\r|\n|\u2028|\u2029/g; - - function escapeChar(match) { - return '\\' + escapes[match]; - } - - // In order to prevent third-party code injection through - // `_.templateSettings.variable`, we test it against the following regular - // expression. It is intentionally a bit more liberal than just matching valid - // identifiers, but still prevents possible loopholes through defaults or - // destructuring assignment. - var bareIdentifier = /^\s*(\w|\$)+\s*$/; - - // JavaScript micro-templating, similar to John Resig's implementation. - // Underscore templating handles arbitrary delimiters, preserves whitespace, - // and correctly escapes quotes within interpolated code. - // NB: `oldSettings` only exists for backwards compatibility. - function template(text, settings, oldSettings) { - if (!settings && oldSettings) settings = oldSettings; - settings = defaults({}, settings, _$1.templateSettings); - - // Combine delimiters into one regular expression via alternation. - var matcher = RegExp([ - (settings.escape || noMatch).source, - (settings.interpolate || noMatch).source, - (settings.evaluate || noMatch).source - ].join('|') + '|$', 'g'); - - // Compile the template source, escaping string literals appropriately. - var index = 0; - var source = "__p+='"; - text.replace(matcher, function(match, escape, interpolate, evaluate, offset) { - source += text.slice(index, offset).replace(escapeRegExp, escapeChar); - index = offset + match.length; - - if (escape) { - source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'"; - } else if (interpolate) { - source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'"; - } else if (evaluate) { - source += "';\n" + evaluate + "\n__p+='"; - } - - // Adobe VMs need the match returned to produce the correct offset. - return match; - }); - source += "';\n"; - - var argument = settings.variable; - if (argument) { - // Insure against third-party code injection. (CVE-2021-23358) - if (!bareIdentifier.test(argument)) throw new Error( - 'variable is not a bare identifier: ' + argument - ); - } else { - // If a variable is not specified, place data values in local scope. - source = 'with(obj||{}){\n' + source + '}\n'; - argument = 'obj'; - } - - source = "var __t,__p='',__j=Array.prototype.join," + - "print=function(){__p+=__j.call(arguments,'');};\n" + - source + 'return __p;\n'; - - var render; - try { - render = new Function(argument, '_', source); - } catch (e) { - e.source = source; - throw e; - } - - var template = function(data) { - return render.call(this, data, _$1); - }; - - // Provide the compiled source as a convenience for precompilation. - template.source = 'function(' + argument + '){\n' + source + '}'; - - return template; - } - - // Traverses the children of `obj` along `path`. If a child is a function, it - // is invoked with its parent as context. Returns the value of the final - // child, or `fallback` if any child is undefined. - function result(obj, path, fallback) { - path = toPath(path); - var length = path.length; - if (!length) { - return isFunction$1(fallback) ? fallback.call(obj) : fallback; - } - for (var i = 0; i < length; i++) { - var prop = obj == null ? void 0 : obj[path[i]]; - if (prop === void 0) { - prop = fallback; - i = length; // Ensure we don't continue iterating. - } - obj = isFunction$1(prop) ? prop.call(obj) : prop; - } - return obj; - } - - // Generate a unique integer id (unique within the entire client session). - // Useful for temporary DOM ids. - var idCounter = 0; - function uniqueId(prefix) { - var id = ++idCounter + ''; - return prefix ? prefix + id : id; - } - - // Start chaining a wrapped Underscore object. - function chain(obj) { - var instance = _$1(obj); - instance._chain = true; - return instance; - } - - // Internal function to execute `sourceFunc` bound to `context` with optional - // `args`. Determines whether to execute a function as a constructor or as a - // normal function. - function executeBound(sourceFunc, boundFunc, context, callingContext, args) { - if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args); - var self = baseCreate(sourceFunc.prototype); - var result = sourceFunc.apply(self, args); - if (isObject(result)) return result; - return self; - } - - // Partially apply a function by creating a version that has had some of its - // arguments pre-filled, without changing its dynamic `this` context. `_` acts - // as a placeholder by default, allowing any combination of arguments to be - // pre-filled. Set `_.partial.placeholder` for a custom placeholder argument. - var partial = restArguments(function(func, boundArgs) { - var placeholder = partial.placeholder; - var bound = function() { - var position = 0, length = boundArgs.length; - var args = Array(length); - for (var i = 0; i < length; i++) { - args[i] = boundArgs[i] === placeholder ? arguments[position++] : boundArgs[i]; - } - while (position < arguments.length) args.push(arguments[position++]); - return executeBound(func, bound, this, this, args); - }; - return bound; - }); - - partial.placeholder = _$1; - - // Create a function bound to a given object (assigning `this`, and arguments, - // optionally). - var bind = restArguments(function(func, context, args) { - if (!isFunction$1(func)) throw new TypeError('Bind must be called on a function'); - var bound = restArguments(function(callArgs) { - return executeBound(func, bound, context, this, args.concat(callArgs)); - }); - return bound; - }); - - // Internal helper for collection methods to determine whether a collection - // should be iterated as an array or as an object. - // Related: https://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength - // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094 - var isArrayLike = createSizePropertyCheck(getLength); - - // Internal implementation of a recursive `flatten` function. - function flatten$1(input, depth, strict, output) { - output = output || []; - if (!depth && depth !== 0) { - depth = Infinity; - } else if (depth <= 0) { - return output.concat(input); - } - var idx = output.length; - for (var i = 0, length = getLength(input); i < length; i++) { - var value = input[i]; - if (isArrayLike(value) && (isArray(value) || isArguments$1(value))) { - // Flatten current level of array or arguments object. - if (depth > 1) { - flatten$1(value, depth - 1, strict, output); - idx = output.length; - } else { - var j = 0, len = value.length; - while (j < len) output[idx++] = value[j++]; - } - } else if (!strict) { - output[idx++] = value; - } - } - return output; - } - - // Bind a number of an object's methods to that object. Remaining arguments - // are the method names to be bound. Useful for ensuring that all callbacks - // defined on an object belong to it. - var bindAll = restArguments(function(obj, keys) { - keys = flatten$1(keys, false, false); - var index = keys.length; - if (index < 1) throw new Error('bindAll must be passed function names'); - while (index--) { - var key = keys[index]; - obj[key] = bind(obj[key], obj); - } - return obj; - }); - - // Memoize an expensive function by storing its results. - function memoize(func, hasher) { - var memoize = function(key) { - var cache = memoize.cache; - var address = '' + (hasher ? hasher.apply(this, arguments) : key); - if (!has$1(cache, address)) cache[address] = func.apply(this, arguments); - return cache[address]; - }; - memoize.cache = {}; - return memoize; - } - - // Delays a function for the given number of milliseconds, and then calls - // it with the arguments supplied. - var delay = restArguments(function(func, wait, args) { - return setTimeout(function() { - return func.apply(null, args); - }, wait); - }); - - // Defers a function, scheduling it to run after the current call stack has - // cleared. - var defer = partial(delay, _$1, 1); - - // Returns a function, that, when invoked, will only be triggered at most once - // during a given window of time. Normally, the throttled function will run - // as much as it can, without ever going more than once per `wait` duration; - // but if you'd like to disable the execution on the leading edge, pass - // `{leading: false}`. To disable execution on the trailing edge, ditto. - function throttle(func, wait, options) { - var timeout, context, args, result; - var previous = 0; - if (!options) options = {}; - - var later = function() { - previous = options.leading === false ? 0 : now(); - timeout = null; - result = func.apply(context, args); - if (!timeout) context = args = null; - }; - - var throttled = function() { - var _now = now(); - if (!previous && options.leading === false) previous = _now; - var remaining = wait - (_now - previous); - context = this; - args = arguments; - if (remaining <= 0 || remaining > wait) { - if (timeout) { - clearTimeout(timeout); - timeout = null; - } - previous = _now; - result = func.apply(context, args); - if (!timeout) context = args = null; - } else if (!timeout && options.trailing !== false) { - timeout = setTimeout(later, remaining); - } - return result; - }; - - throttled.cancel = function() { - clearTimeout(timeout); - previous = 0; - timeout = context = args = null; - }; - - return throttled; - } - - // When a sequence of calls of the returned function ends, the argument - // function is triggered. The end of a sequence is defined by the `wait` - // parameter. If `immediate` is passed, the argument function will be - // triggered at the beginning of the sequence instead of at the end. - function debounce(func, wait, immediate) { - var timeout, previous, args, result, context; - - var later = function() { - var passed = now() - previous; - if (wait > passed) { - timeout = setTimeout(later, wait - passed); - } else { - timeout = null; - if (!immediate) result = func.apply(context, args); - // This check is needed because `func` can recursively invoke `debounced`. - if (!timeout) args = context = null; - } - }; - - var debounced = restArguments(function(_args) { - context = this; - args = _args; - previous = now(); - if (!timeout) { - timeout = setTimeout(later, wait); - if (immediate) result = func.apply(context, args); - } - return result; - }); - - debounced.cancel = function() { - clearTimeout(timeout); - timeout = args = context = null; - }; - - return debounced; - } - - // Returns the first function passed as an argument to the second, - // allowing you to adjust arguments, run code before and after, and - // conditionally execute the original function. - function wrap(func, wrapper) { - return partial(wrapper, func); - } - - // Returns a negated version of the passed-in predicate. - function negate(predicate) { - return function() { - return !predicate.apply(this, arguments); - }; - } - - // Returns a function that is the composition of a list of functions, each - // consuming the return value of the function that follows. - function compose() { - var args = arguments; - var start = args.length - 1; - return function() { - var i = start; - var result = args[start].apply(this, arguments); - while (i--) result = args[i].call(this, result); - return result; - }; - } - - // Returns a function that will only be executed on and after the Nth call. - function after(times, func) { - return function() { - if (--times < 1) { - return func.apply(this, arguments); - } - }; - } - - // Returns a function that will only be executed up to (but not including) the - // Nth call. - function before(times, func) { - var memo; - return function() { - if (--times > 0) { - memo = func.apply(this, arguments); - } - if (times <= 1) func = null; - return memo; - }; - } - - // Returns a function that will be executed at most one time, no matter how - // often you call it. Useful for lazy initialization. - var once = partial(before, 2); - - // Returns the first key on an object that passes a truth test. - function findKey(obj, predicate, context) { - predicate = cb(predicate, context); - var _keys = keys(obj), key; - for (var i = 0, length = _keys.length; i < length; i++) { - key = _keys[i]; - if (predicate(obj[key], key, obj)) return key; - } - } - - // Internal function to generate `_.findIndex` and `_.findLastIndex`. - function createPredicateIndexFinder(dir) { - return function(array, predicate, context) { - predicate = cb(predicate, context); - var length = getLength(array); - var index = dir > 0 ? 0 : length - 1; - for (; index >= 0 && index < length; index += dir) { - if (predicate(array[index], index, array)) return index; - } - return -1; - }; - } - - // Returns the first index on an array-like that passes a truth test. - var findIndex = createPredicateIndexFinder(1); - - // Returns the last index on an array-like that passes a truth test. - var findLastIndex = createPredicateIndexFinder(-1); - - // Use a comparator function to figure out the smallest index at which - // an object should be inserted so as to maintain order. Uses binary search. - function sortedIndex(array, obj, iteratee, context) { - iteratee = cb(iteratee, context, 1); - var value = iteratee(obj); - var low = 0, high = getLength(array); - while (low < high) { - var mid = Math.floor((low + high) / 2); - if (iteratee(array[mid]) < value) low = mid + 1; else high = mid; - } - return low; - } - - // Internal function to generate the `_.indexOf` and `_.lastIndexOf` functions. - function createIndexFinder(dir, predicateFind, sortedIndex) { - return function(array, item, idx) { - var i = 0, length = getLength(array); - if (typeof idx == 'number') { - if (dir > 0) { - i = idx >= 0 ? idx : Math.max(idx + length, i); - } else { - length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1; - } - } else if (sortedIndex && idx && length) { - idx = sortedIndex(array, item); - return array[idx] === item ? idx : -1; - } - if (item !== item) { - idx = predicateFind(slice.call(array, i, length), isNaN$1); - return idx >= 0 ? idx + i : -1; - } - for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) { - if (array[idx] === item) return idx; - } - return -1; - }; - } - - // Return the position of the first occurrence of an item in an array, - // or -1 if the item is not included in the array. - // If the array is large and already in sort order, pass `true` - // for **isSorted** to use binary search. - var indexOf = createIndexFinder(1, findIndex, sortedIndex); - - // Return the position of the last occurrence of an item in an array, - // or -1 if the item is not included in the array. - var lastIndexOf = createIndexFinder(-1, findLastIndex); - - // Return the first value which passes a truth test. - function find(obj, predicate, context) { - var keyFinder = isArrayLike(obj) ? findIndex : findKey; - var key = keyFinder(obj, predicate, context); - if (key !== void 0 && key !== -1) return obj[key]; - } - - // Convenience version of a common use case of `_.find`: getting the first - // object containing specific `key:value` pairs. - function findWhere(obj, attrs) { - return find(obj, matcher(attrs)); - } - - // The cornerstone for collection functions, an `each` - // implementation, aka `forEach`. - // Handles raw objects in addition to array-likes. Treats all - // sparse array-likes as if they were dense. - function each(obj, iteratee, context) { - iteratee = optimizeCb(iteratee, context); - var i, length; - if (isArrayLike(obj)) { - for (i = 0, length = obj.length; i < length; i++) { - iteratee(obj[i], i, obj); - } - } else { - var _keys = keys(obj); - for (i = 0, length = _keys.length; i < length; i++) { - iteratee(obj[_keys[i]], _keys[i], obj); - } - } - return obj; - } - - // Return the results of applying the iteratee to each element. - function map(obj, iteratee, context) { - iteratee = cb(iteratee, context); - var _keys = !isArrayLike(obj) && keys(obj), - length = (_keys || obj).length, - results = Array(length); - for (var index = 0; index < length; index++) { - var currentKey = _keys ? _keys[index] : index; - results[index] = iteratee(obj[currentKey], currentKey, obj); - } - return results; - } - - // Internal helper to create a reducing function, iterating left or right. - function createReduce(dir) { - // Wrap code that reassigns argument variables in a separate function than - // the one that accesses `arguments.length` to avoid a perf hit. (#1991) - var reducer = function(obj, iteratee, memo, initial) { - var _keys = !isArrayLike(obj) && keys(obj), - length = (_keys || obj).length, - index = dir > 0 ? 0 : length - 1; - if (!initial) { - memo = obj[_keys ? _keys[index] : index]; - index += dir; - } - for (; index >= 0 && index < length; index += dir) { - var currentKey = _keys ? _keys[index] : index; - memo = iteratee(memo, obj[currentKey], currentKey, obj); - } - return memo; - }; - - return function(obj, iteratee, memo, context) { - var initial = arguments.length >= 3; - return reducer(obj, optimizeCb(iteratee, context, 4), memo, initial); - }; - } - - // **Reduce** builds up a single result from a list of values, aka `inject`, - // or `foldl`. - var reduce = createReduce(1); - - // The right-associative version of reduce, also known as `foldr`. - var reduceRight = createReduce(-1); - - // Return all the elements that pass a truth test. - function filter(obj, predicate, context) { - var results = []; - predicate = cb(predicate, context); - each(obj, function(value, index, list) { - if (predicate(value, index, list)) results.push(value); - }); - return results; - } - - // Return all the elements for which a truth test fails. - function reject(obj, predicate, context) { - return filter(obj, negate(cb(predicate)), context); - } - - // Determine whether all of the elements pass a truth test. - function every(obj, predicate, context) { - predicate = cb(predicate, context); - var _keys = !isArrayLike(obj) && keys(obj), - length = (_keys || obj).length; - for (var index = 0; index < length; index++) { - var currentKey = _keys ? _keys[index] : index; - if (!predicate(obj[currentKey], currentKey, obj)) return false; - } - return true; - } - - // Determine if at least one element in the object passes a truth test. - function some(obj, predicate, context) { - predicate = cb(predicate, context); - var _keys = !isArrayLike(obj) && keys(obj), - length = (_keys || obj).length; - for (var index = 0; index < length; index++) { - var currentKey = _keys ? _keys[index] : index; - if (predicate(obj[currentKey], currentKey, obj)) return true; - } - return false; - } - - // Determine if the array or object contains a given item (using `===`). - function contains(obj, item, fromIndex, guard) { - if (!isArrayLike(obj)) obj = values(obj); - if (typeof fromIndex != 'number' || guard) fromIndex = 0; - return indexOf(obj, item, fromIndex) >= 0; - } - - // Invoke a method (with arguments) on every item in a collection. - var invoke = restArguments(function(obj, path, args) { - var contextPath, func; - if (isFunction$1(path)) { - func = path; - } else { - path = toPath(path); - contextPath = path.slice(0, -1); - path = path[path.length - 1]; - } - return map(obj, function(context) { - var method = func; - if (!method) { - if (contextPath && contextPath.length) { - context = deepGet(context, contextPath); - } - if (context == null) return void 0; - method = context[path]; - } - return method == null ? method : method.apply(context, args); - }); - }); - - // Convenience version of a common use case of `_.map`: fetching a property. - function pluck(obj, key) { - return map(obj, property(key)); - } - - // Convenience version of a common use case of `_.filter`: selecting only - // objects containing specific `key:value` pairs. - function where(obj, attrs) { - return filter(obj, matcher(attrs)); - } - - // Return the maximum element (or element-based computation). - function max(obj, iteratee, context) { - var result = -Infinity, lastComputed = -Infinity, - value, computed; - if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) { - obj = isArrayLike(obj) ? obj : values(obj); - for (var i = 0, length = obj.length; i < length; i++) { - value = obj[i]; - if (value != null && value > result) { - result = value; - } - } - } else { - iteratee = cb(iteratee, context); - each(obj, function(v, index, list) { - computed = iteratee(v, index, list); - if (computed > lastComputed || computed === -Infinity && result === -Infinity) { - result = v; - lastComputed = computed; - } - }); - } - return result; - } - - // Return the minimum element (or element-based computation). - function min(obj, iteratee, context) { - var result = Infinity, lastComputed = Infinity, - value, computed; - if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) { - obj = isArrayLike(obj) ? obj : values(obj); - for (var i = 0, length = obj.length; i < length; i++) { - value = obj[i]; - if (value != null && value < result) { - result = value; - } - } - } else { - iteratee = cb(iteratee, context); - each(obj, function(v, index, list) { - computed = iteratee(v, index, list); - if (computed < lastComputed || computed === Infinity && result === Infinity) { - result = v; - lastComputed = computed; - } - }); - } - return result; - } - - // Sample **n** random values from a collection using the modern version of the - // [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher–Yates_shuffle). - // If **n** is not specified, returns a single random element. - // The internal `guard` argument allows it to work with `_.map`. - function sample(obj, n, guard) { - if (n == null || guard) { - if (!isArrayLike(obj)) obj = values(obj); - return obj[random(obj.length - 1)]; - } - var sample = isArrayLike(obj) ? clone(obj) : values(obj); - var length = getLength(sample); - n = Math.max(Math.min(n, length), 0); - var last = length - 1; - for (var index = 0; index < n; index++) { - var rand = random(index, last); - var temp = sample[index]; - sample[index] = sample[rand]; - sample[rand] = temp; - } - return sample.slice(0, n); - } - - // Shuffle a collection. - function shuffle(obj) { - return sample(obj, Infinity); - } - - // Sort the object's values by a criterion produced by an iteratee. - function sortBy(obj, iteratee, context) { - var index = 0; - iteratee = cb(iteratee, context); - return pluck(map(obj, function(value, key, list) { - return { - value: value, - index: index++, - criteria: iteratee(value, key, list) - }; - }).sort(function(left, right) { - var a = left.criteria; - var b = right.criteria; - if (a !== b) { - if (a > b || a === void 0) return 1; - if (a < b || b === void 0) return -1; - } - return left.index - right.index; - }), 'value'); - } - - // An internal function used for aggregate "group by" operations. - function group(behavior, partition) { - return function(obj, iteratee, context) { - var result = partition ? [[], []] : {}; - iteratee = cb(iteratee, context); - each(obj, function(value, index) { - var key = iteratee(value, index, obj); - behavior(result, value, key); - }); - return result; - }; - } - - // Groups the object's values by a criterion. Pass either a string attribute - // to group by, or a function that returns the criterion. - var groupBy = group(function(result, value, key) { - if (has$1(result, key)) result[key].push(value); else result[key] = [value]; - }); - - // Indexes the object's values by a criterion, similar to `_.groupBy`, but for - // when you know that your index values will be unique. - var indexBy = group(function(result, value, key) { - result[key] = value; - }); - - // Counts instances of an object that group by a certain criterion. Pass - // either a string attribute to count by, or a function that returns the - // criterion. - var countBy = group(function(result, value, key) { - if (has$1(result, key)) result[key]++; else result[key] = 1; - }); - - // Split a collection into two arrays: one whose elements all pass the given - // truth test, and one whose elements all do not pass the truth test. - var partition = group(function(result, value, pass) { - result[pass ? 0 : 1].push(value); - }, true); - - // Safely create a real, live array from anything iterable. - var reStrSymbol = /[^\ud800-\udfff]|[\ud800-\udbff][\udc00-\udfff]|[\ud800-\udfff]/g; - function toArray(obj) { - if (!obj) return []; - if (isArray(obj)) return slice.call(obj); - if (isString(obj)) { - // Keep surrogate pair characters together. - return obj.match(reStrSymbol); - } - if (isArrayLike(obj)) return map(obj, identity); - return values(obj); - } - - // Return the number of elements in a collection. - function size(obj) { - if (obj == null) return 0; - return isArrayLike(obj) ? obj.length : keys(obj).length; - } - - // Internal `_.pick` helper function to determine whether `key` is an enumerable - // property name of `obj`. - function keyInObj(value, key, obj) { - return key in obj; - } - - // Return a copy of the object only containing the allowed properties. - var pick = restArguments(function(obj, keys) { - var result = {}, iteratee = keys[0]; - if (obj == null) return result; - if (isFunction$1(iteratee)) { - if (keys.length > 1) iteratee = optimizeCb(iteratee, keys[1]); - keys = allKeys(obj); - } else { - iteratee = keyInObj; - keys = flatten$1(keys, false, false); - obj = Object(obj); - } - for (var i = 0, length = keys.length; i < length; i++) { - var key = keys[i]; - var value = obj[key]; - if (iteratee(value, key, obj)) result[key] = value; - } - return result; - }); - - // Return a copy of the object without the disallowed properties. - var omit = restArguments(function(obj, keys) { - var iteratee = keys[0], context; - if (isFunction$1(iteratee)) { - iteratee = negate(iteratee); - if (keys.length > 1) context = keys[1]; - } else { - keys = map(flatten$1(keys, false, false), String); - iteratee = function(value, key) { - return !contains(keys, key); - }; - } - return pick(obj, iteratee, context); - }); - - // Returns everything but the last entry of the array. Especially useful on - // the arguments object. Passing **n** will return all the values in - // the array, excluding the last N. - function initial(array, n, guard) { - return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n))); - } - - // Get the first element of an array. Passing **n** will return the first N - // values in the array. The **guard** check allows it to work with `_.map`. - function first(array, n, guard) { - if (array == null || array.length < 1) return n == null || guard ? void 0 : []; - if (n == null || guard) return array[0]; - return initial(array, array.length - n); - } - - // Returns everything but the first entry of the `array`. Especially useful on - // the `arguments` object. Passing an **n** will return the rest N values in the - // `array`. - function rest(array, n, guard) { - return slice.call(array, n == null || guard ? 1 : n); - } - - // Get the last element of an array. 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