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bump to nightly-2023-03-15-03
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leanprover-community-bot committed Mar 15, 2023
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136 changes: 100 additions & 36 deletions Mathbin/Algebra/CharP/Basic.lean

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32 changes: 16 additions & 16 deletions Mathbin/AlgebraicGeometry/EllipticCurve/Point.lean
Expand Up @@ -129,7 +129,7 @@ theorem negY_negY : W.negY x₁ (W.negY x₁ y₁) = y₁ :=
ring1
#align weierstrass_curve.neg_Y_neg_Y WeierstrassCurve.negY_negY

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2556673791.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2137773769.map_simp -/
theorem baseChange_negY :
(W.base_change A).negY (algebraMap R A x₁) (algebraMap R A y₁) =
algebraMap R A (W.negY x₁ y₁) :=
Expand All @@ -146,7 +146,7 @@ theorem baseChange_negY_of_baseChange (x₁ y₁ : A) :
by rw [← base_change_neg_Y, base_change_base_change]
#align weierstrass_curve.base_change_neg_Y_of_base_change WeierstrassCurve.baseChange_negY_of_baseChange

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
@[simp]
theorem eval_negPolynomial : (W.negPolynomial.eval <| C y₁).eval x₁ = W.negY x₁ y₁ :=
by
Expand All @@ -173,8 +173,8 @@ noncomputable def addPolynomial : R[X] :=
W.Polynomial.eval <| linePolynomial x₁ y₁ L
#align weierstrass_curve.add_polynomial WeierstrassCurve.addPolynomial

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.170323567.C_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.4157056569.C_simp -/
theorem addPolynomial_eq :
W.addPolynomial x₁ y₁ L =
-Cubic.toPoly
Expand All @@ -199,7 +199,7 @@ def addX : R :=
L ^ 2 + W.a₁ * L - W.a₂ - x₁ - x₂
#align weierstrass_curve.add_X WeierstrassCurve.addX

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2556673791.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2137773769.map_simp -/
theorem baseChange_addX :
(W.base_change A).addX (algebraMap R A x₁) (algebraMap R A x₂) (algebraMap R A L) =
algebraMap R A (W.addX x₁ x₂ L) :=
Expand All @@ -225,7 +225,7 @@ def addY' : R :=
L * (W.addX x₁ x₂ L - x₁) + y₁
#align weierstrass_curve.add_Y' WeierstrassCurve.addY'

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2556673791.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2137773769.map_simp -/
theorem baseChange_addY' :
(W.base_change A).addY' (algebraMap R A x₁) (algebraMap R A x₂) (algebraMap R A y₁)
(algebraMap R A L) =
Expand Down Expand Up @@ -266,7 +266,7 @@ theorem baseChange_addY_of_baseChange (x₁ x₂ y₁ L : A) :
by rw [← base_change_add_Y, base_change_base_change]
#align weierstrass_curve.base_change_add_Y_of_base_change WeierstrassCurve.baseChange_addY_of_baseChange

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
theorem equation_add_iff :
W.Equation (W.addX x₁ x₂ L) (W.addY' x₁ x₂ y₁ L) ↔
(W.addPolynomial x₁ y₁ L).eval (W.addX x₁ x₂ L) = 0 :=
Expand All @@ -276,10 +276,10 @@ theorem equation_add_iff :
eval_simp
#align weierstrass_curve.equation_add_iff WeierstrassCurve.equation_add_iff

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.150691367.derivative_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.162409969.derivative_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
theorem nonsingular_add_of_eval_derivative_ne_zero
(hx' : W.Equation (W.addX x₁ x₂ L) (W.addY' x₁ x₂ y₁ L))
(hx : (derivative <| W.addPolynomial x₁ y₁ L).eval (W.addX x₁ x₂ L) ≠ 0) :
Expand Down Expand Up @@ -459,8 +459,8 @@ theorem slope_of_Y_ne_eq_eval (hx : x₁ = x₂) (hy : y₁ ≠ W.negY x₂ y₂
ring1
#align weierstrass_curve.slope_of_Y_ne_eq_eval WeierstrassCurve.slope_of_Y_ne_eq_eval

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2556673791.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2556673791.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2137773769.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2137773769.map_simp -/
theorem baseChange_slope :
(W.base_change K).slope (algebraMap F K x₁) (algebraMap F K x₂) (algebraMap F K y₁)
(algebraMap F K y₂) =
Expand Down Expand Up @@ -537,7 +537,7 @@ theorem addPolynomial_slope (hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂) :
linear_combination (norm := (field_simp [hx] ; ring1)) x₂ * h₁' - x₁ * h₂'
#align weierstrass_curve.add_polynomial_slope WeierstrassCurve.addPolynomial_slope

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.150691367.derivative_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.162409969.derivative_simp -/
theorem derivative_addPolynomial_slope (hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂) :
derivative (W.addPolynomial x₁ y₁ <| W.slope x₁ x₂ y₁ y₂) =
-((X - C x₁) * (X - C x₂) + (X - C x₁) * (X - C (W.addX x₁ x₂ <| W.slope x₁ x₂ y₁ y₂)) +
Expand All @@ -552,7 +552,7 @@ theorem derivative_addPolynomial_slope (hxy : x₁ = x₂ → y₁ ≠ W.negY x
/-! ### The addition law on nonsingular rational points on a Weierstrass curve -/


/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
/-- The addition of two affine points in `W` on a sloped line,
before applying the final negation that maps $Y$ to $-Y - a_1X - a_3$, lies in `W`. -/
theorem equation_add' (hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂) :
Expand All @@ -574,7 +574,7 @@ omit h₁' h₂'

include h₁ h₂

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.1038319287.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3102772865.eval_simp -/
/-- The addition of two nonsingular affine points in `W` on a sloped line,
before applying the final negation that maps $Y$ to $-Y - a_1X - a_3$, is nonsingular. -/
theorem nonsingular_add' (hxy : x₁ = x₂ → y₁ ≠ W.negY x₂ y₂) :
Expand Down
34 changes: 17 additions & 17 deletions Mathbin/AlgebraicGeometry/EllipticCurve/Weierstrass.lean
Expand Up @@ -271,7 +271,7 @@ def baseChange : WeierstrassCurve A :=
algebraMap R A W.a₆⟩
#align weierstrass_curve.base_change WeierstrassCurve.baseChange

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_b₂ : (W.base_change A).b₂ = algebraMap R A W.b₂ :=
by
Expand All @@ -280,7 +280,7 @@ theorem baseChange_b₂ : (W.base_change A).b₂ = algebraMap R A W.b₂ :=
map_simp
#align weierstrass_curve.base_change_b₂ WeierstrassCurve.baseChange_b₂

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_b₄ : (W.base_change A).b₄ = algebraMap R A W.b₄ :=
by
Expand All @@ -289,7 +289,7 @@ theorem baseChange_b₄ : (W.base_change A).b₄ = algebraMap R A W.b₄ :=
map_simp
#align weierstrass_curve.base_change_b₄ WeierstrassCurve.baseChange_b₄

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_b₆ : (W.base_change A).b₆ = algebraMap R A W.b₆ :=
by
Expand All @@ -298,7 +298,7 @@ theorem baseChange_b₆ : (W.base_change A).b₆ = algebraMap R A W.b₆ :=
map_simp
#align weierstrass_curve.base_change_b₆ WeierstrassCurve.baseChange_b₆

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_b₈ : (W.base_change A).b₈ = algebraMap R A W.b₈ :=
by
Expand All @@ -307,7 +307,7 @@ theorem baseChange_b₈ : (W.base_change A).b₈ = algebraMap R A W.b₈ :=
map_simp
#align weierstrass_curve.base_change_b₈ WeierstrassCurve.baseChange_b₈

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_c₄ : (W.base_change A).c₄ = algebraMap R A W.c₄ :=
by
Expand All @@ -316,7 +316,7 @@ theorem baseChange_c₄ : (W.base_change A).c₄ = algebraMap R A W.c₄ :=
map_simp
#align weierstrass_curve.base_change_c₄ WeierstrassCurve.baseChange_c₄

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_c₆ : (W.base_change A).c₆ = algebraMap R A W.c₆ :=
by
Expand All @@ -325,7 +325,7 @@ theorem baseChange_c₆ : (W.base_change A).c₆ = algebraMap R A W.c₆ :=
map_simp
#align weierstrass_curve.base_change_c₆ WeierstrassCurve.baseChange_c₆

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp, nolint simp_nf]
theorem baseChange_Δ : (W.base_change A).Δ = algebraMap R A W.Δ :=
by
Expand Down Expand Up @@ -399,7 +399,7 @@ protected noncomputable def polynomial : R[X][Y] :=
Y ^ 2 + C (C W.a₁ * X + C W.a₃) * Y - C (X ^ 3 + C W.a₂ * X ^ 2 + C W.a₄ * X + C W.a₆)
#align weierstrass_curve.polynomial WeierstrassCurve.polynomial

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3266784253.C_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2327590855.C_simp -/
theorem polynomial_eq :
W.Polynomial =
Cubic.toPoly
Expand Down Expand Up @@ -452,7 +452,7 @@ theorem irreducible_polynomial [IsDomain R] : Irreducible W.Polynomial :=
any_goals rw [degree_add_eq_right_of_degree_lt] <;> simp only [h] <;> decide
#align weierstrass_curve.irreducible_polynomial WeierstrassCurve.irreducible_polynomial

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3143603269.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3687834639.eval_simp -/
@[simp]
theorem eval_polynomial (x y : R) :
(W.Polynomial.eval <| C y).eval x =
Expand Down Expand Up @@ -500,8 +500,8 @@ theorem equation_iff_variableChange (x y : R) :
ring1
#align weierstrass_curve.equation_iff_variable_change WeierstrassCurve.equation_iff_variableChange

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
theorem equation_iff_baseChange [Nontrivial A] [NoZeroSMulDivisors R A] (x y : R) :
W.Equation x y ↔ (W.base_change A).Equation (algebraMap R A x) (algebraMap R A y) :=
by
Expand Down Expand Up @@ -534,7 +534,7 @@ noncomputable def polynomialX : R[X][Y] :=
C (C W.a₁) * Y - C (C 3 * X ^ 2 + C (2 * W.a₂) * X + C W.a₄)
#align weierstrass_curve.polynomial_X WeierstrassCurve.polynomialX

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3143603269.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3687834639.eval_simp -/
@[simp]
theorem eval_polynomialX (x y : R) :
(W.polynomialX.eval <| C y).eval x = W.a₁ * y - (3 * x ^ 2 + 2 * W.a₂ * x + W.a₄) :=
Expand All @@ -557,7 +557,7 @@ noncomputable def polynomialY : R[X][Y] :=
C (C 2) * Y + C (C W.a₁ * X + C W.a₃)
#align weierstrass_curve.polynomial_Y WeierstrassCurve.polynomialY

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3143603269.eval_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3687834639.eval_simp -/
@[simp]
theorem eval_polynomialY (x y : R) : (W.polynomialY.eval <| C y).eval x = 2 * y + W.a₁ * x + W.a₃ :=
by
Expand Down Expand Up @@ -608,8 +608,8 @@ theorem nonsingular_iff_variableChange (x y : R) :
congr 4 <;> ring1
#align weierstrass_curve.nonsingular_iff_variable_change WeierstrassCurve.nonsingular_iff_variableChange

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
theorem nonsingular_iff_baseChange [Nontrivial A] [NoZeroSMulDivisors R A] (x y : R) :
W.Nonsingular x y ↔ (W.base_change A).Nonsingular (algebraMap R A x) (algebraMap R A y) :=
by
Expand Down Expand Up @@ -835,7 +835,7 @@ theorem norm_smul_basis (p q : R[X]) :
ring1
#align weierstrass_curve.coordinate_ring.norm_smul_basis WeierstrassCurve.CoordinateRing.norm_smul_basis

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.3266784253.C_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.2327590855.C_simp -/
theorem coe_norm_smul_basis (p q : R[X]) :
↑(Algebra.norm R[X] <| p • 1 + q • AdjoinRoot.mk W.Polynomial Y) =
AdjoinRoot.mk W.Polynomial ((C p + C q * X) * (C p + C q * (-X - C (C W.a₁ * X + C W.a₃)))) :=
Expand Down Expand Up @@ -1003,7 +1003,7 @@ theorem coe_inv_baseChange_Δ' : ↑(E.base_change A).Δ'⁻¹ = algebraMap R A
rfl
#align elliptic_curve.coe_inv_base_change_Δ' EllipticCurve.coe_inv_baseChange_Δ'

/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.272596109.map_simp -/
/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic _private.367748183.map_simp -/
@[simp]
theorem baseChange_j : (E.base_change A).j = algebraMap R A E.j :=
by
Expand Down

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